* algebra/aggcat.spad.pamphlet (FiniteAggregate): New.

	* algebra/exposed.lsp.pamphlet: Expose it.

5 files changed, 18734 insertions, 18712 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 3c609762..17440831 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(1960126 . 3577545198)       
+(1961956 . 3577666331)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
 (-19 S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . 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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3990 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3986 . T) (-3991 . T) (-3985 . T)) 
+((-3991 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3987 . T) (-3992 . T) (-3986 . T)) 
 NIL 
 (-30) 
 ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,14 +56,14 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3091) 
+(-32 R -3092) 
 ((|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 (-949 (-483))))) 
+((|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)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3993))) 
+((|HasAttribute| |#1| (QUOTE -3994))) 
 (-34) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
@@ -74,7 +74,7 @@ NIL
 NIL 
 (-36 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table.	It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . 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"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 (-39 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3091 UP UPUP -2613) 
+(-40 -3092 UP UPUP -2614) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-3986 |has| (-348 |#2|) (-312)) (-3991 |has| (-348 |#2|) (-312)) (-3985 |has| (-348 |#2|) (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088)))))) (|HasCategory| (-348 |#2|) (QUOTE (-579 (-483)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) 
-(-41 R -3091) 
+((-3987 |has| (-349 |#2|) (-312)) (-3992 |has| (-349 |#2|) (-312)) (-3986 |has| (-349 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-349 |#2|) (QUOTE (-118))) (|HasCategory| (-349 |#2|) (QUOTE (-120))) (|HasCategory| (-349 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-319))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-299))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089)))))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-811 (-1089)))))) (|HasCategory| (-349 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-349 (-484)))))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-349 (-484))))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-319))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-811 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089)))))) 
+(-41 R -3092) 
 ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-258)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) 
-((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) 
+((-3991 |has| |#1| (-495)) (-3989 . T) (-3988 . 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."))) 
-((-3993 . T) (-3994 . T)) 
-((OR (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755)))) (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) 
+((-3994 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#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 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
+((|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
 (-51) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3091) 
+(-54 |Base| R -3092) 
 ((|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}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . 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}"))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
 (-59 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) 
-((-3993 . T) ((-3995 "*") . T) (-3994 . T) (-3990 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3991 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3981 . T) (-3989 . T) (-3992 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3980 . T)) 
+((-3994 . T) ((-3996 "*") . T) (-3995 . T) (-3991 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3992 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3990 . T) (-3993 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3981 . 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}."))) 
-((-3990 . T)) 
+((-3991 . 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}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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)))) 
 (-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 (-3995 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-3996 "*")))) 
 (-75 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
 NIL 
 NIL 
 (-76 S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) 
-((-3994 . T)) 
+((-3995 . 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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-484) (QUOTE (-796 (-329)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1089)))) (|HasCategory| (-484) (QUOTE (-455 (-1089) (-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}"))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-552 (-472)))) (|HasCategory| (-85) (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-551 (-771)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|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}"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
 (-83 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
@@ -280,22 +280,22 @@ NIL
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-88 -3091 UP) 
+(-88 -3092 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}."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-820))) (|HasCategory| (-89 |#1|) (QUOTE (-949 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-472)))) (|HasCategory| (-89 |#1|) (QUOTE (-932))) (|HasCategory| (-89 |#1|) (QUOTE (-739))) (|HasCategory| (-89 |#1|) (QUOTE (-755))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-739))) (|HasCategory| (-89 |#1|) (QUOTE (-755)))) (|HasCategory| (-89 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-1064))) (|HasCategory| (-89 |#1|) (QUOTE (-795 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-795 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-89 |#1|) (QUOTE (-579 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-808 (-1088)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%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 (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-820)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-329)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -455) (QUOTE (-1089)) (|%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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3994))) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
 (-92 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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)))) 
 (-95 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-96) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
 (-97 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -322,24 +322,24 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T)) 
 NIL 
 (-99 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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)))) 
 (-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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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)))) 
 (-101) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
 (-102) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-755)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) (|HasCategory| (-101) (QUOTE (-551 (-771)))) (|HasCategory| (-101) (QUOTE (-552 (-472)))) (OR (|HasCategory| (-101) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-101) (QUOTE (-755))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-101) (QUOTE (-1012))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) 
 (-103) 
 ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) 
 NIL 
@@ -358,13 +358,13 @@ NIL
 NIL 
 (-107) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3995 "*") . T)) 
+(((-3996 "*") . T)) 
 NIL 
-(-108 |minix| -2620 R) 
+(-108 |minix| -2621 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2620 S T$) 
+(-109 |minix| -2621 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}."))) 
-((-3993 . T) (-3983 . T) (-3994 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-552 (-472)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-551 (-771)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) 
+((-3994 . T) (-3984 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-319)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (|HasCategory| (-117) (QUOTE (-319))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) 
 (-115 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
@@ -402,7 +402,7 @@ NIL
 NIL 
 (-118) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-3990 . T)) 
+((-3991 . 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."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-121 -3091 UP UPUP) 
+(-121 -3092 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) 
 NIL 
 NIL 
@@ -423,14 +423,14 @@ NIL
 (-123 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasAttribute| |#1| (QUOTE -3993))) 
+((|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3994))) 
 (-124 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
 (-125 |n| K Q) 
 ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) 
-((-3988 . T) (-3987 . T) (-3990 . T)) 
+((-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
 (-126) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -452,7 +452,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-131 R -3091) 
+(-131 R -3092) 
 ((|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 (-820))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-914))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3989)) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494)))) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1114))) (|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 -3990)) (|HasAttribute| |#2| (QUOTE -3993)) (|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})"))) 
-((-3986 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-820)))) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3989 |has| |#1| (-6 -3989)) (-3992 |has| |#1| (-6 -3992)) (-1374 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3990 |has| |#1| (-6 -3990)) (-3993 |has| |#1| (-6 -3993)) (-1375 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}."))) 
-((-3986 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-258)) (|has| |#1| (-820)))) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3989 |has| |#1| (-6 -3989)) (-3992 |has| |#1| (-6 -3992)) (-1374 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
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+((-3987 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3990 |has| |#1| (-6 -3990)) (-3993 |has| |#1| (-6 -3993)) (-1375 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 (-319))) (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 (-1089)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (|HasCategory| |#1| (QUOTE (-811 (-1089))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 (-1114)))) (|HasCategory| |#1| (QUOTE (-1114))) (|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 (-329))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-329)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1089)) (|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 (-1114)))) (|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 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasAttribute| |#1| (QUOTE -3993)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (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."))) 
-(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}."))) 
-(((-3995 "*") . T) (-3986 . T) (-3991 . T) (-3985 . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") . T) (-3987 . T) (-3992 . T) (-3986 . T) (-3988 . T) (-3989 . T) (-3991 . 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|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -539,7 +539,7 @@ NIL
 (-152 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-856 |#2|) (|%list| (QUOTE -795) (|devaluate| |#1|)))) 
+((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
 (-153 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -576,7 +576,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -3091) 
+(-162 R -3092) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -604,23 +604,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
 NIL 
 NIL 
-(-169 -3091 UP UPUP R) 
+(-169 -3092 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-170 -3091 FP) 
+(-170 -3092 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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-484) (QUOTE (-796 (-329)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1089)))) (|HasCategory| (-484) (QUOTE (-455 (-1089) (-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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-173 R -3091) 
+(-173 R -3092) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -634,19 +634,19 @@ NIL
 NIL 
 (-176 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-178 R -3091) 
+(-178 R -3092) 
 ((|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}."))) 
-((-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}"))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3995 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3994 . T) (-3995 . 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 (-3996 "*"))) (|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."))) 
-((-3994 . T)) 
+((-3995 . 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 \\%."))) 
-((-3990 . T)) 
+((-3991 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -678,7 +678,7 @@ NIL
 NIL 
 (-187 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
 (-188 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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"))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
 (-191) 
 ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) 
@@ -699,28 +699,28 @@ NIL
 (-192 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3993))) 
+((|HasAttribute| |#1| (QUOTE -3994))) 
 (-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}."))) 
-((-3994 . T)) 
+((-3995 . 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 -2620 R) 
+(-195 S -2621 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-716))) (|HasCategory| |#3| (QUOTE (-755))) (|HasAttribute| |#3| (QUOTE -3990)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-662))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-960))) (|HasCategory| |#3| (QUOTE (-1012)))) 
-(-196 -2620 R) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasAttribute| |#3| (QUOTE -3991)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) 
+(-196 -2621 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
-((-3987 |has| |#2| (-960)) (-3988 |has| |#2| (-960)) (-3990 |has| |#2| (-6 -3990)) (-3993 . T)) 
+((-3988 |has| |#2| (-961)) (-3989 |has| |#2| (-961)) (-3991 |has| |#2| (-6 -3991)) (-3994 . T)) 
 NIL 
-(-197 -2620 R) 
+(-197 -2621 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."))) 
-((-3987 |has| |#2| (-960)) (-3988 |has| |#2| (-960)) (-3990 |has| |#2| (-6 -3990)) (-3993 . T)) 
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+(-198 -2621 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}."))) 
-((-3986 . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) (-3988 . T) (-3989 . T) (-3991 . 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}"))) 
-((-3994 . T) (-3993 . T)) 
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+((-3995 . T) (-3994 . 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"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 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"))) 
-(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-495)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-391))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
 (-207) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
@@ -770,23 +770,23 @@ NIL
 NIL 
 (-210 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-3990 OR (-2561 (|has| |#4| (-960)) (|has| |#4| (-190))) (|has| |#4| (-6 -3990)) (-2561 (|has| |#4| (-960)) (|has| |#4| (-808 (-1088))))) (-3987 |has| |#4| (-960)) (-3988 |has| |#4| (-960)) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-662))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-716))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-755))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-960))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-312))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-960)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312)))) (|HasCategory| |#4| (QUOTE (-960))) (|HasCategory| |#4| (QUOTE (-662))) (|HasCategory| |#4| (QUOTE (-716))) (OR (|HasCategory| |#4| (QUOTE (-716))) (|HasCategory| |#4| (QUOTE (-755)))) (|HasCategory| |#4| (QUOTE (-755))) (|HasCategory| |#4| (QUOTE (-318))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-579 (-483)))) (|HasCategory| |#4| (QUOTE (-808 (-1088))))) (-12 (|HasCategory| |#4| (QUOTE (-579 (-483)))) (|HasCategory| |#4| (QUOTE (-960))))) (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (OR (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-960)))) (|HasCategory| |#4| (QUOTE (-190))) (OR (|HasCategory| |#4| (QUOTE (-190))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-960))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1088)))) (|HasCategory| |#4| (QUOTE (-960)))) (|HasCategory| |#4| (QUOTE (-808 (-1088))))) (|HasCategory| |#4| (QUOTE (-1012))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-662))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-716))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-755))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-960)))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-1012))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-716))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-755))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-662))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (|HasCategory| |#4| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-716))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-755))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-662))) (|HasCategory| |#4| (QUOTE (-949 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-483)))) (|HasCategory| |#4| (QUOTE (-960))))) (|HasCategory| (-483) (QUOTE (-755))) (-12 (|HasCategory| |#4| (QUOTE (-579 (-483)))) (|HasCategory| |#4| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-960)))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1088)))) (|HasCategory| |#4| (QUOTE (-960))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-960)))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-960))))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-949 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (|HasCategory| |#4| (QUOTE (-960)))) (-12 (|HasCategory| |#4| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-808 (-1088)))) (|HasCategory| |#4| (QUOTE (-960)))) (|HasAttribute| |#4| (QUOTE -3990)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-960))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-960)))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1088)))) (|HasCategory| |#4| (QUOTE (-960)))) (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-23))) (|HasCategory| |#4| (QUOTE (-104))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72))) (-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) 
+((-3991 OR (-2562 (|has| |#4| (-961)) (|has| |#4| (-190))) (|has| |#4| (-6 -3991)) (-2562 (|has| |#4| (-961)) (|has| |#4| (-809 (-1089))))) (-3988 |has| |#4| (-961)) (-3989 |has| |#4| (-961)) (-3994 . T)) 
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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 (-319))) (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 (-1089))))) (-12 (|HasCategory| |#4| (QUOTE (-580 (-484)))) (|HasCategory| |#4| (QUOTE (-961))))) (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasCategory| |#4| (QUOTE (-190))) (OR (|HasCategory| |#4| (QUOTE (-190))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-811 (-1089)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasCategory| |#4| (QUOTE (-809 (-1089))))) (|HasCategory| |#4| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#4| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (|HasCategory| |#4| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-484)))) (|HasCategory| |#4| (QUOTE (-961))))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#4| (QUOTE (-580 (-484)))) (|HasCategory| |#4| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-811 (-1089)))) (|HasCategory| |#4| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-961))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-950 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#4| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-809 (-1089)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasAttribute| |#4| (QUOTE -3991)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-961))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-811 (-1089)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-23))) (|HasCategory| |#4| (QUOTE (-104))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) 
 (-211 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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(QUOTE (-1012)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-949 (-483)))) (|HasCategory| |#3| (QUOTE (-1012)))) (|HasCategory| |#3| (QUOTE (-960)))) (-12 (|HasCategory| |#3| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#3| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-808 (-1088)))) (|HasCategory| |#3| (QUOTE (-960)))) (|HasAttribute| |#3| (QUOTE -3990)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-960))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-960)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1088)))) (|HasCategory| |#3| (QUOTE (-960)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-551 (-771)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) 
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(-1089))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|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 (-1089)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-809 (-1089))))) (|HasCategory| |#3| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE 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 (-212 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-190)))) 
 (-213 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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}."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . 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 (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-189)))) 
+((|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-189)))) 
 (-225 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
 (-226 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#3| (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#3| (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#3| (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#3| (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#3| (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| |#3| (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#3| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-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 -3091) 
+(-230 R -3092) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the	inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-231 R -3091) 
+(-231 R -3092) 
 ((|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 (-755))) (|HasCategory| |#2| (QUOTE (-1012)))) 
+((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) 
 (-237 S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
-((-3994 . T)) 
+((-3995 . 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 -3994))) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
 (-243 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-244 S R |Mod| -2036 -3516 |exactQuo|) 
+(-244 S R |Mod| -2037 -3517 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 (-245 S) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
@@ -914,7 +914,7 @@ NIL
 NIL 
 (-246) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3986 . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 (-247) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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."))) 
-((-3990 OR (|has| |#1| (-960)) (|has| |#1| (-411))) (-3987 |has| |#1| (-960)) (-3988 |has| |#1| (-960))) 
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+((-3991 OR (|has| |#1| (-961)) (|has| |#1| (-412))) (-3988 |has| |#1| (-961)) (-3989 |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 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|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 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-412))) (|HasCategory| |#1| (QUOTE (-663)))) (|HasCategory| |#1| (QUOTE (-412))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-412))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-412))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1089)) (|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 (-412)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-412))) (|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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
 (-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 (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) 
+((|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 -3091 S) 
+(-255 -3092 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 -3091) 
+(-256 E -3092) 
 ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 (-259 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -3091) 
+(-261 -3092) 
 ((|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))}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-949 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-472)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-932))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-739))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-755))) (OR (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-739))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-755)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-949 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-1064))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-795 (-328)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-795 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-579 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-808 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-820)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-473)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-329)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -455) (QUOTE (-1089)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1165 |#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."))) 
-((-3990 OR (-12 (|has| |#1| (-494)) (OR (|has| |#1| (-960)) (|has| |#1| (-411)))) (|has| |#1| (-960)) (|has| |#1| (-411))) (-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) ((-3995 "*") |has| |#1| (-494)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-494)) (-3985 |has| |#1| (-494))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-579 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960))))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-1024)))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960)))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-960)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-949 (-483)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) 
+((-3991 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-961)) (|has| |#1| (-412)))) (|has| |#1| (-961)) (|has| |#1| (-412))) (-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) ((-3996 "*") |has| |#1| (-495)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-495)) (-3986 |has| |#1| (-495))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 (-349 (-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 (-412))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-412))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-796 (-329)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|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 (-391))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-412))) (|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 (-412))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 -3091) 
+(-268 R -3092) 
 ((|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."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
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+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-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 -349) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|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."))) 
-((-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-715)))) 
+((-3989 . T) (-3988 . 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1031,26 +1031,26 @@ NIL
 (-275 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-693) (QUOTE (-715)))) 
+((|HasCategory| (-694) (QUOTE (-716)))) 
 (-276 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) 
+((|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
 (-277 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . 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."))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-279 S -3091) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-279 S -3092) 
 ((|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 (-318)))) 
-(-280 -3091) 
+((|HasCategory| |#2| (QUOTE (-319)))) 
+(-280 -3092) 
 ((|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 -3091 UP UPUP R) 
+(-283 -3092 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 -3091 UP UPUP R) 
+(-285 S -3092 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 -3091 UP UPUP R) 
+(-286 -3092 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|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-288 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#1|) (QUOTE (-118)))) 
-(-290 S -3091 UP UPUP) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-319)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-319))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+(-290 S -3092 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 (-318))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-291 -3091 UP UPUP) 
+((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-291 -3092 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."))) 
-((-3986 |has| (-348 |#2|) (-312)) (-3991 |has| (-348 |#2|) (-312)) (-3985 |has| (-348 |#2|) (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 |has| (-349 |#2|) (-312)) (-3992 |has| (-349 |#2|) (-312)) (-3986 |has| (-349 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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}."))) 
@@ -1102,16 +1102,16 @@ 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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#1|) (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-319)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-319))) (|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-296 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1126,51 +1126,51 @@ 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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-300 R UP -3091) 
+(-300 R UP -3092) 
 ((|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| (-816 |#1|) (QUOTE (-118))) (|HasCategory| (-816 |#1|) (QUOTE (-318)))) (|HasCategory| (-816 |#1|) (QUOTE (-120))) (|HasCategory| (-816 |#1|) (QUOTE (-318))) (|HasCategory| (-816 |#1|) (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-319)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-319))) (|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|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 -3091 GF) 
+(-306 -3092 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 -3091 FP FPP) 
+(-307 -3092 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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118)))) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-309 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
 NIL 
 NIL 
 (-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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
 (-311 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1178,7 +1178,7 @@ NIL
 NIL 
 (-312) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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."))) 
@@ -1191,3574 +1191,3578 @@ 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 (-494)))) 
+((|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."))) 
-((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . T)) 
+((-3991 |has| |#1| (-495)) (-3989 . T) (-3988 . T)) 
 NIL 
 (-317 S) 
+((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\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|) |#1|) $) "\\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|) |#1|) $) "\\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|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) 
+NIL 
+NIL 
+(-318 S) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
 NIL 
 NIL 
-(-318) 
+(-319) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
 NIL 
 NIL 
-(-319 S R UP) 
+(-320 S R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-320 R UP) 
+(-321 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-321 A S) 
+(-322 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012)))) 
-(-322 S) 
+((|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) 
+(-323 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-323 S A R B) 
+(-324 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-324 |VarSet| R) 
+(-325 |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) (-3988 . T) (-3987 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3989 . T) (-3988 . T)) 
 NIL 
-(-325 S V) 
+(-326 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
 NIL 
 NIL 
-(-326 S R) 
+(-327 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 (-579 (-483))))) 
-(-327 R) 
+((|HasCategory| |#2| (QUOTE (-580 (-484))))) 
+(-328 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 
-(-328) 
+(-329) 
 ((|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}."))) 
-((-3976 . T) (-3984 . T) (-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3977 . T) (-3985 . T) (-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-329 |Par|) 
+(-330 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
 NIL 
 NIL 
-(-330 |Par|) 
+(-331 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in lp,{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-331 R S) 
-((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
 (-332 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."))) 
+((-3989 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-333 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}"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146)))) 
-(-333 R |Basis|) 
+(-334 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}."))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-334 S) 
+(-335 S) 
 ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
 NIL 
-(-335 S) 
+(-336 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-336) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-337) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
 NIL 
-(-337) 
+(-338) 
 ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used."))) 
 NIL 
 NIL 
-(-338 |n| |class| R) 
+(-339 |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|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-339 -3091 UP UPUP R) 
+(-340 -3092 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-340 -3091 UP) 
+(-341 -3092 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
-(-341 R) 
+(-342 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
 NIL 
 NIL 
-(-342 S) 
+(-343 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
 NIL 
 NIL 
-(-343) 
+(-344) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-344 S) 
+(-345 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3976)) (|HasAttribute| |#1| (QUOTE -3984))) 
-(-345) 
+((|HasAttribute| |#1| (QUOTE -3977)) (|HasAttribute| |#1| (QUOTE -3985))) 
+(-346) 
 ((|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\"."))) 
-((-3768 . T) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3769 . T) (-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-346 R) 
+(-347 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."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
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-(-347 R S) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-455 (-1089) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1133))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1089)) (|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 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-391)))) 
+(-348 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 
-(-348 S) 
+(-349 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."))) 
-((-3980 -12 (|has| |#1| (-6 -3991)) (|has| |#1| (-390)) (|has| |#1| (-6 -3980))) (-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
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-(-349 A B) 
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+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| |#1| (QUOTE (-796 (-329)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1089)) (|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 -3981)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-350 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 
 NIL 
-(-350 S R UP) 
+(-351 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 NIL 
-(-351 R UP) 
+(-352 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-352 A S) 
+(-353 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483))))) 
-(-353 S) 
+((|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) 
+(-354 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-354 R -3091 UP A) 
+(-355 R -3092 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-355 R1 F1 U1 A1 R2 F2 U2 A2) 
+(-356 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 
-(-356 R -3091 UP A |ibasis|) 
+(-357 R -3092 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -949) (|devaluate| |#2|)))) 
-(-357 AR R AS S) 
+((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) 
+(-358 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
 NIL 
-(-358 S R) 
+(-359 S R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-359 R) 
+(-360 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) 
-((-3990 |has| |#1| (-494)) (-3988 . T) (-3987 . T)) 
+((-3991 |has| |#1| (-495)) (-3989 . T) (-3988 . T)) 
 NIL 
-(-360 R) 
+(-361 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
 NIL 
 NIL 
-(-361 S R) 
+(-362 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 (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) 
-(-362 R) 
+((|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 (-412))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) 
+(-363 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}."))) 
-((-3990 OR (|has| |#1| (-960)) (|has| |#1| (-411))) (-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) ((-3995 "*") |has| |#1| (-494)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-494)) (-3985 |has| |#1| (-494))) 
+((-3991 OR (|has| |#1| (-961)) (|has| |#1| (-412))) (-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) ((-3996 "*") |has| |#1| (-495)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-495)) (-3986 |has| |#1| (-495))) 
 NIL 
-(-363 R A S B) 
+(-364 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) 
 NIL 
 NIL 
-(-364 R FE |x| |cen|) 
+(-365 R FE |x| |cen|) 
 ((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) 
 NIL 
 NIL 
-(-365 R FE |Expon| UPS TRAN |x|) 
+(-366 R FE |Expon| UPS TRAN |x|) 
 ((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) 
 NIL 
 NIL 
-(-366 A S) 
+(-367 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 (-755))) (|HasCategory| |#2| (QUOTE (-318)))) 
-(-367 S) 
+((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-368 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3993 . T) (-3983 . T) (-3994 . T)) 
+((-3994 . T) (-3984 . T) (-3995 . T)) 
 NIL 
-(-368 S A R B) 
+(-369 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-369 R -3091) 
+(-370 R -3092) 
 ((|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 
-(-370 R E) 
+(-371 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"))) 
-((-3980 -12 (|has| |#1| (-6 -3980)) (|has| |#2| (-6 -3980))) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3980)) (|HasAttribute| |#2| (QUOTE -3980)))) 
-(-371 R -3091) 
+((-3981 -12 (|has| |#1| (-6 -3981)) (|has| |#2| (-6 -3981))) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#2| (QUOTE -3981)))) 
+(-372 R -3092) 
 ((|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 
-(-372 R -3091) 
+(-373 R -3092) 
 ((|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 
-(-373 R -3091) 
+(-374 R -3092) 
 ((|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)))) 
-(-374 R -3091) 
+(-375 R -3092) 
 ((|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 
-(-375) 
+(-376) 
 ((|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 
-(-376 R -3091 UP) 
+(-377 R -3092 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 (-949 (-48))))) 
-(-377) 
+((|HasCategory| |#2| (QUOTE (-950 (-48))))) 
+(-378) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
 NIL 
-(-378 |f|) 
+(-379 |f|) 
 ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-379) 
+(-380) 
 ((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) 
 NIL 
 NIL 
-(-380 UP) 
+(-381 UP) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-381 R UP -3091) 
+(-382 R UP -3092) 
 ((|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 
-(-382 R UP) 
+(-383 R UP) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) 
 NIL 
 NIL 
-(-383 R) 
+(-384 R) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-345)))) 
-(-384) 
+((|HasCategory| |#1| (QUOTE (-346)))) 
+(-385) 
 ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer \\spad{zi}."))) 
 NIL 
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-(-385 |Dom| |Expon| |VarSet| |Dpol|) 
+(-386 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp, infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-312)))) 
-(-386 |Dom| |Expon| |VarSet| |Dpol|) 
+(-387 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp, infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) 
 NIL 
 NIL 
-(-387 |Dom| |Expon| |VarSet| |Dpol|) 
+(-388 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) 
 NIL 
 NIL 
-(-388 |Dom| |Expon| |VarSet| |Dpol|) 
+(-389 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) 
 NIL 
 NIL 
-(-389 S) 
+(-390 S) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-390) 
+(-391) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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}."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-391 R |n| |ls| |gamma|) 
+(-392 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"))) 
-((-3990 |has| (-348 (-856 |#1|)) (-494)) (-3988 . T) (-3987 . T)) 
-((|HasCategory| (-348 (-856 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-348 (-856 |#1|)) (QUOTE (-494)))) 
-(-392 |vl| R E) 
+((-3991 |has| (-349 (-857 |#1|)) (-495)) (-3989 . T) (-3988 . T)) 
+((|HasCategory| (-349 (-857 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-349 (-857 |#1|)) (QUOTE (-495)))) 
+(-393 |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"))) 
-(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-393 R BP) 
+(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-495)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-391))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-394 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) 
 NIL 
 NIL 
-(-394 OV E S R P) 
+(-395 OV E S R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-395 E OV R P) 
+(-396 E OV R P) 
 ((|constructor| (NIL "This package provides operations for GCD computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the GCD of \\spad{p} and \\spad{q}"))) 
 NIL 
 NIL 
-(-396 R) 
+(-397 R) 
 ((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) 
 NIL 
 NIL 
-(-397 R FE) 
+(-398 R FE) 
 ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}."))) 
 NIL 
 NIL 
-(-398 RP TP) 
+(-399 RP TP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) 
 NIL 
 NIL 
-(-399 |vl| R IS E |ff| P) 
+(-400 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-400 E V R P Q) 
+(-401 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
 NIL 
 NIL 
-(-401 R E |VarSet| P) 
+(-402 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-402 S R E) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-403 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) 
 NIL 
 NIL 
-(-403 R E) 
+(-404 R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) 
 NIL 
 NIL 
-(-404) 
+(-405) 
 ((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(vv) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect."))) 
 NIL 
 NIL 
-(-405) 
+(-406) 
 ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) 
 NIL 
 NIL 
-(-406) 
+(-407) 
 ((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) 
 NIL 
 NIL 
-(-407 S R E) 
+(-408 S R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-408 R E) 
+(-409 R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-409 |lv| -3091 R) 
+(-410 |lv| -3092 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
-(-410 S) 
+(-411 S) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
 NIL 
 NIL 
-(-411) 
+(-412) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-412 |Coef| |var| |cen|) 
+(-413 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-413 |Key| |Entry| |Tbl| |dent|) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-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 -349) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) 
+(-414 |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."))) 
-((-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) 
-(-414 R E V P) 
+((-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) 
+(-415 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)}"))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-415) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-416) 
 ((|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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-416) 
+(-417) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) 
 NIL 
 NIL 
-(-417 |Key| |Entry| |hashfn|) 
+(-418 |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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-418) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+(-419) 
 ((|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 
-(-419 |vl| R) 
+(-420 |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"))) 
-(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
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 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(-961))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-809 (-1089))))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-349 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(|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|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 (-319))) (|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 (-1089)))) (|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 (-319))) (|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| (-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 (-1089)))) (|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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3991)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) 
+(-422) 
 ((|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 
-(-422 S) 
+(-423 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}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-423 -3091 UP UPUP R) 
+((-3994 . T) (-3995 . 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)))) 
+(-424 -3092 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 
-(-424 BP) 
+(-425 BP) 
 ((|constructor| (NIL "This package provides the functions for the heuristic integer gcd. Geddes's algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,..,ak])} = gcd of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,..,fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,..fk])} = gcd and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,..fk])} = gcd and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,..,fk])} = gcd of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,..,fk])} = gcd of the polynomials \\spad{fi}."))) 
 NIL 
 NIL 
-(-425) 
+(-426) 
 ((|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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (QUOTE (-118))))) 
-(-426 A S) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-484) (QUOTE (-796 (-329)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1089)))) (|HasCategory| (-484) (QUOTE (-455 (-1089) (-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))))) 
+(-427 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) 
-(-427 S) 
+((|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) 
+(-428 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
 NIL 
-(-428 S) 
+(-429 S) 
 ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) 
 NIL 
 NIL 
-(-429) 
+(-430) 
 ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name `n'."))) 
 NIL 
 NIL 
-(-430 S) 
+(-431 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-431) 
+(-432) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-432 -3091 UP |AlExt| |AlPol|) 
+(-433 -3092 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
-(-433) 
+(-434) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| $ (QUOTE (-960))) (|HasCategory| $ (QUOTE (-949 (-483))))) 
-(-434 S |mn|) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
+(-435 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-435 R |Row| |Col|) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-436 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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-436 K R UP) 
+((-3994 . T) (-3995 . 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)))) 
+(-437 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 
-(-437 R UP -3091) 
+(-438 R UP -3092) 
 ((|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 
-(-438 |mn|) 
+(-439 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-552 (-472)))) (|HasCategory| (-85) (QUOTE (-755))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-551 (-771)))) (|HasCategory| (-85) (QUOTE (-72)))) 
-(-439 K R UP L) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+(-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 
-(-440) 
+(-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 
-(-441 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 
-(-442 -3091 |Expon| |VarSet| |DPoly|) 
+(-443 -3092 |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 (-552 (-1088))))) 
-(-443 |vl| |nv|) 
+((|HasCategory| |#3| (QUOTE (-553 (-1089))))) 
+(-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 
-(-444 T$) 
+(-445 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3055 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3056 (|f| |x| |x|) |x|))) . T)) 
 NIL 
-(-445) 
+(-446) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-446 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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-447 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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-448 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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-449 A S) 
+(-450 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-450 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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-451 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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-452 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 
-(-453 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 
-(-454 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 
-(-455 S E |un|) 
+(-456 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-715)))) 
-(-456 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}"))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-457) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|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 
-(-458 |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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((OR (|HasCategory| (-516 |#1|) (QUOTE (-118))) (|HasCategory| (-516 |#1|) (QUOTE (-318)))) (|HasCategory| (-516 |#1|) (QUOTE (-120))) (|HasCategory| (-516 |#1|) (QUOTE (-318))) (|HasCategory| (-516 |#1|) (QUOTE (-118)))) 
-(-459 R |Row| |Col| M) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-319)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-319))) (|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 
-((|HasAttribute| |#3| (QUOTE -3994))) 
-(-460 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasAttribute| |#3| (QUOTE -3995))) 
+(-461 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasAttribute| |#7| (QUOTE -3994))) 
-(-461) 
+((|HasAttribute| |#7| (QUOTE -3995))) 
+(-462) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
 NIL 
-(-462) 
+(-463) 
 ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) 
 NIL 
 NIL 
-(-463 S) 
+(-464 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-464) 
+(-465) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-465 GF) 
+(-466 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) 
 NIL 
 NIL 
-(-466) 
+(-467) 
 ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-467 R) 
+(-468 R) 
 ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) 
 NIL 
 NIL 
-(-468 |Varset|) 
+(-469 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-693) (QUOTE (-1012))))) 
-(-469 K -3091 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-694) (QUOTE (-1013))))) 
+(-470 K -3092 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
-(-470) 
+(-471) 
 NIL 
 NIL 
 NIL 
-(-471) 
+(-472) 
 ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) 
 NIL 
 NIL 
-(-472) 
+(-473) 
 ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-473 R) 
+(-474 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-474 |Coef| UTS) 
+(-475 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-475 K -3091 |Par|) 
+(-476 K -3092 |Par|) 
 ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-476 R BP |pMod| |nextMod|) 
+(-477 R BP |pMod| |nextMod|) 
 ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) 
 NIL 
 NIL 
-(-477 OV E R P) 
+(-478 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) 
 NIL 
 NIL 
-(-478 K UP |Coef| UTS) 
+(-479 K UP |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-479 |Coef| UTS) 
+(-480 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-480 R UP) 
+(-481 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-481 S) 
+(-482 S) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-482) 
+(-483) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
-((-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-483) 
+(-484) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-484) 
+(-485) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-485) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-486) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-487) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-488 |Key| |Entry| |addDom|) 
+(-489 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-489 R -3091) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+(-490 R -3092) 
 ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) 
 NIL 
 NIL 
-(-490 R0 -3091 UP UPUP R) 
+(-491 R0 -3092 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) 
 NIL 
 NIL 
-(-491) 
+(-492) 
 ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) 
 NIL 
 NIL 
-(-492 R) 
+(-493 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-3768 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3769 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-493 S) 
+(-494 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
 NIL 
 NIL 
-(-494) 
+(-495) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-495 R -3091) 
+(-496 R -3092) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-496 I) 
+(-497 I) 
 ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) 
 NIL 
 NIL 
-(-497 R -3091 L) 
+(-498 R -3092 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 -599) (|devaluate| |#2|)))) 
-(-498) 
+((|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 
-(-499 -3091 UP UPUP R) 
+(-500 -3092 UP UPUP R) 
 ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) 
 NIL 
 NIL 
-(-500 -3091 UP) 
+(-501 -3092 UP) 
 ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) 
 NIL 
 NIL 
-(-501 R -3091 L) 
+(-502 R -3092 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 -599) (|devaluate| |#2|)))) 
-(-502 R -3091) 
+((|HasCategory| |#3| (|%list| (QUOTE -600) (|devaluate| |#2|)))) 
+(-503 R -3092) 
 ((|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 (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-568))))) 
-(-503 -3091 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-1052)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-569))))) 
+(-504 -3092 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
-(-504 S) 
+(-505 S) 
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-505 -3091) 
+(-506 -3092) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
-(-506 R) 
+(-507 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) 
-((-3768 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3769 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-507) 
+(-508) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
-(-508 R -3091) 
+(-509 R -3092) 
 ((|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 (-552 (-799 (-483))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-949 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-494)))) 
-(-509 -3091 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-510 -3092 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-510 R -3091) 
+(-511 R -3092) 
 ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) 
 NIL 
 NIL 
-(-511) 
+(-512) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-512) 
+(-513) 
 ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) 
 NIL 
 NIL 
-(-513) 
+(-514) 
 ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) 
 NIL 
 NIL 
-(-514) 
+(-515) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-515 |p| |unBalanced?|) 
+(-516 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-516 |p|) 
+(-517 |p|) 
 ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) 
-(-517) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-319)))) 
+(-518) 
 ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) 
 NIL 
 NIL 
-(-518 -3091) 
+(-519 -3092) 
 ((|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}."))) 
-((-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-949 (-1088))))) 
-(-519 E -3091) 
+((-3989 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-950 (-1089))))) 
+(-520 E -3092) 
 ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) 
 NIL 
 NIL 
-(-520 R -3091) 
+(-521 R -3092) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-521) 
+(-522) 
 ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) 
 NIL 
 NIL 
-(-522 I) 
+(-523 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
 NIL 
-(-523 GF) 
+(-524 GF) 
 ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) 
 NIL 
 NIL 
-(-524 R) 
+(-525 R) 
 ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-120)))) 
-(-525) 
+(-526) 
 ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) 
 NIL 
 NIL 
-(-526 R E V P TS) 
+(-527 R E V P TS) 
 ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) 
 NIL 
 NIL 
-(-527) 
+(-528) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-528 E V R P) 
+(-529 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-529 |Coef|) 
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))) (|HasCategory| (-483) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483)))))) 
 (-530 |Coef|) 
+((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (|HasCategory| (-484) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484)))))) 
+(-531 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-3995 "*") |has| |#1| (-494)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-494)))) 
-(-531) 
+(((-3996 "*") |has| |#1| (-495)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-532) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) 
 NIL 
 NIL 
-(-532 A B) 
+(-533 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-533 A B C) 
+(-534 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-534 R -3091 FG) 
+(-535 R -3092 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
-(-535 S) 
+(-536 S) 
 ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) 
 NIL 
 NIL 
-(-536 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 -3994)) (|HasCategory| |#2| (QUOTE (-755))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#3| (QUOTE (-1012)))) 
-(-537 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-756))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-1013)))) 
+(-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 
-(-538) 
+(-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 
-(-539 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)."))) 
-((-3990 OR (-2561 (|has| |#2| (-316 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-494)))) (-3988 . T) (-3987 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-540) 
+((-3991 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-360 |#1|)) (|has| |#1| (-495)))) (-3989 . T) (-3988 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-541) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
 NIL 
-(-541) 
+(-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| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-542) 
+(-543) 
 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "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 
-(-543) 
+(-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| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-544) 
+(-545) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "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 
-(-545) 
+(-546) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-546 |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."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3858 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-755))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-547 S |Key| |Entry|) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3859 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |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 
-(-548 |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}."))) 
-((-3994 . T)) 
+((-3995 . T)) 
 NIL 
-(-549 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 (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#1| (QUOTE (-552 (-799 (-483)))))) 
-(-550 R S) 
+((|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|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 
-(-551 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 
-(-552 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-553 -3091 UP) 
+(-554 -3092 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-554 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 
-(-555) 
+(-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| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-556 S) 
+(-557 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-557 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}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-754)))) 
-(-558 S R) 
+((-3988 . T) (-3989 . T) (-3991 . 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 
-(-559 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."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-560 R -3091) 
+(-561 R -3092) 
 ((|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 
-(-561 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"))) 
-((-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3986 . T) (-3990 . T)) 
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-(-562 R E V P TS ST) 
+((-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3987 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 
-(-563 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 
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 ((|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 
-(-565 |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}}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-566 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 
-(-567 R -3091) 
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 ((|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 
-(-568) 
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 ((|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 
-(-569 |lv| -3091) 
+(-570 |lv| -3092) 
 ((|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 
-(-570) 
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 ((|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."))) 
-((-3994 . T)) 
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-(-571 R A) 
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+((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3859 (-1072)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-1072) (QUOTE (-756))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) 
+(-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)."))) 
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-(-572 S R) 
+((-3991 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-360 |#1|)) (|has| |#1| (-495)))) (-3989 . T) (-3988 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-573 R) 
+(-574 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3988 . T) (-3987 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3989 . T) (-3988 . T)) 
 NIL 
-(-574 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 
-(-575 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 
-(-576 |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 
-(-577 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 
-((-2559 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-578 K B) 
+((-2560 (|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}."))) 
-((-3988 . T) (-3987 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-576 |#2|) (QUOTE (-1012))))) 
-(-579 R) 
+((-3989 . T) (-3988 . 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 
-(-580 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}."))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-581 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 
-(-582 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."))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-583 A B) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|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 
-(-584 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 
-(-585 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 
-(-586 T$) 
+(-587 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-587 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| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-588 S) 
+(-589 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-589 R) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-590 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-590 S E |un|) 
+(-591 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 
-(-591 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 -3994))) 
-(-592 S) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
+(-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 
-(-593 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}."))) 
-((-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-713)))) 
-(-594 R -3091 L) 
+((-3989 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-714)))) 
+(-595 R -3092 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 
-(-595 A -2491) 
+(-596 A -2492) 
 ((|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}}"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-596 A) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-391))) (|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}}"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-597 A M) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-391))) (|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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-598 S A) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-599 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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)))) 
-(-599 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}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-600 -3091 UP) 
+(-601 -3092 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)))) 
-(-601 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 
-(-602 S) 
+(-603 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-603) 
+(-604) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-604 R) 
+(-605 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-605 |VarSet| R) 
+(-606 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3988 . T) (-3987 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3989 . T) (-3988 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-606 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 
-(-607 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}."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-608 -3091 |Row| |Col| M) 
+(-609 -3092 |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 
-(-609 -3091) 
+(-610 -3092) 
 ((|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 
-(-610 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 
-(-611 |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."))) 
-((-3990 . T) (-3993 . T) (-3987 . T) (-3988 . T)) 
-((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3995 #1="*"))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494))) (OR (|HasAttribute| |#2| (QUOTE (-3995 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088))))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-612) 
+((-3991 . T) (-3994 . T) (-3988 . T) (-3989 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3996 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-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 (-1089)))) (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3996 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-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 
-(-613 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-614 A S) 
+(-615 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-615 S) 
+(-616 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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 
-(-616) 
+(-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 
-(-617 |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 
-(-618 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 
-(-619 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 
-(-620 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 
-(-621) 
+(-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 
-(-622 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 
-(-623 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 
-(-624 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 
-(-625 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 (-3995 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-494)))) 
-(-626 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3996 "*"))) (|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."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T)) 
 NIL 
-(-627 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 
-(-628 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 (-494)))) 
-(-629 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."))) 
-((-3993 . T) (-3994 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3995 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((|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."))) 
+((-3994 . T) (-3995 . 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 (-3996 "*"))) (|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 
-(-631 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 
-(-632 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 
-(-633 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}."))) 
-((-3994 . T)) 
+((-3995 . T)) 
 NIL 
-(-634 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 
-(-635) 
+(-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 
-(-636 OV E -3091 PG) 
+(-637 OV E -3092 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 
-(-637 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 
-(-638 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 
-(-639 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 
-(-640 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 
-(-641 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 
-(-642 S -2668 I) 
+(-643 S -2669 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 
-(-643 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 
-(-644 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)}.}"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-645 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 
-(-646) 
+(-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 
-(-647 R |Mod| -2036 -3516 |exactQuo|) 
+(-648 R |Mod| -2037 -3517 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-648 R P) 
+(-649 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
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-(-649 IS E |ff|) 
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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 (-329)))) (|HasCategory| (-994) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-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| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-650 R M) 
+(-651 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) 
+((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-651 R |Mod| -2036 -3516 |exactQuo|) 
+(-652 R |Mod| -2037 -3517 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-652 S R) 
+(-653 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-653 R) 
+(-654 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-654 -3091) 
+(-655 -3092) 
 ((|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]]}."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-655 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-656) 
+(-657) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 
-(-657 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 
-(-658) 
+(-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 
-(-659 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 (-318)))) 
-(-660 R UP) 
+((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-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."))) 
-((-3986 |has| |#1| (-312)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 |has| |#1| (-312)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-661 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 
-(-662) 
+(-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| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-663 T$) 
+(-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 (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-664 T$) 
+(-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 (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-665 -3091 UP) 
+(-666 -3092 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 
-(-666 |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 
-(-667 |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 
-(-668 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 
-(-669 |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."))) 
-(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-820))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-772 |#1|) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-772 |#1|) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-670 E OV R PRF) 
+(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-495)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-391))) (-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 
-(-671 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 
-(-672 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 
-(-673 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}."))) 
-((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-755)))) 
-(-674 S) 
-((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
-((-3993 . T) (-3983 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-756)))) 
 (-675 S) 
+((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
+((-3994 . T) (-3984 . T) (-3995 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-676 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-3983 . T) (-3994 . T)) 
+((-3984 . T) (-3995 . T)) 
 NIL 
-(-676) 
+(-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 
-(-677 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 
-(-678 |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}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-679 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 
-(-680 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 
-(-681 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 
-(-682 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}."))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-683 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-684) 
+(-685) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-685 S) 
+(-686 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 
-(-686) 
+(-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 
-(-687 |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 
-(-688 -3091) 
+(-689 -3092) 
 ((|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 
-(-689 P -3091) 
+(-690 P -3092) 
 ((|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 
-(-690 T$) 
+(-691 T$) 
 NIL 
 NIL 
 NIL 
-(-691 UP -3091) 
+(-692 UP -3092) 
 ((|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 
-(-692 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 
-(-693) 
+(-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."))) 
-(((-3995 "*") . T)) 
+(((-3996 "*") . T)) 
 NIL 
-(-694 R -3091) 
+(-695 R -3092) 
 ((|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 
-(-695) 
+(-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 
-(-696 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 
-(-697 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 
-(-698 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 
-(-699 -3091 |ExtF| |SUEx| |ExtP| |n|) 
+(-700 -3092 |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 
-(-700 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 
-(-701 |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 
-(-702 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."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-552 (-1088))))) (|HasCategory| |#2| (QUOTE (-552 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-1088))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-552 (-1088)))) (-2559 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-1088)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-552 (-1088)))) (-2559 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) (-2559 (|HasCategory| |#1| (QUOTE (-38 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-552 (-1088)))) (-2559 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) (-2559 (|HasCategory| |#1| (QUOTE (-482))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-1088)))) (-2559 (|HasCategory| |#1| (QUOTE (-903 (-483))))))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-703 R) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
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+(-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)}"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-993) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-993) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-993) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-704 R S) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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 (-329)))) (|HasCategory| (-994) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-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 
-(-705 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 (-348 (-483)))))) 
-(-706 R E V P) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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.}"))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-707 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 (-494))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-708) 
+((-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 
-(-709) 
+(-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}."))) 
 NIL 
 NIL 
-(-710) 
+(-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."))) 
 NIL 
 NIL 
-(-711 |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}."))) 
 NIL 
 NIL 
-(-712 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|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-713) 
+(-714) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\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 
-(-714 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 
 NIL 
-(-715) 
+(-716) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-716) 
+(-717) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-717) 
+(-718) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-718 S R) 
+(-719 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-318)))) 
-(-719 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-720 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-720) 
+(-721) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
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-(-721 R) 
+(-722 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-348 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-908 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) 
-(-722 OR R OS S) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-349 (-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 (-349 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 
-(-723 R -3091 L) 
+(-724 R -3092 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 
-(-724 R -3091) 
+(-725 R -3092) 
 ((|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 
-(-725 R -3091) 
+(-726 R -3092) 
 ((|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 
-(-726 -3091 UP UPUP R) 
+(-727 -3092 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 
-(-727 -3091 UP L LQ) 
+(-728 -3092 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 
-(-728 -3091 UP L LQ) 
+(-729 -3092 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 
-(-729 -3091 UP) 
+(-730 -3092 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 
-(-730 -3091 L UP A LO) 
+(-731 -3092 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 
-(-731 -3091 UP) 
+(-732 -3092 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)))) 
-(-732 -3091 LO) 
+(-733 -3092 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 
-(-733 -3091 LODO) 
+(-734 -3092 LODO) 
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 NIL 
 NIL 
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 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|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 (-319))) (|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 (-1089)))) (|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 (-319))) (|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| (-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 (-1089)))) (|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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3991)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|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"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-737 (-1088)) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-737 (-1088)) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-737 (-1088)) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-736 |Kernels| R |var|) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-738 (-1089)) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-738 (-1089)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-800 (-329)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-738 (-1089)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-737 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-3995 "*") |has| |#2| (-312)) (-3986 |has| |#2| (-312)) (-3991 |has| |#2| (-312)) (-3985 |has| |#2| (-312)) (-3990 . T) (-3988 . T) (-3987 . T)) 
+(((-3996 "*") |has| |#2| (-312)) (-3987 |has| |#2| (-312)) (-3992 |has| |#2| (-312)) (-3986 |has| |#2| (-312)) (-3991 . T) (-3989 . T) (-3988 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-737 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 
-(-738 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| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-739) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-740) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-740 P R) 
+(-741 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) 
-(-741 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}."))) 
-((-3993 . T) (-3983 . T) (-3994 . T)) 
+((-3994 . T) (-3984 . T) (-3995 . T)) 
 NIL 
-(-742 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."))) 
-((-3990 |has| |#1| (-754))) 
-((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-754)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-743 R S) 
+((-3991 |has| |#1| (-755))) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 
-(-744 R) 
+(-745 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) 
+((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-745 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 
-(-746 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-747) 
+(-748) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-748) 
+(-749) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 
-(-749 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3990 |has| |#1| (-754))) 
-((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-754)))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-750 R S) 
+((-3991 |has| |#1| (-755))) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-751 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-751) 
+(-752) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-752 -2620 S) 
+(-753 -2621 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-753) 
+(-754) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-754) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-755) 
+(-756) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-756 T$ |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 (-551 (-771))))) 
-(-757 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-758) 
+(-759) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-759 S R) 
+(-760 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-760 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-761 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-761 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 (-494)))) 
-(-762 R |sigma| -3243) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-763 R |sigma| -3244) 
 ((|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."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-763 |x| R |sigma| -3243) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-764 |x| R |sigma| -3244) 
 ((|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}."))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-764 R) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-391))) (|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 (-348 (-483)))))) 
-(-765) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-484)))))) 
+(-766) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-766) 
+(-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 
-(-767) 
+(-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 
-(-768 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 
-(-769) 
+(-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 
-(-770) 
+(-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 
-(-771) 
+(-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 
-(-772 |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 
-(-773) 
+(-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 
-(-774 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)"))) 
-((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) 
+((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-775 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 
-(-776 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 
-(-777 |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)."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-778 |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}."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-779 |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)."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-777 |#1|) (QUOTE (-820))) (|HasCategory| (-777 |#1|) (QUOTE (-949 (-1088)))) (|HasCategory| (-777 |#1|) (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-120))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-472)))) (|HasCategory| (-777 |#1|) (QUOTE (-932))) (|HasCategory| (-777 |#1|) (QUOTE (-739))) (|HasCategory| (-777 |#1|) (QUOTE (-755))) (OR (|HasCategory| (-777 |#1|) (QUOTE (-739))) (|HasCategory| (-777 |#1|) (QUOTE (-755)))) (|HasCategory| (-777 |#1|) (QUOTE (-949 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-1064))) (|HasCategory| (-777 |#1|) (QUOTE (-795 (-328)))) (|HasCategory| (-777 |#1|) (QUOTE (-795 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-777 |#1|) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-777 |#1|) (QUOTE (-579 (-483)))) (|HasCategory| (-777 |#1|) (QUOTE (-189))) (|HasCategory| (-777 |#1|) (QUOTE (-810 (-1088)))) (|HasCategory| (-777 |#1|) (QUOTE (-190))) (|HasCategory| (-777 |#1|) (QUOTE (-808 (-1088)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -454) (QUOTE (-1088)) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -777) (|devaluate| |#1|)) (|%list| (QUOTE -777) (|devaluate| |#1|)))) (|HasCategory| (-777 |#1|) (QUOTE (-258))) (|HasCategory| (-777 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-777 |#1|) (QUOTE (-820)))) (|HasCategory| (-777 |#1|) (QUOTE (-118))))) 
-(-780 |p| PADIC) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-329)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1089)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1089)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -455) (QUOTE (-1089)) (|%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)}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-949 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755)))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-482))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-781 S T$) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| |#2| (QUOTE (-796 (-329)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1089)) (|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 (-1012))) (|HasCategory| |#2| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-12 (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771)))))) 
-(-782) 
+((-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 
-(-783) 
+(-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 
-(-784) 
+(-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 
-(-785 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 
-(-786 |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 
-(-787 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 
-(-788 |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 
-(-789) 
+(-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 
-(-790 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 
-(-791 |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 
-(-792) 
+(-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 
-(-793 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 
-(-794 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 
-(-795 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 
-(-796 |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 (-2559 (|HasCategory| |#2| (QUOTE (-949 (-1088))))) (-2559 (|HasCategory| |#2| (QUOTE (-960))))) (-12 (|HasCategory| |#2| (QUOTE (-960))) (-2559 (|HasCategory| |#2| (QUOTE (-949 (-1088)))))) (|HasCategory| |#2| (QUOTE (-949 (-1088))))) 
-(-797 R S) 
+((-12 (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1089))))) (-2560 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1089)))))) (|HasCategory| |#2| (QUOTE (-950 (-1089))))) 
+(-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 
-(-798 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 
-(-799 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 
-(-800 R -2668) 
+(-801 R -2669) 
 ((|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 
-(-801 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 
-(-802 |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 
-(-803 UP R) 
+(-804 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-804 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 
-(-805 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 
-(-806 UP -3091) 
+(-807 UP -3092) 
 ((|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 
-(-807 R S) 
+(-808 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-808 S) 
+(-809 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-809 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 
-(-810 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 
-(-811 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 (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-812 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)))) 
+(-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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-755)))) 
-(-813 |n| R) 
+((-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-756)))) 
+(-814 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 
-(-814 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."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-815 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 
-(-816 |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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318)))) 
-(-817 R E |VarSet| S) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-319)))) 
+(-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 
-(-818 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 
-(-819 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)))) 
-(-820) 
+(-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}."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-821 R0 -3091 UP UPUP R) 
+(-822 R0 -3092 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 
-(-822 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 
-(-823 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 
-(-824 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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-825 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 
-(-826 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 
-(-827) 
+(-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 
-(-828 -3091) 
+(-829 -3092) 
 ((|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 
-(-829) 
+(-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}."))) 
-(((-3995 "*") . T)) 
+(((-3996 "*") . T)) 
 NIL 
-(-830 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 
-(-831) 
+(-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)}"))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-832 |xx| -3091) 
+(-833 |xx| -3092) 
 ((|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 
-(-833 -3091 P) 
+(-834 -3092 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-834 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 
-(-835) 
+(-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 
-(-836 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 
-(-837) 
+(-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 
-(-838) 
+(-839) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-839) 
+(-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 
-(-840 R -3091) 
+(-841 R -3092) 
 ((|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 
-(-841 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 
-(-842 S R -3091) 
+(-843 S R -3092) 
 ((|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 
-(-843 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 
-(-844 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 
-(-845 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 
-(-846 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 -795) (|devaluate| |#1|)))) 
-(-847 -2668) 
+((|HasCategory| |#3| (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
+(-848 -2669) 
 ((|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 
-(-848 R -3091 -2668) 
+(-849 R -3092 -2669) 
 ((|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 
-(-849 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 
-(-850 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 
-(-851 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 
-(-852) 
+(-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 
-(-853 R) 
+(-854 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#1| (QUOTE (-960))) (-12 (|HasCategory| |#1| (QUOTE (-914))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-854 |lv| R) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|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 
-(-855 |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 (-754)))) 
-(-856 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}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-1088) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-1088) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-1088) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-1088) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-1088) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-857 R S) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-1089) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1089) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-1089) (QUOTE (-553 (-800 (-329)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1089) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1089) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-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 
-(-858 |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 
-(-859 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 (-820))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| |#4| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| |#4| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#4| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) 
-(-860 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-329)))) (|HasCategory| |#2| (QUOTE (-796 (-329)))) (|HasCategory| |#4| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-329))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|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}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-861 E V R P -3091) 
+(-862 E V R P -3092) 
 ((|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 
-(-862 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 
-(-863 E V R P -3091) 
+(-864 E V R P -3092) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-390)))) 
-(-864) 
+((|HasCategory| |#3| (QUOTE (-391)))) 
+(-865) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-865) 
+(-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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-866 R E) 
+(-867 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3991))) 
-(-867 R L) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3992))) 
+(-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 
-(-868 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"))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-869 A B) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|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 
-(-870) 
+(-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 
-(-871 -3091) 
+(-872 -3092) 
 ((|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 
-(-872 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 
-(-873) 
+(-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 
-(-874 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"))) 
-((-3990 -12 (|has| |#2| (-411)) (|has| |#1| (-411)))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-755))))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-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 (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-662))))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-716))) (|HasCategory| |#2| (QUOTE (-716)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-662))))) (-12 (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-662)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-755))))) 
-(-875) 
+((-3991 -12 (|has| |#2| (-412)) (|has| |#1| (-412)))) 
+((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 (-412))) (|HasCategory| |#2| (QUOTE (-412)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-412))) (|HasCategory| |#2| (QUOTE (-412)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-319)))) (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 (-412))) (|HasCategory| |#2| (QUOTE (-412)))) (-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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-876 T$) 
+(-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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-877 T$) 
+(-878 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-878 S T$) 
+(-879 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-879) 
+(-880) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-880 S) 
+(-881 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T)) 
 NIL 
-(-881 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 (-390)))) 
-(-882) 
+((|HasCategory| |#1| (QUOTE (-391)))) 
+(-883) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-883) 
+(-884) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-884 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 
-(-885 |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}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-886) 
+(-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 
-(-887 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 (-494)))) 
-(-888 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."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-889 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."))) 
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-((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-390)))) 
-(-890 K) 
+((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-391)))) 
+(-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."))) 
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-(-891 |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."))) 
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-(-892 R) 
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 ((|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}."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
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-(-893 R1 R2) 
+(-894 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
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-(-894 R) 
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 ((|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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-(-895 K) 
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 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
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-(-896 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"))) 
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-(-897 K R UP -3091) 
+(-898 K R UP -3092) 
 ((|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 
-(-898 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))))) 
-(-899 |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 
-(-900 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 
-(-901) 
+(-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 
-(-902 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 (-820))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-949 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-739))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-1064)))) 
-(-903 S) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-950 (-1089)))) (|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 (-1065)))) 
+(-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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-904 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 
-(-905 |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 
-(-906) 
+(-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 
-(-907 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."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T)) 
 NIL 
-(-908 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.}"))) 
-((-3986 |has| |#1| (-246)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1088)) (|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 (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-909 S R) 
+((-3987 |has| |#1| (-246)) (-3988 . T) (-3989 . T) (-3991 . 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 (-1089)) (|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 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-246)))) 
-(-910 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3986 |has| |#1| (-246)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 |has| |#1| (-246)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-911 QR R QS S) 
+(-912 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-912 S) 
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-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}."))) 
+((-3994 . T) (-3995 . 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-914) 
+(-915) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-915 -3091 UP UPUP |radicnd| |n|) 
+(-916 -3092 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-3986 |has| (-348 |#2|) (-312)) (-3991 |has| (-348 |#2|) (-312)) (-3985 |has| (-348 |#2|) (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088)))))) (|HasCategory| (-348 |#2|) (QUOTE (-579 (-483)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 |#2|) (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-810 (-1088))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-808 (-1088)))))) 
-(-916 |bb|) 
+((-3987 |has| (-349 |#2|) (-312)) (-3992 |has| (-349 |#2|) (-312)) (-3986 |has| (-349 |#2|) (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-349 |#2|) (QUOTE (-118))) (|HasCategory| (-349 |#2|) (QUOTE (-120))) (|HasCategory| (-349 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-319))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (|HasCategory| (-349 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-299))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089)))))) (OR (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-811 (-1089)))))) (|HasCategory| (-349 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-349 (-484)))))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-349 (-484))))) (|HasCategory| (-349 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-319))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-811 (-1089))))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-190))) (|HasCategory| (-349 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-349 |#2|) (QUOTE (-312))) (|HasCategory| (-349 |#2|) (QUOTE (-809 (-1089)))))) 
+(-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."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-483) (QUOTE (-820))) (|HasCategory| (-483) (QUOTE (-949 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-932))) (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755))) (OR (|HasCategory| (-483) (QUOTE (-739))) (|HasCategory| (-483) (QUOTE (-755)))) (|HasCategory| (-483) (QUOTE (-949 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-795 (-328)))) (|HasCategory| (-483) (QUOTE (-795 (-483)))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-483) (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-810 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-808 (-1088)))) (|HasCategory| (-483) (QUOTE (-454 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-260 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-258))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-579 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-820)))) (|HasCategory| (-483) (QUOTE (-118))))) 
-(-917) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1089)))) (|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 (-1065))) (|HasCategory| (-484) (QUOTE (-796 (-329)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1089)))) (|HasCategory| (-484) (QUOTE (-455 (-1089) (-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 
-(-918) 
+(-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 
-(-919 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 
-(-920 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 
-(-921 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 
-((|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-1012)))) 
-(-922 S) 
+((|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-1013)))) 
+(-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 
-(-923 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 
-(-924) 
+(-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}}"))) 
-((-3986 . T) (-3991 . T) (-3985 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3990 . T)) 
+((-3987 . T) (-3992 . T) (-3986 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3991 . T)) 
 NIL 
-(-925 R -3091) 
+(-926 R -3092) 
 ((|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 
-(-926 R -3091) 
+(-927 R -3092) 
 ((|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 
-(-927 -3091 UP) 
+(-928 -3092 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 
-(-928 -3091 UP) 
+(-929 -3092 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 
-(-929 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 
-(-930 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 
-(-931) 
+(-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 
-(-932) 
+(-933) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-933 |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 
-(-934 |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 
-(-935) 
+(-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 
-(-936 |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"))) 
-((-3986 . T) (-3991 . T) (-3985 . T) (-3988 . T) (-3987 . T) ((-3995 "*") . T) (-3990 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-348 (-483)) (QUOTE (-949 (-483))))) 
-(-937 -3091 L) 
+((-3987 . T) (-3992 . T) (-3986 . T) (-3989 . T) (-3988 . T) ((-3996 "*") . T) (-3991 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-349 (-484)) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-349 (-484)) (QUOTE (-950 (-349 (-484))))) (|HasCategory| (-349 (-484)) (QUOTE (-950 (-484))))) 
+(-938 -3092 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 
-(-938 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 
-(-939 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."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-940) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-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 
-(-941 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 (-3995 "*")))) 
-(-942 R) 
+((|HasAttribute| |#1| (QUOTE (-3996 "*")))) 
+(-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 (-318)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) 
-(-943 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) 
+(-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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-944 S) 
+(-945 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-945 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 
-(-946 -3091 |Expon| |VarSet| |FPol| |LFPol|) 
+(-947 -3092 |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"))) 
-(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-947) 
+(-948) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-948 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 
-(-949 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 
-(-950 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 
-(-951 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 
-(-952) 
+(-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 
-(-953 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 
-(-954 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 
-(-955 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| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-956 T$) 
+(-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 
-(-957 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}."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-1012))) (|HasCategory| (-702 |#1| (-772 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -702) (|devaluate| |#1|) (|%list| (QUOTE -772) (|devaluate| |#2|)))))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-552 (-472)))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-772 |#2|) (QUOTE (-318))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-702 |#1| (-772 |#2|)) (QUOTE (-72)))) 
-(-958) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-773 |#2|) (QUOTE (-319))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) 
+(-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 
-(-959 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 
-(-960) 
+(-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."))) 
-((-3990 . T)) 
+((-3991 . T)) 
 NIL 
-(-961 |xx| -3091) 
+(-962 |xx| -3092) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-962 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 
-(-963 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.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-146)))) 
-(-964 |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.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
-((-3993 . T) (-3988 . T) (-3987 . T)) 
+((-3994 . T) (-3989 . T) (-3988 . T)) 
 NIL 
-(-965 |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}."))) 
-((-3993 . T) (-3988 . T) (-3987 . 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 (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-494))) (-12 (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-551 (-771))))) 
-(-966 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3994 . T) (-3989 . T) (-3988 . 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 (-1013))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|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 
-(-967 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 
-(-968 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 
-(-969) 
+(-970) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-970 S T$) 
+(-971 S T$) 
 ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1012)))) 
-(-971 S) 
+((|HasCategory| |#1| (QUOTE (-1013)))) 
+(-972 S) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-972) 
+(-973) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-973 |TheField| |ThePolDom|) 
+(-974 |TheField| |ThePolDom|) 
 ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-974) 
+(-975) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-975 S R E V) 
+(-976 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-903 (-483)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#4| (QUOTE (-552 (-1088))))) 
-(-976 R E V) 
+((|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-904 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-1089))))) 
+(-977 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-977) 
+(-978) 
 ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) 
 NIL 
 NIL 
-(-978 S |TheField| |ThePols|) 
+(-979 S |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-979 |TheField| |ThePols|) 
+(-980 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-980 R E V P TS) 
+(-981 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-981 S R E V P) 
+(-982 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-982 R E V P) 
+(-983 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-983 R E V P TS) 
+(-984 R E V P TS) 
 ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-984) 
+(-985) 
 ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-985) 
+(-986) 
 ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) 
 NIL 
 NIL 
-(-986 |Base| R -3091) 
+(-987 |Base| R -3092) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-987 |f|) 
+(-988 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-988 |Base| R -3091) 
+(-989 |Base| R -3092) 
 ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) 
 NIL 
 NIL 
-(-989 R |ls|) 
+(-990 R |ls|) 
 ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) 
 NIL 
 NIL 
-(-990 R UP M) 
+(-991 R UP M) 
 ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) 
-((-3986 |has| |#1| (-312)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . 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 (-318))) (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 (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1088))))) (-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 (-808 (-1088)))))) 
-(-991 UP SAE UPA) 
+((-3987 |has| |#1| (-312)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . 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 (-319))) (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 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-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 (-1089))))) (-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 (-1089)))))) 
+(-992 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-992 UP SAE UPA) 
+(-993 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-993) 
+(-994) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-994) 
+(-995) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-995 S) 
+(-996 S) 
 ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) 
 NIL 
 NIL 
-(-996) 
+(-997) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-997 R) 
+(-998 R) 
 ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) 
 NIL 
 NIL 
-(-998 R) 
+(-999 R) 
 ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| (-999 (-1088)) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| (-999 (-1088)) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-999 (-1088)) (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1088)))) (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-999 S) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-800 (-329)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-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 
-(-1000 S) 
+(-1001 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-1012)))) 
-(-1001 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 (-754)))) 
-(-1002) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-1003) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1003 S) 
+(-1004 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1000 |#1|) (QUOTE (-1012)))) 
-(-1004 R S) 
+((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) 
+(-1005 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1005 S) 
+(-1006 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
 NIL 
 NIL 
-(-1006 S L) 
+(-1007 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) 
 NIL 
 NIL 
-(-1007) 
+(-1008) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1008 S) 
+(-1009 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) 
-((-3993 . T) (-3983 . T) (-3994 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-1009 A S) 
+((-3994 . T) (-3984 . T) (-3995 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-319))) (|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 (-319))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-1010 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1010 S) 
+(-1011 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
-((-3983 . T)) 
+((-3984 . T)) 
 NIL 
-(-1011 S) 
+(-1012 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1012) 
+(-1013) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1013 |m| |n|) 
+(-1014 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1014) 
+(-1015) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1015 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1016 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1016 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1017 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1017 R E V P TS) 
+(-1018 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1018 R E V P TS) 
+(-1019 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1019 R E V P) 
+(-1020 R E V P) 
 ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-1020) 
+(-1021) 
 ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1021 T$) 
+(-1022 T$) 
 ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) 
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1022 T$) 
+(-1023 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) 
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1023 S) 
+(-1024 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1024) 
+(-1025) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1025 |dimtot| |dim1| S) 
+(-1026 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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-(-1026 R |x|) 
+((-3988 |has| |#3| (-961)) (-3989 |has| |#3| (-961)) (-3991 |has| |#3| (-6 -3991)) (-3994 . T)) 
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|#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-319))) (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 (-1089))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (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 (-319))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|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 (-319))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|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 (-1089)))) (|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 (-1089)))) (|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 (-1089)))) (|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 (-1089)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|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 (-1089)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-809 (-1089))))) (|HasCategory| |#3| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|HasCategory| |#3| (QUOTE (-950 (-349 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-349 (-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 (-1089)))) (|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 (-319))) (|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 (-1089)))) (|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 (-319))) (|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| (-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 (-1089)))) (|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 (-349 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasAttribute| |#3| (QUOTE -3991)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1089)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|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 (-390)))) 
-(-1027) 
+((|HasCategory| |#1| (QUOTE (-391)))) 
+(-1028) 
 ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) 
 NIL 
 NIL 
-(-1028) 
+(-1029) 
 ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) 
 NIL 
 NIL 
-(-1029 R -3091) 
+(-1030 R -3092) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1030 R) 
+(-1031 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1031) 
+(-1032) 
 ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) 
 NIL 
 NIL 
-(-1032) 
+(-1033) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) 
-((-3981 . T) (-3985 . T) (-3980 . T) (-3991 . T) (-3992 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3982 . T) (-3986 . T) (-3981 . T) (-3992 . T) (-3993 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1033 S) 
+(-1034 S) 
 ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-3993 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T)) 
 NIL 
-(-1034 S |ndim| R |Row| |Col|) 
+(-1035 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3995 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
-(-1035 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3996 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
+(-1036 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
-((-3993 . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3994 . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1036 R |Row| |Col| M) 
+(-1037 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1037 R |VarSet|) 
+(-1038 R |VarSet|) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-820))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-820)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-820)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-328)))) (|HasCategory| |#2| (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-795 (-483)))) (|HasCategory| |#2| (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-328))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-799 (-483))))) (|HasCategory| |#2| (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-552 (-472))))) (|HasCategory| |#1| (QUOTE (-579 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1038 |Coef| |Var| SMP) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-391))) (|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 (-329)))) (|HasCategory| |#2| (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1039 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1039 R E V P) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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)))) 
+(-1040 R E V P) 
 ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-1040 UP -3091) 
+(-1041 UP -3092) 
 ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) 
 NIL 
 NIL 
-(-1041 R) 
+(-1042 R) 
 ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) 
 NIL 
 NIL 
-(-1042 R) 
+(-1043 R) 
 ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1043 R) 
+(-1044 R) 
 ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) 
 NIL 
 NIL 
-(-1044 S A) 
+(-1045 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-1045 R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1046 R) 
 ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) 
 NIL 
 NIL 
-(-1046 R) 
+(-1047 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1047) 
+(-1048) 
 ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) 
 NIL 
 NIL 
-(-1048) 
+(-1049) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) 
 NIL 
 NIL 
-(-1049) 
+(-1050) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) 
 NIL 
 NIL 
-(-1050) 
+(-1051) 
 ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) 
 NIL 
 NIL 
-(-1051) 
+(-1052) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1052 V C) 
+(-1053 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1053 V C) 
+(-1054 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-1052 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012))) (OR (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1012)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-551 (-771)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-72)))) 
-(-1054 |ndim| R) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-1053 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1053) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-552 (-772)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72)))) 
+(-1055 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) 
-((-3990 . T) (-3982 |has| |#2| (-6 (-3995 "*"))) (-3993 . T) (-3987 . T) (-3988 . T)) 
-((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3995 #1="*"))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3995 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-808 (-1088))))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-1055 S) 
+((-3991 . T) (-3983 |has| |#2| (-6 (-3996 "*"))) (-3994 . T) (-3988 . T) (-3989 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3996 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-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 (-1089)))) (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3996 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1089))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-1056 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1056) 
+(-1057) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-1057 R E V P TS) 
+(-1058 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1058 R E V P) 
+(-1059 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1059) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-1060) 
 ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) 
 NIL 
 NIL 
-(-1060 S) 
+(-1061 S) 
 ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1061 A S) 
+((-3994 . T) (-3995 . 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)))) 
+(-1062 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1062 S) 
+(-1063 S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1063 |Key| |Ent| |dent|) 
+(-1064 |Key| |Ent| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
-((-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) 
-(-1064) 
+((-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) 
+(-1065) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1065) 
+(-1066) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1066 |Coef|) 
+(-1067 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1067 S) 
-((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
-((-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-1068 S) 
+((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
+((-3995 . 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)))) 
+(-1069 S) 
 ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) 
 NIL 
 NIL 
-(-1069 A B) 
+(-1070 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-1070 A B C) 
+(-1071 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) 
 NIL 
 NIL 
-(-1071) 
+(-1072) 
 ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-755)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-551 (-771)))) (|HasCategory| (-117) (QUOTE (-552 (-472)))) (OR (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-117) (QUOTE (-755))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) 
-(-1072 |Entry|) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) 
+(-1073 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3858 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-1073 A) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3859 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
+(-1074 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) 
-(-1074 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-349 (-484)))))) 
+(-1075 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1075 |Coef|) 
+(-1076 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1076 R UP) 
+(-1077 R UP) 
 ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-258)))) 
-(-1077 |n| R) 
+(-1078 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1078 S1 S2) 
+(-1079 S1 S2) 
 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) 
 NIL 
 NIL 
-(-1079) 
+(-1080) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1080 |Coef| |var| |cen|) 
+(-1081 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-3995 "*") OR (-2561 (|has| |#1| (-312)) (|has| (-1087 |#1| |#2| |#3|) (-739))) (|has| |#1| (-146)) (-2561 (|has| |#1| (-312)) (|has| (-1087 |#1| |#2| |#3|) (-820)))) (-3986 OR (-2561 (|has| |#1| (-312)) (|has| (-1087 |#1| |#2| |#3|) (-739))) (|has| |#1| (-494)) (-2561 (|has| |#1| (-312)) (|has| (-1087 |#1| |#2| |#3|) (-820)))) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1087 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1087 |#1| |#2| |#3|) (QUOTE (-739)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1087 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1087 |#1| |#2| |#3|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1087 |#1| |#2| |#3|) (QUOTE (-808 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| 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-(-1081 R -3091) 
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(QUOTE (-312))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-756)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1082 R -3092) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
 NIL 
-(-1082 R) 
+(-1083 R) 
 ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) 
 NIL 
 NIL 
-(-1083 R) 
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 ((|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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-(-1084 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 (-329)))) (|HasCategory| (-994) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-811 (-1089)))) (|HasCategory| |#1| (QUOTE (-809 (-1089)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#1| (QUOTE (-391))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1085 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1085 E OV R P) 
+(-1086 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) 
 NIL 
 NIL 
-(-1086 |Coef| |var| |cen|) 
-((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
 (-1087 |Coef| |var| |cen|) 
+((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-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 -349) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) 
+(-1088 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|)))) (|HasCategory| (-693) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1088) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|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 -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) 
+(-1089) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1089 R) 
+(-1090 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1090 R) 
+(-1091 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-6 -3991)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#1| (QUOTE (-949 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-949 (-483)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-883) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3991))) 
-(-1091) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-6 -3992)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-391))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3992))) 
+(-1092) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1092) 
+(-1093) 
 ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) 
 NIL 
 NIL 
-(-1093) 
+(-1094) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1094 N) 
+(-1095 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1095 N) 
+(-1096 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) 
 NIL 
 NIL 
-(-1096) 
+(-1097) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1097 R) 
+(-1098 R) 
 ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-1098) 
+(-1099) 
 ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) 
 NIL 
 NIL 
-(-1099 S) 
+(-1100 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1100 |Key| |Entry|) 
+(-1101 |Key| |Entry|) 
 ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) 
-((-3993 . T) (-3994 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3858) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| |#2| (QUOTE (-551 (-771))))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-551 (-771)))) (|HasCategory| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-1101 S) 
+((-3994 . T) (-3995 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3859 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+(-1102 S) 
 ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) 
 NIL 
 NIL 
-(-1102 S) 
+(-1103 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
 NIL 
-(-1103 R) 
+(-1104 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1104 S |Key| |Entry|) 
+(-1105 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1105 |Key| |Entry|) 
+(-1106 |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-3994 . T)) 
+((-3995 . T)) 
 NIL 
-(-1106 |Key| |Entry|) 
+(-1107 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) 
 NIL 
 NIL 
-(-1107) 
+(-1108) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1108 S) 
+(-1109 S) 
 ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) 
 NIL 
 NIL 
-(-1109) 
+(-1110) 
 ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) 
 NIL 
 NIL 
-(-1110 R) 
+(-1111 R) 
 ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-1111) 
+(-1112) 
 ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1112 S) 
+(-1113 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1113) 
+(-1114) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1114 S) 
-((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-1115 S) 
+((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1116 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1116) 
+(-1117) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1117 R -3091) 
+(-1118 R -3092) 
 ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
-(-1118 R |Row| |Col| M) 
+(-1119 R |Row| |Col| M) 
 ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) 
 NIL 
 NIL 
-(-1119 R -3091) 
+(-1120 R -3092) 
 ((|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 -552) (|%list| (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -795) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -552) (|%list| (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -795) (|devaluate| |#1|))))) 
-(-1120 |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|))))) 
+(-1121 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1121 S R E V P) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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)))) 
+(-1122 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-318)))) 
-(-1122 R E V P) 
+((|HasCategory| |#4| (QUOTE (-319)))) 
+(-1123 R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-1123 |Curve|) 
+(-1124 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) 
 NIL 
 NIL 
-(-1124) 
+(-1125) 
 ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) 
 NIL 
 NIL 
-(-1125 S) 
+(-1126 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-551 (-771))))) 
-(-1126 -3091) 
+((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) 
+(-1127 -3092) 
 ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) 
 NIL 
 NIL 
-(-1127) 
+(-1128) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1128) 
+(-1129) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1129 S) 
+(-1130 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-1130) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1131) 
 ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) 
 NIL 
 NIL 
-(-1131 S) 
+(-1132 S) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
 NIL 
 NIL 
-(-1132) 
+(-1133) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1133) 
+(-1134) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1134) 
+(-1135) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1135) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1136) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1137 |Coef| |var| |cen|) 
+(-1138 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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-(-1138 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
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(-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-821))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-811 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-756)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1139 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1139 |Coef|) 
+(-1140 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1140 S |Coef| UTS) 
+(-1141 S |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-1141 |Coef| UTS) 
+(-1142 |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
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 NIL 
-(-1142 |Coef| UTS) 
+(-1143 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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-(-1143 ZP) 
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+(-1144 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1144 S) 
+(-1145 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-754))) (|HasCategory| |#1| (QUOTE (-1012)))) 
-(-1145 R S) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) 
+(-1146 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-754)))) 
-(-1146 |x| R) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-1147 |x| R) 
 ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3995 "*") |has| |#2| (-146)) (-3986 |has| |#2| (-494)) (-3989 |has| |#2| (-312)) (-3991 |has| |#2| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-328)))) (|HasCategory| (-993) (QUOTE (-795 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-795 (-483)))) (|HasCategory| (-993) (QUOTE (-795 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-328))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-799 (-483))))) (|HasCategory| (-993) (QUOTE (-552 (-799 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-552 (-472)))) (|HasCategory| (-993) (QUOTE (-552 (-472))))) (|HasCategory| |#2| (QUOTE (-579 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483)))))) (|HasCategory| |#2| (QUOTE (-949 (-348 (-483))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-820)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-820)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-810 (-1088)))) (|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1147 |x| R |y| S) 
+(((-3996 "*") |has| |#2| (-146)) (-3987 |has| |#2| (-495)) (-3990 |has| |#2| (-312)) (-3992 |has| |#2| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . 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 (-329)))) (|HasCategory| (-994) (QUOTE (-796 (-329))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-329))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-329)))))) (-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 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-349 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-811 (-1089)))) (|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-391))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-1148 |x| R |y| S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1148 R Q UP) 
+(-1149 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1149 R UP) 
+(-1150 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1150 R UP) 
+(-1151 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) 
 NIL 
 NIL 
-(-1151 R U) 
+(-1152 R U) 
 ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) 
 NIL 
 NIL 
-(-1152 S R) 
+(-1153 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1064)))) 
-(-1153 R) 
+((|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-391))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1065)))) 
+(-1154 R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3989 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3990 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-1154 R PR S PS) 
+(-1155 R PR S PS) 
 ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) 
 NIL 
 NIL 
-(-1155 S |Coef| |Expon|) 
+(-1156 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-808 (-1088)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1024))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#2|) (QUOTE (-1088)))))) 
-(-1156 |Coef| |Expon|) 
+((|HasCategory| |#2| (QUOTE (-809 (-1089)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#2|) (QUOTE (-1089)))))) 
+(-1157 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1157 RC P) 
+(-1158 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1158 |Coef| |var| |cen|) 
+(-1159 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1159 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-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 -349) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) 
+(-1160 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1160 |Coef|) 
+(-1161 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1161 S |Coef| ULS) 
+(-1162 S |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
 NIL 
 NIL 
-(-1162 |Coef| ULS) 
+(-1163 |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1163 |Coef| ULS) 
+(-1164 |Coef| ULS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3991 |has| |#1| (-312)) (-3985 |has| |#1| (-312)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-483)))))) 
-(-1164 R FE |var| |cen|) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3986 |has| |#1| (-312)) (-3988 . T) (-3989 . T) (-3991 . 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 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-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 -349) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-349 (-484)))))) 
+(-1165 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
-(((-3995 "*") |has| (-1158 |#2| |#3| |#4|) (-146)) (-3986 |has| (-1158 |#2| |#3| |#4|) (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-348 (-483)))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-348 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-949 (-483)))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-494)))) 
-(-1165 A S) 
+(((-3996 "*") |has| (-1159 |#2| |#3| |#4|) (-146)) (-3987 |has| (-1159 |#2| |#3| |#4|) (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-349 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-349 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-349 (-484)))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-349 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-391))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-495)))) 
+(-1166 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3994))) 
-(-1166 S) 
+((|HasAttribute| |#1| (QUOTE -3995))) 
+(-1167 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1167 |Coef| |var| |cen|) 
+(-1168 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-808 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-693)) (|devaluate| |#1|)))) (|HasCategory| (-693) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasSignature| |#1| (|%list| (QUOTE -3944) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-693))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1168 |Coef1| |Coef2| UTS1 UTS2) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-349 (-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 (-1089)))) (|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 -3945) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-349 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#1|))))))) 
+(-1169 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1169 S |Coef|) 
+(-1170 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-29 (-483)))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasSignature| |#2| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -582) (QUOTE (-1088))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3810) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1088))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-483))))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-1170 |Coef|) 
+((|HasCategory| |#2| (QUOTE (-29 (-484)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasSignature| |#2| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3811) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (QUOTE (-38 (-349 (-484))))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-1171 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
-(((-3995 "*") |has| |#1| (-146)) (-3986 |has| |#1| (-494)) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") |has| |#1| (-146)) (-3987 |has| |#1| (-495)) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1171 |Coef| UTS) 
+(-1172 |Coef| UTS) 
 ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) 
 NIL 
 NIL 
-(-1172 -3091 UP L UTS) 
+(-1173 -3092 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 (-494)))) 
-(-1173) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-1174) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
 NIL 
 NIL 
-(-1174 |sym|) 
+(-1175 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1175 S R) 
+(-1176 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-914))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-662))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1176 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)))) 
+(-1177 R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-3994 . T) (-3993 . T)) 
+((-3995 . T) (-3994 . T)) 
 NIL 
-(-1177 R) 
+(-1178 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-3994 . T) (-3993 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-551 (-771)))) (|HasCategory| |#1| (QUOTE (-552 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-755))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-662))) (|HasCategory| |#1| (QUOTE (-960))) (-12 (|HasCategory| |#1| (QUOTE (-914))) (|HasCategory| |#1| (QUOTE (-960)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-1178 A B) 
+((-3995 . T) (-3994 . 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 (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-1179 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1179) 
+(-1180) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1180) 
+(-1181) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1181) 
+(-1182) 
 ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) 
 NIL 
 NIL 
-(-1182) 
+(-1183) 
 ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) 
 NIL 
 NIL 
-(-1183) 
+(-1184) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1184 A S) 
+(-1185 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1185 S) 
+(-1186 S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
-((-3988 . T) (-3987 . T)) 
+((-3989 . T) (-3988 . T)) 
 NIL 
-(-1186 R) 
+(-1187 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1187 K R UP -3091) 
+(-1188 K R UP -3092) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1188) 
+(-1189) 
 ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) 
 NIL 
 NIL 
-(-1189) 
+(-1190) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1190 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1191 R |VarSet| E P |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-3988 |has| |#1| (-146)) (-3987 |has| |#1| (-146)) (-3990 . T)) 
+((-3989 |has| |#1| (-146)) (-3988 |has| |#1| (-146)) (-3991 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1191 R E V P) 
+(-1192 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) 
-((-3994 . T) (-3993 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-552 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-551 (-771)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1192 R) 
+((-3995 . T) (-3994 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+(-1193 R) 
 ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) 
-((-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1193 |vl| R) 
+(-1194 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) 
-((-3990 . T) (-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3986))) 
-(-1194 R |VarSet| XPOLY) 
+((-3991 . T) (-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3987))) 
+(-1195 R |VarSet| XPOLY) 
 ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) 
 NIL 
 NIL 
-(-1195 S -3091) 
+(-1196 S -3092) 
 ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1196 -3091) 
+((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
+(-1197 -3092) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3985 . T) (-3991 . T) (-3986 . T) ((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+((-3986 . T) (-3992 . T) (-3987 . T) ((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
-(-1197 |vl| R) 
+(-1198 |vl| R) 
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-1198 |VarSet| R) 
+(-1199 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) 
-((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-653 (-348 (-483))))) (|HasAttribute| |#2| (QUOTE -3986))) 
-(-1199 R) 
+((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-349 (-484))))) (|HasAttribute| |#2| (QUOTE -3987))) 
+(-1200 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-3986 |has| |#1| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3986))) 
-(-1200 |vl| R) 
+((-3987 |has| |#1| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3987))) 
+(-1201 |vl| R) 
 ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) 
+((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) 
 NIL 
-(-1201 R E) 
+(-1202 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-3990 . T) (-3991 |has| |#1| (-6 -3991)) (-3986 |has| |#1| (-6 -3986)) (-3988 . T) (-3987 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3986))) 
-(-1202 |VarSet| R) 
+((-3991 . T) (-3992 |has| |#1| (-6 -3992)) (-3987 |has| |#1| (-6 -3987)) (-3989 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3987))) 
+(-1203 |VarSet| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) 
-((-3986 |has| |#2| (-6 -3986)) (-3988 . T) (-3987 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3986))) 
-(-1203) 
+((-3987 |has| |#2| (-6 -3987)) (-3989 . T) (-3988 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3987))) 
+(-1204) 
 ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) 
 NIL 
 NIL 
-(-1204 A) 
+(-1205 A) 
 ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) 
 NIL 
 NIL 
-(-1205 R |ls| |ls2|) 
+(-1206 R |ls| |ls2|) 
 ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1206 R) 
+(-1207 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1207 |p|) 
+(-1208 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-3995 "*") . T) (-3987 . T) (-3988 . T) (-3990 . T)) 
+(((-3996 "*") . T) (-3988 . T) (-3989 . T) (-3991 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4776,4 +4780,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1960106 1960111 1960116 1960121) (-2 NIL 1960086 1960091 1960096 1960101) (-1 NIL 1960066 1960071 1960076 1960081) (0 NIL 1960046 1960051 1960056 1960061) (-1207 "ZMOD.spad" 1959855 1959868 1959984 1960041) (-1206 "ZLINDEP.spad" 1958953 1958964 1959845 1959850) (-1205 "ZDSOLVE.spad" 1948914 1948936 1958943 1958948) (-1204 "YSTREAM.spad" 1948409 1948420 1948904 1948909) (-1203 "YDIAGRAM.spad" 1948043 1948052 1948399 1948404) (-1202 "XRPOLY.spad" 1947263 1947283 1947899 1947968) (-1201 "XPR.spad" 1945058 1945071 1946981 1947080) (-1200 "XPOLYC.spad" 1944377 1944393 1944984 1945053) (-1199 "XPOLY.spad" 1943932 1943943 1944233 1944302) (-1198 "XPBWPOLY.spad" 1942403 1942423 1943738 1943807) (-1197 "XFALG.spad" 1939451 1939467 1942329 1942398) (-1196 "XF.spad" 1937914 1937929 1939353 1939446) (-1195 "XF.spad" 1936357 1936374 1937798 1937803) (-1194 "XEXPPKG.spad" 1935616 1935642 1936347 1936352) (-1193 "XDPOLY.spad" 1935230 1935246 1935472 1935541) (-1192 "XALG.spad" 1934898 1934909 1935186 1935225) (-1191 "WUTSET.spad" 1930901 1930918 1934532 1934559) (-1190 "WP.spad" 1930108 1930152 1930759 1930826) (-1189 "WHILEAST.spad" 1929906 1929915 1930098 1930103) (-1188 "WHEREAST.spad" 1929577 1929586 1929896 1929901) (-1187 "WFFINTBS.spad" 1927240 1927262 1929567 1929572) (-1186 "WEIER.spad" 1925462 1925473 1927230 1927235) (-1185 "VSPACE.spad" 1925135 1925146 1925430 1925457) (-1184 "VSPACE.spad" 1924828 1924841 1925125 1925130) (-1183 "VOID.spad" 1924505 1924514 1924818 1924823) (-1182 "VIEWDEF.spad" 1919706 1919715 1924495 1924500) (-1181 "VIEW3D.spad" 1903667 1903676 1919696 1919701) (-1180 "VIEW2D.spad" 1891566 1891575 1903657 1903662) (-1179 "VIEW.spad" 1889286 1889295 1891556 1891561) (-1178 "VECTOR2.spad" 1887925 1887938 1889276 1889281) (-1177 "VECTOR.spad" 1886644 1886655 1886895 1886922) (-1176 "VECTCAT.spad" 1884556 1884567 1886612 1886639) (-1175 "VECTCAT.spad" 1882277 1882290 1884335 1884340) (-1174 "VARIABLE.spad" 1882057 1882072 1882267 1882272) (-1173 "UTYPE.spad" 1881701 1881710 1882047 1882052) (-1172 "UTSODETL.spad" 1880996 1881020 1881657 1881662) (-1171 "UTSODE.spad" 1879212 1879232 1880986 1880991) (-1170 "UTSCAT.spad" 1876691 1876707 1879110 1879207) (-1169 "UTSCAT.spad" 1873838 1873856 1876259 1876264) (-1168 "UTS2.spad" 1873433 1873468 1873828 1873833) (-1167 "UTS.spad" 1868445 1868473 1871965 1872062) (-1166 "URAGG.spad" 1863166 1863177 1868435 1868440) (-1165 "URAGG.spad" 1857851 1857864 1863122 1863127) (-1164 "UPXSSING.spad" 1855619 1855645 1857055 1857188) (-1163 "UPXSCONS.spad" 1853437 1853457 1853810 1853959) (-1162 "UPXSCCA.spad" 1852008 1852028 1853283 1853432) (-1161 "UPXSCCA.spad" 1850721 1850743 1851998 1852003) (-1160 "UPXSCAT.spad" 1849310 1849326 1850567 1850716) (-1159 "UPXS2.spad" 1848853 1848906 1849300 1849305) (-1158 "UPXS.spad" 1846208 1846236 1847044 1847193) (-1157 "UPSQFREE.spad" 1844623 1844637 1846198 1846203) (-1156 "UPSCAT.spad" 1842418 1842442 1844521 1844618) (-1155 "UPSCAT.spad" 1839914 1839940 1842019 1842024) (-1154 "UPOLYC2.spad" 1839385 1839404 1839904 1839909) (-1153 "UPOLYC.spad" 1834465 1834476 1839227 1839380) (-1152 "UPOLYC.spad" 1829463 1829476 1834227 1834232) (-1151 "UPMP.spad" 1828395 1828408 1829453 1829458) (-1150 "UPDIVP.spad" 1827960 1827974 1828385 1828390) (-1149 "UPDECOMP.spad" 1826221 1826235 1827950 1827955) (-1148 "UPCDEN.spad" 1825438 1825454 1826211 1826216) (-1147 "UP2.spad" 1824802 1824823 1825428 1825433) (-1146 "UP.spad" 1822272 1822287 1822659 1822812) (-1145 "UNISEG2.spad" 1821769 1821782 1822228 1822233) (-1144 "UNISEG.spad" 1821122 1821133 1821688 1821693) (-1143 "UNIFACT.spad" 1820225 1820237 1821112 1821117) (-1142 "ULSCONS.spad" 1814071 1814091 1814441 1814590) (-1141 "ULSCCAT.spad" 1811808 1811828 1813917 1814066) (-1140 "ULSCCAT.spad" 1809653 1809675 1811764 1811769) (-1139 "ULSCAT.spad" 1807893 1807909 1809499 1809648) (-1138 "ULS2.spad" 1807407 1807460 1807883 1807888) (-1137 "ULS.spad" 1799440 1799468 1800385 1800808) (-1136 "UINT8.spad" 1799317 1799326 1799430 1799435) (-1135 "UINT64.spad" 1799193 1799202 1799307 1799312) (-1134 "UINT32.spad" 1799069 1799078 1799183 1799188) (-1133 "UINT16.spad" 1798945 1798954 1799059 1799064) (-1132 "UFD.spad" 1798010 1798019 1798871 1798940) (-1131 "UFD.spad" 1797137 1797148 1798000 1798005) (-1130 "UDVO.spad" 1796018 1796027 1797127 1797132) (-1129 "UDPO.spad" 1793599 1793610 1795974 1795979) (-1128 "TYPEAST.spad" 1793518 1793527 1793589 1793594) (-1127 "TYPE.spad" 1793450 1793459 1793508 1793513) (-1126 "TWOFACT.spad" 1792102 1792117 1793440 1793445) (-1125 "TUPLE.spad" 1791609 1791620 1792014 1792019) (-1124 "TUBETOOL.spad" 1788476 1788485 1791599 1791604) (-1123 "TUBE.spad" 1787123 1787140 1788466 1788471) (-1122 "TSETCAT.spad" 1775194 1775211 1787091 1787118) (-1121 "TSETCAT.spad" 1763251 1763270 1775150 1775155) (-1120 "TS.spad" 1761879 1761895 1762845 1762942) (-1119 "TRMANIP.spad" 1756243 1756260 1761567 1761572) (-1118 "TRIMAT.spad" 1755206 1755231 1756233 1756238) (-1117 "TRIGMNIP.spad" 1753733 1753750 1755196 1755201) (-1116 "TRIGCAT.spad" 1753245 1753254 1753723 1753728) (-1115 "TRIGCAT.spad" 1752755 1752766 1753235 1753240) (-1114 "TREE.spad" 1751395 1751406 1752427 1752454) (-1113 "TRANFUN.spad" 1751234 1751243 1751385 1751390) (-1112 "TRANFUN.spad" 1751071 1751082 1751224 1751229) (-1111 "TOPSP.spad" 1750745 1750754 1751061 1751066) (-1110 "TOOLSIGN.spad" 1750408 1750419 1750735 1750740) (-1109 "TEXTFILE.spad" 1748969 1748978 1750398 1750403) (-1108 "TEX1.spad" 1748525 1748536 1748959 1748964) (-1107 "TEX.spad" 1745719 1745728 1748515 1748520) (-1106 "TBCMPPK.spad" 1743820 1743843 1745709 1745714) (-1105 "TBAGG.spad" 1742878 1742901 1743800 1743815) (-1104 "TBAGG.spad" 1741944 1741969 1742868 1742873) (-1103 "TANEXP.spad" 1741352 1741363 1741934 1741939) (-1102 "TALGOP.spad" 1741076 1741087 1741342 1741347) (-1101 "TABLEAU.spad" 1740557 1740568 1741066 1741071) (-1100 "TABLE.spad" 1738832 1738855 1739102 1739129) (-1099 "TABLBUMP.spad" 1735611 1735622 1738822 1738827) (-1098 "SYSTEM.spad" 1734839 1734848 1735601 1735606) (-1097 "SYSSOLP.spad" 1732322 1732333 1734829 1734834) (-1096 "SYSPTR.spad" 1732221 1732230 1732312 1732317) (-1095 "SYSNNI.spad" 1731444 1731455 1732211 1732216) (-1094 "SYSINT.spad" 1730848 1730859 1731434 1731439) (-1093 "SYNTAX.spad" 1727182 1727191 1730838 1730843) (-1092 "SYMTAB.spad" 1725250 1725259 1727172 1727177) (-1091 "SYMS.spad" 1721279 1721288 1725240 1725245) (-1090 "SYMPOLY.spad" 1720412 1720423 1720494 1720621) (-1089 "SYMFUNC.spad" 1719913 1719924 1720402 1720407) (-1088 "SYMBOL.spad" 1717408 1717417 1719903 1719908) (-1087 "SUTS.spad" 1714521 1714549 1715940 1716037) (-1086 "SUPXS.spad" 1711863 1711891 1712712 1712861) (-1085 "SUPFRACF.spad" 1710968 1710986 1711853 1711858) (-1084 "SUP2.spad" 1710360 1710373 1710958 1710963) (-1083 "SUP.spad" 1707444 1707455 1708217 1708370) (-1082 "SUMRF.spad" 1706418 1706429 1707434 1707439) (-1081 "SUMFS.spad" 1706047 1706064 1706408 1706413) (-1080 "SULS.spad" 1698067 1698095 1699025 1699448) (-1079 "syntax.spad" 1697836 1697845 1698057 1698062) (-1078 "SUCH.spad" 1697526 1697541 1697826 1697831) (-1077 "SUBSPACE.spad" 1689657 1689672 1697516 1697521) (-1076 "SUBRESP.spad" 1688827 1688841 1689613 1689618) (-1075 "STTFNC.spad" 1685295 1685311 1688817 1688822) (-1074 "STTF.spad" 1681394 1681410 1685285 1685290) (-1073 "STTAYLOR.spad" 1674071 1674082 1681301 1681306) (-1072 "STRTBL.spad" 1672458 1672475 1672607 1672634) (-1071 "STRING.spad" 1671326 1671335 1671711 1671738) (-1070 "STREAM3.spad" 1670899 1670914 1671316 1671321) (-1069 "STREAM2.spad" 1670027 1670040 1670889 1670894) (-1068 "STREAM1.spad" 1669733 1669744 1670017 1670022) (-1067 "STREAM.spad" 1666729 1666740 1669336 1669351) (-1066 "STINPROD.spad" 1665665 1665681 1666719 1666724) (-1065 "STEPAST.spad" 1664899 1664908 1665655 1665660) (-1064 "STEP.spad" 1664216 1664225 1664889 1664894) (-1063 "STBL.spad" 1662606 1662634 1662773 1662788) (-1062 "STAGG.spad" 1661305 1661316 1662596 1662601) (-1061 "STAGG.spad" 1660002 1660015 1661295 1661300) (-1060 "STACK.spad" 1659424 1659435 1659674 1659701) (-1059 "SRING.spad" 1659184 1659193 1659414 1659419) (-1058 "SREGSET.spad" 1656916 1656933 1658818 1658845) (-1057 "SRDCMPK.spad" 1655493 1655513 1656906 1656911) (-1056 "SRAGG.spad" 1650676 1650685 1655461 1655488) (-1055 "SRAGG.spad" 1645879 1645890 1650666 1650671) (-1054 "SQMATRIX.spad" 1643556 1643574 1644472 1644559) (-1053 "SPLTREE.spad" 1638298 1638311 1643094 1643121) (-1052 "SPLNODE.spad" 1634918 1634931 1638288 1638293) (-1051 "SPFCAT.spad" 1633727 1633736 1634908 1634913) (-1050 "SPECOUT.spad" 1632279 1632288 1633717 1633722) (-1049 "SPADXPT.spad" 1624370 1624379 1632269 1632274) (-1048 "spad-parser.spad" 1623835 1623844 1624360 1624365) (-1047 "SPADAST.spad" 1623536 1623545 1623825 1623830) (-1046 "SPACEC.spad" 1607751 1607762 1623526 1623531) (-1045 "SPACE3.spad" 1607527 1607538 1607741 1607746) (-1044 "SORTPAK.spad" 1607076 1607089 1607483 1607488) (-1043 "SOLVETRA.spad" 1604839 1604850 1607066 1607071) (-1042 "SOLVESER.spad" 1603295 1603306 1604829 1604834) (-1041 "SOLVERAD.spad" 1599321 1599332 1603285 1603290) (-1040 "SOLVEFOR.spad" 1597783 1597801 1599311 1599316) (-1039 "SNTSCAT.spad" 1597383 1597400 1597751 1597778) (-1038 "SMTS.spad" 1595700 1595726 1596977 1597074) (-1037 "SMP.spad" 1593508 1593528 1593898 1594025) (-1036 "SMITH.spad" 1592353 1592378 1593498 1593503) (-1035 "SMATCAT.spad" 1590471 1590501 1592297 1592348) (-1034 "SMATCAT.spad" 1588521 1588553 1590349 1590354) (-1033 "SKAGG.spad" 1587490 1587501 1588489 1588516) (-1032 "SINT.spad" 1586789 1586798 1587356 1587485) (-1031 "SIMPAN.spad" 1586517 1586526 1586779 1586784) (-1030 "SIGNRF.spad" 1585642 1585653 1586507 1586512) (-1029 "SIGNEF.spad" 1584928 1584945 1585632 1585637) (-1028 "syntax.spad" 1584345 1584354 1584918 1584923) (-1027 "SIG.spad" 1583707 1583716 1584335 1584340) (-1026 "SHP.spad" 1581651 1581666 1583663 1583668) (-1025 "SHDP.spad" 1571144 1571171 1571661 1571758) (-1024 "SGROUP.spad" 1570752 1570761 1571134 1571139) (-1023 "SGROUP.spad" 1570358 1570369 1570742 1570747) (-1022 "catdef.spad" 1570068 1570080 1570179 1570353) (-1021 "catdef.spad" 1569624 1569636 1569889 1570063) (-1020 "SGCF.spad" 1562763 1562772 1569614 1569619) (-1019 "SFRTCAT.spad" 1561709 1561726 1562731 1562758) (-1018 "SFRGCD.spad" 1560772 1560792 1561699 1561704) (-1017 "SFQCMPK.spad" 1555585 1555605 1560762 1560767) (-1016 "SEXOF.spad" 1555428 1555468 1555575 1555580) (-1015 "SEXCAT.spad" 1553256 1553296 1555418 1555423) (-1014 "SEX.spad" 1553148 1553157 1553246 1553251) (-1013 "SETMN.spad" 1551608 1551625 1553138 1553143) (-1012 "SETCAT.spad" 1551093 1551102 1551598 1551603) (-1011 "SETCAT.spad" 1550576 1550587 1551083 1551088) (-1010 "SETAGG.spad" 1547125 1547136 1550556 1550571) (-1009 "SETAGG.spad" 1543682 1543695 1547115 1547120) (-1008 "SET.spad" 1541991 1542002 1543088 1543127) (-1007 "syntax.spad" 1541694 1541703 1541981 1541986) (-1006 "SEGXCAT.spad" 1540850 1540863 1541684 1541689) (-1005 "SEGCAT.spad" 1539775 1539786 1540840 1540845) (-1004 "SEGBIND2.spad" 1539473 1539486 1539765 1539770) (-1003 "SEGBIND.spad" 1539231 1539242 1539420 1539425) (-1002 "SEGAST.spad" 1538961 1538970 1539221 1539226) (-1001 "SEG2.spad" 1538396 1538409 1538917 1538922) (-1000 "SEG.spad" 1538209 1538220 1538315 1538320) (-999 "SDVAR.spad" 1537486 1537496 1538199 1538204) (-998 "SDPOL.spad" 1535184 1535194 1535474 1535601) (-997 "SCPKG.spad" 1533274 1533284 1535174 1535179) (-996 "SCOPE.spad" 1532452 1532460 1533264 1533269) (-995 "SCACHE.spad" 1531149 1531159 1532442 1532447) (-994 "SASTCAT.spad" 1531059 1531067 1531139 1531144) (-993 "SAOS.spad" 1530932 1530940 1531049 1531054) (-992 "SAERFFC.spad" 1530646 1530665 1530922 1530927) (-991 "SAEFACT.spad" 1530348 1530367 1530636 1530641) (-990 "SAE.spad" 1527999 1528014 1528609 1528744) (-989 "RURPK.spad" 1525659 1525674 1527989 1527994) (-988 "RULESET.spad" 1525113 1525136 1525649 1525654) (-987 "RULECOLD.spad" 1524966 1524978 1525103 1525108) (-986 "RULE.spad" 1523215 1523238 1524956 1524961) (-985 "RTVALUE.spad" 1522951 1522959 1523205 1523210) (-984 "syntax.spad" 1522669 1522677 1522941 1522946) (-983 "RSETGCD.spad" 1519112 1519131 1522659 1522664) (-982 "RSETCAT.spad" 1509081 1509097 1519080 1519107) (-981 "RSETCAT.spad" 1499070 1499088 1509071 1509076) (-980 "RSDCMPK.spad" 1497571 1497590 1499060 1499065) (-979 "RRCC.spad" 1495956 1495985 1497561 1497566) (-978 "RRCC.spad" 1494339 1494370 1495946 1495951) (-977 "RPTAST.spad" 1494042 1494050 1494329 1494334) (-976 "RPOLCAT.spad" 1473547 1473561 1493910 1494037) (-975 "RPOLCAT.spad" 1452845 1452861 1473210 1473215) (-974 "ROMAN.spad" 1452174 1452182 1452711 1452840) (-973 "ROIRC.spad" 1451255 1451286 1452164 1452169) (-972 "RNS.spad" 1450232 1450240 1451157 1451250) (-971 "RNS.spad" 1449295 1449305 1450222 1450227) (-970 "RNGBIND.spad" 1448456 1448469 1449250 1449255) (-969 "RNG.spad" 1448065 1448073 1448446 1448451) (-968 "RNG.spad" 1447672 1447682 1448055 1448060) (-967 "RMODULE.spad" 1447454 1447464 1447662 1447667) (-966 "RMCAT2.spad" 1446875 1446931 1447444 1447449) (-965 "RMATRIX.spad" 1445685 1445703 1446027 1446066) (-964 "RMATCAT.spad" 1441265 1441295 1445641 1445680) (-963 "RMATCAT.spad" 1436735 1436767 1441113 1441118) (-962 "RLINSET.spad" 1436440 1436450 1436725 1436730) (-961 "RINTERP.spad" 1436329 1436348 1436430 1436435) (-960 "RING.spad" 1435800 1435808 1436309 1436324) (-959 "RING.spad" 1435279 1435289 1435790 1435795) (-958 "RIDIST.spad" 1434672 1434680 1435269 1435274) (-957 "RGCHAIN.spad" 1433227 1433242 1434120 1434147) (-956 "RGBCSPC.spad" 1433017 1433028 1433217 1433222) (-955 "RGBCMDL.spad" 1432580 1432591 1433007 1433012) (-954 "RFFACTOR.spad" 1432043 1432053 1432570 1432575) (-953 "RFFACT.spad" 1431779 1431790 1432033 1432038) (-952 "RFDIST.spad" 1430776 1430784 1431769 1431774) (-951 "RF.spad" 1428451 1428461 1430766 1430771) (-950 "RETSOL.spad" 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957674) (-646 "MMLFORM.spad" 955901 955909 957031 957036) (-645 "MMAP.spad" 955643 955677 955891 955896) (-644 "MLO.spad" 954102 954112 955599 955638) (-643 "MLIFT.spad" 952714 952731 954092 954097) (-642 "MKUCFUNC.spad" 952249 952267 952704 952709) (-641 "MKRECORD.spad" 951837 951850 952239 952244) (-640 "MKFUNC.spad" 951244 951254 951827 951832) (-639 "MKFLCFN.spad" 950212 950222 951234 951239) (-638 "MKBCFUNC.spad" 949707 949725 950202 950207) (-637 "MHROWRED.spad" 948218 948228 949697 949702) (-636 "MFINFACT.spad" 947618 947640 948208 948213) (-635 "MESH.spad" 945413 945421 947608 947613) (-634 "MDDFACT.spad" 943632 943642 945403 945408) (-633 "MDAGG.spad" 942923 942933 943612 943627) (-632 "MCDEN.spad" 942133 942145 942913 942918) (-631 "MAYBE.spad" 941433 941444 942123 942128) (-630 "MATSTOR.spad" 938749 938759 941423 941428) (-629 "MATRIX.spad" 937528 937538 938012 938039) (-628 "MATLIN.spad" 934896 934920 937412 937417) (-627 "MATCAT2.spad" 934178 934226 934886 934891) (-626 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895394 895406 895695 895700) (-605 "LPOLY.spad" 894356 894375 895250 895319) (-604 "LPEFRAC.spad" 893627 893637 894346 894351) (-603 "LOGIC.spad" 893229 893237 893617 893622) (-602 "LOGIC.spad" 892829 892839 893219 893224) (-601 "LODOOPS.spad" 891759 891771 892819 892824) (-600 "LODOF.spad" 890805 890822 891716 891721) (-599 "LODOCAT.spad" 889471 889481 890761 890800) (-598 "LODOCAT.spad" 888135 888147 889427 889432) (-597 "LODO2.spad" 887449 887461 887856 887895) (-596 "LODO1.spad" 886890 886900 887170 887209) (-595 "LODO.spad" 886315 886331 886611 886650) (-594 "LODEEF.spad" 885117 885135 886305 886310) (-593 "LO.spad" 884518 884532 885051 885078) (-592 "LNAGG.spad" 880705 880715 884508 884513) (-591 "LNAGG.spad" 876856 876868 880661 880666) (-590 "LMOPS.spad" 873624 873641 876846 876851) (-589 "LMODULE.spad" 873408 873418 873614 873619) (-588 "LMDICT.spad" 872789 872799 873037 873064) (-587 "LLINSET.spad" 872496 872506 872779 872784) (-586 "LITERAL.spad" 872402 872413 872486 872491) (-585 "LIST3.spad" 871713 871727 872392 872397) (-584 "LIST2MAP.spad" 868640 868652 871703 871708) (-583 "LIST2.spad" 867342 867354 868630 868635) (-582 "LIST.spad" 865224 865234 866567 866594) (-581 "LINSET.spad" 865003 865013 865214 865219) (-580 "LINFORM.spad" 864466 864478 864971 864998) (-579 "LINEXP.spad" 863209 863219 864456 864461) (-578 "LINELT.spad" 862580 862592 863092 863119) (-577 "LINDEP.spad" 861429 861441 862492 862497) (-576 "LINBASIS.spad" 861065 861080 861419 861424) (-575 "LIMITRF.spad" 859012 859022 861055 861060) (-574 "LIMITPS.spad" 857922 857935 859002 859007) (-573 "LIECAT.spad" 857406 857416 857848 857917) (-572 "LIECAT.spad" 856918 856930 857362 857367) (-571 "LIE.spad" 854922 854934 856196 856338) (-570 "LIB.spad" 853093 853101 853539 853554) (-569 "LGROBP.spad" 850446 850465 853083 853088) (-568 "LFCAT.spad" 849505 849513 850436 850441) (-567 "LF.spad" 848460 848476 849495 849500) (-566 "LEXTRIPK.spad" 844083 844098 848450 848455) (-565 "LEXP.spad" 842102 842129 844063 844078) (-564 "LETAST.spad" 841801 841809 842092 842097) (-563 "LEADCDET.spad" 840207 840224 841791 841796) (-562 "LAZM3PK.spad" 838951 838973 840197 840202) (-561 "LAUPOL.spad" 837618 837631 838518 838587) (-560 "LAPLACE.spad" 837201 837217 837608 837613) (-559 "LALG.spad" 836977 836987 837181 837196) (-558 "LALG.spad" 836761 836773 836967 836972) (-557 "LA.spad" 836201 836215 836683 836722) (-556 "KVTFROM.spad" 835944 835954 836191 836196) (-555 "KTVLOGIC.spad" 835488 835496 835934 835939) (-554 "KRCFROM.spad" 835234 835244 835478 835483) (-553 "KOVACIC.spad" 833965 833982 835224 835229) (-552 "KONVERT.spad" 833687 833697 833955 833960) (-551 "KOERCE.spad" 833424 833434 833677 833682) (-550 "KERNEL2.spad" 833127 833139 833414 833419) (-549 "KERNEL.spad" 831847 831857 832976 832981) (-548 "KDAGG.spad" 830956 830978 831827 831842) (-547 "KDAGG.spad" 830073 830097 830946 830951) (-546 "KAFILE.spad" 828963 828979 829198 829225) (-545 "JVMOP.spad" 828876 828884 828953 828958) (-544 "JVMMDACC.spad" 827930 827938 828866 828871) (-543 "JVMFDACC.spad" 827246 827254 827920 827925) (-542 "JVMCSTTG.spad" 825975 825983 827236 827241) (-541 "JVMCFACC.spad" 825421 825429 825965 825970) (-540 "JVMBCODE.spad" 825332 825340 825411 825416) (-539 "JORDAN.spad" 823149 823161 824610 824752) (-538 "JOINAST.spad" 822851 822859 823139 823144) (-537 "IXAGG.spad" 820984 821008 822841 822846) (-536 "IXAGG.spad" 818972 818998 820831 820836) (-535 "ITUPLE.spad" 818148 818158 818962 818967) (-534 "ITRIGMNP.spad" 816995 817014 818138 818143) (-533 "ITFUN3.spad" 816501 816515 816985 816990) (-532 "ITFUN2.spad" 816245 816257 816491 816496) (-531 "ITFORM.spad" 815600 815608 816235 816240) (-530 "ITAYLOR.spad" 813594 813609 815464 815561) (-529 "ISUPS.spad" 806043 806058 812580 812677) (-528 "ISUMP.spad" 805544 805560 806033 806038) (-527 "ISAST.spad" 805263 805271 805534 805539) (-526 "IRURPK.spad" 803980 803999 805253 805258) (-525 "IRSN.spad" 801984 801992 803970 803975) (-524 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778861 779409 779414) (-503 "INTRAT.spad" 777586 777603 778841 778846) (-502 "INTPM.spad" 776049 776065 777307 777312) (-501 "INTPAF.spad" 773925 773943 775978 775983) (-500 "INTHERTR.spad" 773199 773216 773915 773920) (-499 "INTHERAL.spad" 772869 772893 773189 773194) (-498 "INTHEORY.spad" 769308 769316 772859 772864) (-497 "INTG0.spad" 763072 763090 769237 769242) (-496 "INTFACT.spad" 762139 762149 763062 763067) (-495 "INTEF.spad" 760550 760566 762129 762134) (-494 "INTDOM.spad" 759173 759181 760476 760545) (-493 "INTDOM.spad" 757858 757868 759163 759168) (-492 "INTCAT.spad" 756125 756135 757772 757853) (-491 "INTBIT.spad" 755632 755640 756115 756120) (-490 "INTALG.spad" 754820 754847 755622 755627) (-489 "INTAF.spad" 754320 754336 754810 754815) (-488 "INTABL.spad" 752702 752733 752865 752892) (-487 "INT8.spad" 752582 752590 752692 752697) (-486 "INT64.spad" 752461 752469 752572 752577) (-485 "INT32.spad" 752340 752348 752451 752456) (-484 "INT16.spad" 752219 752227 752330 752335) (-483 "INT.spad" 751745 751753 752085 752214) (-482 "INS.spad" 749248 749256 751647 751740) (-481 "INS.spad" 746837 746847 749238 749243) (-480 "INPSIGN.spad" 746307 746320 746827 746832) (-479 "INPRODPF.spad" 745403 745422 746297 746302) (-478 "INPRODFF.spad" 744491 744515 745393 745398) (-477 "INNMFACT.spad" 743466 743483 744481 744486) (-476 "INMODGCD.spad" 742970 743000 743456 743461) (-475 "INFSP.spad" 741267 741289 742960 742965) (-474 "INFPROD0.spad" 740347 740366 741257 741262) (-473 "INFORM1.spad" 739972 739982 740337 740342) (-472 "INFORM.spad" 737183 737191 739962 739967) (-471 "INFINITY.spad" 736735 736743 737173 737178) (-470 "INETCLTS.spad" 736712 736720 736725 736730) (-469 "INEP.spad" 735258 735280 736702 736707) (-468 "INDE.spad" 734907 734924 735168 735173) (-467 "INCRMAPS.spad" 734344 734354 734897 734902) (-466 "INBFILE.spad" 733440 733448 734334 734339) (-465 "INBFF.spad" 729290 729301 733430 733435) (-464 "INBCON.spad" 727556 727564 729280 729285) (-463 "INBCON.spad" 725820 725830 727546 727551) (-462 "INAST.spad" 725481 725489 725810 725815) (-461 "IMPTAST.spad" 725189 725197 725471 725476) (-460 "IMATQF.spad" 724283 724327 725145 725150) (-459 "IMATLIN.spad" 722904 722928 724239 724244) (-458 "IFF.spad" 722317 722333 722588 722681) (-457 "IFAST.spad" 721931 721939 722307 722312) (-456 "IFARRAY.spad" 719458 719473 721156 721183) (-455 "IFAMON.spad" 719320 719337 719414 719419) (-454 "IEVALAB.spad" 718733 718745 719310 719315) (-453 "IEVALAB.spad" 718144 718158 718723 718728) (-452 "indexedp.spad" 717700 717712 718134 718139) (-451 "IDPOAMS.spad" 717378 717390 717612 717617) (-450 "IDPOAM.spad" 717020 717032 717290 717295) (-449 "IDPO.spad" 716434 716446 716932 716937) (-448 "IDPC.spad" 715149 715161 716424 716429) (-447 "IDPAM.spad" 714816 714828 715061 715066) (-446 "IDPAG.spad" 714485 714497 714728 714733) (-445 "IDENT.spad" 714137 714145 714475 714480) (-444 "catdef.spad" 713908 713919 714020 714132) (-443 "IDECOMP.spad" 711147 711165 713898 713903) (-442 "IDEAL.spad" 706109 706148 711095 711100) (-441 "ICDEN.spad" 705322 705338 706099 706104) (-440 "ICARD.spad" 704715 704723 705312 705317) (-439 "IBPTOOLS.spad" 703322 703339 704705 704710) (-438 "IBITS.spad" 702835 702848 702968 702995) (-437 "IBATOOL.spad" 699820 699839 702825 702830) (-436 "IBACHIN.spad" 698327 698342 699810 699815) (-435 "array2.spad" 697812 697834 697999 698026) (-434 "IARRAY1.spad" 696891 696906 697037 697064) (-433 "IAN.spad" 695273 695281 696722 696815) (-432 "IALGFACT.spad" 694884 694917 695263 695268) (-431 "HYPCAT.spad" 694308 694316 694874 694879) (-430 "HYPCAT.spad" 693730 693740 694298 694303) (-429 "HOSTNAME.spad" 693546 693554 693720 693725) (-428 "HOMOTOP.spad" 693289 693299 693536 693541) (-427 "HOAGG.spad" 690571 690581 693279 693284) (-426 "HOAGG.spad" 687603 687615 690313 690318) (-425 "HEXADEC.spad" 685828 685836 686193 686286) (-424 "HEUGCD.spad" 684919 684930 685818 685823) (-423 "HELLFDIV.spad" 684525 684549 684909 684914) (-422 "HEAP.spad" 683982 683992 684197 684224) (-421 "HEADAST.spad" 683523 683531 683972 683977) (-420 "HDP.spad" 673156 673172 673533 673630) (-419 "HDMP.spad" 670703 670718 671319 671446) (-418 "HB.spad" 668978 668986 670693 670698) (-417 "HASHTBL.spad" 667312 667343 667523 667550) (-416 "HASAST.spad" 667028 667036 667302 667307) (-415 "HACKPI.spad" 666519 666527 666930 667023) (-414 "GTSET.spad" 665446 665462 666153 666180) (-413 "GSTBL.spad" 663829 663864 664003 664018) (-412 "GSERIES.spad" 661201 661228 662020 662169) (-411 "GROUP.spad" 660474 660482 661181 661196) (-410 "GROUP.spad" 659755 659765 660464 660469) (-409 "GROEBSOL.spad" 658249 658270 659745 659750) (-408 "GRMOD.spad" 656830 656842 658239 658244) (-407 "GRMOD.spad" 655409 655423 656820 656825) (-406 "GRIMAGE.spad" 648322 648330 655399 655404) (-405 "GRDEF.spad" 646701 646709 648312 648317) (-404 "GRAY.spad" 645172 645180 646691 646696) (-403 "GRALG.spad" 644267 644279 645162 645167) (-402 "GRALG.spad" 643360 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607807 607812) (-381 "GALFACTU.spad" 604484 604503 606261 606266) (-380 "GALFACT.spad" 594697 594708 604474 604479) (-379 "FUNDESC.spad" 594375 594383 594687 594692) (-378 "FUNCTION.spad" 594224 594236 594365 594370) (-377 "FT.spad" 592524 592532 594214 594219) (-376 "FSUPFACT.spad" 591438 591457 592474 592479) (-375 "FST.spad" 589524 589532 591428 591433) (-374 "FSRED.spad" 589004 589020 589514 589519) (-373 "FSPRMELT.spad" 587870 587886 588961 588966) (-372 "FSPECF.spad" 585961 585977 587860 587865) (-371 "FSINT.spad" 585621 585637 585951 585956) (-370 "FSERIES.spad" 584812 584824 585441 585540) (-369 "FSCINT.spad" 584129 584145 584802 584807) (-368 "FSAGG2.spad" 582864 582880 584119 584124) (-367 "FSAGG.spad" 581981 581991 582820 582859) (-366 "FSAGG.spad" 581060 581072 581901 581906) (-365 "FS2UPS.spad" 575575 575609 581050 581055) (-364 "FS2EXPXP.spad" 574716 574739 575565 575570) (-363 "FS2.spad" 574371 574387 574706 574711) (-362 "FS.spad" 568643 568653 574150 574366) (-361 "FS.spad" 562717 562729 568226 568231) (-360 "FRUTIL.spad" 561671 561681 562707 562712) (-359 "FRNAALG.spad" 556948 556958 561613 561666) (-358 "FRNAALG.spad" 552237 552249 556904 556909) (-357 "FRNAAF2.spad" 551685 551703 552227 552232) (-356 "FRMOD.spad" 551093 551123 551614 551619) (-355 "FRIDEAL2.spad" 550697 550729 551083 551088) (-354 "FRIDEAL.spad" 549922 549943 550677 550692) (-353 "FRETRCT.spad" 549441 549451 549912 549917) (-352 "FRETRCT.spad" 548867 548879 549340 549345) (-351 "FRAMALG.spad" 547247 547260 548823 548862) (-350 "FRAMALG.spad" 545659 545674 547237 547242) (-349 "FRAC2.spad" 545264 545276 545649 545654) (-348 "FRAC.spad" 543251 543261 543638 543811) (-347 "FR2.spad" 542587 542599 543241 543246) (-346 "FR.spad" 536375 536385 541648 541717) (-345 "FPS.spad" 533214 533222 536265 536370) (-344 "FPS.spad" 530081 530091 533134 533139) (-343 "FPC.spad" 529127 529135 529983 530076) (-342 "FPC.spad" 528259 528269 529117 529122) (-341 "FPATMAB.spad" 528021 528031 528249 528254) (-340 "FPARFRAC.spad" 526863 526880 528011 528016) (-339 "FORDER.spad" 526554 526578 526853 526858) (-338 "FNLA.spad" 525978 526000 526522 526549) (-337 "FNCAT.spad" 524573 524581 525968 525973) (-336 "FNAME.spad" 524465 524473 524563 524568) (-335 "FMONOID.spad" 524146 524156 524421 524426) (-334 "FMONCAT.spad" 521315 521325 524136 524141) (-333 "FMCAT.spad" 518991 519009 521283 521310) (-332 "FM1.spad" 518356 518368 518925 518952) (-331 "FM.spad" 517971 517983 518210 518237) (-330 "FLOATRP.spad" 515714 515728 517961 517966) (-329 "FLOATCP.spad" 513153 513167 515704 515709) (-328 "FLOAT.spad" 510244 510252 513019 513148) (-327 "FLINEXP.spad" 509966 509976 510234 510239) (-326 "FLINEXP.spad" 509645 509657 509915 509920) (-325 "FLASORT.spad" 508971 508983 509635 509640) (-324 "FLALG.spad" 506641 506660 508897 508966) (-323 "FLAGG2.spad" 505358 505374 506631 506636) (-322 "FLAGG.spad" 502424 502434 505338 505353) (-321 "FLAGG.spad" 499391 499403 502307 502312) (-320 "FINRALG.spad" 497476 497489 499347 499386) (-319 "FINRALG.spad" 495487 495502 497360 497365) (-318 "FINITE.spad" 494639 494647 495477 495482) (-317 "FINITE.spad" 493789 493799 494629 494634) (-316 "FINAALG.spad" 482974 482984 493731 493784) (-315 "FINAALG.spad" 472171 472183 482930 482935) (-314 "FILECAT.spad" 470705 470722 472161 472166) (-313 "FILE.spad" 470288 470298 470695 470700) (-312 "FIELD.spad" 469694 469702 470190 470283) (-311 "FIELD.spad" 469186 469196 469684 469689) (-310 "FGROUP.spad" 467849 467859 469166 469181) (-309 "FGLMICPK.spad" 466644 466659 467839 467844) (-308 "FFX.spad" 466030 466045 466363 466456) (-307 "FFSLPE.spad" 465541 465562 466020 466025) (-306 "FFPOLY2.spad" 464601 464618 465531 465536) (-305 "FFPOLY.spad" 455943 455954 464591 464596) (-304 "FFP.spad" 455351 455371 455662 455755) (-303 "FFNBX.spad" 453874 453894 455070 455163) (-302 "FFNBP.spad" 452398 452415 453593 453686) (-301 "FFNB.spad" 450866 450887 452082 452175) (-300 "FFINTBAS.spad" 448380 448399 450856 450861) (-299 "FFIELDC.spad" 445965 445973 448282 448375) (-298 "FFIELDC.spad" 443636 443646 445955 445960) (-297 "FFHOM.spad" 442408 442425 443626 443631) (-296 "FFF.spad" 439851 439862 442398 442403) (-295 "FFCGX.spad" 438709 438729 439570 439663) (-294 "FFCGP.spad" 437609 437629 438428 438521) (-293 "FFCG.spad" 436404 436425 437293 437386) (-292 "FFCAT2.spad" 436151 436191 436394 436399) (-291 "FFCAT.spad" 429316 429338 435990 436146) (-290 "FFCAT.spad" 422560 422584 429236 429241) (-289 "FF.spad" 422011 422027 422244 422337) (-288 "FEVALAB.spad" 421719 421729 422001 422006) (-287 "FEVALAB.spad" 421203 421215 421487 421492) (-286 "FDIVCAT.spad" 419299 419323 421193 421198) (-285 "FDIVCAT.spad" 417393 417419 419289 419294) (-284 "FDIV2.spad" 417049 417089 417383 417388) (-283 "FDIV.spad" 416507 416531 417039 417044) (-282 "FCTRDATA.spad" 415515 415523 416497 416502) (-281 "FCOMP.spad" 414894 414904 415505 415510) (-280 "FAXF.spad" 407929 407943 414796 414889) (-279 "FAXF.spad" 401016 401032 407885 407890) (-278 "FARRAY.spad" 399208 399218 400241 400268) (-277 "FAMR.spad" 397352 397364 399106 399203) (-276 "FAMR.spad" 395480 395494 397236 397241) (-275 "FAMONOID.spad" 395164 395174 395434 395439) (-274 "FAMONC.spad" 393484 393496 395154 395159) (-273 "FAGROUP.spad" 393124 393134 393380 393407) (-272 "FACUTIL.spad" 391336 391353 393114 393119) (-271 "FACTFUNC.spad" 390538 390548 391326 391331) (-270 "EXPUPXS.spad" 387430 387453 388729 388878) (-269 "EXPRTUBE.spad" 384718 384726 387420 387425) (-268 "EXPRODE.spad" 381886 381902 384708 384713) (-267 "EXPR2UPS.spad" 378008 378021 381876 381881) (-266 "EXPR2.spad" 377713 377725 377998 378003) (-265 "EXPR.spad" 373358 373368 374072 374359) (-264 "EXPEXPAN.spad" 370303 370328 370935 371028) (-263 "EXITAST.spad" 370039 370047 370293 370298) (-262 "EXIT.spad" 369710 369718 370029 370034) (-261 "EVALCYC.spad" 369170 369184 369700 369705) (-260 "EVALAB.spad" 368750 368760 369160 369165) (-259 "EVALAB.spad" 368328 368340 368740 368745) (-258 "EUCDOM.spad" 365918 365926 368254 368323) (-257 "EUCDOM.spad" 363570 363580 365908 365913) (-256 "ES2.spad" 363083 363099 363560 363565) (-255 "ES1.spad" 362653 362669 363073 363078) (-254 "ES.spad" 355524 355532 362643 362648) (-253 "ES.spad" 348316 348326 355437 355442) (-252 "ERROR.spad" 345643 345651 348306 348311) (-251 "EQTBL.spad" 343979 344001 344188 344215) (-250 "EQ2.spad" 343697 343709 343969 343974) (-249 "EQ.spad" 338603 338613 341398 341504) (-248 "EP.spad" 334929 334939 338593 338598) (-247 "ENV.spad" 333607 333615 334919 334924) (-246 "ENTIRER.spad" 333275 333283 333551 333602) (-245 "ENTIRER.spad" 332987 332997 333265 333270) (-244 "EMR.spad" 332275 332316 332913 332982) (-243 "ELTAGG.spad" 330529 330548 332265 332270) (-242 "ELTAGG.spad" 328747 328768 330485 330490) (-241 "ELTAB.spad" 328222 328235 328737 328742) (-240 "ELFUTS.spad" 327657 327676 328212 328217) (-239 "ELEMFUN.spad" 327346 327354 327647 327652) (-238 "ELEMFUN.spad" 327033 327043 327336 327341) (-237 "ELAGG.spad" 325004 325014 327013 327028) (-236 "ELAGG.spad" 322912 322924 324923 324928) (-235 "ELABOR.spad" 322258 322266 322902 322907) (-234 "ELABEXPR.spad" 321190 321198 322248 322253) (-233 "EFUPXS.spad" 317966 317996 321146 321151) (-232 "EFULS.spad" 314802 314825 317922 317927) (-231 "EFSTRUC.spad" 312817 312833 314792 314797) (-230 "EF.spad" 307593 307609 312807 312812) (-229 "EAB.spad" 305893 305901 307583 307588) (-228 "DVARCAT.spad" 302899 302909 305883 305888) (-227 "DVARCAT.spad" 299903 299915 302889 302894) (-226 "DSMP.spad" 297636 297650 297941 298068) (-225 "DSEXT.spad" 296938 296948 297626 297631) (-224 "DSEXT.spad" 296160 296172 296850 296855) (-223 "DROPT1.spad" 295825 295835 296150 296155) (-222 "DROPT0.spad" 290690 290698 295815 295820) (-221 "DROPT.spad" 284649 284657 290680 290685) (-220 "DRAWPT.spad" 282822 282830 284639 284644) (-219 "DRAWHACK.spad" 282130 282140 282812 282817) (-218 "DRAWCX.spad" 279608 279616 282120 282125) (-217 "DRAWCURV.spad" 279155 279170 279598 279603) (-216 "DRAWCFUN.spad" 268687 268695 279145 279150) (-215 "DRAW.spad" 261563 261576 268677 268682) (-214 "DQAGG.spad" 259741 259751 261531 261558) (-213 "DPOLCAT.spad" 255098 255114 259609 259736) (-212 "DPOLCAT.spad" 250541 250559 255054 255059) (-211 "DPMO.spad" 243244 243260 243382 243588) (-210 "DPMM.spad" 235960 235978 236085 236291) (-209 "DOMTMPLT.spad" 235731 235739 235950 235955) (-208 "DOMCTOR.spad" 235486 235494 235721 235726) (-207 "DOMAIN.spad" 234597 234605 235476 235481) (-206 "DMP.spad" 232190 232205 232760 232887) (-205 "DMEXT.spad" 232057 232067 232158 232185) (-204 "DLP.spad" 231417 231427 232047 232052) (-203 "DLIST.spad" 230038 230048 230642 230669) (-202 "DLAGG.spad" 228455 228465 230028 230033) (-201 "DIVRING.spad" 227997 228005 228399 228450) (-200 "DIVRING.spad" 227583 227593 227987 227992) (-199 "DISPLAY.spad" 225773 225781 227573 227578) (-198 "DIRPROD2.spad" 224591 224609 225763 225768) (-197 "DIRPROD.spad" 213961 213977 214601 214698) (-196 "DIRPCAT.spad" 213156 213172 213859 213956) (-195 "DIRPCAT.spad" 211977 211995 212682 212687) (-194 "DIOSP.spad" 210802 210810 211967 211972) (-193 "DIOPS.spad" 209798 209808 210782 210797) (-192 "DIOPS.spad" 208768 208780 209754 209759) (-191 "catdef.spad" 208626 208634 208758 208763) (-190 "DIFRING.spad" 208464 208472 208606 208621) (-189 "DIFFSPC.spad" 208043 208051 208454 208459) (-188 "DIFFSPC.spad" 207620 207630 208033 208038) (-187 "DIFFMOD.spad" 207109 207119 207588 207615) (-186 "DIFFDOM.spad" 206274 206285 207099 207104) (-185 "DIFFDOM.spad" 205437 205450 206264 206269) (-184 "DIFEXT.spad" 205256 205266 205417 205432) (-183 "DIAGG.spad" 204886 204896 205236 205251) (-182 "DIAGG.spad" 204524 204536 204876 204881) (-181 "DHMATRIX.spad" 202901 202911 204046 204073) (-180 "DFSFUN.spad" 196541 196549 202891 202896) (-179 "DFLOAT.spad" 193148 193156 196431 196536) (-178 "DFINTTLS.spad" 191379 191395 193138 193143) (-177 "DERHAM.spad" 189293 189325 191359 191374) (-176 "DEQUEUE.spad" 188682 188692 188965 188992) (-175 "DEGRED.spad" 188299 188313 188672 188677) (-174 "DEFINTRF.spad" 185881 185891 188289 188294) (-173 "DEFINTEF.spad" 184419 184435 185871 185876) (-172 "DEFAST.spad" 183803 183811 184409 184414) (-171 "DECIMAL.spad" 182032 182040 182393 182486) (-170 "DDFACT.spad" 179853 179870 182022 182027) (-169 "DBLRESP.spad" 179453 179477 179843 179848) (-168 "DBASIS.spad" 179079 179094 179443 179448) (-167 "DBASE.spad" 177743 177753 179069 179074) (-166 "DATAARY.spad" 177229 177242 177733 177738) (-165 "CYCLOTOM.spad" 176735 176743 177219 177224) (-164 "CYCLES.spad" 173527 173535 176725 176730) (-163 "CVMP.spad" 172944 172954 173517 173522) (-162 "CTRIGMNP.spad" 171444 171460 172934 172939) (-161 "CTORKIND.spad" 171047 171055 171434 171439) (-160 "CTORCAT.spad" 170288 170296 171037 171042) (-159 "CTORCAT.spad" 169527 169537 170278 170283) (-158 "CTORCALL.spad" 169116 169126 169517 169522) (-157 "CTOR.spad" 168807 168815 169106 169111) (-156 "CSTTOOLS.spad" 168052 168065 168797 168802) (-155 "CRFP.spad" 161824 161837 168042 168047) (-154 "CRCEAST.spad" 161544 161552 161814 161819) (-153 "CRAPACK.spad" 160611 160621 161534 161539) (-152 "CPMATCH.spad" 160112 160127 160533 160538) (-151 "CPIMA.spad" 159817 159836 160102 160107) (-150 "COORDSYS.spad" 154826 154836 159807 159812) (-149 "CONTOUR.spad" 154253 154261 154816 154821) (-148 "CONTFRAC.spad" 150003 150013 154155 154248) (-147 "CONDUIT.spad" 149761 149769 149993 149998) (-146 "COMRING.spad" 149435 149443 149699 149756) (-145 "COMPPROP.spad" 148953 148961 149425 149430) (-144 "COMPLPAT.spad" 148720 148735 148943 148948) (-143 "COMPLEX2.spad" 148435 148447 148710 148715) (-142 "COMPLEX.spad" 144141 144151 144385 144643) (-141 "COMPILER.spad" 143690 143698 144131 144136) (-140 "COMPFACT.spad" 143292 143306 143680 143685) (-139 "COMPCAT.spad" 141367 141377 143029 143287) (-138 "COMPCAT.spad" 139183 139195 140847 140852) (-137 "COMMUPC.spad" 138931 138949 139173 139178) (-136 "COMMONOP.spad" 138464 138472 138921 138926) (-135 "COMMAAST.spad" 138227 138235 138454 138459) (-134 "COMM.spad" 138038 138046 138217 138222) (-133 "COMBOPC.spad" 136961 136969 138028 138033) (-132 "COMBINAT.spad" 135728 135738 136951 136956) (-131 "COMBF.spad" 133150 133166 135718 135723) (-130 "COLOR.spad" 131987 131995 133140 133145) (-129 "COLONAST.spad" 131653 131661 131977 131982) (-128 "CMPLXRT.spad" 131364 131381 131643 131648) (-127 "CLLCTAST.spad" 131026 131034 131354 131359) (-126 "CLIP.spad" 127134 127142 131016 131021) (-125 "CLIF.spad" 125789 125805 127090 127129) (-124 "CLAGG.spad" 122326 122336 125779 125784) (-123 "CLAGG.spad" 118747 118759 122202 122207) (-122 "CINTSLPE.spad" 118102 118115 118737 118742) (-121 "CHVAR.spad" 116240 116262 118092 118097) (-120 "CHARZ.spad" 116155 116163 116220 116235) (-119 "CHARPOL.spad" 115681 115691 116145 116150) (-118 "CHARNZ.spad" 115443 115451 115661 115676) (-117 "CHAR.spad" 112811 112819 115433 115438) (-116 "CFCAT.spad" 112139 112147 112801 112806) (-115 "CDEN.spad" 111359 111373 112129 112134) (-114 "CCLASS.spad" 109539 109547 110801 110840) (-113 "CATEGORY.spad" 108613 108621 109529 109534) (-112 "CATCTOR.spad" 108504 108512 108603 108608) (-111 "CATAST.spad" 108130 108138 108494 108499) (-110 "CASEAST.spad" 107844 107852 108120 108125) (-109 "CARTEN2.spad" 107234 107261 107834 107839) (-108 "CARTEN.spad" 102986 103010 107224 107229) (-107 "CARD.spad" 100281 100289 102960 102981) (-106 "CAPSLAST.spad" 100063 100071 100271 100276) (-105 "CACHSET.spad" 99687 99695 100053 100058) (-104 "CABMON.spad" 99242 99250 99677 99682) (-103 "BYTEORD.spad" 98917 98925 99232 99237) (-102 "BYTEBUF.spad" 96884 96892 98170 98197) (-101 "BYTE.spad" 96359 96367 96874 96879) (-100 "BTREE.spad" 95497 95507 96031 96058) (-99 "BTOURN.spad" 94568 94577 95169 95196) (-98 "BTCAT.spad" 93961 93970 94536 94563) (-97 "BTCAT.spad" 93374 93385 93951 93956) (-96 "BTAGG.spad" 92841 92848 93342 93369) (-95 "BTAGG.spad" 92328 92337 92831 92836) (-94 "BSTREE.spad" 91135 91144 92000 92027) (-93 "BRILL.spad" 89341 89351 91125 91130) (-92 "BRAGG.spad" 88298 88307 89331 89336) (-91 "BRAGG.spad" 87219 87230 88254 88259) (-90 "BPADICRT.spad" 85279 85290 85525 85618) (-89 "BPADIC.spad" 84952 84963 85205 85274) (-88 "BOUNDZRO.spad" 84609 84625 84942 84947) (-87 "BOP1.spad" 82068 82077 84599 84604) (-86 "BOP.spad" 77211 77218 82058 82063) (-85 "BOOLEAN.spad" 76760 76767 77201 77206) (-84 "BOOLE.spad" 76411 76418 76750 76755) (-83 "BOOLE.spad" 76060 76069 76401 76406) (-82 "BMODULE.spad" 75773 75784 76028 76055) (-81 "BITS.spad" 75205 75212 75419 75446) (-80 "catdef.spad" 75088 75098 75195 75200) (-79 "catdef.spad" 74839 74849 75078 75083) (-78 "BINDING.spad" 74261 74268 74829 74834) (-77 "BINARY.spad" 72496 72503 72851 72944) (-76 "BGAGG.spad" 71702 71711 72476 72491) (-75 "BGAGG.spad" 70916 70927 71692 71697) (-74 "BEZOUT.spad" 70057 70083 70866 70871) (-73 "BBTREE.spad" 67000 67009 69729 69756) (-72 "BASTYPE.spad" 66500 66507 66990 66995) (-71 "BASTYPE.spad" 65998 66007 66490 66495) (-70 "BALFACT.spad" 65458 65470 65988 65993) (-69 "AUTOMOR.spad" 64909 64918 65438 65453) (-68 "ATTREG.spad" 61632 61639 64661 64904) (-67 "ATTRAST.spad" 61349 61356 61622 61627) (-66 "ATRIG.spad" 60819 60826 61339 61344) (-65 "ATRIG.spad" 60287 60296 60809 60814) (-64 "ASTCAT.spad" 60191 60198 60277 60282) (-63 "ASTCAT.spad" 60093 60102 60181 60186) (-62 "ASTACK.spad" 59497 59506 59765 59792) (-61 "ASSOCEQ.spad" 58331 58342 59453 59458) (-60 "ARRAY2.spad" 57854 57863 58003 58030) (-59 "ARRAY12.spad" 56567 56578 57844 57849) (-58 "ARRAY1.spad" 55446 55455 55792 55819) (-57 "ARR2CAT.spad" 51340 51361 55414 55441) (-56 "ARR2CAT.spad" 47254 47277 51330 51335) (-55 "ARITY.spad" 46626 46633 47244 47249) (-54 "APPRULE.spad" 45910 45932 46616 46621) (-53 "APPLYORE.spad" 45529 45542 45900 45905) (-52 "ANY1.spad" 44600 44609 45519 45524) (-51 "ANY.spad" 43451 43458 44590 44595) (-50 "ANTISYM.spad" 41896 41912 43431 43446) (-49 "ANON.spad" 41605 41612 41886 41891) (-48 "AN.spad" 40073 40080 41436 41529) (-47 "AMR.spad" 38258 38269 39971 40068) (-46 "AMR.spad" 36306 36319 38021 38026) (-45 "ALIST.spad" 33544 33565 33894 33921) (-44 "ALGSC.spad" 32679 32705 33416 33469) (-43 "ALGPKG.spad" 28462 28473 32635 32640) (-42 "ALGMFACT.spad" 27655 27669 28452 28457) (-41 "ALGMANIP.spad" 25156 25171 27499 27504) (-40 "ALGFF.spad" 22974 23001 23191 23347) (-39 "ALGFACT.spad" 22093 22103 22964 22969) (-38 "ALGEBRA.spad" 21926 21935 22049 22088) (-37 "ALGEBRA.spad" 21791 21802 21916 21921) (-36 "ALAGG.spad" 21303 21324 21759 21786) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-3 NIL 1961936 1961941 1961946 1961951) (-2 NIL 1961916 1961921 1961926 1961931) (-1 NIL 1961896 1961901 1961906 1961911) (0 NIL 1961876 1961881 1961886 1961891) (-1208 "ZMOD.spad" 1961685 1961698 1961814 1961871) (-1207 "ZLINDEP.spad" 1960783 1960794 1961675 1961680) (-1206 "ZDSOLVE.spad" 1950744 1950766 1960773 1960778) (-1205 "YSTREAM.spad" 1950239 1950250 1950734 1950739) (-1204 "YDIAGRAM.spad" 1949873 1949882 1950229 1950234) (-1203 "XRPOLY.spad" 1949093 1949113 1949729 1949798) (-1202 "XPR.spad" 1946888 1946901 1948811 1948910) (-1201 "XPOLYC.spad" 1946207 1946223 1946814 1946883) (-1200 "XPOLY.spad" 1945762 1945773 1946063 1946132) (-1199 "XPBWPOLY.spad" 1944233 1944253 1945568 1945637) (-1198 "XFALG.spad" 1941281 1941297 1944159 1944228) (-1197 "XF.spad" 1939744 1939759 1941183 1941276) (-1196 "XF.spad" 1938187 1938204 1939628 1939633) (-1195 "XEXPPKG.spad" 1937446 1937472 1938177 1938182) (-1194 "XDPOLY.spad" 1937060 1937076 1937302 1937371) (-1193 "XALG.spad" 1936728 1936739 1937016 1937055) (-1192 "WUTSET.spad" 1932731 1932748 1936362 1936389) (-1191 "WP.spad" 1931938 1931982 1932589 1932656) (-1190 "WHILEAST.spad" 1931736 1931745 1931928 1931933) (-1189 "WHEREAST.spad" 1931407 1931416 1931726 1931731) (-1188 "WFFINTBS.spad" 1929070 1929092 1931397 1931402) (-1187 "WEIER.spad" 1927292 1927303 1929060 1929065) (-1186 "VSPACE.spad" 1926965 1926976 1927260 1927287) (-1185 "VSPACE.spad" 1926658 1926671 1926955 1926960) (-1184 "VOID.spad" 1926335 1926344 1926648 1926653) (-1183 "VIEWDEF.spad" 1921536 1921545 1926325 1926330) (-1182 "VIEW3D.spad" 1905497 1905506 1921526 1921531) (-1181 "VIEW2D.spad" 1893396 1893405 1905487 1905492) (-1180 "VIEW.spad" 1891116 1891125 1893386 1893391) (-1179 "VECTOR2.spad" 1889755 1889768 1891106 1891111) (-1178 "VECTOR.spad" 1888474 1888485 1888725 1888752) (-1177 "VECTCAT.spad" 1886386 1886397 1888442 1888469) (-1176 "VECTCAT.spad" 1884107 1884120 1886165 1886170) (-1175 "VARIABLE.spad" 1883887 1883902 1884097 1884102) (-1174 "UTYPE.spad" 1883531 1883540 1883877 1883882) (-1173 "UTSODETL.spad" 1882826 1882850 1883487 1883492) (-1172 "UTSODE.spad" 1881042 1881062 1882816 1882821) (-1171 "UTSCAT.spad" 1878521 1878537 1880940 1881037) (-1170 "UTSCAT.spad" 1875668 1875686 1878089 1878094) (-1169 "UTS2.spad" 1875263 1875298 1875658 1875663) (-1168 "UTS.spad" 1870275 1870303 1873795 1873892) (-1167 "URAGG.spad" 1864996 1865007 1870265 1870270) (-1166 "URAGG.spad" 1859681 1859694 1864952 1864957) (-1165 "UPXSSING.spad" 1857449 1857475 1858885 1859018) (-1164 "UPXSCONS.spad" 1855267 1855287 1855640 1855789) (-1163 "UPXSCCA.spad" 1853838 1853858 1855113 1855262) (-1162 "UPXSCCA.spad" 1852551 1852573 1853828 1853833) (-1161 "UPXSCAT.spad" 1851140 1851156 1852397 1852546) (-1160 "UPXS2.spad" 1850683 1850736 1851130 1851135) (-1159 "UPXS.spad" 1848038 1848066 1848874 1849023) (-1158 "UPSQFREE.spad" 1846453 1846467 1848028 1848033) (-1157 "UPSCAT.spad" 1844248 1844272 1846351 1846448) (-1156 "UPSCAT.spad" 1841744 1841770 1843849 1843854) (-1155 "UPOLYC2.spad" 1841215 1841234 1841734 1841739) (-1154 "UPOLYC.spad" 1836295 1836306 1841057 1841210) (-1153 "UPOLYC.spad" 1831293 1831306 1836057 1836062) (-1152 "UPMP.spad" 1830225 1830238 1831283 1831288) (-1151 "UPDIVP.spad" 1829790 1829804 1830215 1830220) (-1150 "UPDECOMP.spad" 1828051 1828065 1829780 1829785) (-1149 "UPCDEN.spad" 1827268 1827284 1828041 1828046) (-1148 "UP2.spad" 1826632 1826653 1827258 1827263) (-1147 "UP.spad" 1824102 1824117 1824489 1824642) (-1146 "UNISEG2.spad" 1823599 1823612 1824058 1824063) (-1145 "UNISEG.spad" 1822952 1822963 1823518 1823523) (-1144 "UNIFACT.spad" 1822055 1822067 1822942 1822947) (-1143 "ULSCONS.spad" 1815901 1815921 1816271 1816420) (-1142 "ULSCCAT.spad" 1813638 1813658 1815747 1815896) (-1141 "ULSCCAT.spad" 1811483 1811505 1813594 1813599) (-1140 "ULSCAT.spad" 1809723 1809739 1811329 1811478) (-1139 "ULS2.spad" 1809237 1809290 1809713 1809718) (-1138 "ULS.spad" 1801270 1801298 1802215 1802638) (-1137 "UINT8.spad" 1801147 1801156 1801260 1801265) (-1136 "UINT64.spad" 1801023 1801032 1801137 1801142) (-1135 "UINT32.spad" 1800899 1800908 1801013 1801018) (-1134 "UINT16.spad" 1800775 1800784 1800889 1800894) (-1133 "UFD.spad" 1799840 1799849 1800701 1800770) (-1132 "UFD.spad" 1798967 1798978 1799830 1799835) (-1131 "UDVO.spad" 1797848 1797857 1798957 1798962) (-1130 "UDPO.spad" 1795429 1795440 1797804 1797809) (-1129 "TYPEAST.spad" 1795348 1795357 1795419 1795424) (-1128 "TYPE.spad" 1795280 1795289 1795338 1795343) (-1127 "TWOFACT.spad" 1793932 1793947 1795270 1795275) (-1126 "TUPLE.spad" 1793439 1793450 1793844 1793849) (-1125 "TUBETOOL.spad" 1790306 1790315 1793429 1793434) (-1124 "TUBE.spad" 1788953 1788970 1790296 1790301) (-1123 "TSETCAT.spad" 1777024 1777041 1788921 1788948) (-1122 "TSETCAT.spad" 1765081 1765100 1776980 1776985) (-1121 "TS.spad" 1763709 1763725 1764675 1764772) (-1120 "TRMANIP.spad" 1758073 1758090 1763397 1763402) (-1119 "TRIMAT.spad" 1757036 1757061 1758063 1758068) (-1118 "TRIGMNIP.spad" 1755563 1755580 1757026 1757031) (-1117 "TRIGCAT.spad" 1755075 1755084 1755553 1755558) (-1116 "TRIGCAT.spad" 1754585 1754596 1755065 1755070) (-1115 "TREE.spad" 1753225 1753236 1754257 1754284) (-1114 "TRANFUN.spad" 1753064 1753073 1753215 1753220) (-1113 "TRANFUN.spad" 1752901 1752912 1753054 1753059) (-1112 "TOPSP.spad" 1752575 1752584 1752891 1752896) (-1111 "TOOLSIGN.spad" 1752238 1752249 1752565 1752570) (-1110 "TEXTFILE.spad" 1750799 1750808 1752228 1752233) (-1109 "TEX1.spad" 1750355 1750366 1750789 1750794) (-1108 "TEX.spad" 1747549 1747558 1750345 1750350) (-1107 "TBCMPPK.spad" 1745650 1745673 1747539 1747544) (-1106 "TBAGG.spad" 1744708 1744731 1745630 1745645) (-1105 "TBAGG.spad" 1743774 1743799 1744698 1744703) (-1104 "TANEXP.spad" 1743182 1743193 1743764 1743769) (-1103 "TALGOP.spad" 1742906 1742917 1743172 1743177) (-1102 "TABLEAU.spad" 1742387 1742398 1742896 1742901) (-1101 "TABLE.spad" 1740662 1740685 1740932 1740959) (-1100 "TABLBUMP.spad" 1737441 1737452 1740652 1740657) (-1099 "SYSTEM.spad" 1736669 1736678 1737431 1737436) (-1098 "SYSSOLP.spad" 1734152 1734163 1736659 1736664) (-1097 "SYSPTR.spad" 1734051 1734060 1734142 1734147) (-1096 "SYSNNI.spad" 1733274 1733285 1734041 1734046) (-1095 "SYSINT.spad" 1732678 1732689 1733264 1733269) (-1094 "SYNTAX.spad" 1729012 1729021 1732668 1732673) (-1093 "SYMTAB.spad" 1727080 1727089 1729002 1729007) (-1092 "SYMS.spad" 1723109 1723118 1727070 1727075) (-1091 "SYMPOLY.spad" 1722242 1722253 1722324 1722451) (-1090 "SYMFUNC.spad" 1721743 1721754 1722232 1722237) (-1089 "SYMBOL.spad" 1719238 1719247 1721733 1721738) (-1088 "SUTS.spad" 1716351 1716379 1717770 1717867) (-1087 "SUPXS.spad" 1713693 1713721 1714542 1714691) (-1086 "SUPFRACF.spad" 1712798 1712816 1713683 1713688) (-1085 "SUP2.spad" 1712190 1712203 1712788 1712793) (-1084 "SUP.spad" 1709274 1709285 1710047 1710200) (-1083 "SUMRF.spad" 1708248 1708259 1709264 1709269) (-1082 "SUMFS.spad" 1707877 1707894 1708238 1708243) (-1081 "SULS.spad" 1699897 1699925 1700855 1701278) (-1080 "syntax.spad" 1699666 1699675 1699887 1699892) (-1079 "SUCH.spad" 1699356 1699371 1699656 1699661) (-1078 "SUBSPACE.spad" 1691487 1691502 1699346 1699351) (-1077 "SUBRESP.spad" 1690657 1690671 1691443 1691448) (-1076 "STTFNC.spad" 1687125 1687141 1690647 1690652) (-1075 "STTF.spad" 1683224 1683240 1687115 1687120) (-1074 "STTAYLOR.spad" 1675901 1675912 1683131 1683136) (-1073 "STRTBL.spad" 1674288 1674305 1674437 1674464) (-1072 "STRING.spad" 1673156 1673165 1673541 1673568) (-1071 "STREAM3.spad" 1672729 1672744 1673146 1673151) (-1070 "STREAM2.spad" 1671857 1671870 1672719 1672724) (-1069 "STREAM1.spad" 1671563 1671574 1671847 1671852) (-1068 "STREAM.spad" 1668559 1668570 1671166 1671181) (-1067 "STINPROD.spad" 1667495 1667511 1668549 1668554) (-1066 "STEPAST.spad" 1666729 1666738 1667485 1667490) (-1065 "STEP.spad" 1666046 1666055 1666719 1666724) (-1064 "STBL.spad" 1664436 1664464 1664603 1664618) (-1063 "STAGG.spad" 1663135 1663146 1664426 1664431) (-1062 "STAGG.spad" 1661832 1661845 1663125 1663130) (-1061 "STACK.spad" 1661254 1661265 1661504 1661531) (-1060 "SRING.spad" 1661014 1661023 1661244 1661249) (-1059 "SREGSET.spad" 1658746 1658763 1660648 1660675) (-1058 "SRDCMPK.spad" 1657323 1657343 1658736 1658741) (-1057 "SRAGG.spad" 1652506 1652515 1657291 1657318) (-1056 "SRAGG.spad" 1647709 1647720 1652496 1652501) (-1055 "SQMATRIX.spad" 1645386 1645404 1646302 1646389) (-1054 "SPLTREE.spad" 1640128 1640141 1644924 1644951) (-1053 "SPLNODE.spad" 1636748 1636761 1640118 1640123) (-1052 "SPFCAT.spad" 1635557 1635566 1636738 1636743) (-1051 "SPECOUT.spad" 1634109 1634118 1635547 1635552) (-1050 "SPADXPT.spad" 1626200 1626209 1634099 1634104) (-1049 "spad-parser.spad" 1625665 1625674 1626190 1626195) (-1048 "SPADAST.spad" 1625366 1625375 1625655 1625660) (-1047 "SPACEC.spad" 1609581 1609592 1625356 1625361) (-1046 "SPACE3.spad" 1609357 1609368 1609571 1609576) (-1045 "SORTPAK.spad" 1608906 1608919 1609313 1609318) (-1044 "SOLVETRA.spad" 1606669 1606680 1608896 1608901) (-1043 "SOLVESER.spad" 1605125 1605136 1606659 1606664) (-1042 "SOLVERAD.spad" 1601151 1601162 1605115 1605120) (-1041 "SOLVEFOR.spad" 1599613 1599631 1601141 1601146) (-1040 "SNTSCAT.spad" 1599213 1599230 1599581 1599608) (-1039 "SMTS.spad" 1597530 1597556 1598807 1598904) (-1038 "SMP.spad" 1595338 1595358 1595728 1595855) (-1037 "SMITH.spad" 1594183 1594208 1595328 1595333) (-1036 "SMATCAT.spad" 1592301 1592331 1594127 1594178) (-1035 "SMATCAT.spad" 1590351 1590383 1592179 1592184) (-1034 "SKAGG.spad" 1589320 1589331 1590319 1590346) (-1033 "SINT.spad" 1588619 1588628 1589186 1589315) (-1032 "SIMPAN.spad" 1588347 1588356 1588609 1588614) (-1031 "SIGNRF.spad" 1587472 1587483 1588337 1588342) (-1030 "SIGNEF.spad" 1586758 1586775 1587462 1587467) (-1029 "syntax.spad" 1586175 1586184 1586748 1586753) (-1028 "SIG.spad" 1585537 1585546 1586165 1586170) (-1027 "SHP.spad" 1583481 1583496 1585493 1585498) (-1026 "SHDP.spad" 1572974 1573001 1573491 1573588) (-1025 "SGROUP.spad" 1572582 1572591 1572964 1572969) (-1024 "SGROUP.spad" 1572188 1572199 1572572 1572577) (-1023 "catdef.spad" 1571898 1571910 1572009 1572183) (-1022 "catdef.spad" 1571454 1571466 1571719 1571893) (-1021 "SGCF.spad" 1564593 1564602 1571444 1571449) (-1020 "SFRTCAT.spad" 1563539 1563556 1564561 1564588) (-1019 "SFRGCD.spad" 1562602 1562622 1563529 1563534) (-1018 "SFQCMPK.spad" 1557415 1557435 1562592 1562597) (-1017 "SEXOF.spad" 1557258 1557298 1557405 1557410) (-1016 "SEXCAT.spad" 1555086 1555126 1557248 1557253) (-1015 "SEX.spad" 1554978 1554987 1555076 1555081) (-1014 "SETMN.spad" 1553438 1553455 1554968 1554973) (-1013 "SETCAT.spad" 1552923 1552932 1553428 1553433) (-1012 "SETCAT.spad" 1552406 1552417 1552913 1552918) (-1011 "SETAGG.spad" 1548955 1548966 1552386 1552401) (-1010 "SETAGG.spad" 1545512 1545525 1548945 1548950) (-1009 "SET.spad" 1543821 1543832 1544918 1544957) (-1008 "syntax.spad" 1543524 1543533 1543811 1543816) (-1007 "SEGXCAT.spad" 1542680 1542693 1543514 1543519) (-1006 "SEGCAT.spad" 1541605 1541616 1542670 1542675) (-1005 "SEGBIND2.spad" 1541303 1541316 1541595 1541600) (-1004 "SEGBIND.spad" 1541061 1541072 1541250 1541255) (-1003 "SEGAST.spad" 1540791 1540800 1541051 1541056) (-1002 "SEG2.spad" 1540226 1540239 1540747 1540752) (-1001 "SEG.spad" 1540039 1540050 1540145 1540150) (-1000 "SDVAR.spad" 1539315 1539326 1540029 1540034) (-999 "SDPOL.spad" 1537008 1537018 1537298 1537425) (-998 "SCPKG.spad" 1535098 1535108 1536998 1537003) (-997 "SCOPE.spad" 1534276 1534284 1535088 1535093) (-996 "SCACHE.spad" 1532973 1532983 1534266 1534271) (-995 "SASTCAT.spad" 1532883 1532891 1532963 1532968) (-994 "SAOS.spad" 1532756 1532764 1532873 1532878) (-993 "SAERFFC.spad" 1532470 1532489 1532746 1532751) (-992 "SAEFACT.spad" 1532172 1532191 1532460 1532465) (-991 "SAE.spad" 1529823 1529838 1530433 1530568) (-990 "RURPK.spad" 1527483 1527498 1529813 1529818) (-989 "RULESET.spad" 1526937 1526960 1527473 1527478) (-988 "RULECOLD.spad" 1526790 1526802 1526927 1526932) (-987 "RULE.spad" 1525039 1525062 1526780 1526785) (-986 "RTVALUE.spad" 1524775 1524783 1525029 1525034) (-985 "syntax.spad" 1524493 1524501 1524765 1524770) (-984 "RSETGCD.spad" 1520936 1520955 1524483 1524488) (-983 "RSETCAT.spad" 1510905 1510921 1520904 1520931) (-982 "RSETCAT.spad" 1500894 1500912 1510895 1510900) (-981 "RSDCMPK.spad" 1499395 1499414 1500884 1500889) (-980 "RRCC.spad" 1497780 1497809 1499385 1499390) (-979 "RRCC.spad" 1496163 1496194 1497770 1497775) (-978 "RPTAST.spad" 1495866 1495874 1496153 1496158) (-977 "RPOLCAT.spad" 1475371 1475385 1495734 1495861) (-976 "RPOLCAT.spad" 1454669 1454685 1475034 1475039) (-975 "ROMAN.spad" 1453998 1454006 1454535 1454664) (-974 "ROIRC.spad" 1453079 1453110 1453988 1453993) (-973 "RNS.spad" 1452056 1452064 1452981 1453074) (-972 "RNS.spad" 1451119 1451129 1452046 1452051) (-971 "RNGBIND.spad" 1450280 1450293 1451074 1451079) (-970 "RNG.spad" 1449889 1449897 1450270 1450275) (-969 "RNG.spad" 1449496 1449506 1449879 1449884) (-968 "RMODULE.spad" 1449278 1449288 1449486 1449491) (-967 "RMCAT2.spad" 1448699 1448755 1449268 1449273) (-966 "RMATRIX.spad" 1447509 1447527 1447851 1447890) (-965 "RMATCAT.spad" 1443089 1443119 1447465 1447504) (-964 "RMATCAT.spad" 1438559 1438591 1442937 1442942) (-963 "RLINSET.spad" 1438264 1438274 1438549 1438554) (-962 "RINTERP.spad" 1438153 1438172 1438254 1438259) (-961 "RING.spad" 1437624 1437632 1438133 1438148) (-960 "RING.spad" 1437103 1437113 1437614 1437619) (-959 "RIDIST.spad" 1436496 1436504 1437093 1437098) (-958 "RGCHAIN.spad" 1435051 1435066 1435944 1435971) (-957 "RGBCSPC.spad" 1434841 1434852 1435041 1435046) (-956 "RGBCMDL.spad" 1434404 1434415 1434831 1434836) (-955 "RFFACTOR.spad" 1433867 1433877 1434394 1434399) (-954 "RFFACT.spad" 1433603 1433614 1433857 1433862) (-953 "RFDIST.spad" 1432600 1432608 1433593 1433598) (-952 "RF.spad" 1430275 1430285 1432590 1432595) (-951 "RETSOL.spad" 1429695 1429707 1430265 1430270) (-950 "RETRACT.spad" 1429124 1429134 1429685 1429690) (-949 "RETRACT.spad" 1428551 1428563 1429114 1429119) (-948 "RETAST.spad" 1428364 1428372 1428541 1428546) (-947 "RESRING.spad" 1427712 1427758 1428302 1428359) (-946 "RESLATC.spad" 1427037 1427047 1427702 1427707) (-945 "REPSQ.spad" 1426769 1426779 1427027 1427032) (-944 "REPDB.spad" 1426477 1426487 1426759 1426764) (-943 "REP2.spad" 1416192 1416202 1426319 1426324) (-942 "REP1.spad" 1410413 1410423 1416142 1416147) (-941 "REP.spad" 1407968 1407976 1410403 1410408) (-940 "REGSET.spad" 1405794 1405810 1407602 1407629) (-939 "REF.spad" 1405313 1405323 1405784 1405789) (-938 "REDORDER.spad" 1404520 1404536 1405303 1405308) (-937 "RECLOS.spad" 1403417 1403436 1404120 1404213) (-936 "REALSOLV.spad" 1402558 1402566 1403407 1403412) (-935 "REAL0Q.spad" 1399857 1399871 1402548 1402553) (-934 "REAL0.spad" 1396702 1396716 1399847 1399852) (-933 "REAL.spad" 1396575 1396583 1396692 1396697) (-932 "RDUCEAST.spad" 1396297 1396305 1396565 1396570) (-931 "RDIV.spad" 1395953 1395977 1396287 1396292) (-930 "RDIST.spad" 1395521 1395531 1395943 1395948) (-929 "RDETRS.spad" 1394386 1394403 1395511 1395516) (-928 "RDETR.spad" 1392526 1392543 1394376 1394381) (-927 "RDEEFS.spad" 1391626 1391642 1392516 1392521) (-926 "RDEEF.spad" 1390637 1390653 1391616 1391621) (-925 "RCFIELD.spad" 1387856 1387864 1390539 1390632) (-924 "RCFIELD.spad" 1385161 1385171 1387846 1387851) (-923 "RCAGG.spad" 1383098 1383108 1385151 1385156) (-922 "RCAGG.spad" 1380962 1380974 1383017 1383022) (-921 "RATRET.spad" 1380323 1380333 1380952 1380957) (-920 "RATFACT.spad" 1380016 1380027 1380313 1380318) (-919 "RANDSRC.spad" 1379336 1379344 1380006 1380011) (-918 "RADUTIL.spad" 1379093 1379101 1379326 1379331) (-917 "RADIX.spad" 1376138 1376151 1377683 1377776) (-916 "RADFF.spad" 1374055 1374091 1374173 1374329) (-915 "RADCAT.spad" 1373651 1373659 1374045 1374050) (-914 "RADCAT.spad" 1373245 1373255 1373641 1373646) (-913 "QUEUE.spad" 1372659 1372669 1372917 1372944) (-912 "QUATCT2.spad" 1372280 1372298 1372649 1372654) (-911 "QUATCAT.spad" 1370451 1370461 1372210 1372275) (-910 "QUATCAT.spad" 1368387 1368399 1370148 1370153) (-909 "QUAT.spad" 1366994 1367004 1367336 1367401) (-908 "QUAGG.spad" 1365828 1365838 1366962 1366989) (-907 "QQUTAST.spad" 1365597 1365605 1365818 1365823) (-906 "QFORM.spad" 1365216 1365230 1365587 1365592) (-905 "QFCAT2.spad" 1364909 1364925 1365206 1365211) (-904 "QFCAT.spad" 1363612 1363622 1364811 1364904) (-903 "QFCAT.spad" 1361948 1361960 1363149 1363154) (-902 "QEQUAT.spad" 1361507 1361515 1361938 1361943) (-901 "QCMPACK.spad" 1356422 1356441 1361497 1361502) (-900 "QALGSET2.spad" 1354418 1354436 1356412 1356417) (-899 "QALGSET.spad" 1350523 1350555 1354332 1354337) (-898 "PWFFINTB.spad" 1347939 1347960 1350513 1350518) (-897 "PUSHVAR.spad" 1347278 1347297 1347929 1347934) (-896 "PTRANFN.spad" 1343414 1343424 1347268 1347273) (-895 "PTPACK.spad" 1340502 1340512 1343404 1343409) (-894 "PTFUNC2.spad" 1340325 1340339 1340492 1340497) (-893 "PTCAT.spad" 1339580 1339590 1340293 1340320) (-892 "PSQFR.spad" 1338895 1338919 1339570 1339575) (-891 "PSEUDLIN.spad" 1337781 1337791 1338885 1338890) (-890 "PSETPK.spad" 1324486 1324502 1337659 1337664) (-889 "PSETCAT.spad" 1318886 1318909 1324466 1324481) (-888 "PSETCAT.spad" 1313260 1313285 1318842 1318847) (-887 "PSCURVE.spad" 1312259 1312267 1313250 1313255) (-886 "PSCAT.spad" 1311042 1311071 1312157 1312254) (-885 "PSCAT.spad" 1309915 1309946 1311032 1311037) (-884 "PRTITION.spad" 1308613 1308621 1309905 1309910) (-883 "PRTDAST.spad" 1308332 1308340 1308603 1308608) (-882 "PRS.spad" 1297950 1297967 1308288 1308293) (-881 "PRQAGG.spad" 1297385 1297395 1297918 1297945) (-880 "PROPLOG.spad" 1296989 1296997 1297375 1297380) (-879 "PROPFUN2.spad" 1296612 1296625 1296979 1296984) (-878 "PROPFUN1.spad" 1296018 1296029 1296602 1296607) (-877 "PROPFRML.spad" 1294586 1294597 1296008 1296013) (-876 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1264412 1264417) (-857 "POLY.spad" 1261687 1261697 1262202 1262329) (-856 "POLUTIL.spad" 1260652 1260681 1261643 1261648) (-855 "POLTOPOL.spad" 1259400 1259415 1260642 1260647) (-854 "POINT.spad" 1258283 1258293 1258370 1258397) (-853 "PNTHEORY.spad" 1254985 1254993 1258273 1258278) (-852 "PMTOOLS.spad" 1253760 1253774 1254975 1254980) (-851 "PMSYM.spad" 1253309 1253319 1253750 1253755) (-850 "PMQFCAT.spad" 1252900 1252914 1253299 1253304) (-849 "PMPREDFS.spad" 1252362 1252384 1252890 1252895) (-848 "PMPRED.spad" 1251849 1251863 1252352 1252357) (-847 "PMPLCAT.spad" 1250926 1250944 1251778 1251783) (-846 "PMLSAGG.spad" 1250511 1250525 1250916 1250921) (-845 "PMKERNEL.spad" 1250090 1250102 1250501 1250506) (-844 "PMINS.spad" 1249670 1249680 1250080 1250085) (-843 "PMFS.spad" 1249247 1249265 1249660 1249665) (-842 "PMDOWN.spad" 1248537 1248551 1249237 1249242) (-841 "PMASSFS.spad" 1247512 1247528 1248527 1248532) (-840 "PMASS.spad" 1246530 1246538 1247502 1247507) (-839 "PLOTTOOL.spad" 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1200519 1202727 1202732) (-819 "PFBRU.spad" 1198397 1198409 1200499 1200504) (-818 "PFBR.spad" 1195957 1195980 1198387 1198392) (-817 "PF.spad" 1195531 1195543 1195762 1195855) (-816 "PERMGRP.spad" 1190301 1190311 1195521 1195526) (-815 "PERMCAT.spad" 1188962 1188972 1190281 1190296) (-814 "PERMAN.spad" 1187518 1187532 1188952 1188957) (-813 "PERM.spad" 1183328 1183338 1187351 1187366) (-812 "PENDTREE.spad" 1182742 1182752 1183022 1183027) (-811 "PDSPC.spad" 1181555 1181565 1182732 1182737) (-810 "PDSPC.spad" 1180366 1180378 1181545 1181550) (-809 "PDRING.spad" 1180208 1180218 1180346 1180361) (-808 "PDMOD.spad" 1180024 1180036 1180176 1180203) (-807 "PDECOMP.spad" 1179494 1179511 1180014 1180019) (-806 "PDDOM.spad" 1178932 1178945 1179484 1179489) (-805 "PDDOM.spad" 1178368 1178383 1178922 1178927) (-804 "PCOMP.spad" 1178221 1178234 1178358 1178363) (-803 "PBWLB.spad" 1176819 1176836 1178211 1178216) (-802 "PATTERN2.spad" 1176557 1176569 1176809 1176814) (-801 "PATTERN1.spad" 1174901 1174917 1176547 1176552) (-800 "PATTERN.spad" 1169476 1169486 1174891 1174896) (-799 "PATRES2.spad" 1169148 1169162 1169466 1169471) (-798 "PATRES.spad" 1166731 1166743 1169138 1169143) (-797 "PATMATCH.spad" 1164972 1165003 1166483 1166488) (-796 "PATMAB.spad" 1164401 1164411 1164962 1164967) (-795 "PATLRES.spad" 1163487 1163501 1164391 1164396) (-794 "PATAB.spad" 1163251 1163261 1163477 1163482) (-793 "PARTPERM.spad" 1161307 1161315 1163241 1163246) (-792 "PARSURF.spad" 1160741 1160769 1161297 1161302) (-791 "PARSU2.spad" 1160538 1160554 1160731 1160736) (-790 "script-parser.spad" 1160058 1160066 1160528 1160533) (-789 "PARSCURV.spad" 1159492 1159520 1160048 1160053) (-788 "PARSC2.spad" 1159283 1159299 1159482 1159487) (-787 "PARPCURV.spad" 1158745 1158773 1159273 1159278) (-786 "PARPC2.spad" 1158536 1158552 1158735 1158740) (-785 "PARAMAST.spad" 1157664 1157672 1158526 1158531) (-784 "PAN2EXPR.spad" 1157076 1157084 1157654 1157659) (-783 "PALETTE.spad" 1156190 1156198 1157066 1157071) (-782 "PAIR.spad" 1155264 1155277 1155833 1155838) (-781 "PADICRC.spad" 1152669 1152687 1153832 1153925) (-780 "PADICRAT.spad" 1150729 1150741 1150942 1151035) (-779 "PADICCT.spad" 1149278 1149290 1150655 1150724) (-778 "PADIC.spad" 1148981 1148993 1149204 1149273) (-777 "PADEPAC.spad" 1147670 1147689 1148971 1148976) (-776 "PADE.spad" 1146422 1146438 1147660 1147665) (-775 "OWP.spad" 1145670 1145700 1146280 1146347) (-774 "OVERSET.spad" 1145243 1145251 1145660 1145665) (-773 "OVAR.spad" 1145024 1145047 1145233 1145238) (-772 "OUTFORM.spad" 1134432 1134440 1145014 1145019) (-771 "OUTBFILE.spad" 1133866 1133874 1134422 1134427) (-770 "OUTBCON.spad" 1132936 1132944 1133856 1133861) (-769 "OUTBCON.spad" 1132004 1132014 1132926 1132931) (-768 "OUT.spad" 1131122 1131130 1131994 1131999) (-767 "OSI.spad" 1130597 1130605 1131112 1131117) (-766 "OSGROUP.spad" 1130515 1130523 1130587 1130592) (-765 "ORTHPOL.spad" 1129026 1129036 1130458 1130463) (-764 "OREUP.spad" 1128520 1128548 1128747 1128786) (-763 "ORESUP.spad" 1127862 1127886 1128241 1128280) (-762 "OREPCTO.spad" 1125751 1125763 1127782 1127787) (-761 "OREPCAT.spad" 1119938 1119948 1125707 1125746) (-760 "OREPCAT.spad" 1114015 1114027 1119786 1119791) (-759 "ORDTYPE.spad" 1113252 1113260 1114005 1114010) (-758 "ORDTYPE.spad" 1112487 1112497 1113242 1113247) (-757 "ORDSTRCT.spad" 1112273 1112288 1112436 1112441) (-756 "ORDSET.spad" 1111973 1111981 1112263 1112268) (-755 "ORDRING.spad" 1111790 1111798 1111953 1111968) (-754 "ORDMON.spad" 1111645 1111653 1111780 1111785) (-753 "ORDFUNS.spad" 1110777 1110793 1111635 1111640) (-752 "ORDFIN.spad" 1110597 1110605 1110767 1110772) (-751 "ORDCOMP2.spad" 1109890 1109902 1110587 1110592) (-750 "ORDCOMP.spad" 1108416 1108426 1109498 1109527) (-749 "OPSIG.spad" 1108078 1108086 1108406 1108411) (-748 "OPQUERY.spad" 1107659 1107667 1108068 1108073) (-747 "OPERCAT.spad" 1107125 1107135 1107649 1107654) (-746 "OPERCAT.spad" 1106589 1106601 1107115 1107120) (-745 "OP.spad" 1106331 1106341 1106411 1106478) (-744 "ONECOMP2.spad" 1105755 1105767 1106321 1106326) (-743 "ONECOMP.spad" 1104561 1104571 1105363 1105392) (-742 "OMSAGG.spad" 1104349 1104359 1104517 1104556) (-741 "OMLO.spad" 1103782 1103794 1104235 1104274) (-740 "OINTDOM.spad" 1103545 1103553 1103708 1103777) (-739 "OFMONOID.spad" 1101684 1101694 1103501 1103506) (-738 "ODVAR.spad" 1100945 1100955 1101674 1101679) (-737 "ODR.spad" 1100589 1100615 1100757 1100906) (-736 "ODPOL.spad" 1098237 1098247 1098577 1098704) (-735 "ODP.spad" 1087874 1087894 1088247 1088344) (-734 "ODETOOLS.spad" 1086523 1086542 1087864 1087869) (-733 "ODESYS.spad" 1084217 1084234 1086513 1086518) (-732 "ODERTRIC.spad" 1080250 1080267 1084174 1084179) (-731 "ODERED.spad" 1079649 1079673 1080240 1080245) (-730 "ODERAT.spad" 1077282 1077299 1079639 1079644) (-729 "ODEPRRIC.spad" 1074375 1074397 1077272 1077277) (-728 "ODEPRIM.spad" 1071773 1071795 1074365 1074370) (-727 "ODEPAL.spad" 1071159 1071183 1071763 1071768) (-726 "ODEINT.spad" 1070594 1070610 1071149 1071154) (-725 "ODEEF.spad" 1066089 1066105 1070584 1070589) (-724 "ODECONST.spad" 1065634 1065652 1066079 1066084) (-723 "OCTCT2.spad" 1065275 1065293 1065624 1065629) (-722 "OCT.spad" 1063590 1063600 1064304 1064343) (-721 "OCAMON.spad" 1063438 1063446 1063580 1063585) (-720 "OC.spad" 1061234 1061244 1063394 1063433) (-719 "OC.spad" 1058769 1058781 1060931 1060936) (-718 "OASGP.spad" 1058584 1058592 1058759 1058764) (-717 "OAMONS.spad" 1058106 1058114 1058574 1058579) (-716 "OAMON.spad" 1057864 1057872 1058096 1058101) (-715 "OAMON.spad" 1057620 1057630 1057854 1057859) (-714 "OAGROUP.spad" 1057158 1057166 1057610 1057615) (-713 "OAGROUP.spad" 1056694 1056704 1057148 1057153) (-712 "NUMTUBE.spad" 1056285 1056301 1056684 1056689) (-711 "NUMQUAD.spad" 1044261 1044269 1056275 1056280) (-710 "NUMODE.spad" 1035613 1035621 1044251 1044256) (-709 "NUMFMT.spad" 1034453 1034461 1035603 1035608) (-708 "NUMERIC.spad" 1026568 1026578 1034259 1034264) (-707 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"NCEP.spad" 999261 999275 1001085 1001090) (-687 "NASRING.spad" 998865 998873 999251 999256) (-686 "NASRING.spad" 998467 998477 998855 998860) (-685 "NARNG.spad" 997867 997875 998457 998462) (-684 "NARNG.spad" 997265 997275 997857 997862) (-683 "NAALG.spad" 996830 996840 997233 997260) (-682 "NAALG.spad" 996415 996427 996820 996825) (-681 "MULTSQFR.spad" 993373 993390 996405 996410) (-680 "MULTFACT.spad" 992756 992773 993363 993368) (-679 "MTSCAT.spad" 990850 990871 992654 992751) (-678 "MTHING.spad" 990509 990519 990840 990845) (-677 "MSYSCMD.spad" 989943 989951 990499 990504) (-676 "MSETAGG.spad" 989788 989798 989911 989938) (-675 "MSET.spad" 987734 987744 989482 989521) (-674 "MRING.spad" 984711 984723 987442 987509) (-673 "MRF2.spad" 984273 984287 984701 984706) (-672 "MRATFAC.spad" 983819 983836 984263 984268) (-671 "MPRFF.spad" 981859 981878 983809 983814) (-670 "MPOLY.spad" 979663 979678 980022 980149) (-669 "MPCPF.spad" 978927 978946 979653 979658) (-668 "MPC3.spad" 978744 978784 978917 978922) (-667 "MPC2.spad" 978398 978431 978734 978739) (-666 "MONOTOOL.spad" 976749 976766 978388 978393) (-665 "catdef.spad" 976182 976193 976403 976744) (-664 "catdef.spad" 975580 975591 975836 976177) (-663 "MONOID.spad" 974901 974909 975570 975575) (-662 "MONOID.spad" 974220 974230 974891 974896) (-661 "MONOGEN.spad" 972968 972981 974080 974215) (-660 "MONOGEN.spad" 971738 971753 972852 972857) (-659 "MONADWU.spad" 969818 969826 971728 971733) (-658 "MONADWU.spad" 967896 967906 969808 969813) (-657 "MONAD.spad" 967056 967064 967886 967891) (-656 "MONAD.spad" 966214 966224 967046 967051) (-655 "MOEBIUS.spad" 964950 964964 966194 966209) (-654 "MODULE.spad" 964820 964830 964918 964945) (-653 "MODULE.spad" 964710 964722 964810 964815) (-652 "MODRING.spad" 964045 964084 964690 964705) (-651 "MODOP.spad" 962702 962714 963867 963934) (-650 "MODMONOM.spad" 962433 962451 962692 962697) (-649 "MODMON.spad" 959503 959515 960218 960371) (-648 "MODFIELD.spad" 958865 958904 959405 959498) (-647 "MMLFORM.spad" 957725 957733 958855 958860) (-646 "MMAP.spad" 957467 957501 957715 957720) (-645 "MLO.spad" 955926 955936 957423 957462) (-644 "MLIFT.spad" 954538 954555 955916 955921) (-643 "MKUCFUNC.spad" 954073 954091 954528 954533) (-642 "MKRECORD.spad" 953661 953674 954063 954068) (-641 "MKFUNC.spad" 953068 953078 953651 953656) (-640 "MKFLCFN.spad" 952036 952046 953058 953063) (-639 "MKBCFUNC.spad" 951531 951549 952026 952031) (-638 "MHROWRED.spad" 950042 950052 951521 951526) (-637 "MFINFACT.spad" 949442 949464 950032 950037) (-636 "MESH.spad" 947237 947245 949432 949437) (-635 "MDDFACT.spad" 945456 945466 947227 947232) (-634 "MDAGG.spad" 944747 944757 945436 945451) (-633 "MCDEN.spad" 943957 943969 944737 944742) (-632 "MAYBE.spad" 943257 943268 943947 943952) (-631 "MATSTOR.spad" 940573 940583 943247 943252) (-630 "MATRIX.spad" 939352 939362 939836 939863) (-629 "MATLIN.spad" 936720 936744 939236 939241) (-628 "MATCAT2.spad" 936002 936050 936710 936715) (-627 "MATCAT.spad" 927698 927720 935970 935997) (-626 "MATCAT.spad" 919266 919290 927540 927545) (-625 "MAPPKG3.spad" 918181 918195 919256 919261) (-624 "MAPPKG2.spad" 917519 917531 918171 918176) (-623 "MAPPKG1.spad" 916347 916357 917509 917514) (-622 "MAPPAST.spad" 915686 915694 916337 916342) (-621 "MAPHACK3.spad" 915498 915512 915676 915681) (-620 "MAPHACK2.spad" 915267 915279 915488 915493) (-619 "MAPHACK1.spad" 914911 914921 915257 915262) (-618 "MAGMA.spad" 912717 912734 914901 914906) (-617 "MACROAST.spad" 912312 912320 912707 912712) (-616 "LZSTAGG.spad" 909566 909576 912302 912307) (-615 "LZSTAGG.spad" 906818 906830 909556 909561) (-614 "LWORD.spad" 903563 903580 906808 906813) (-613 "LSTAST.spad" 903347 903355 903553 903558) (-612 "LSQM.spad" 901625 901639 902019 902070) (-611 "LSPP.spad" 901160 901177 901615 901620) (-610 "LSMP1.spad" 899003 899017 901150 901155) (-609 "LSMP.spad" 897860 897888 898993 898998) (-608 "LSAGG.spad" 897529 897539 897828 897855) (-607 "LSAGG.spad" 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282817) (-218 "DRAWCX.spad" 279608 279616 282120 282125) (-217 "DRAWCURV.spad" 279155 279170 279598 279603) (-216 "DRAWCFUN.spad" 268687 268695 279145 279150) (-215 "DRAW.spad" 261563 261576 268677 268682) (-214 "DQAGG.spad" 259741 259751 261531 261558) (-213 "DPOLCAT.spad" 255098 255114 259609 259736) (-212 "DPOLCAT.spad" 250541 250559 255054 255059) (-211 "DPMO.spad" 243244 243260 243382 243588) (-210 "DPMM.spad" 235960 235978 236085 236291) (-209 "DOMTMPLT.spad" 235731 235739 235950 235955) (-208 "DOMCTOR.spad" 235486 235494 235721 235726) (-207 "DOMAIN.spad" 234597 234605 235476 235481) (-206 "DMP.spad" 232190 232205 232760 232887) (-205 "DMEXT.spad" 232057 232067 232158 232185) (-204 "DLP.spad" 231417 231427 232047 232052) (-203 "DLIST.spad" 230038 230048 230642 230669) (-202 "DLAGG.spad" 228455 228465 230028 230033) (-201 "DIVRING.spad" 227997 228005 228399 228450) (-200 "DIVRING.spad" 227583 227593 227987 227992) (-199 "DISPLAY.spad" 225773 225781 227573 227578) (-198 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 45c0fee2..e5115451 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,279 +1,279 @@
 
-(198452 . 3577545201)        
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 (((|#1|) |has| |#1| (-146))) 
 (((|#1|) |has| |#1| (-146))) 
 (((|#1|) |has| |#1| (-146))) 
@@ -3926,17 +3926,17 @@
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-(((|#4|) . T) (((-771)) . T)) 
-(((|#1|) |has| |#1| (-146)) (($) . T) (((-483)) . T)) 
+(((|#4|) . T) (((-772)) . T)) 
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 (((|#1| |#2| |#3| |#4|) . T)) 
-((((-472)) |has| |#4| (-552 (-472)))) 
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 (((|#4|) . T)) 
-(((|#4| |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1012)))) 
-(((|#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1012)))) 
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+(((|#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013)))) 
 (((|#4|) . T)) 
-((((-771)) . T) (((-582 |#4|)) . T)) 
+((((-772)) . T) (((-583 |#4|)) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#2|) |has| |#2| (-146))) 
@@ -3945,15 +3945,15 @@
 (((|#2| |#2|) . T)) 
 (((|#2|) . T)) 
 (((|#2|) . T)) 
-((((-771)) . T)) 
-((($) . T) (((-483)) . T) ((|#2|) . T)) 
+((((-772)) . T)) 
+((($) . T) (((-484)) . T) ((|#2|) . T)) 
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-(((|#2| (-738 |#1|)) . T)) 
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+(((|#2| (-739 |#1|)) . T)) 
+(((|#2| (-803 |#1|)) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#2|) |has| |#2| (-146))) 
 (((|#2| |#2|) . T)) 
@@ -3963,12 +3963,12 @@
 (((|#2|) |has| |#2| (-146))) 
 (((|#2|) . T)) 
 (((|#2|) . T) (($) . T)) 
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-(((|#2|) . T) (($) . T) (((-483)) . T)) 
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-((((-802 |#1|)) . T) (((-738 |#1|)) . T)) 
+((((-772)) . T)) 
+(((|#2|) . T) (($) . T) (((-484)) . T)) 
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+((((-803 |#1|)) . T) (((-739 |#1|)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-1088) |#1|) . T)) 
+((((-1089) |#1|) . T)) 
 (((|#1|) |has| |#1| (-146))) 
 (((|#1| |#1|) . T)) 
 (((|#1|) . T)) 
@@ -3977,11 +3977,11 @@
 (((|#1|) |has| |#1| (-146))) 
 (((|#1|) . T)) 
 (((|#1|) . T) (($) . T)) 
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-(((|#1|) . T) (((-483)) . T) (((-738 (-1088))) . T)) 
-((((-738 (-1088))) . T)) 
-((((-1088) |#1|) . T)) 
+((((-772)) . T)) 
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+((((-739 (-1089))) . T)) 
+((((-1089) |#1|) . T)) 
 (((|#2|) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#1|) |has| |#1| (-146))) 
@@ -3991,10 +3991,10 @@
 (((|#1|) |has| |#1| (-146))) 
 (((|#1|) |has| |#1| (-146))) 
 (((|#1|) . T)) 
-(((|#2|) . T) ((|#1|) . T) (((-483)) . T)) 
+(((|#2|) . T) ((|#1|) . T) (((-484)) . T)) 
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-((((-771)) . T)) 
-(((|#1|) . T) (($) . T) (((-483)) . T)) 
+((((-772)) . T)) 
+(((|#1|) . T) (($) . T) (((-484)) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#2|) |has| |#2| (-146))) 
 (((|#2| |#2|) . T)) 
@@ -4004,20 +4004,20 @@
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-((((-483)) . T)) 
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+((((-484)) . T)) 
 ((($ $) . T)) 
 ((($) . T)) 
 ((($) . T)) 
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 ((($) . T)) 
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. -104) T) ((-1202 . -589) 198067) ((-1202 . -1192) 198051) ((-1202 . -653) 198021) ((-1202 . -581) 197991) ((-1202 . -967) 197975) ((-1202 . -962) 197959) ((-1202 . -82) 197938) ((-1202 . -38) 197908) ((-1202 . -1197) 197887) ((-1201 . -960) T) ((-1201 . -662) T) ((-1201 . -1059) T) ((-1201 . -1024) T) ((-1201 . -969) T) ((-1201 . -21) T) ((-1201 . -587) 197846) ((-1201 . -23) T) ((-1201 . -1012) T) ((-1201 . -551) 197828) ((-1201 . -1127) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -589) 197802) ((-1201 . -554) 197758) ((-1201 . -1192) 197742) ((-1201 . -653) 197712) ((-1201 . -581) 197682) ((-1201 . -967) 197666) ((-1201 . -962) 197650) ((-1201 . -82) 197629) ((-1201 . -38) 197599) ((-1201 . -333) 197578) ((-1201 . -949) 197562) ((-1199 . -1200) 197538) ((-1199 . -949) 197512) ((-1199 . -554) 197458) ((-1199 . -960) T) ((-1199 . -662) T) ((-1199 . -1059) T) ((-1199 . -1024) T) ((-1199 . -969) T) ((-1199 . -21) T) ((-1199 . -587) 197417) ((-1199 . -23) T) ((-1199 . -1012) T) ((-1199 . -551) 197399) ((-1199 . -1127) T) ((-1199 . -13) T) ((-1199 . -72) T) ((-1199 . -25) T) ((-1199 . -104) T) ((-1199 . -589) 197373) ((-1199 . -1192) 197357) ((-1199 . -653) 197327) ((-1199 . -581) 197297) ((-1199 . -967) 197281) ((-1199 . -962) 197265) ((-1199 . -82) 197244) ((-1199 . -38) 197214) ((-1199 . -1197) 197190) ((-1198 . -1200) 197169) ((-1198 . -949) 197126) ((-1198 . -554) 197055) ((-1198 . -960) T) ((-1198 . -662) T) ((-1198 . -1059) T) ((-1198 . -1024) T) ((-1198 . -969) T) ((-1198 . -21) T) ((-1198 . -587) 197014) ((-1198 . -23) T) ((-1198 . -1012) T) ((-1198 . -551) 196996) ((-1198 . -1127) T) ((-1198 . -13) T) ((-1198 . -72) T) ((-1198 . -25) T) ((-1198 . -104) T) ((-1198 . -589) 196970) ((-1198 . -1192) 196954) ((-1198 . -653) 196924) ((-1198 . -581) 196894) ((-1198 . -967) 196878) ((-1198 . -962) 196862) ((-1198 . -82) 196841) ((-1198 . -38) 196811) ((-1198 . -1197) 196790) ((-1198 . -333) 196762) ((-1193 . -333) 196734) ((-1193 . -554) 196683) ((-1193 . -949) 196660) ((-1193 . -581) 196630) ((-1193 . -653) 196600) ((-1193 . -589) 196574) ((-1193 . -587) 196533) ((-1193 . -104) T) ((-1193 . -25) T) ((-1193 . -72) T) ((-1193 . -13) T) ((-1193 . -1127) T) ((-1193 . -551) 196515) ((-1193 . -1012) T) ((-1193 . -23) T) ((-1193 . -21) T) ((-1193 . -967) 196499) ((-1193 . -962) 196483) ((-1193 . -82) 196462) ((-1193 . -1200) 196441) ((-1193 . -960) T) ((-1193 . -662) T) ((-1193 . -1059) T) ((-1193 . -1024) T) ((-1193 . -969) T) ((-1193 . -1192) 196425) ((-1193 . -38) 196395) ((-1193 . -1197) 196374) ((-1191 . -1122) 196343) ((-1191 . -551) 196305) ((-1191 . -124) 196289) ((-1191 . -34) T) ((-1191 . -13) T) ((-1191 . -1127) T) ((-1191 . -72) T) ((-1191 . -260) 196227) ((-1191 . -454) 196160) ((-1191 . -1012) T) ((-1191 . -427) 196144) ((-1191 . -552) 196105) ((-1191 . -888) 196074) ((-1190 . -960) T) ((-1190 . -662) T) ((-1190 . -1059) T) ((-1190 . -1024) T) ((-1190 . -969) T) ((-1190 . -21) T) ((-1190 . -587) 196019) ((-1190 . -23) T) ((-1190 . -1012) T) ((-1190 . -551) 195988) ((-1190 . -1127) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -25) T) ((-1190 . -104) T) ((-1190 . -589) 195948) ((-1190 . -554) 195890) ((-1190 . -428) 195874) ((-1190 . -38) 195844) ((-1190 . -82) 195809) ((-1190 . -962) 195779) ((-1190 . -967) 195749) ((-1190 . -581) 195719) ((-1190 . -653) 195689) ((-1189 . -994) T) ((-1189 . -428) 195670) ((-1189 . -551) 195636) ((-1189 . -554) 195617) ((-1189 . -1012) T) ((-1189 . -1127) T) ((-1189 . -13) T) ((-1189 . -72) T) ((-1189 . -64) T) ((-1188 . -994) T) ((-1188 . -428) 195598) ((-1188 . -551) 195564) ((-1188 . -554) 195545) ((-1188 . -1012) T) ((-1188 . -1127) T) ((-1188 . -13) T) ((-1188 . -72) T) ((-1188 . -64) T) ((-1183 . -551) 195527) ((-1181 . -1012) T) ((-1181 . -551) 195509) ((-1181 . -1127) T) ((-1181 . -13) T) ((-1181 . -72) T) ((-1180 . -1012) T) ((-1180 . -551) 195491) ((-1180 . -1127) T) ((-1180 . -13) T) ((-1180 . -72) T) ((-1177 . -1176) 195475) ((-1177 . -322) 195459) ((-1177 . -758) 195438) ((-1177 . -755) 195417) ((-1177 . -124) 195401) ((-1177 . -34) T) ((-1177 . -13) T) ((-1177 . -1127) T) ((-1177 . -72) 195335) ((-1177 . -551) 195250) ((-1177 . -260) 195188) ((-1177 . -454) 195121) ((-1177 . -1012) 195074) ((-1177 . -427) 195058) ((-1177 . -552) 195019) ((-1177 . -241) 194971) ((-1177 . -537) 194948) ((-1177 . -243) 194925) ((-1177 . -592) 194909) ((-1177 . -19) 194893) ((-1174 . -1012) T) ((-1174 . -551) 194859) ((-1174 . -1127) T) ((-1174 . -13) T) ((-1174 . -72) T) ((-1167 . -1170) 194843) ((-1167 . -190) 194802) ((-1167 . -554) 194684) ((-1167 . -589) 194609) ((-1167 . -587) 194519) ((-1167 . -104) T) ((-1167 . -25) T) ((-1167 . -72) T) ((-1167 . -551) 194501) ((-1167 . -1012) T) ((-1167 . -23) T) ((-1167 . -21) T) ((-1167 . -969) T) ((-1167 . -1024) T) ((-1167 . -1059) T) ((-1167 . -662) T) ((-1167 . -960) T) ((-1167 . -186) 194454) ((-1167 . -13) T) ((-1167 . -1127) T) ((-1167 . -189) 194413) ((-1167 . 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191956) ((-1164 . -1127) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -581) 191813) ((-1164 . -653) 191670) ((-1164 . -118) 191631) ((-1164 . -120) 191592) ((-1164 . -146) T) ((-1164 . -494) T) ((-1164 . -246) T) ((-1164 . -47) 191536) ((-1163 . -1162) 191515) ((-1163 . -312) 191494) ((-1163 . -1132) 191473) ((-1163 . -831) 191452) ((-1163 . -494) 191406) ((-1163 . -146) 191340) ((-1163 . -554) 191159) ((-1163 . -653) 191006) ((-1163 . -581) 190853) ((-1163 . -38) 190700) ((-1163 . -390) 190679) ((-1163 . -258) 190658) ((-1163 . -589) 190558) ((-1163 . -587) 190443) ((-1163 . -969) T) ((-1163 . -1024) T) ((-1163 . -1059) T) ((-1163 . -662) T) ((-1163 . -960) T) ((-1163 . -82) 190263) ((-1163 . -962) 190104) ((-1163 . -967) 189945) ((-1163 . -21) T) ((-1163 . -23) T) ((-1163 . -1012) T) ((-1163 . -551) 189927) ((-1163 . -1127) T) ((-1163 . -13) T) ((-1163 . -72) T) ((-1163 . -25) T) ((-1163 . -104) T) ((-1163 . -246) 189881) ((-1163 . -201) 189860) ((-1163 . -914) 189826) ((-1163 . -1113) 189792) ((-1163 . -1116) 189758) ((-1163 . -431) 189724) ((-1163 . -239) 189690) ((-1163 . -66) 189656) ((-1163 . -35) 189622) ((-1163 . -1156) 189592) ((-1163 . -47) 189562) ((-1163 . -120) 189541) ((-1163 . -118) 189520) ((-1163 . -885) 189483) ((-1163 . -810) 189389) ((-1163 . -805) 189293) ((-1163 . -808) 189199) ((-1163 . -241) 189157) ((-1163 . -189) 189109) ((-1163 . -186) 189055) ((-1163 . -190) 189007) ((-1163 . -1160) 188991) ((-1163 . -949) 188975) ((-1158 . -1162) 188936) ((-1158 . -312) 188915) ((-1158 . -1132) 188894) ((-1158 . -831) 188873) ((-1158 . -494) 188827) ((-1158 . -146) 188761) ((-1158 . -554) 188510) ((-1158 . -653) 188357) ((-1158 . -581) 188204) ((-1158 . -38) 188051) ((-1158 . -390) 188030) ((-1158 . -258) 188009) ((-1158 . -589) 187909) ((-1158 . -587) 187794) ((-1158 . -969) T) ((-1158 . -1024) T) ((-1158 . -1059) T) ((-1158 . -662) T) ((-1158 . -960) T) ((-1158 . -82) 187614) ((-1158 . -962) 187455) ((-1158 . -967) 187296) ((-1158 . -21) T) ((-1158 . -23) T) ((-1158 . -1012) T) ((-1158 . -551) 187278) ((-1158 . -1127) T) ((-1158 . -13) T) ((-1158 . -72) T) ((-1158 . -25) T) ((-1158 . -104) T) ((-1158 . -246) 187232) ((-1158 . -201) 187211) ((-1158 . -914) 187177) ((-1158 . -1113) 187143) ((-1158 . -1116) 187109) ((-1158 . -431) 187075) ((-1158 . -239) 187041) ((-1158 . -66) 187007) ((-1158 . -35) 186973) ((-1158 . -1156) 186943) ((-1158 . -47) 186913) ((-1158 . -120) 186892) ((-1158 . -118) 186871) ((-1158 . -885) 186834) ((-1158 . -810) 186740) ((-1158 . -805) 186621) ((-1158 . -808) 186527) ((-1158 . -241) 186485) ((-1158 . -189) 186437) ((-1158 . -186) 186383) ((-1158 . -190) 186335) ((-1158 . -1160) 186319) ((-1158 . -949) 186254) ((-1146 . -1153) 186238) ((-1146 . -1064) 186216) ((-1146 . -552) NIL) ((-1146 . -260) 186203) ((-1146 . -454) 186151) ((-1146 . -277) 186128) ((-1146 . -949) 186011) ((-1146 . -353) 185995) ((-1146 . -38) 185827) ((-1146 . -82) 185632) ((-1146 . -962) 185458) ((-1146 . -967) 185284) ((-1146 . -587) 185194) ((-1146 . -589) 185083) ((-1146 . -581) 184915) ((-1146 . -653) 184747) ((-1146 . -554) 184503) ((-1146 . -118) 184482) ((-1146 . -120) 184461) ((-1146 . -47) 184438) ((-1146 . -327) 184422) ((-1146 . -579) 184370) ((-1146 . -808) 184314) ((-1146 . -805) 184221) ((-1146 . -810) 184132) ((-1146 . -795) NIL) ((-1146 . -820) 184111) ((-1146 . -1132) 184090) ((-1146 . -860) 184060) ((-1146 . -831) 184039) ((-1146 . -494) 183953) ((-1146 . -246) 183867) ((-1146 . -146) 183761) ((-1146 . -390) 183695) ((-1146 . -258) 183674) ((-1146 . -241) 183601) ((-1146 . -190) T) ((-1146 . -104) T) ((-1146 . -25) T) ((-1146 . -72) T) ((-1146 . -551) 183583) ((-1146 . -1012) T) ((-1146 . -23) T) ((-1146 . -21) T) ((-1146 . -969) T) ((-1146 . -1024) T) ((-1146 . -1059) T) ((-1146 . -662) T) ((-1146 . -960) T) ((-1146 . -186) 183570) ((-1146 . -13) T) ((-1146 . -1127) T) ((-1146 . -189) T) ((-1146 . -225) 183554) ((-1146 . -184) 183538) ((-1144 . -1005) 183522) ((-1144 . -556) 183506) ((-1144 . -1012) 183484) ((-1144 . -551) 183451) ((-1144 . -1127) 183429) ((-1144 . -13) 183407) ((-1144 . -72) 183385) ((-1144 . -1006) 183342) ((-1142 . -1141) 183321) ((-1142 . -914) 183287) ((-1142 . -1113) 183253) ((-1142 . -1116) 183219) ((-1142 . -431) 183185) ((-1142 . -239) 183151) ((-1142 . -66) 183117) ((-1142 . -35) 183083) ((-1142 . -1156) 183060) ((-1142 . -47) 183037) ((-1142 . -554) 182792) ((-1142 . -653) 182612) ((-1142 . -581) 182432) ((-1142 . -589) 182243) ((-1142 . -587) 182101) ((-1142 . -967) 181915) ((-1142 . -962) 181729) ((-1142 . -82) 181517) ((-1142 . -38) 181337) ((-1142 . -885) 181307) ((-1142 . -241) 181207) ((-1142 . -1139) 181191) ((-1142 . -969) T) ((-1142 . -1024) T) ((-1142 . -1059) T) ((-1142 . -662) T) ((-1142 . -960) T) ((-1142 . -21) T) ((-1142 . -23) T) ((-1142 . -1012) T) ((-1142 . -551) 181173) ((-1142 . -1127) T) ((-1142 . -13) T) ((-1142 . -72) T) ((-1142 . -25) T) ((-1142 . -104) T) ((-1142 . -118) 181101) ((-1142 . -120) 180983) ((-1142 . -552) 180656) ((-1142 . -184) 180626) ((-1142 . -808) 180480) ((-1142 . -810) 180280) ((-1142 . -805) 180078) ((-1142 . -225) 180048) ((-1142 . -189) 179910) ((-1142 . -186) 179766) ((-1142 . -190) 179674) ((-1142 . -312) 179653) ((-1142 . -1132) 179632) ((-1142 . -831) 179611) ((-1142 . -494) 179565) ((-1142 . -146) 179499) ((-1142 . -390) 179478) ((-1142 . -258) 179457) ((-1142 . -246) 179411) ((-1142 . -201) 179390) ((-1142 . -288) 179360) ((-1142 . -454) 179220) ((-1142 . -260) 179159) ((-1142 . -327) 179129) ((-1142 . -579) 179037) ((-1142 . -341) 179007) ((-1142 . -795) 178880) ((-1142 . -739) 178833) ((-1142 . -713) 178786) ((-1142 . -715) 178739) ((-1142 . -755) 178641) ((-1142 . -758) 178543) ((-1142 . -717) 178496) ((-1142 . -720) 178449) ((-1142 . -754) 178402) ((-1142 . -793) 178372) ((-1142 . -820) 178325) ((-1142 . -932) 178278) ((-1142 . -949) 178067) ((-1142 . -1064) 178019) ((-1142 . -903) 177989) ((-1137 . -1141) 177950) ((-1137 . -914) 177916) ((-1137 . -1113) 177882) ((-1137 . -1116) 177848) ((-1137 . -431) 177814) ((-1137 . -239) 177780) ((-1137 . -66) 177746) ((-1137 . -35) 177712) ((-1137 . -1156) 177689) ((-1137 . -47) 177666) ((-1137 . -554) 177467) ((-1137 . -653) 177269) ((-1137 . -581) 177071) ((-1137 . -589) 176926) ((-1137 . -587) 176766) ((-1137 . -967) 176562) ((-1137 . -962) 176358) ((-1137 . -82) 176110) ((-1137 . -38) 175912) ((-1137 . -885) 175882) ((-1137 . -241) 175710) ((-1137 . -1139) 175694) ((-1137 . -969) T) ((-1137 . -1024) T) ((-1137 . -1059) T) ((-1137 . -662) T) ((-1137 . -960) T) ((-1137 . -21) T) ((-1137 . -23) T) ((-1137 . -1012) T) ((-1137 . -551) 175676) ((-1137 . -1127) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -25) T) ((-1137 . -104) T) ((-1137 . -118) 175586) ((-1137 . -120) 175496) ((-1137 . -552) NIL) ((-1137 . -184) 175448) ((-1137 . -808) 175284) ((-1137 . -810) 175048) ((-1137 . -805) 174787) ((-1137 . -225) 174739) ((-1137 . -189) 174565) ((-1137 . -186) 174385) ((-1137 . -190) 174275) ((-1137 . -312) 174254) ((-1137 . -1132) 174233) ((-1137 . -831) 174212) ((-1137 . -494) 174166) ((-1137 . -146) 174100) ((-1137 . -390) 174079) ((-1137 . -258) 174058) ((-1137 . -246) 174012) ((-1137 . -201) 173991) ((-1137 . -288) 173943) ((-1137 . -454) 173677) ((-1137 . -260) 173562) ((-1137 . -327) 173514) ((-1137 . -579) 173466) ((-1137 . -341) 173418) ((-1137 . -795) NIL) ((-1137 . -739) NIL) ((-1137 . -713) NIL) ((-1137 . -715) NIL) ((-1137 . -755) NIL) ((-1137 . -758) NIL) ((-1137 . -717) NIL) ((-1137 . -720) NIL) ((-1137 . -754) NIL) ((-1137 . -793) 173370) ((-1137 . -820) NIL) ((-1137 . -932) NIL) ((-1137 . -949) 173336) ((-1137 . -1064) NIL) ((-1137 . -903) 173288) ((-1136 . -751) T) ((-1136 . -758) T) ((-1136 . -755) T) ((-1136 . -1012) T) ((-1136 . -551) 173270) ((-1136 . -1127) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -603) T) ((-1135 . -751) T) ((-1135 . -758) T) ((-1135 . -755) T) ((-1135 . -1012) T) ((-1135 . -551) 173252) ((-1135 . -1127) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -318) T) ((-1135 . -603) T) ((-1134 . -751) T) ((-1134 . -758) T) ((-1134 . -755) T) ((-1134 . -1012) T) ((-1134 . -551) 173234) ((-1134 . -1127) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -318) T) ((-1134 . -603) T) ((-1133 . -751) T) ((-1133 . -758) T) ((-1133 . -755) T) ((-1133 . -1012) T) ((-1133 . -551) 173216) ((-1133 . -1127) T) ((-1133 . -13) T) ((-1133 . -72) T) ((-1133 . -318) T) ((-1133 . -603) T) ((-1128 . -994) T) ((-1128 . -428) 173197) ((-1128 . -551) 173163) ((-1128 . -554) 173144) ((-1128 . -1012) T) ((-1128 . -1127) T) ((-1128 . -13) T) ((-1128 . -72) T) ((-1128 . -64) T) ((-1125 . -428) 173121) ((-1125 . -551) 173062) ((-1125 . -554) 173039) ((-1125 . -1012) 173017) ((-1125 . -1127) 172995) ((-1125 . -13) 172973) ((-1125 . -72) 172951) ((-1120 . -678) 172927) ((-1120 . -35) 172893) ((-1120 . -66) 172859) ((-1120 . -239) 172825) ((-1120 . -431) 172791) ((-1120 . -1116) 172757) ((-1120 . -1113) 172723) ((-1120 . -914) 172689) ((-1120 . -47) 172658) ((-1120 . -38) 172555) ((-1120 . -581) 172452) ((-1120 . -653) 172349) ((-1120 . -554) 172231) ((-1120 . -246) 172210) ((-1120 . -494) 172189) ((-1120 . -82) 172054) ((-1120 . -962) 171940) ((-1120 . -967) 171826) ((-1120 . -146) 171780) ((-1120 . -120) 171759) ((-1120 . -118) 171738) ((-1120 . -589) 171663) ((-1120 . -587) 171573) ((-1120 . -885) 171534) ((-1120 . -810) 171515) ((-1120 . -1127) T) ((-1120 . -13) T) ((-1120 . -805) 171494) ((-1120 . -960) T) ((-1120 . -662) T) ((-1120 . -1059) T) ((-1120 . -1024) T) ((-1120 . -969) T) ((-1120 . -21) T) ((-1120 . -23) T) ((-1120 . -1012) T) ((-1120 . -551) 171476) ((-1120 . -72) T) ((-1120 . -25) T) ((-1120 . -104) T) ((-1120 . -808) 171457) ((-1120 . -454) 171424) ((-1120 . -260) 171411) ((-1114 . -922) 171395) ((-1114 . -34) T) ((-1114 . -13) T) ((-1114 . -1127) T) ((-1114 . -72) 171349) ((-1114 . -551) 171284) ((-1114 . -260) 171222) ((-1114 . -454) 171155) ((-1114 . -1012) 171133) ((-1114 . -427) 171117) ((-1109 . -314) 171091) ((-1109 . -72) T) ((-1109 . -13) T) ((-1109 . -1127) T) ((-1109 . -551) 171073) ((-1109 . -1012) T) ((-1107 . -1012) T) ((-1107 . -551) 171055) ((-1107 . -1127) T) ((-1107 . -13) T) ((-1107 . -72) T) ((-1107 . -554) 171037) ((-1102 . -746) 171021) ((-1102 . -72) T) ((-1102 . -13) T) ((-1102 . -1127) T) ((-1102 . -551) 171003) ((-1102 . -1012) T) ((-1100 . -1105) 170982) ((-1100 . -183) 170930) ((-1100 . -76) 170878) ((-1100 . -260) 170676) ((-1100 . -454) 170428) ((-1100 . -427) 170363) ((-1100 . -124) 170311) ((-1100 . -552) NIL) ((-1100 . -193) 170259) ((-1100 . -548) 170238) ((-1100 . -243) 170217) ((-1100 . -1127) T) ((-1100 . -13) T) ((-1100 . -241) 170196) ((-1100 . -1012) T) ((-1100 . -551) 170178) ((-1100 . -72) T) ((-1100 . -34) T) ((-1100 . -537) 170157) ((-1096 . -1012) T) ((-1096 . -551) 170139) ((-1096 . -1127) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1095 . -751) T) ((-1095 . -758) T) ((-1095 . -755) T) ((-1095 . -1012) T) ((-1095 . -551) 170121) ((-1095 . -1127) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -318) T) ((-1095 . -603) T) ((-1094 . -751) T) ((-1094 . -758) T) ((-1094 . -755) T) ((-1094 . -1012) T) ((-1094 . -551) 170103) ((-1094 . -1127) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -318) T) ((-1093 . -1173) T) ((-1093 . -1012) T) ((-1093 . -551) 170070) ((-1093 . -1127) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -949) 170006) ((-1093 . -554) 169942) ((-1092 . -551) 169924) ((-1091 . -551) 169906) ((-1090 . -277) 169883) ((-1090 . -949) 169781) ((-1090 . -353) 169765) ((-1090 . -38) 169662) ((-1090 . -554) 169519) ((-1090 . -589) 169444) ((-1090 . -587) 169354) ((-1090 . -969) T) ((-1090 . -1024) T) ((-1090 . -1059) T) ((-1090 . -662) T) ((-1090 . -960) T) ((-1090 . -82) 169219) ((-1090 . -962) 169105) ((-1090 . -967) 168991) ((-1090 . -21) T) ((-1090 . -23) T) ((-1090 . -1012) T) ((-1090 . -551) 168973) ((-1090 . -1127) T) ((-1090 . -13) T) ((-1090 . -72) T) ((-1090 . -25) T) ((-1090 . -104) T) ((-1090 . -581) 168870) ((-1090 . -653) 168767) ((-1090 . -118) 168746) ((-1090 . -120) 168725) ((-1090 . -146) 168679) ((-1090 . -494) 168658) ((-1090 . -246) 168637) ((-1090 . -47) 168614) ((-1088 . -755) T) ((-1088 . -551) 168596) ((-1088 . -1012) T) ((-1088 . -72) T) ((-1088 . -13) T) ((-1088 . -1127) T) ((-1088 . -758) T) ((-1088 . -552) 168518) ((-1088 . -554) 168484) ((-1088 . -949) 168466) ((-1088 . -795) 168433) ((-1087 . -1170) 168417) ((-1087 . -190) 168376) ((-1087 . -554) 168258) ((-1087 . -589) 168183) ((-1087 . -587) 168093) ((-1087 . -104) T) ((-1087 . -25) T) ((-1087 . -72) T) ((-1087 . -551) 168075) ((-1087 . -1012) T) ((-1087 . -23) T) ((-1087 . -21) T) ((-1087 . -969) T) ((-1087 . -1024) T) ((-1087 . -1059) T) ((-1087 . -662) T) ((-1087 . -960) T) ((-1087 . -186) 168028) ((-1087 . -13) T) ((-1087 . -1127) T) ((-1087 . -189) 167987) ((-1087 . -241) 167952) ((-1087 . -808) 167865) ((-1087 . -805) 167753) ((-1087 . -810) 167666) ((-1087 . -885) 167636) ((-1087 . -38) 167533) ((-1087 . -82) 167398) ((-1087 . -962) 167284) ((-1087 . -967) 167170) ((-1087 . -581) 167067) ((-1087 . -653) 166964) ((-1087 . -118) 166943) ((-1087 . -120) 166922) ((-1087 . -146) 166876) ((-1087 . -494) 166855) ((-1087 . -246) 166834) ((-1087 . -47) 166811) ((-1087 . -1156) 166788) ((-1087 . -35) 166754) ((-1087 . -66) 166720) ((-1087 . -239) 166686) ((-1087 . -431) 166652) ((-1087 . -1116) 166618) ((-1087 . -1113) 166584) ((-1087 . -914) 166550) ((-1086 . -1162) 166511) ((-1086 . -312) 166490) ((-1086 . -1132) 166469) ((-1086 . -831) 166448) ((-1086 . -494) 166402) ((-1086 . -146) 166336) ((-1086 . -554) 166085) ((-1086 . -653) 165932) ((-1086 . -581) 165779) ((-1086 . -38) 165626) ((-1086 . -390) 165605) ((-1086 . -258) 165584) ((-1086 . -589) 165484) ((-1086 . -587) 165369) ((-1086 . -969) T) ((-1086 . -1024) T) ((-1086 . -1059) T) ((-1086 . -662) T) ((-1086 . -960) T) ((-1086 . -82) 165189) ((-1086 . -962) 165030) ((-1086 . -967) 164871) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1012) T) ((-1086 . -551) 164853) ((-1086 . -1127) T) ((-1086 . -13) T) ((-1086 . -72) T) ((-1086 . -25) T) ((-1086 . -104) T) ((-1086 . -246) 164807) ((-1086 . -201) 164786) ((-1086 . -914) 164752) ((-1086 . -1113) 164718) ((-1086 . -1116) 164684) ((-1086 . -431) 164650) ((-1086 . -239) 164616) ((-1086 . -66) 164582) ((-1086 . -35) 164548) ((-1086 . -1156) 164518) ((-1086 . -47) 164488) ((-1086 . -120) 164467) ((-1086 . -118) 164446) ((-1086 . -885) 164409) ((-1086 . -810) 164315) ((-1086 . -805) 164196) ((-1086 . -808) 164102) ((-1086 . -241) 164060) ((-1086 . -189) 164012) ((-1086 . -186) 163958) ((-1086 . -190) 163910) ((-1086 . -1160) 163894) ((-1086 . -949) 163829) ((-1083 . -1153) 163813) ((-1083 . -1064) 163791) ((-1083 . -552) NIL) ((-1083 . -260) 163778) ((-1083 . -454) 163726) ((-1083 . -277) 163703) ((-1083 . -949) 163586) ((-1083 . -353) 163570) ((-1083 . -38) 163402) ((-1083 . -82) 163207) ((-1083 . -962) 163033) ((-1083 . -967) 162859) ((-1083 . -587) 162769) ((-1083 . -589) 162658) ((-1083 . -581) 162490) ((-1083 . -653) 162322) ((-1083 . -554) 162099) ((-1083 . -118) 162078) ((-1083 . -120) 162057) ((-1083 . -47) 162034) ((-1083 . -327) 162018) ((-1083 . -579) 161966) ((-1083 . -808) 161910) ((-1083 . -805) 161817) ((-1083 . -810) 161728) ((-1083 . -795) NIL) ((-1083 . -820) 161707) ((-1083 . -1132) 161686) ((-1083 . -860) 161656) ((-1083 . -831) 161635) ((-1083 . -494) 161549) ((-1083 . -246) 161463) ((-1083 . -146) 161357) ((-1083 . -390) 161291) ((-1083 . -258) 161270) ((-1083 . -241) 161197) ((-1083 . -190) T) ((-1083 . -104) T) ((-1083 . -25) T) ((-1083 . -72) T) ((-1083 . -551) 161179) ((-1083 . -1012) T) ((-1083 . -23) T) ((-1083 . -21) T) ((-1083 . -969) T) ((-1083 . -1024) T) ((-1083 . -1059) T) ((-1083 . -662) T) ((-1083 . -960) T) ((-1083 . -186) 161166) ((-1083 . -13) T) ((-1083 . -1127) T) ((-1083 . -189) T) ((-1083 . -225) 161150) ((-1083 . -184) 161134) ((-1080 . -1141) 161095) ((-1080 . -914) 161061) ((-1080 . -1113) 161027) ((-1080 . -1116) 160993) ((-1080 . -431) 160959) ((-1080 . -239) 160925) ((-1080 . -66) 160891) ((-1080 . -35) 160857) ((-1080 . -1156) 160834) ((-1080 . -47) 160811) ((-1080 . -554) 160612) ((-1080 . -653) 160414) ((-1080 . -581) 160216) ((-1080 . -589) 160071) ((-1080 . -587) 159911) ((-1080 . -967) 159707) ((-1080 . -962) 159503) ((-1080 . -82) 159255) ((-1080 . -38) 159057) ((-1080 . -885) 159027) ((-1080 . -241) 158855) ((-1080 . -1139) 158839) ((-1080 . -969) T) ((-1080 . -1024) T) ((-1080 . -1059) T) ((-1080 . -662) T) ((-1080 . -960) T) ((-1080 . -21) T) ((-1080 . -23) T) ((-1080 . -1012) T) ((-1080 . -551) 158821) ((-1080 . -1127) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -25) T) ((-1080 . -104) T) ((-1080 . -118) 158731) ((-1080 . -120) 158641) ((-1080 . -552) NIL) ((-1080 . -184) 158593) ((-1080 . -808) 158429) ((-1080 . -810) 158193) ((-1080 . -805) 157932) ((-1080 . -225) 157884) ((-1080 . -189) 157710) ((-1080 . -186) 157530) ((-1080 . -190) 157420) ((-1080 . -312) 157399) ((-1080 . -1132) 157378) ((-1080 . -831) 157357) ((-1080 . -494) 157311) ((-1080 . -146) 157245) ((-1080 . -390) 157224) ((-1080 . -258) 157203) ((-1080 . -246) 157157) ((-1080 . -201) 157136) ((-1080 . -288) 157088) ((-1080 . -454) 156822) ((-1080 . -260) 156707) ((-1080 . -327) 156659) ((-1080 . -579) 156611) ((-1080 . -341) 156563) ((-1080 . -795) NIL) ((-1080 . -739) NIL) ((-1080 . -713) NIL) ((-1080 . -715) NIL) ((-1080 . -755) NIL) ((-1080 . -758) NIL) ((-1080 . -717) NIL) ((-1080 . -720) NIL) ((-1080 . -754) NIL) ((-1080 . -793) 156515) ((-1080 . -820) NIL) ((-1080 . -932) NIL) ((-1080 . -949) 156481) ((-1080 . -1064) NIL) ((-1080 . -903) 156433) ((-1079 . -994) T) ((-1079 . -428) 156414) ((-1079 . -551) 156380) ((-1079 . -554) 156361) ((-1079 . -1012) T) ((-1079 . -1127) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1079 . -64) T) ((-1078 . -1012) T) ((-1078 . -551) 156343) ((-1078 . -1127) T) 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. -615) 155204) ((-1067 . -592) 155188) ((-1067 . -243) 155165) ((-1067 . -241) 155117) ((-1067 . -537) 155094) ((-1067 . -552) 155055) ((-1067 . -427) 155039) ((-1067 . -1012) 155017) ((-1067 . -454) 154950) ((-1067 . -260) 154888) ((-1067 . -551) 154823) ((-1067 . -72) 154777) ((-1067 . -1127) T) ((-1067 . -13) T) ((-1067 . -34) T) ((-1067 . -124) 154761) ((-1067 . -1166) 154745) ((-1067 . -922) 154729) ((-1067 . -1062) 154713) ((-1067 . -554) 154690) ((-1065 . -994) T) ((-1065 . -428) 154671) ((-1065 . -551) 154637) ((-1065 . -554) 154618) ((-1065 . -1012) T) ((-1065 . -1127) T) ((-1065 . -13) T) ((-1065 . -72) T) ((-1065 . -64) T) ((-1063 . -1105) 154597) ((-1063 . -183) 154545) ((-1063 . -76) 154493) ((-1063 . -260) 154291) ((-1063 . -454) 154043) ((-1063 . -427) 153978) ((-1063 . -124) 153926) ((-1063 . -552) NIL) ((-1063 . -193) 153874) ((-1063 . -548) 153853) ((-1063 . -243) 153832) ((-1063 . -1127) T) ((-1063 . -13) T) ((-1063 . -241) 153811) ((-1063 . -1012) T) ((-1063 . 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T) ((-1047 . -1127) T) ((-1047 . -551) 151534) ((-1047 . -1012) T) ((-1047 . -554) 151515) ((-1047 . -428) 151496) ((-1047 . -994) T) ((-1045 . -1046) 151480) ((-1045 . -72) T) ((-1045 . -13) T) ((-1045 . -1127) T) ((-1045 . -551) 151462) ((-1045 . -1012) T) ((-1038 . -678) 151441) ((-1038 . -35) 151407) ((-1038 . -66) 151373) ((-1038 . -239) 151339) ((-1038 . -431) 151305) ((-1038 . -1116) 151271) ((-1038 . -1113) 151237) ((-1038 . -914) 151203) ((-1038 . -47) 151175) ((-1038 . -38) 151072) ((-1038 . -581) 150969) ((-1038 . -653) 150866) ((-1038 . -554) 150748) ((-1038 . -246) 150727) ((-1038 . -494) 150706) ((-1038 . -82) 150571) ((-1038 . -962) 150457) ((-1038 . -967) 150343) ((-1038 . -146) 150297) ((-1038 . -120) 150276) ((-1038 . -118) 150255) ((-1038 . -589) 150180) ((-1038 . -587) 150090) ((-1038 . -885) 150057) ((-1038 . -810) 150041) ((-1038 . -1127) T) ((-1038 . -13) T) ((-1038 . -805) 150023) ((-1038 . -960) T) ((-1038 . -662) T) ((-1038 . -1059) T) ((-1038 . -1024) T) 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T) ((-1025 . -537) 146464) ((-1025 . -949) 146293) ((-1025 . -554) 146097) ((-1025 . -353) 146066) ((-1025 . -579) 145974) ((-1025 . -589) 145813) ((-1025 . -327) 145783) ((-1025 . -318) 145762) ((-1025 . -190) 145715) ((-1025 . -587) 145503) ((-1025 . -969) 145482) ((-1025 . -1024) 145461) ((-1025 . -1059) 145440) ((-1025 . -662) 145419) ((-1025 . -960) 145398) ((-1025 . -186) 145294) ((-1025 . -189) 145196) ((-1025 . -225) 145166) ((-1025 . -805) 145038) ((-1025 . -810) 144912) ((-1025 . -808) 144845) ((-1025 . -184) 144815) ((-1025 . -551) 144512) ((-1025 . -967) 144437) ((-1025 . -962) 144342) ((-1025 . -82) 144262) ((-1025 . -104) 144137) ((-1025 . -25) 143974) ((-1025 . -72) 143711) ((-1025 . -13) T) ((-1025 . -1127) T) ((-1025 . -1012) 143467) ((-1025 . -23) 143323) ((-1025 . -21) 143238) ((-1021 . -1022) 143222) ((-1021 . |MappingCategory|) 143196) ((-1021 . -1127) T) ((-1021 . -80) 143180) ((-1021 . -1012) T) ((-1021 . -551) 143162) ((-1021 . -13) T) ((-1021 . -72) T) ((-1016 . -1015) 143126) ((-1016 . -72) T) ((-1016 . -551) 143108) ((-1016 . -1012) T) ((-1016 . -241) 143064) ((-1016 . -1127) T) ((-1016 . -13) T) ((-1016 . -556) 142979) ((-1014 . -1015) 142931) ((-1014 . -72) T) ((-1014 . -551) 142913) ((-1014 . -1012) T) ((-1014 . -241) 142869) ((-1014 . -1127) T) ((-1014 . -13) T) ((-1014 . -556) 142772) ((-1013 . -318) T) ((-1013 . -72) T) ((-1013 . -13) T) ((-1013 . -1127) T) ((-1013 . -551) 142754) ((-1013 . -1012) T) ((-1008 . -367) 142738) ((-1008 . -1010) 142722) ((-1008 . -318) 142701) ((-1008 . -193) 142685) ((-1008 . -552) 142646) ((-1008 . -124) 142630) ((-1008 . -427) 142614) ((-1008 . -1012) T) ((-1008 . -454) 142547) ((-1008 . -260) 142485) ((-1008 . -551) 142467) ((-1008 . -72) T) ((-1008 . -1127) T) ((-1008 . -13) T) ((-1008 . -34) T) ((-1008 . -76) 142451) ((-1008 . -183) 142435) ((-1007 . -994) T) ((-1007 . -428) 142416) ((-1007 . -551) 142382) ((-1007 . -554) 142363) ((-1007 . -1012) T) ((-1007 . -1127) T) ((-1007 . -13) T) ((-1007 . -72) T) ((-1007 . -64) T) ((-1003 . -1127) T) ((-1003 . -13) T) ((-1003 . -1012) 142333) ((-1003 . -551) 142292) ((-1003 . -72) 142262) ((-1002 . -994) T) ((-1002 . -428) 142243) ((-1002 . -551) 142209) ((-1002 . -554) 142190) ((-1002 . -1012) T) ((-1002 . -1127) T) ((-1002 . -13) T) ((-1002 . -72) T) ((-1002 . -64) T) ((-1000 . -1005) 142174) ((-1000 . -556) 142158) ((-1000 . -1012) 142136) ((-1000 . -551) 142103) ((-1000 . -1127) 142081) ((-1000 . -13) 142059) ((-1000 . -72) 142037) ((-1000 . -1006) 141995) ((-999 . -228) 141979) ((-999 . -554) 141963) ((-999 . -949) 141947) ((-999 . -758) T) ((-999 . -72) T) ((-999 . -1012) T) ((-999 . -551) 141929) ((-999 . -755) T) ((-999 . -186) 141916) ((-999 . -13) T) ((-999 . -1127) T) ((-999 . -189) T) ((-998 . -213) 141855) ((-998 . -554) 141599) ((-998 . -949) 141429) ((-998 . -552) NIL) ((-998 . -277) 141391) ((-998 . -353) 141375) ((-998 . -38) 141227) ((-998 . -82) 141052) ((-998 . -962) 140898) ((-998 . -967) 140744) ((-998 . -587) 140654) ((-998 . -589) 140543) ((-998 . -581) 140395) ((-998 . -653) 140247) ((-998 . -118) 140226) ((-998 . -120) 140205) ((-998 . -146) 140119) ((-998 . -494) 140053) ((-998 . -246) 139987) ((-998 . -47) 139949) ((-998 . -327) 139933) ((-998 . -579) 139881) ((-998 . -390) 139835) ((-998 . -454) 139700) ((-998 . -808) 139636) ((-998 . -805) 139535) ((-998 . -810) 139438) ((-998 . -795) NIL) ((-998 . -820) 139417) ((-998 . -1132) 139396) ((-998 . -860) 139343) ((-998 . -260) 139330) ((-998 . -190) 139309) ((-998 . -104) T) ((-998 . -25) T) ((-998 . -72) T) ((-998 . -551) 139291) ((-998 . -1012) T) ((-998 . -23) T) ((-998 . -21) T) ((-998 . -969) T) ((-998 . -1024) T) ((-998 . -1059) T) ((-998 . -662) T) ((-998 . -960) T) ((-998 . -186) 139239) ((-998 . -13) T) ((-998 . -1127) T) ((-998 . -189) 139193) ((-998 . -225) 139177) ((-998 . -184) 139161) ((-996 . -551) 139143) ((-993 . -755) T) ((-993 . -551) 139125) ((-993 . -1012) T) ((-993 . -72) T) ((-993 . -13) T) ((-993 . -1127) T) ((-993 . -758) T) ((-993 . -552) 139106) ((-990 . -660) 139085) ((-990 . -949) 138983) ((-990 . -353) 138967) ((-990 . -579) 138915) ((-990 . -589) 138792) ((-990 . -327) 138776) ((-990 . -320) 138755) ((-990 . -120) 138734) ((-990 . -554) 138559) ((-990 . -653) 138433) ((-990 . -581) 138307) ((-990 . -587) 138205) ((-990 . -967) 138118) ((-990 . -962) 138031) ((-990 . -82) 137923) ((-990 . -38) 137797) ((-990 . -351) 137776) ((-990 . -343) 137755) ((-990 . -118) 137709) ((-990 . -1064) 137688) ((-990 . -299) 137667) ((-990 . -318) 137621) ((-990 . -201) 137575) ((-990 . -246) 137529) ((-990 . -258) 137483) ((-990 . -390) 137437) ((-990 . -494) 137391) ((-990 . -831) 137345) ((-990 . -1132) 137299) ((-990 . -312) 137253) ((-990 . -190) 137181) ((-990 . -186) 137057) ((-990 . -189) 136939) ((-990 . -225) 136909) ((-990 . -805) 136781) ((-990 . -810) 136655) ((-990 . -808) 136588) ((-990 . -184) 136558) ((-990 . -552) 136542) ((-990 . -21) T) ((-990 . -23) T) ((-990 . -1012) T) ((-990 . -551) 136524) ((-990 . -1127) T) ((-990 . -13) T) ((-990 . -72) T) ((-990 . -25) T) ((-990 . -104) T) ((-990 . -960) T) ((-990 . -662) T) ((-990 . -1059) T) ((-990 . -1024) T) ((-990 . -969) T) ((-990 . -146) T) ((-988 . -1012) T) ((-988 . -551) 136506) ((-988 . -1127) T) ((-988 . -13) T) ((-988 . -72) T) ((-988 . -241) 136485) ((-987 . -1012) T) ((-987 . -551) 136467) ((-987 . -1127) T) ((-987 . -13) T) ((-987 . -72) T) ((-986 . -1012) T) ((-986 . -551) 136449) ((-986 . -1127) T) ((-986 . -13) T) ((-986 . -72) T) ((-986 . -241) 136428) ((-986 . -949) 136405) ((-986 . -554) 136382) ((-985 . -1127) T) ((-985 . -13) T) ((-984 . -994) T) ((-984 . -428) 136363) ((-984 . -551) 136329) ((-984 . -554) 136310) ((-984 . -1012) T) ((-984 . -1127) T) ((-984 . -13) T) ((-984 . -72) T) ((-984 . -64) T) ((-977 . -994) T) ((-977 . -428) 136291) ((-977 . -551) 136257) ((-977 . -554) 136238) ((-977 . -1012) T) ((-977 . -1127) T) ((-977 . -13) T) ((-977 . -72) T) ((-977 . -64) T) ((-974 . -482) T) 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135864) ((-973 . -72) T) ((-973 . -13) T) ((-973 . -1127) T) ((-973 . -551) 135846) ((-973 . -1012) T) ((-970 . -1127) T) ((-970 . -13) T) ((-970 . -1012) 135824) ((-970 . -551) 135791) ((-970 . -72) 135769) ((-965 . -964) 135709) ((-965 . -581) 135654) ((-965 . -653) 135599) ((-965 . -34) T) ((-965 . -260) 135537) ((-965 . -454) 135470) ((-965 . -427) 135454) ((-965 . -589) 135438) ((-965 . -587) 135407) ((-965 . -104) T) ((-965 . -25) T) ((-965 . -72) T) ((-965 . -13) T) ((-965 . -1127) T) ((-965 . -551) 135369) ((-965 . -1012) T) ((-965 . -23) T) ((-965 . -21) T) ((-965 . -967) 135353) ((-965 . -962) 135337) ((-965 . -82) 135316) ((-965 . -1185) 135286) ((-965 . -552) 135247) ((-957 . -982) 135176) ((-957 . -888) 135105) ((-957 . -552) 135047) ((-957 . -427) 135012) ((-957 . -1012) T) ((-957 . -454) 134896) ((-957 . -260) 134804) ((-957 . -551) 134747) ((-957 . -72) T) ((-957 . -1127) T) ((-957 . -13) T) ((-957 . -34) T) ((-957 . -124) 134712) ((-957 . -1122) 134641) ((-947 . -994) 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-72) T) ((-784 . -64) T) ((-784 . -1173) T) ((-782 . -1012) T) ((-782 . -551) 120541) ((-782 . -1127) T) ((-782 . -13) T) ((-782 . -72) T) ((-782 . -554) 120523) ((-781 . -1127) T) ((-781 . -13) T) ((-781 . -551) 120398) ((-781 . -1012) 120349) ((-781 . -72) 120300) ((-780 . -903) 120284) ((-780 . -1064) 120262) ((-780 . -949) 120129) ((-780 . -554) 120028) ((-780 . -552) 119831) ((-780 . -932) 119810) ((-780 . -820) 119789) ((-780 . -793) 119773) ((-780 . -754) 119752) ((-780 . -720) 119731) ((-780 . -717) 119710) ((-780 . -758) 119664) ((-780 . -755) 119618) ((-780 . -715) 119597) ((-780 . -713) 119576) ((-780 . -739) 119555) ((-780 . -795) 119480) ((-780 . -341) 119464) ((-780 . -579) 119412) ((-780 . -589) 119328) ((-780 . -327) 119312) ((-780 . -241) 119270) ((-780 . -260) 119235) ((-780 . -454) 119147) ((-780 . -288) 119131) ((-780 . -201) T) ((-780 . -82) 119062) ((-780 . -962) 119014) ((-780 . -967) 118966) ((-780 . -246) T) ((-780 . -653) 118918) ((-780 . -581) 118870) ((-780 . -587) 118807) ((-780 . -38) 118759) ((-780 . -258) T) ((-780 . -390) T) ((-780 . -146) T) ((-780 . -494) T) ((-780 . -831) T) ((-780 . -1132) T) ((-780 . -312) T) ((-780 . -190) 118738) ((-780 . -186) 118686) ((-780 . -189) 118640) ((-780 . -225) 118624) ((-780 . -805) 118548) ((-780 . -810) 118474) ((-780 . -808) 118433) ((-780 . -184) 118417) ((-780 . -120) 118371) ((-780 . -118) 118350) ((-780 . -104) T) ((-780 . -25) T) ((-780 . -72) T) ((-780 . -13) T) ((-780 . -1127) T) ((-780 . -551) 118332) ((-780 . -1012) T) ((-780 . -23) T) ((-780 . -21) T) ((-780 . -960) T) ((-780 . -662) T) ((-780 . -1059) T) ((-780 . -1024) T) ((-780 . -969) T) ((-779 . -903) 118309) ((-779 . -1064) NIL) ((-779 . -949) 118286) ((-779 . -554) 118216) ((-779 . -552) NIL) ((-779 . -932) NIL) ((-779 . -820) NIL) ((-779 . -793) 118193) ((-779 . -754) NIL) ((-779 . -720) NIL) ((-779 . -717) NIL) ((-779 . -758) NIL) ((-779 . -755) NIL) ((-779 . -715) NIL) ((-779 . -713) NIL) ((-779 . -739) NIL) ((-779 . -795) NIL) ((-779 . -341) 118170) ((-779 . -579) 118147) ((-779 . -589) 118092) ((-779 . -327) 118069) ((-779 . -241) 117999) ((-779 . -260) 117943) ((-779 . -454) 117806) ((-779 . -288) 117783) ((-779 . -201) T) ((-779 . -82) 117700) ((-779 . -962) 117645) ((-779 . -967) 117590) ((-779 . -246) T) ((-779 . -653) 117535) ((-779 . -581) 117480) ((-779 . -587) 117410) ((-779 . -38) 117355) ((-779 . -258) T) ((-779 . -390) T) ((-779 . -146) T) ((-779 . -494) T) ((-779 . -831) T) ((-779 . -1132) T) ((-779 . -312) T) ((-779 . -190) NIL) ((-779 . -186) NIL) ((-779 . -189) NIL) ((-779 . -225) 117332) ((-779 . -805) NIL) ((-779 . -810) NIL) ((-779 . -808) NIL) ((-779 . -184) 117309) ((-779 . -120) T) ((-779 . -118) NIL) ((-779 . -104) T) ((-779 . -25) T) ((-779 . -72) T) ((-779 . -13) T) ((-779 . -1127) T) ((-779 . -551) 117291) ((-779 . -1012) T) ((-779 . -23) T) ((-779 . -21) T) ((-779 . -960) T) ((-779 . -662) T) ((-779 . -1059) T) ((-779 . -1024) T) ((-779 . -969) T) ((-777 . -778) 117275) ((-777 . -831) T) ((-777 . -494) T) ((-777 . -246) T) ((-777 . -146) T) ((-777 . -554) 117247) ((-777 . -653) 117234) ((-777 . -581) 117221) ((-777 . -967) 117208) ((-777 . -962) 117195) ((-777 . -82) 117180) ((-777 . -38) 117167) ((-777 . -390) T) ((-777 . -258) T) ((-777 . -960) T) ((-777 . -662) T) ((-777 . -1059) T) ((-777 . -1024) T) ((-777 . -969) T) ((-777 . -21) T) ((-777 . -587) 117139) ((-777 . -23) T) ((-777 . -1012) T) ((-777 . -551) 117121) ((-777 . -1127) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -25) T) ((-777 . -104) T) ((-777 . -589) 117108) ((-777 . -120) T) ((-774 . -960) T) ((-774 . -662) T) ((-774 . -1059) T) ((-774 . -1024) T) ((-774 . -969) T) ((-774 . -21) T) ((-774 . -587) 117053) ((-774 . -23) T) ((-774 . -1012) T) ((-774 . -551) 117015) ((-774 . -1127) T) ((-774 . -13) T) ((-774 . -72) T) ((-774 . -25) T) ((-774 . -104) T) ((-774 . -589) 116975) ((-774 . -554) 116910) ((-774 . -428) 116887) ((-774 . -38) 116857) ((-774 . -82) 116822) ((-774 . -962) 116792) 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115280) ((-749 . -21) 115235) ((-749 . -587) 115155) ((-749 . -23) 115110) ((-749 . -25) 115065) ((-749 . -104) 115020) ((-749 . -754) 114999) ((-749 . -720) 114978) ((-749 . -717) 114957) ((-749 . -758) 114936) ((-749 . -755) 114915) ((-749 . -715) 114894) ((-749 . -713) 114873) ((-749 . -960) 114852) ((-749 . -662) 114831) ((-749 . -1059) 114810) ((-749 . -1024) 114789) ((-749 . -969) 114768) ((-749 . -589) 114741) ((-749 . -120) 114720) ((-748 . -746) 114702) ((-748 . -72) T) ((-748 . -13) T) ((-748 . -1127) T) ((-748 . -551) 114684) ((-748 . -1012) T) ((-744 . -960) T) ((-744 . -662) T) ((-744 . -1059) T) ((-744 . -1024) T) ((-744 . -969) T) ((-744 . -21) T) ((-744 . -587) 114629) ((-744 . -23) T) ((-744 . -1012) T) ((-744 . -551) 114611) ((-744 . -1127) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -25) T) ((-744 . -104) T) ((-744 . -589) 114571) ((-744 . -554) 114526) ((-744 . -949) 114496) ((-744 . -241) 114475) ((-744 . -120) 114454) ((-744 . -118) 114433) ((-744 . -38) 114403) 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T) ((-736 . -25) T) ((-736 . -104) T) ((-736 . -589) 112615) ((-736 . -190) T) ((-736 . -554) 112524) ((-736 . -969) T) ((-736 . -1024) T) ((-736 . -1059) T) ((-736 . -662) T) ((-736 . -960) T) ((-736 . -186) 112511) ((-736 . -189) T) ((-736 . -428) 112495) ((-736 . -312) 112474) ((-736 . -1132) 112453) ((-736 . -831) 112432) ((-736 . -494) 112411) ((-736 . -146) 112390) ((-736 . -653) 112327) ((-736 . -581) 112264) ((-736 . -38) 112201) ((-736 . -390) 112180) ((-736 . -258) 112159) ((-736 . -246) 112138) ((-736 . -201) 112117) ((-735 . -213) 112056) ((-735 . -554) 111800) ((-735 . -949) 111630) ((-735 . -552) NIL) ((-735 . -277) 111592) ((-735 . -353) 111576) ((-735 . -38) 111428) ((-735 . -82) 111253) ((-735 . -962) 111099) ((-735 . -967) 110945) ((-735 . -587) 110855) ((-735 . -589) 110744) ((-735 . -581) 110596) ((-735 . -653) 110448) ((-735 . -118) 110427) ((-735 . -120) 110406) ((-735 . -146) 110320) ((-735 . -494) 110254) ((-735 . -246) 110188) ((-735 . -47) 110150) ((-735 . 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((-734 . -537) 108791) ((-734 . -949) 108620) ((-734 . -554) 108424) ((-734 . -353) 108393) ((-734 . -579) 108301) ((-734 . -589) 108140) ((-734 . -327) 108110) ((-734 . -318) 108089) ((-734 . -190) 108042) ((-734 . -587) 107830) ((-734 . -969) 107809) ((-734 . -1024) 107788) ((-734 . -1059) 107767) ((-734 . -662) 107746) ((-734 . -960) 107725) ((-734 . -186) 107621) ((-734 . -189) 107523) ((-734 . -225) 107493) ((-734 . -805) 107365) ((-734 . -810) 107239) ((-734 . -808) 107172) ((-734 . -184) 107142) ((-734 . -551) 106839) ((-734 . -967) 106764) ((-734 . -962) 106669) ((-734 . -82) 106589) ((-734 . -104) 106464) ((-734 . -25) 106301) ((-734 . -72) 106038) ((-734 . -13) T) ((-734 . -1127) T) ((-734 . -1012) 105794) ((-734 . -23) 105650) ((-734 . -21) 105565) ((-721 . -719) 105549) ((-721 . -758) 105528) ((-721 . -755) 105507) ((-721 . -949) 105300) ((-721 . -554) 105153) ((-721 . -353) 105117) ((-721 . -241) 105075) ((-721 . -260) 105040) ((-721 . -454) 104952) ((-721 . -288) 104936) 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102795) ((-703 . -579) 102743) ((-703 . -808) 102687) ((-703 . -805) 102594) ((-703 . -810) 102505) ((-703 . -795) NIL) ((-703 . -820) 102484) ((-703 . -1132) 102463) ((-703 . -860) 102433) ((-703 . -831) 102412) ((-703 . -494) 102326) ((-703 . -246) 102240) ((-703 . -146) 102134) ((-703 . -390) 102068) ((-703 . -258) 102047) ((-703 . -241) 101974) ((-703 . -190) T) ((-703 . -104) T) ((-703 . -25) T) ((-703 . -72) T) ((-703 . -551) 101935) ((-703 . -1012) T) ((-703 . -23) T) ((-703 . -21) T) ((-703 . -969) T) ((-703 . -1024) T) ((-703 . -1059) T) ((-703 . -662) T) ((-703 . -960) T) ((-703 . -186) 101922) ((-703 . -13) T) ((-703 . -1127) T) ((-703 . -189) T) ((-703 . -225) 101906) ((-703 . -184) 101890) ((-702 . -976) 101857) ((-702 . -552) 101492) ((-702 . -260) 101479) ((-702 . -454) 101431) ((-702 . -277) 101403) ((-702 . -949) 101262) ((-702 . -353) 101246) ((-702 . -38) 101098) ((-702 . -554) 100871) ((-702 . -589) 100760) ((-702 . -587) 100670) ((-702 . -969) T) ((-702 . -1024) T) 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. -241) 56072) ((-348 . -260) 56037) ((-348 . -454) 55949) ((-348 . -288) 55933) ((-348 . -201) T) ((-348 . -82) 55864) ((-348 . -962) 55816) ((-348 . -967) 55768) ((-348 . -246) T) ((-348 . -653) 55720) ((-348 . -581) 55672) ((-348 . -587) 55609) ((-348 . -38) 55561) ((-348 . -258) T) ((-348 . -390) T) ((-348 . -146) T) ((-348 . -494) T) ((-348 . -831) T) ((-348 . -1132) T) ((-348 . -312) T) ((-348 . -190) 55540) ((-348 . -186) 55488) ((-348 . -189) 55442) ((-348 . -225) 55426) ((-348 . -805) 55350) ((-348 . -810) 55276) ((-348 . -808) 55235) ((-348 . -184) 55219) ((-348 . -120) 55173) ((-348 . -118) 55152) ((-348 . -104) T) ((-348 . -25) T) ((-348 . -72) T) ((-348 . -13) T) ((-348 . -1127) T) ((-348 . -551) 55134) ((-348 . -1012) T) ((-348 . -23) T) ((-348 . -21) T) ((-348 . -960) T) ((-348 . -662) T) ((-348 . -1059) T) ((-348 . -1024) T) ((-348 . -969) T) ((-346 . -494) T) ((-346 . -246) T) ((-346 . -146) T) ((-346 . -554) 55043) ((-346 . -653) 55017) ((-346 . -581) 54991) ((-346 . 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. -494) T) ((-301 . -146) T) ((-301 . -653) 48806) ((-301 . -581) 48751) ((-301 . -38) 48716) ((-301 . -390) T) ((-301 . -258) T) ((-301 . -82) 48633) ((-301 . -962) 48578) ((-301 . -967) 48523) ((-301 . -246) T) ((-301 . -201) T) ((-301 . -343) T) ((-301 . -118) T) ((-301 . -949) 48500) ((-301 . -1185) 48477) ((-301 . -1196) 48454) ((-295 . -280) 48438) ((-295 . -190) 48417) ((-295 . -186) 48390) ((-295 . -189) 48369) ((-295 . -318) 48348) ((-295 . -1064) 48327) ((-295 . -299) 48306) ((-295 . -120) 48285) ((-295 . -554) 48222) ((-295 . -589) 48174) ((-295 . -587) 48111) ((-295 . -104) T) ((-295 . -25) T) ((-295 . -72) T) ((-295 . -13) T) ((-295 . -1127) T) ((-295 . -551) 48093) ((-295 . -1012) T) ((-295 . -23) T) ((-295 . -21) T) ((-295 . -969) T) ((-295 . -1024) T) ((-295 . -1059) T) ((-295 . -662) T) ((-295 . -960) T) ((-295 . -312) T) ((-295 . -1132) T) ((-295 . -831) T) ((-295 . -494) T) ((-295 . -146) T) ((-295 . -653) 48045) ((-295 . -581) 47997) ((-295 . -38) 47962) ((-295 . 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. -23) T) ((-177 . -1012) T) ((-177 . -551) 16389) ((-177 . -1127) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -949) 16366) ((-176 . -214) 16350) ((-176 . -1033) 16334) ((-176 . -76) 16318) ((-176 . -34) T) ((-176 . -13) T) ((-176 . -1127) T) ((-176 . -72) 16272) ((-176 . -551) 16207) ((-176 . -260) 16145) ((-176 . -454) 16078) ((-176 . -1012) 16056) ((-176 . -427) 16040) ((-176 . -907) 16024) ((-172 . -994) T) ((-172 . -428) 16005) ((-172 . -551) 15971) ((-172 . -554) 15952) ((-172 . -1012) T) ((-172 . -1127) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -903) 15934) ((-171 . -1064) T) ((-171 . -554) 15884) ((-171 . -949) 15844) ((-171 . -552) 15774) ((-171 . -932) T) ((-171 . -820) NIL) ((-171 . -793) 15756) ((-171 . -754) T) ((-171 . -720) T) ((-171 . -717) T) ((-171 . -758) T) ((-171 . -755) T) ((-171 . -715) T) ((-171 . -713) T) ((-171 . -739) T) ((-171 . -795) 15738) ((-171 . -341) 15720) ((-171 . -579) 15702) ((-171 . -327) 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. -552) NIL) ((-102 . -427) 9347) ((-102 . -1012) T) ((-102 . -454) NIL) ((-102 . -260) NIL) ((-102 . -551) 9291) ((-102 . -72) T) ((-102 . -1127) T) ((-102 . -13) T) ((-102 . -34) T) ((-102 . -124) 9273) ((-102 . -755) T) ((-102 . -758) T) ((-102 . -322) 9255) ((-101 . -751) T) ((-101 . -758) T) ((-101 . -755) T) ((-101 . -1012) T) ((-101 . -551) 9237) ((-101 . -1127) T) ((-101 . -13) T) ((-101 . -72) T) ((-101 . -318) T) ((-101 . -603) T) ((-100 . -98) 9221) ((-100 . -922) 9205) ((-100 . -34) T) ((-100 . -13) T) ((-100 . -1127) T) ((-100 . -72) 9159) ((-100 . -551) 9094) ((-100 . -260) 9032) ((-100 . -454) 8965) ((-100 . -1012) 8943) ((-100 . -427) 8927) ((-100 . -92) 8911) ((-99 . -98) 8895) ((-99 . -922) 8879) ((-99 . -34) T) ((-99 . -13) T) ((-99 . -1127) T) ((-99 . -72) 8833) ((-99 . -551) 8768) ((-99 . -260) 8706) ((-99 . -454) 8639) ((-99 . -1012) 8617) ((-99 . -427) 8601) ((-99 . -92) 8585) ((-94 . -98) 8569) ((-94 . -922) 8553) ((-94 . -34) T) ((-94 . -13) T) ((-94 . -1127) T) ((-94 . -72) 8507) ((-94 . -551) 8442) ((-94 . -260) 8380) ((-94 . -454) 8313) ((-94 . -1012) 8291) ((-94 . -427) 8275) ((-94 . -92) 8259) ((-90 . -903) 8237) ((-90 . -1064) NIL) ((-90 . -949) 8215) ((-90 . -554) 8146) ((-90 . -552) NIL) ((-90 . -932) NIL) ((-90 . -820) NIL) ((-90 . -793) 8124) ((-90 . -754) NIL) ((-90 . -720) NIL) ((-90 . -717) NIL) ((-90 . -758) NIL) ((-90 . -755) NIL) ((-90 . -715) NIL) ((-90 . -713) NIL) ((-90 . -739) NIL) ((-90 . -795) NIL) ((-90 . -341) 8102) ((-90 . -579) 8080) ((-90 . -589) 8026) ((-90 . -327) 8004) ((-90 . -241) 7938) ((-90 . -260) 7885) ((-90 . -454) 7755) ((-90 . -288) 7733) ((-90 . -201) T) ((-90 . -82) 7652) ((-90 . -962) 7598) ((-90 . -967) 7544) ((-90 . -246) T) ((-90 . -653) 7490) ((-90 . -581) 7436) ((-90 . -587) 7367) ((-90 . -38) 7313) ((-90 . -258) T) ((-90 . -390) T) ((-90 . -146) T) ((-90 . -494) T) ((-90 . -831) T) ((-90 . -1132) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7291) ((-90 . -805) NIL) ((-90 . -810) NIL) ((-90 . -808) NIL) ((-90 . -184) 7269) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1127) T) ((-90 . -551) 7251) ((-90 . -1012) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -960) T) ((-90 . -662) T) ((-90 . -1059) T) ((-90 . -1024) T) ((-90 . -969) T) ((-89 . -778) 7235) ((-89 . -831) T) ((-89 . -494) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -554) 7207) ((-89 . -653) 7194) ((-89 . -581) 7181) ((-89 . -967) 7168) ((-89 . -962) 7155) ((-89 . -82) 7140) ((-89 . -38) 7127) ((-89 . -390) T) ((-89 . -258) T) ((-89 . -960) T) ((-89 . -662) T) ((-89 . -1059) T) ((-89 . -1024) T) ((-89 . -969) T) ((-89 . -21) T) ((-89 . -587) 7099) ((-89 . -23) T) ((-89 . -1012) T) ((-89 . -551) 7081) ((-89 . -1127) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -589) 7068) ((-89 . -120) T) ((-86 . -755) T) ((-86 . -551) 7050) ((-86 . -1012) T) ((-86 . -72) T) ((-86 . -13) T) 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((-77 . -754) T) ((-77 . -720) T) ((-77 . -717) T) ((-77 . -758) T) ((-77 . -755) T) ((-77 . -715) T) ((-77 . -713) T) ((-77 . -739) T) ((-77 . -795) 6485) ((-77 . -341) 6467) ((-77 . -579) 6449) ((-77 . -327) 6431) ((-77 . -241) NIL) ((-77 . -260) NIL) ((-77 . -454) NIL) ((-77 . -288) 6413) ((-77 . -201) T) ((-77 . -82) 6340) ((-77 . -962) 6290) ((-77 . -967) 6240) ((-77 . -246) T) ((-77 . -653) 6190) ((-77 . -581) 6140) ((-77 . -589) 6090) ((-77 . -587) 6040) ((-77 . -38) 5990) ((-77 . -258) T) ((-77 . -390) T) ((-77 . -146) T) ((-77 . -494) T) ((-77 . -831) T) ((-77 . -1132) T) ((-77 . -312) T) ((-77 . -190) T) ((-77 . -186) 5977) ((-77 . -189) T) ((-77 . -225) 5959) ((-77 . -805) NIL) ((-77 . -810) NIL) ((-77 . -808) NIL) ((-77 . -184) 5941) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1127) T) ((-77 . -551) 5884) ((-77 . -1012) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -960) T) ((-77 . -662) T) ((-77 . -1059) T) 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4805) ((-58 . -592) 4789) ((-58 . -243) 4766) ((-58 . -241) 4718) ((-58 . -537) 4695) ((-58 . -552) 4656) ((-58 . -427) 4640) ((-58 . -1012) 4593) ((-58 . -454) 4526) ((-58 . -260) 4464) ((-58 . -551) 4379) ((-58 . -72) 4313) ((-58 . -1127) T) ((-58 . -13) T) ((-58 . -34) T) ((-58 . -124) 4297) ((-58 . -755) 4276) ((-58 . -758) 4255) ((-58 . -322) 4239) ((-55 . -1012) T) ((-55 . -551) 4221) ((-55 . -1127) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -949) 4203) ((-55 . -554) 4185) ((-51 . -1012) T) ((-51 . -551) 4167) ((-51 . -1127) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -559) 4151) ((-50 . -554) 4120) ((-50 . -589) 4094) ((-50 . -587) 4053) ((-50 . -969) T) ((-50 . -1024) T) ((-50 . -1059) T) ((-50 . -662) T) ((-50 . -960) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1012) T) ((-50 . -551) 4035) ((-50 . -1127) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -949) 4019) ((-49 . -1012) T) ((-49 . -551) 4001) ((-49 . -1127) T) ((-49 . -13) T) ((-49 . -72) T) 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|EnumerationCategory|) T) ((0 . -551) 84) ((0 . -1012) T) ((0 . -72) T) ((0 . -1127) T) ((-2 . |RecordCategory|) T) ((-2 . -551) 66) ((-2 . -1012) T) ((-2 . -72) T) ((-2 . -1127) T) ((-3 . |UnionCategory|) T) ((-3 . -551) 48) ((-3 . -1012) T) ((-3 . -72) T) ((-3 . -1127) T) ((-1 . -1012) T) ((-1 . -551) 30) ((-1 . -1127) T) ((-1 . -13) T) ((-1 . -72) T)) 
\ No newline at end of file
+((((-484)) . T)) 
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. -104) T) ((-1203 . -590) 198080) ((-1203 . -1193) 198064) ((-1203 . -654) 198034) ((-1203 . -582) 198004) ((-1203 . -968) 197988) ((-1203 . -963) 197972) ((-1203 . -82) 197951) ((-1203 . -38) 197921) ((-1203 . -1198) 197900) ((-1202 . -961) T) ((-1202 . -663) T) ((-1202 . -1060) T) ((-1202 . -1025) T) ((-1202 . -970) T) ((-1202 . -21) T) ((-1202 . -588) 197859) ((-1202 . -23) T) ((-1202 . -1013) T) ((-1202 . -552) 197841) ((-1202 . -1128) T) ((-1202 . -13) T) ((-1202 . -72) T) ((-1202 . -25) T) ((-1202 . -104) T) ((-1202 . -590) 197815) ((-1202 . -555) 197771) ((-1202 . -1193) 197755) ((-1202 . -654) 197725) ((-1202 . -582) 197695) ((-1202 . -968) 197679) ((-1202 . -963) 197663) ((-1202 . -82) 197642) ((-1202 . -38) 197612) ((-1202 . -334) 197591) ((-1202 . -950) 197575) ((-1200 . -1201) 197551) ((-1200 . -950) 197525) ((-1200 . -555) 197471) ((-1200 . -961) T) ((-1200 . -663) T) ((-1200 . -1060) T) ((-1200 . -1025) T) ((-1200 . -970) T) ((-1200 . -21) T) ((-1200 . -588) 197430) 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. -588) 196032) ((-1191 . -23) T) ((-1191 . -1013) T) ((-1191 . -552) 196001) ((-1191 . -1128) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -25) T) ((-1191 . -104) T) ((-1191 . -590) 195961) ((-1191 . -555) 195903) ((-1191 . -429) 195887) ((-1191 . -38) 195857) ((-1191 . -82) 195822) ((-1191 . -963) 195792) ((-1191 . -968) 195762) ((-1191 . -582) 195732) ((-1191 . -654) 195702) ((-1190 . -995) T) ((-1190 . -429) 195683) ((-1190 . -552) 195649) ((-1190 . -555) 195630) ((-1190 . -1013) T) ((-1190 . -1128) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -64) T) ((-1189 . -995) T) ((-1189 . -429) 195611) ((-1189 . -552) 195577) ((-1189 . -555) 195558) ((-1189 . -1013) T) ((-1189 . -1128) T) ((-1189 . -13) T) ((-1189 . -72) T) ((-1189 . -64) T) ((-1184 . -552) 195540) ((-1182 . -1013) T) ((-1182 . -552) 195522) ((-1182 . -1128) T) ((-1182 . -13) T) ((-1182 . -72) T) ((-1181 . -1013) T) ((-1181 . -552) 195504) ((-1181 . -1128) T) ((-1181 . -13) T) ((-1181 . -72) T) ((-1178 . -1177) 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-963) 185471) ((-1147 . -968) 185297) ((-1147 . -588) 185207) ((-1147 . -590) 185096) ((-1147 . -582) 184928) ((-1147 . -654) 184760) ((-1147 . -555) 184516) ((-1147 . -118) 184495) ((-1147 . -120) 184474) ((-1147 . -47) 184451) ((-1147 . -328) 184435) ((-1147 . -580) 184383) ((-1147 . -809) 184327) ((-1147 . -806) 184234) ((-1147 . -811) 184145) ((-1147 . -796) NIL) ((-1147 . -821) 184124) ((-1147 . -1133) 184103) ((-1147 . -861) 184073) ((-1147 . -832) 184052) ((-1147 . -495) 183966) ((-1147 . -246) 183880) ((-1147 . -146) 183774) ((-1147 . -391) 183708) ((-1147 . -258) 183687) ((-1147 . -241) 183614) ((-1147 . -190) T) ((-1147 . -104) T) ((-1147 . -25) T) ((-1147 . -72) T) ((-1147 . -552) 183596) ((-1147 . -1013) T) ((-1147 . -23) T) ((-1147 . -21) T) ((-1147 . -970) T) ((-1147 . -1025) T) ((-1147 . -1060) T) ((-1147 . -663) T) ((-1147 . -961) T) ((-1147 . -186) 183583) ((-1147 . -13) T) ((-1147 . -1128) T) ((-1147 . -189) T) ((-1147 . -225) 183567) ((-1147 . -184) 183551) ((-1145 . -1006) 183535) ((-1145 . -557) 183519) ((-1145 . -1013) 183497) ((-1145 . -552) 183464) ((-1145 . -1128) 183442) ((-1145 . -13) 183420) ((-1145 . -72) 183398) ((-1145 . -1007) 183355) ((-1143 . -1142) 183334) ((-1143 . -915) 183300) ((-1143 . -1114) 183266) ((-1143 . -1117) 183232) ((-1143 . -432) 183198) ((-1143 . -239) 183164) ((-1143 . -66) 183130) ((-1143 . -35) 183096) ((-1143 . -1157) 183073) ((-1143 . -47) 183050) ((-1143 . -555) 182805) ((-1143 . -654) 182625) ((-1143 . -582) 182445) ((-1143 . -590) 182256) ((-1143 . -588) 182114) ((-1143 . -968) 181928) ((-1143 . -963) 181742) ((-1143 . -82) 181530) ((-1143 . -38) 181350) ((-1143 . -886) 181320) ((-1143 . -241) 181220) ((-1143 . -1140) 181204) ((-1143 . -970) T) ((-1143 . -1025) T) ((-1143 . -1060) T) ((-1143 . -663) T) ((-1143 . -961) T) ((-1143 . -21) T) ((-1143 . -23) T) ((-1143 . -1013) T) ((-1143 . -552) 181186) ((-1143 . -1128) T) ((-1143 . -13) T) ((-1143 . -72) T) ((-1143 . -25) T) ((-1143 . -104) T) ((-1143 . -118) 181114) ((-1143 . -120) 180996) ((-1143 . -553) 180669) ((-1143 . -184) 180639) ((-1143 . -809) 180493) ((-1143 . -811) 180293) ((-1143 . -806) 180091) ((-1143 . -225) 180061) ((-1143 . -189) 179923) ((-1143 . -186) 179779) ((-1143 . -190) 179687) ((-1143 . -312) 179666) ((-1143 . -1133) 179645) ((-1143 . -832) 179624) ((-1143 . -495) 179578) ((-1143 . -146) 179512) ((-1143 . -391) 179491) ((-1143 . -258) 179470) ((-1143 . -246) 179424) ((-1143 . -201) 179403) ((-1143 . -288) 179373) ((-1143 . -455) 179233) ((-1143 . -260) 179172) ((-1143 . -328) 179142) ((-1143 . -580) 179050) ((-1143 . -342) 179020) ((-1143 . -796) 178893) ((-1143 . -740) 178846) ((-1143 . -714) 178799) ((-1143 . -716) 178752) ((-1143 . -756) 178654) ((-1143 . -759) 178556) ((-1143 . -718) 178509) ((-1143 . -721) 178462) ((-1143 . -755) 178415) ((-1143 . -794) 178385) ((-1143 . -821) 178338) ((-1143 . -933) 178291) ((-1143 . -950) 178080) ((-1143 . -1065) 178032) ((-1143 . -904) 178002) ((-1138 . -1142) 177963) ((-1138 . -915) 177929) ((-1138 . -1114) 177895) ((-1138 . -1117) 177861) ((-1138 . -432) 177827) ((-1138 . -239) 177793) ((-1138 . -66) 177759) ((-1138 . -35) 177725) ((-1138 . -1157) 177702) ((-1138 . -47) 177679) ((-1138 . -555) 177480) ((-1138 . -654) 177282) ((-1138 . -582) 177084) ((-1138 . -590) 176939) ((-1138 . -588) 176779) ((-1138 . -968) 176575) ((-1138 . -963) 176371) ((-1138 . -82) 176123) ((-1138 . -38) 175925) ((-1138 . -886) 175895) ((-1138 . -241) 175723) ((-1138 . -1140) 175707) ((-1138 . -970) T) ((-1138 . -1025) T) ((-1138 . -1060) T) ((-1138 . -663) T) ((-1138 . -961) T) ((-1138 . -21) T) ((-1138 . -23) T) ((-1138 . -1013) T) ((-1138 . -552) 175689) ((-1138 . -1128) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -25) T) ((-1138 . -104) T) ((-1138 . -118) 175599) ((-1138 . -120) 175509) ((-1138 . -553) NIL) ((-1138 . -184) 175461) ((-1138 . -809) 175297) ((-1138 . -811) 175061) ((-1138 . -806) 174800) ((-1138 . -225) 174752) ((-1138 . -189) 174578) ((-1138 . -186) 174398) ((-1138 . -190) 174288) ((-1138 . -312) 174267) ((-1138 . -1133) 174246) ((-1138 . -832) 174225) ((-1138 . -495) 174179) ((-1138 . -146) 174113) ((-1138 . -391) 174092) ((-1138 . -258) 174071) ((-1138 . -246) 174025) ((-1138 . -201) 174004) ((-1138 . -288) 173956) ((-1138 . -455) 173690) ((-1138 . -260) 173575) ((-1138 . -328) 173527) ((-1138 . -580) 173479) ((-1138 . -342) 173431) ((-1138 . -796) NIL) ((-1138 . -740) NIL) ((-1138 . -714) NIL) ((-1138 . -716) NIL) ((-1138 . -756) NIL) ((-1138 . -759) NIL) ((-1138 . -718) NIL) ((-1138 . -721) NIL) ((-1138 . -755) NIL) ((-1138 . -794) 173383) ((-1138 . -821) NIL) ((-1138 . -933) NIL) ((-1138 . -950) 173349) ((-1138 . -1065) NIL) ((-1138 . -904) 173301) ((-1137 . -752) T) ((-1137 . -759) T) ((-1137 . -756) T) ((-1137 . -1013) T) ((-1137 . -552) 173283) ((-1137 . -1128) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -319) T) ((-1137 . -604) T) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1013) T) ((-1136 . -552) 173265) ((-1136 . -1128) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -319) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1013) T) ((-1135 . -552) 173247) ((-1135 . -1128) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -319) T) ((-1135 . -604) T) ((-1134 . -752) T) ((-1134 . -759) T) ((-1134 . -756) T) ((-1134 . -1013) T) ((-1134 . -552) 173229) ((-1134 . -1128) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -319) T) ((-1134 . -604) T) ((-1129 . -995) T) ((-1129 . -429) 173210) ((-1129 . -552) 173176) ((-1129 . -555) 173157) ((-1129 . -1013) T) ((-1129 . -1128) T) ((-1129 . -13) T) ((-1129 . -72) T) ((-1129 . -64) T) ((-1126 . -429) 173134) ((-1126 . -552) 173075) ((-1126 . -555) 173052) ((-1126 . -1013) 173030) ((-1126 . -1128) 173008) ((-1126 . -13) 172986) ((-1126 . -72) 172964) ((-1121 . -679) 172940) ((-1121 . -35) 172906) ((-1121 . -66) 172872) ((-1121 . -239) 172838) ((-1121 . -432) 172804) ((-1121 . -1117) 172770) ((-1121 . -1114) 172736) ((-1121 . -915) 172702) ((-1121 . -47) 172671) ((-1121 . -38) 172568) ((-1121 . -582) 172465) ((-1121 . -654) 172362) ((-1121 . -555) 172244) ((-1121 . -246) 172223) ((-1121 . -495) 172202) ((-1121 . -82) 172067) ((-1121 . -963) 171953) ((-1121 . -968) 171839) ((-1121 . -146) 171793) ((-1121 . -120) 171772) ((-1121 . -118) 171751) ((-1121 . -590) 171676) ((-1121 . -588) 171586) ((-1121 . -886) 171547) ((-1121 . -811) 171528) ((-1121 . -1128) T) ((-1121 . -13) T) ((-1121 . -806) 171507) ((-1121 . -961) T) ((-1121 . -663) T) ((-1121 . -1060) T) ((-1121 . -1025) T) ((-1121 . -970) T) ((-1121 . -21) T) ((-1121 . -23) T) ((-1121 . -1013) T) ((-1121 . -552) 171489) ((-1121 . -72) T) ((-1121 . -25) T) ((-1121 . -104) T) ((-1121 . -809) 171470) ((-1121 . -455) 171437) ((-1121 . -260) 171424) ((-1115 . -923) 171408) ((-1115 . -34) T) ((-1115 . -13) T) ((-1115 . -1128) T) ((-1115 . -72) 171362) ((-1115 . -552) 171297) ((-1115 . -260) 171235) ((-1115 . -455) 171168) ((-1115 . -1013) 171146) ((-1115 . -428) 171130) ((-1110 . -314) 171104) ((-1110 . -72) T) ((-1110 . -13) T) ((-1110 . -1128) T) ((-1110 . -552) 171086) ((-1110 . -1013) T) ((-1108 . -1013) T) ((-1108 . -552) 171068) ((-1108 . -1128) T) ((-1108 . -13) T) ((-1108 . -72) T) ((-1108 . -555) 171050) ((-1103 . -747) 171034) ((-1103 . -72) T) ((-1103 . -13) T) ((-1103 . -1128) T) ((-1103 . -552) 171016) ((-1103 . -1013) T) ((-1101 . -1106) 170995) ((-1101 . -183) 170943) ((-1101 . -76) 170891) ((-1101 . -260) 170689) ((-1101 . -455) 170441) ((-1101 . -428) 170376) ((-1101 . -124) 170324) ((-1101 . -553) NIL) ((-1101 . -193) 170272) ((-1101 . -549) 170251) ((-1101 . -243) 170230) ((-1101 . -1128) T) ((-1101 . -13) T) ((-1101 . -241) 170209) ((-1101 . -1013) T) ((-1101 . -552) 170191) ((-1101 . -72) T) ((-1101 . -34) T) ((-1101 . -538) 170170) ((-1097 . -1013) T) ((-1097 . -552) 170152) ((-1097 . -1128) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1096 . -752) T) ((-1096 . -759) T) ((-1096 . -756) T) ((-1096 . -1013) T) ((-1096 . -552) 170134) ((-1096 . -1128) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -319) T) ((-1096 . -604) T) ((-1095 . -752) T) ((-1095 . -759) T) ((-1095 . -756) T) ((-1095 . -1013) T) ((-1095 . -552) 170116) ((-1095 . -1128) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -319) T) ((-1094 . -1174) T) ((-1094 . -1013) T) ((-1094 . -552) 170083) ((-1094 . -1128) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -950) 170019) ((-1094 . -555) 169955) ((-1093 . -552) 169937) ((-1092 . -552) 169919) ((-1091 . -277) 169896) ((-1091 . -950) 169794) ((-1091 . -354) 169778) ((-1091 . -38) 169675) ((-1091 . -555) 169532) ((-1091 . -590) 169457) ((-1091 . -588) 169367) ((-1091 . -970) T) ((-1091 . -1025) T) ((-1091 . -1060) T) ((-1091 . -663) T) ((-1091 . -961) T) ((-1091 . -82) 169232) ((-1091 . -963) 169118) ((-1091 . -968) 169004) ((-1091 . -21) T) ((-1091 . -23) T) ((-1091 . -1013) T) ((-1091 . -552) 168986) ((-1091 . -1128) T) ((-1091 . -13) T) ((-1091 . -72) T) ((-1091 . -25) T) ((-1091 . -104) T) ((-1091 . -582) 168883) ((-1091 . -654) 168780) ((-1091 . -118) 168759) ((-1091 . -120) 168738) ((-1091 . -146) 168692) ((-1091 . -495) 168671) ((-1091 . -246) 168650) ((-1091 . -47) 168627) ((-1089 . -756) T) ((-1089 . -552) 168609) ((-1089 . -1013) T) ((-1089 . -72) T) ((-1089 . -13) T) ((-1089 . -1128) T) ((-1089 . -759) T) ((-1089 . -553) 168531) ((-1089 . -555) 168497) ((-1089 . -950) 168479) ((-1089 . -796) 168446) ((-1088 . -1171) 168430) ((-1088 . -190) 168389) ((-1088 . -555) 168271) ((-1088 . -590) 168196) ((-1088 . -588) 168106) ((-1088 . -104) T) ((-1088 . -25) T) ((-1088 . -72) T) ((-1088 . -552) 168088) ((-1088 . -1013) T) ((-1088 . -23) T) ((-1088 . -21) T) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1060) T) ((-1088 . -663) T) ((-1088 . -961) T) ((-1088 . -186) 168041) ((-1088 . -13) T) ((-1088 . -1128) T) ((-1088 . -189) 168000) ((-1088 . -241) 167965) ((-1088 . -809) 167878) ((-1088 . -806) 167766) ((-1088 . -811) 167679) ((-1088 . -886) 167649) ((-1088 . -38) 167546) ((-1088 . -82) 167411) ((-1088 . -963) 167297) ((-1088 . -968) 167183) ((-1088 . -582) 167080) ((-1088 . -654) 166977) ((-1088 . -118) 166956) ((-1088 . -120) 166935) ((-1088 . -146) 166889) ((-1088 . -495) 166868) ((-1088 . -246) 166847) ((-1088 . -47) 166824) ((-1088 . -1157) 166801) ((-1088 . -35) 166767) ((-1088 . -66) 166733) ((-1088 . -239) 166699) ((-1088 . -432) 166665) ((-1088 . -1117) 166631) ((-1088 . -1114) 166597) ((-1088 . -915) 166563) ((-1087 . -1163) 166524) ((-1087 . -312) 166503) ((-1087 . -1133) 166482) ((-1087 . -832) 166461) ((-1087 . -495) 166415) ((-1087 . -146) 166349) ((-1087 . -555) 166098) ((-1087 . -654) 165945) ((-1087 . -582) 165792) ((-1087 . -38) 165639) ((-1087 . -391) 165618) ((-1087 . -258) 165597) ((-1087 . -590) 165497) ((-1087 . -588) 165382) ((-1087 . -970) T) ((-1087 . -1025) T) ((-1087 . -1060) T) ((-1087 . -663) T) ((-1087 . -961) T) ((-1087 . -82) 165202) ((-1087 . -963) 165043) ((-1087 . -968) 164884) ((-1087 . -21) T) ((-1087 . -23) T) ((-1087 . -1013) T) ((-1087 . -552) 164866) ((-1087 . -1128) T) ((-1087 . -13) T) ((-1087 . -72) T) ((-1087 . -25) T) ((-1087 . -104) T) ((-1087 . -246) 164820) ((-1087 . -201) 164799) ((-1087 . -915) 164765) ((-1087 . -1114) 164731) ((-1087 . -1117) 164697) ((-1087 . -432) 164663) ((-1087 . -239) 164629) ((-1087 . -66) 164595) ((-1087 . -35) 164561) ((-1087 . -1157) 164531) ((-1087 . -47) 164501) ((-1087 . -120) 164480) ((-1087 . -118) 164459) ((-1087 . -886) 164422) ((-1087 . -811) 164328) ((-1087 . -806) 164209) ((-1087 . -809) 164115) ((-1087 . -241) 164073) ((-1087 . -189) 164025) ((-1087 . -186) 163971) ((-1087 . -190) 163923) ((-1087 . -1161) 163907) ((-1087 . -950) 163842) ((-1084 . -1154) 163826) ((-1084 . -1065) 163804) ((-1084 . -553) NIL) ((-1084 . -260) 163791) ((-1084 . -455) 163739) ((-1084 . -277) 163716) ((-1084 . -950) 163599) ((-1084 . -354) 163583) ((-1084 . -38) 163415) ((-1084 . -82) 163220) ((-1084 . -963) 163046) ((-1084 . -968) 162872) ((-1084 . -588) 162782) ((-1084 . -590) 162671) ((-1084 . -582) 162503) ((-1084 . -654) 162335) ((-1084 . -555) 162112) ((-1084 . -118) 162091) ((-1084 . -120) 162070) ((-1084 . -47) 162047) ((-1084 . -328) 162031) ((-1084 . -580) 161979) ((-1084 . -809) 161923) ((-1084 . -806) 161830) ((-1084 . -811) 161741) ((-1084 . -796) NIL) ((-1084 . -821) 161720) ((-1084 . -1133) 161699) ((-1084 . -861) 161669) ((-1084 . -832) 161648) ((-1084 . -495) 161562) ((-1084 . -246) 161476) ((-1084 . -146) 161370) ((-1084 . -391) 161304) ((-1084 . -258) 161283) ((-1084 . -241) 161210) ((-1084 . -190) T) ((-1084 . -104) T) ((-1084 . -25) T) ((-1084 . -72) T) ((-1084 . -552) 161192) ((-1084 . -1013) T) ((-1084 . -23) T) ((-1084 . -21) T) ((-1084 . -970) T) ((-1084 . -1025) T) ((-1084 . -1060) T) ((-1084 . -663) T) ((-1084 . -961) T) ((-1084 . -186) 161179) ((-1084 . -13) T) ((-1084 . -1128) T) ((-1084 . -189) T) ((-1084 . -225) 161163) ((-1084 . -184) 161147) ((-1081 . -1142) 161108) ((-1081 . -915) 161074) ((-1081 . -1114) 161040) ((-1081 . -1117) 161006) ((-1081 . -432) 160972) ((-1081 . -239) 160938) ((-1081 . -66) 160904) ((-1081 . -35) 160870) ((-1081 . -1157) 160847) ((-1081 . -47) 160824) ((-1081 . -555) 160625) ((-1081 . -654) 160427) ((-1081 . -582) 160229) ((-1081 . -590) 160084) ((-1081 . -588) 159924) ((-1081 . -968) 159720) ((-1081 . -963) 159516) ((-1081 . -82) 159268) ((-1081 . -38) 159070) ((-1081 . -886) 159040) ((-1081 . -241) 158868) ((-1081 . -1140) 158852) ((-1081 . -970) T) ((-1081 . -1025) T) ((-1081 . -1060) T) ((-1081 . -663) T) ((-1081 . -961) T) ((-1081 . -21) T) ((-1081 . -23) T) ((-1081 . -1013) T) ((-1081 . -552) 158834) ((-1081 . -1128) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -25) T) ((-1081 . -104) T) ((-1081 . -118) 158744) ((-1081 . -120) 158654) ((-1081 . -553) NIL) ((-1081 . -184) 158606) ((-1081 . -809) 158442) ((-1081 . -811) 158206) ((-1081 . -806) 157945) ((-1081 . -225) 157897) ((-1081 . -189) 157723) ((-1081 . -186) 157543) ((-1081 . -190) 157433) ((-1081 . -312) 157412) ((-1081 . -1133) 157391) ((-1081 . -832) 157370) ((-1081 . -495) 157324) ((-1081 . -146) 157258) ((-1081 . -391) 157237) ((-1081 . -258) 157216) ((-1081 . -246) 157170) ((-1081 . -201) 157149) ((-1081 . -288) 157101) ((-1081 . -455) 156835) ((-1081 . -260) 156720) ((-1081 . -328) 156672) ((-1081 . -580) 156624) ((-1081 . -342) 156576) ((-1081 . -796) NIL) ((-1081 . -740) NIL) ((-1081 . -714) NIL) ((-1081 . -716) NIL) ((-1081 . -756) NIL) ((-1081 . -759) NIL) ((-1081 . -718) NIL) ((-1081 . -721) NIL) ((-1081 . -755) NIL) ((-1081 . -794) 156528) ((-1081 . -821) NIL) ((-1081 . -933) NIL) ((-1081 . -950) 156494) ((-1081 . -1065) NIL) ((-1081 . -904) 156446) ((-1080 . -995) T) ((-1080 . -429) 156427) ((-1080 . -552) 156393) ((-1080 . -555) 156374) ((-1080 . -1013) T) ((-1080 . -1128) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -64) T) ((-1079 . -1013) T) ((-1079 . -552) 156356) ((-1079 . -1128) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1078 . -1013) T) ((-1078 . -552) 156338) ((-1078 . -1128) T) ((-1078 . -13) T) ((-1078 . -72) T) ((-1073 . -1106) 156314) ((-1073 . -183) 156259) ((-1073 . -76) 156204) ((-1073 . -260) 155993) ((-1073 . -455) 155733) ((-1073 . -428) 155665) ((-1073 . -124) 155610) ((-1073 . -553) NIL) ((-1073 . -193) 155555) ((-1073 . -549) 155531) ((-1073 . -243) 155507) ((-1073 . -1128) T) ((-1073 . -13) T) ((-1073 . -241) 155483) ((-1073 . -1013) T) ((-1073 . -552) 155465) ((-1073 . -72) T) ((-1073 . -34) T) ((-1073 . -538) 155441) ((-1072 . -1057) T) ((-1072 . -323) 155423) ((-1072 . -759) T) ((-1072 . -756) T) ((-1072 . -124) 155405) ((-1072 . -34) T) ((-1072 . -13) T) ((-1072 . -1128) T) ((-1072 . -72) T) ((-1072 . -552) 155387) ((-1072 . -260) NIL) ((-1072 . -455) NIL) ((-1072 . -1013) T) ((-1072 . -428) 155369) ((-1072 . -553) NIL) ((-1072 . -241) 155319) ((-1072 . -538) 155294) ((-1072 . -243) 155269) ((-1072 . -593) 155251) ((-1072 . -19) 155233) ((-1068 . -616) 155217) ((-1068 . -593) 155201) ((-1068 . -243) 155178) ((-1068 . -241) 155130) ((-1068 . -538) 155107) ((-1068 . -553) 155068) ((-1068 . -428) 155052) ((-1068 . -1013) 155030) ((-1068 . -455) 154963) ((-1068 . -260) 154901) ((-1068 . -552) 154836) ((-1068 . -72) 154790) ((-1068 . -1128) T) ((-1068 . -13) T) ((-1068 . -34) T) ((-1068 . -124) 154774) ((-1068 . -1167) 154758) ((-1068 . -923) 154742) ((-1068 . -1063) 154726) ((-1068 . -555) 154703) ((-1066 . -995) T) ((-1066 . -429) 154684) ((-1066 . -552) 154650) ((-1066 . -555) 154631) ((-1066 . -1013) T) ((-1066 . -1128) T) ((-1066 . -13) T) ((-1066 . -72) T) ((-1066 . -64) T) ((-1064 . -1106) 154610) ((-1064 . -183) 154558) ((-1064 . -76) 154506) ((-1064 . -260) 154304) ((-1064 . -455) 154056) ((-1064 . -428) 153991) ((-1064 . -124) 153939) ((-1064 . -553) NIL) ((-1064 . -193) 153887) ((-1064 . -549) 153866) ((-1064 . -243) 153845) ((-1064 . -1128) T) ((-1064 . -13) T) ((-1064 . -241) 153824) ((-1064 . -1013) T) ((-1064 . 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T) ((-1026 . -538) 146477) ((-1026 . -950) 146306) ((-1026 . -555) 146110) ((-1026 . -354) 146079) ((-1026 . -580) 145987) ((-1026 . -590) 145826) ((-1026 . -328) 145796) ((-1026 . -319) 145775) ((-1026 . -190) 145728) ((-1026 . -588) 145516) ((-1026 . -970) 145495) ((-1026 . -1025) 145474) ((-1026 . -1060) 145453) ((-1026 . -663) 145432) ((-1026 . -961) 145411) ((-1026 . -186) 145307) ((-1026 . -189) 145209) ((-1026 . -225) 145179) ((-1026 . -806) 145051) ((-1026 . -811) 144925) ((-1026 . -809) 144858) ((-1026 . -184) 144828) ((-1026 . -552) 144525) ((-1026 . -968) 144450) ((-1026 . -963) 144355) ((-1026 . -82) 144275) ((-1026 . -104) 144150) ((-1026 . -25) 143987) ((-1026 . -72) 143724) ((-1026 . -13) T) ((-1026 . -1128) T) ((-1026 . -1013) 143480) ((-1026 . -23) 143336) ((-1026 . -21) 143251) ((-1022 . -1023) 143235) ((-1022 . |MappingCategory|) 143209) ((-1022 . -1128) T) ((-1022 . -80) 143193) ((-1022 . -1013) T) ((-1022 . -552) 143175) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 143139) ((-1017 . -72) T) ((-1017 . -552) 143121) ((-1017 . -1013) T) ((-1017 . -241) 143077) ((-1017 . -1128) T) ((-1017 . -13) T) ((-1017 . -557) 142992) ((-1015 . -1016) 142944) ((-1015 . -72) T) ((-1015 . -552) 142926) ((-1015 . -1013) T) ((-1015 . -241) 142882) ((-1015 . -1128) T) ((-1015 . -13) T) ((-1015 . -557) 142785) ((-1014 . -319) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1128) T) ((-1014 . -552) 142767) ((-1014 . -1013) T) ((-1009 . -368) 142751) ((-1009 . -1011) 142735) ((-1009 . -319) 142714) ((-1009 . -193) 142698) ((-1009 . -553) 142659) ((-1009 . -124) 142643) ((-1009 . -428) 142627) ((-1009 . -1013) T) ((-1009 . -455) 142560) ((-1009 . -260) 142498) ((-1009 . -552) 142480) ((-1009 . -72) T) ((-1009 . -1128) T) ((-1009 . -13) T) ((-1009 . -34) T) ((-1009 . -76) 142464) ((-1009 . -183) 142448) ((-1008 . -995) T) ((-1008 . -429) 142429) ((-1008 . -552) 142395) ((-1008 . -555) 142376) ((-1008 . -1013) T) ((-1008 . -1128) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1128) T) ((-1004 . -13) T) ((-1004 . -1013) 142346) ((-1004 . -552) 142305) ((-1004 . -72) 142275) ((-1003 . -995) T) ((-1003 . -429) 142256) ((-1003 . -552) 142222) ((-1003 . -555) 142203) ((-1003 . -1013) T) ((-1003 . -1128) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 142187) ((-1001 . -557) 142171) ((-1001 . -1013) 142149) ((-1001 . -552) 142116) ((-1001 . -1128) 142094) ((-1001 . -13) 142072) ((-1001 . -72) 142050) ((-1001 . -1007) 142008) ((-1000 . -228) 141992) ((-1000 . -555) 141976) ((-1000 . -950) 141960) ((-1000 . -759) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -552) 141942) ((-1000 . -756) T) ((-1000 . -186) 141929) ((-1000 . -13) T) ((-1000 . -1128) T) ((-1000 . -189) T) ((-999 . -213) 141866) ((-999 . -555) 141609) ((-999 . -950) 141438) ((-999 . -553) NIL) ((-999 . -277) 141399) ((-999 . -354) 141383) ((-999 . -38) 141235) ((-999 . -82) 141060) ((-999 . -963) 140906) ((-999 . -968) 140752) ((-999 . -588) 140662) ((-999 . -590) 140551) ((-999 . -582) 140403) ((-999 . -654) 140255) ((-999 . -118) 140234) ((-999 . -120) 140213) ((-999 . -146) 140127) ((-999 . -495) 140061) ((-999 . -246) 139995) ((-999 . -47) 139956) ((-999 . -328) 139940) ((-999 . -580) 139888) ((-999 . -391) 139842) ((-999 . -455) 139705) ((-999 . -809) 139640) ((-999 . -806) 139538) ((-999 . -811) 139440) ((-999 . -796) NIL) ((-999 . -821) 139419) ((-999 . -1133) 139398) ((-999 . -861) 139343) ((-999 . -260) 139330) ((-999 . -190) 139309) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -552) 139291) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1060) T) ((-999 . -663) T) ((-999 . -961) T) ((-999 . -186) 139239) ((-999 . -13) T) ((-999 . -1128) T) ((-999 . -189) 139193) ((-999 . -225) 139177) ((-999 . -184) 139161) ((-997 . -552) 139143) ((-994 . -756) T) ((-994 . -552) 139125) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1128) T) ((-994 . -759) T) ((-994 . -553) 139106) ((-991 . -661) 139085) ((-991 . -950) 138983) ((-991 . -354) 138967) ((-991 . -580) 138915) ((-991 . -590) 138792) ((-991 . -328) 138776) ((-991 . -321) 138755) ((-991 . -120) 138734) ((-991 . -555) 138559) ((-991 . -654) 138433) ((-991 . -582) 138307) ((-991 . -588) 138205) ((-991 . -968) 138118) ((-991 . -963) 138031) ((-991 . -82) 137923) ((-991 . -38) 137797) ((-991 . -352) 137776) ((-991 . -344) 137755) ((-991 . -118) 137709) ((-991 . -1065) 137688) ((-991 . -299) 137667) ((-991 . -319) 137621) ((-991 . -201) 137575) ((-991 . -246) 137529) ((-991 . -258) 137483) ((-991 . -391) 137437) ((-991 . -495) 137391) ((-991 . -832) 137345) ((-991 . -1133) 137299) ((-991 . -312) 137253) ((-991 . -190) 137181) ((-991 . -186) 137057) ((-991 . -189) 136939) ((-991 . -225) 136909) ((-991 . -806) 136781) ((-991 . -811) 136655) ((-991 . -809) 136588) ((-991 . -184) 136558) ((-991 . -553) 136542) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -552) 136524) ((-991 . -1128) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -961) T) ((-991 . -663) T) ((-991 . -1060) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -552) 136506) ((-989 . -1128) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 136485) ((-988 . -1013) T) ((-988 . -552) 136467) ((-988 . -1128) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -552) 136449) ((-987 . -1128) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 136428) ((-987 . -950) 136405) ((-987 . -555) 136382) ((-986 . -1128) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -429) 136363) ((-985 . -552) 136329) ((-985 . -555) 136310) ((-985 . -1013) T) ((-985 . -1128) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -429) 136291) ((-978 . -552) 136257) ((-978 . -555) 136238) ((-978 . -1013) T) ((-978 . -1128) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) 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135864) ((-974 . -72) T) ((-974 . -13) T) ((-974 . -1128) T) ((-974 . -552) 135846) ((-974 . -1013) T) ((-971 . -1128) T) ((-971 . -13) T) ((-971 . -1013) 135824) ((-971 . -552) 135791) ((-971 . -72) 135769) ((-966 . -965) 135709) ((-966 . -582) 135654) ((-966 . -654) 135599) ((-966 . -34) T) ((-966 . -260) 135537) ((-966 . -455) 135470) ((-966 . -428) 135454) ((-966 . -590) 135438) ((-966 . -588) 135407) ((-966 . -104) T) ((-966 . -25) T) ((-966 . -72) T) ((-966 . -13) T) ((-966 . -1128) T) ((-966 . -552) 135369) ((-966 . -1013) T) ((-966 . -23) T) ((-966 . -21) T) ((-966 . -968) 135353) ((-966 . -963) 135337) ((-966 . -82) 135316) ((-966 . -1186) 135286) ((-966 . -553) 135247) ((-958 . -983) 135176) ((-958 . -889) 135105) ((-958 . -553) 135047) ((-958 . -428) 135012) ((-958 . -1013) T) ((-958 . -455) 134896) ((-958 . -260) 134804) ((-958 . -552) 134747) ((-958 . -72) T) ((-958 . -1128) T) ((-958 . -13) T) ((-958 . -34) T) ((-958 . -124) 134712) ((-958 . -1123) 134641) ((-948 . -995) 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-72) T) ((-785 . -64) T) ((-785 . -1174) T) ((-783 . -1013) T) ((-783 . -552) 120541) ((-783 . -1128) T) ((-783 . -13) T) ((-783 . -72) T) ((-783 . -555) 120523) ((-782 . -1128) T) ((-782 . -13) T) ((-782 . -552) 120398) ((-782 . -1013) 120349) ((-782 . -72) 120300) ((-781 . -904) 120284) ((-781 . -1065) 120262) ((-781 . -950) 120129) ((-781 . -555) 120028) ((-781 . -553) 119831) ((-781 . -933) 119810) ((-781 . -821) 119789) ((-781 . -794) 119773) ((-781 . -755) 119752) ((-781 . -721) 119731) ((-781 . -718) 119710) ((-781 . -759) 119664) ((-781 . -756) 119618) ((-781 . -716) 119597) ((-781 . -714) 119576) ((-781 . -740) 119555) ((-781 . -796) 119480) ((-781 . -342) 119464) ((-781 . -580) 119412) ((-781 . -590) 119328) ((-781 . -328) 119312) ((-781 . -241) 119270) ((-781 . -260) 119235) ((-781 . -455) 119147) ((-781 . -288) 119131) ((-781 . -201) T) ((-781 . -82) 119062) ((-781 . -963) 119014) ((-781 . -968) 118966) ((-781 . -246) T) ((-781 . -654) 118918) ((-781 . -582) 118870) ((-781 . -588) 118807) ((-781 . -38) 118759) ((-781 . -258) T) ((-781 . -391) T) ((-781 . -146) T) ((-781 . -495) T) ((-781 . -832) T) ((-781 . -1133) T) ((-781 . -312) T) ((-781 . -190) 118738) ((-781 . -186) 118686) ((-781 . -189) 118640) ((-781 . -225) 118624) ((-781 . -806) 118548) ((-781 . -811) 118474) ((-781 . -809) 118433) ((-781 . -184) 118417) ((-781 . -120) 118371) ((-781 . -118) 118350) ((-781 . -104) T) ((-781 . -25) T) ((-781 . -72) T) ((-781 . -13) T) ((-781 . -1128) T) ((-781 . -552) 118332) ((-781 . -1013) T) ((-781 . -23) T) ((-781 . -21) T) ((-781 . -961) T) ((-781 . -663) T) ((-781 . -1060) T) ((-781 . -1025) T) ((-781 . -970) T) ((-780 . -904) 118309) ((-780 . -1065) NIL) ((-780 . -950) 118286) ((-780 . -555) 118216) ((-780 . -553) NIL) ((-780 . -933) NIL) ((-780 . -821) NIL) ((-780 . -794) 118193) ((-780 . -755) NIL) ((-780 . -721) NIL) ((-780 . -718) NIL) ((-780 . -759) NIL) ((-780 . -756) NIL) ((-780 . -716) NIL) ((-780 . -714) NIL) ((-780 . -740) NIL) ((-780 . -796) 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. -832) T) ((-778 . -495) T) ((-778 . -246) T) ((-778 . -146) T) ((-778 . -555) 117247) ((-778 . -654) 117234) ((-778 . -582) 117221) ((-778 . -968) 117208) ((-778 . -963) 117195) ((-778 . -82) 117180) ((-778 . -38) 117167) ((-778 . -391) T) ((-778 . -258) T) ((-778 . -961) T) ((-778 . -663) T) ((-778 . -1060) T) ((-778 . -1025) T) ((-778 . -970) T) ((-778 . -21) T) ((-778 . -588) 117139) ((-778 . -23) T) ((-778 . -1013) T) ((-778 . -552) 117121) ((-778 . -1128) T) ((-778 . -13) T) ((-778 . -72) T) ((-778 . -25) T) ((-778 . -104) T) ((-778 . -590) 117108) ((-778 . -120) T) ((-775 . -961) T) ((-775 . -663) T) ((-775 . -1060) T) ((-775 . -1025) T) ((-775 . -970) T) ((-775 . -21) T) ((-775 . -588) 117053) ((-775 . -23) T) ((-775 . -1013) T) ((-775 . -552) 117015) ((-775 . -1128) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -25) T) ((-775 . -104) T) ((-775 . -590) 116975) ((-775 . -555) 116910) ((-775 . -429) 116887) ((-775 . -38) 116857) ((-775 . -82) 116822) ((-775 . -963) 116792) 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((-741 . -21) T) ((-741 . -968) 113203) ((-741 . -963) 113187) ((-741 . -82) 113166) ((-741 . -961) T) ((-741 . -663) T) ((-741 . -1060) T) ((-741 . -1025) T) ((-741 . -970) T) ((-741 . -38) 113136) ((-741 . -190) 113115) ((-741 . -186) 113088) ((-741 . -189) 113067) ((-739 . -335) 113051) ((-739 . -555) 113035) ((-739 . -950) 113019) ((-739 . -759) T) ((-739 . -756) T) ((-739 . -1025) T) ((-739 . -72) T) ((-739 . -13) T) ((-739 . -1128) T) ((-739 . -552) 113001) ((-739 . -1013) T) ((-739 . -663) T) ((-739 . -754) T) ((-739 . -766) T) ((-738 . -228) 112985) ((-738 . -555) 112969) ((-738 . -950) 112953) ((-738 . -759) T) ((-738 . -72) T) ((-738 . -1013) T) ((-738 . -552) 112935) ((-738 . -756) T) ((-738 . -186) 112922) ((-738 . -13) T) ((-738 . -1128) T) ((-738 . -189) T) ((-737 . -82) 112857) ((-737 . -963) 112808) ((-737 . -968) 112759) ((-737 . -21) T) ((-737 . -588) 112695) ((-737 . -23) T) ((-737 . -1013) T) ((-737 . -552) 112664) ((-737 . -1128) T) ((-737 . -13) T) ((-737 . -72) T) ((-737 . -25) T) ((-737 . -104) T) ((-737 . -590) 112615) ((-737 . -190) T) ((-737 . -555) 112524) ((-737 . -970) T) ((-737 . -1025) T) ((-737 . -1060) T) ((-737 . -663) T) ((-737 . -961) T) ((-737 . -186) 112511) ((-737 . -189) T) ((-737 . -429) 112495) ((-737 . -312) 112474) ((-737 . -1133) 112453) ((-737 . -832) 112432) ((-737 . -495) 112411) ((-737 . -146) 112390) ((-737 . -654) 112327) ((-737 . -582) 112264) ((-737 . -38) 112201) ((-737 . -391) 112180) ((-737 . -258) 112159) ((-737 . -246) 112138) ((-737 . -201) 112117) ((-736 . -213) 112056) ((-736 . -555) 111800) ((-736 . -950) 111630) ((-736 . -553) NIL) ((-736 . -277) 111592) ((-736 . -354) 111576) ((-736 . -38) 111428) ((-736 . -82) 111253) ((-736 . -963) 111099) ((-736 . -968) 110945) ((-736 . -588) 110855) ((-736 . -590) 110744) ((-736 . -582) 110596) ((-736 . -654) 110448) ((-736 . -118) 110427) ((-736 . -120) 110406) ((-736 . -146) 110320) ((-736 . -495) 110254) ((-736 . -246) 110188) ((-736 . -47) 110150) ((-736 . 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102795) ((-704 . -580) 102743) ((-704 . -809) 102687) ((-704 . -806) 102594) ((-704 . -811) 102505) ((-704 . -796) NIL) ((-704 . -821) 102484) ((-704 . -1133) 102463) ((-704 . -861) 102433) ((-704 . -832) 102412) ((-704 . -495) 102326) ((-704 . -246) 102240) ((-704 . -146) 102134) ((-704 . -391) 102068) ((-704 . -258) 102047) ((-704 . -241) 101974) ((-704 . -190) T) ((-704 . -104) T) ((-704 . -25) T) ((-704 . -72) T) ((-704 . -552) 101935) ((-704 . -1013) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1060) T) ((-704 . -663) T) ((-704 . -961) T) ((-704 . -186) 101922) ((-704 . -13) T) ((-704 . -1128) T) ((-704 . -189) T) ((-704 . -225) 101906) ((-704 . -184) 101890) ((-703 . -977) 101857) ((-703 . -553) 101492) ((-703 . -260) 101479) ((-703 . -455) 101431) ((-703 . -277) 101403) ((-703 . -950) 101262) ((-703 . -354) 101246) ((-703 . -38) 101098) ((-703 . -555) 100871) ((-703 . -590) 100760) ((-703 . -588) 100670) ((-703 . -970) T) ((-703 . -1025) T) 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-915) 60999) ((-413 . -201) 60978) ((-413 . -246) 60932) ((-413 . -104) T) ((-413 . -25) T) ((-413 . -72) T) ((-413 . -13) T) ((-413 . -1128) T) ((-413 . -552) 60914) ((-413 . -1013) T) ((-413 . -23) T) ((-413 . -21) T) ((-413 . -961) T) ((-413 . -663) T) ((-413 . -1060) T) ((-413 . -1025) T) ((-413 . -970) T) ((-413 . -258) 60893) ((-413 . -391) 60872) ((-413 . -146) 60806) ((-413 . -495) 60760) ((-413 . -832) 60739) ((-413 . -1133) 60718) ((-413 . -312) 60697) ((-407 . -1013) T) ((-407 . -552) 60679) ((-407 . -1128) T) ((-407 . -13) T) ((-407 . -72) T) ((-402 . -889) 60648) ((-402 . -553) 60609) ((-402 . -428) 60593) ((-402 . -1013) T) ((-402 . -455) 60526) ((-402 . -260) 60464) ((-402 . -552) 60426) ((-402 . -72) T) ((-402 . -1128) T) ((-402 . -13) T) ((-402 . -34) T) ((-402 . -124) 60410) ((-400 . -654) 60381) ((-400 . -582) 60352) ((-400 . -590) 60323) ((-400 . -588) 60279) ((-400 . -104) T) ((-400 . -25) T) ((-400 . -72) T) ((-400 . -13) T) ((-400 . -1128) T) ((-400 . -552) 60261) ((-400 . -1013) T) ((-400 . -23) T) ((-400 . -21) T) ((-400 . -968) 60232) ((-400 . -963) 60203) ((-400 . -82) 60164) ((-393 . -861) 60131) ((-393 . -555) 59923) ((-393 . -950) 59801) ((-393 . -1133) 59780) ((-393 . -821) 59759) ((-393 . -796) NIL) ((-393 . -811) 59736) ((-393 . -806) 59711) ((-393 . -809) 59688) ((-393 . -455) 59626) ((-393 . -391) 59580) ((-393 . -580) 59528) ((-393 . -590) 59417) ((-393 . -328) 59401) ((-393 . -47) 59380) ((-393 . -38) 59232) ((-393 . -582) 59084) ((-393 . -654) 58936) ((-393 . -246) 58870) ((-393 . -495) 58804) ((-393 . -82) 58629) ((-393 . -963) 58475) ((-393 . -968) 58321) ((-393 . -146) 58235) ((-393 . -120) 58214) ((-393 . -118) 58193) ((-393 . -588) 58103) ((-393 . -104) T) ((-393 . -25) T) ((-393 . -72) T) ((-393 . -13) T) ((-393 . -1128) T) ((-393 . -552) 58085) ((-393 . -1013) T) ((-393 . -23) T) ((-393 . -21) T) ((-393 . -961) T) ((-393 . -663) T) ((-393 . -1060) T) ((-393 . -1025) T) ((-393 . -970) T) ((-393 . -354) 58069) ((-393 . -277) 58048) ((-393 . -260) 58035) ((-393 . -553) 57896) ((-392 . -360) 57866) ((-392 . -683) 57836) ((-392 . -657) T) ((-392 . -685) T) ((-392 . -82) 57787) ((-392 . -963) 57757) ((-392 . -968) 57727) ((-392 . -21) T) ((-392 . -588) 57642) ((-392 . -23) T) ((-392 . -1013) T) ((-392 . -552) 57624) ((-392 . -72) T) ((-392 . -25) T) ((-392 . -104) T) ((-392 . -590) 57554) ((-392 . -582) 57524) ((-392 . -654) 57494) ((-392 . -316) 57464) ((-392 . -1128) T) ((-392 . -13) T) ((-392 . -241) 57427) ((-380 . -1013) T) ((-380 . -552) 57409) ((-380 . -1128) T) ((-380 . -13) T) ((-380 . -72) T) ((-379 . -1013) T) ((-379 . -552) 57391) ((-379 . -1128) T) ((-379 . -13) T) ((-379 . -72) T) ((-378 . -1013) T) ((-378 . -552) 57373) ((-378 . -1128) T) ((-378 . -13) T) ((-378 . -72) T) ((-376 . -552) 57355) ((-371 . -38) 57339) ((-371 . -555) 57308) ((-371 . -590) 57282) ((-371 . -588) 57241) ((-371 . -970) T) ((-371 . -1025) T) ((-371 . -1060) T) ((-371 . -663) T) ((-371 . -961) T) ((-371 . -82) 57220) 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. -241) 56072) ((-349 . -260) 56037) ((-349 . -455) 55949) ((-349 . -288) 55933) ((-349 . -201) T) ((-349 . -82) 55864) ((-349 . -963) 55816) ((-349 . -968) 55768) ((-349 . -246) T) ((-349 . -654) 55720) ((-349 . -582) 55672) ((-349 . -588) 55609) ((-349 . -38) 55561) ((-349 . -258) T) ((-349 . -391) T) ((-349 . -146) T) ((-349 . -495) T) ((-349 . -832) T) ((-349 . -1133) T) ((-349 . -312) T) ((-349 . -190) 55540) ((-349 . -186) 55488) ((-349 . -189) 55442) ((-349 . -225) 55426) ((-349 . -806) 55350) ((-349 . -811) 55276) ((-349 . -809) 55235) ((-349 . -184) 55219) ((-349 . -120) 55173) ((-349 . -118) 55152) ((-349 . -104) T) ((-349 . -25) T) ((-349 . -72) T) ((-349 . -13) T) ((-349 . -1128) T) ((-349 . -552) 55134) ((-349 . -1013) T) ((-349 . -23) T) ((-349 . -21) T) ((-349 . -961) T) ((-349 . -663) T) ((-349 . -1060) T) ((-349 . -1025) T) ((-349 . -970) T) ((-347 . -495) T) ((-347 . -246) T) ((-347 . -146) T) ((-347 . -555) 55043) ((-347 . -654) 55017) ((-347 . -582) 54991) ((-347 . -590) 54965) ((-347 . -588) 54924) ((-347 . -104) T) ((-347 . -25) T) ((-347 . -72) T) ((-347 . -13) T) ((-347 . -1128) T) ((-347 . -552) 54906) ((-347 . -1013) T) ((-347 . -23) T) ((-347 . -21) T) ((-347 . -968) 54880) ((-347 . -963) 54854) ((-347 . -82) 54821) ((-347 . -961) T) ((-347 . -663) T) ((-347 . -1060) T) ((-347 . -1025) T) ((-347 . -970) T) ((-347 . -38) 54795) ((-347 . -184) 54779) ((-347 . -809) 54738) ((-347 . -811) 54664) ((-347 . -806) 54588) ((-347 . -225) 54572) ((-347 . -189) 54526) ((-347 . -186) 54474) ((-347 . -190) 54453) ((-347 . -288) 54437) ((-347 . -455) 54279) ((-347 . -260) 54218) ((-347 . -241) 54146) ((-347 . -354) 54130) ((-347 . -950) 54028) ((-347 . -391) 53981) ((-347 . -933) 53960) ((-347 . -553) 53863) ((-347 . -1133) 53841) ((-341 . -1013) T) ((-341 . -552) 53823) ((-341 . -1128) T) ((-341 . -13) T) ((-341 . -72) T) ((-341 . -189) T) ((-341 . -186) 53810) ((-341 . -553) 53787) ((-339 . -683) 53771) ((-339 . -657) T) ((-339 . -685) T) ((-339 . -82) 53750) ((-339 . -963) 53734) ((-339 . -968) 53718) ((-339 . -21) T) ((-339 . -588) 53687) ((-339 . -23) T) ((-339 . -1013) T) ((-339 . -552) 53669) ((-339 . -1128) T) ((-339 . -13) T) ((-339 . -72) T) ((-339 . -25) T) ((-339 . -104) T) ((-339 . -590) 53653) ((-339 . -582) 53637) ((-339 . -654) 53621) ((-337 . -338) T) ((-337 . -72) T) ((-337 . -13) T) ((-337 . -1128) T) ((-337 . -552) 53587) ((-337 . -1013) T) ((-337 . -555) 53568) ((-337 . -429) 53549) ((-336 . -335) 53533) ((-336 . -555) 53517) ((-336 . -950) 53501) ((-336 . -759) 53480) ((-336 . -756) 53459) ((-336 . -1025) T) ((-336 . -72) T) ((-336 . -13) T) ((-336 . -1128) T) ((-336 . -552) 53441) ((-336 . -1013) T) ((-336 . -663) T) ((-333 . -334) 53420) ((-333 . -555) 53404) ((-333 . -950) 53388) ((-333 . -582) 53358) ((-333 . -654) 53328) ((-333 . -590) 53312) ((-333 . -588) 53281) ((-333 . -104) T) ((-333 . -25) T) ((-333 . -72) T) ((-333 . -13) T) ((-333 . -1128) T) ((-333 . -552) 53263) ((-333 . -1013) T) ((-333 . -23) T) 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((-329 . -258) T) ((-329 . -82) 52566) ((-329 . -963) 52531) ((-329 . -968) 52496) ((-329 . -246) T) ((-329 . -201) T) ((-329 . -755) T) ((-329 . -721) T) ((-329 . -718) T) ((-329 . -759) T) ((-329 . -756) T) ((-329 . -716) T) ((-329 . -714) T) ((-329 . -796) 52478) ((-329 . -915) T) ((-329 . -933) T) ((-329 . -950) 52438) ((-329 . -973) T) ((-329 . -190) T) ((-329 . -186) 52425) ((-329 . -189) T) ((-329 . -1114) T) ((-329 . -1117) T) ((-329 . -432) T) ((-329 . -239) T) ((-329 . -66) T) ((-329 . -35) T) ((-329 . -557) 52407) ((-313 . -314) 52384) ((-313 . -72) T) ((-313 . -13) T) ((-313 . -1128) T) ((-313 . -552) 52366) ((-313 . -1013) T) ((-310 . -412) T) ((-310 . -1025) T) ((-310 . -72) T) ((-310 . -13) T) ((-310 . -1128) T) ((-310 . -552) 52348) ((-310 . -1013) T) ((-310 . -663) T) ((-310 . -950) 52332) ((-310 . -555) 52316) ((-308 . -280) 52300) ((-308 . -190) 52279) ((-308 . -186) 52252) ((-308 . -189) 52231) ((-308 . -319) 52210) ((-308 . -1065) 52189) ((-308 . -299) 52168) ((-308 . -120) 52147) ((-308 . -555) 52084) ((-308 . -590) 52036) ((-308 . -588) 51973) ((-308 . -104) T) ((-308 . -25) T) ((-308 . -72) T) ((-308 . -13) T) ((-308 . -1128) T) ((-308 . -552) 51955) ((-308 . -1013) T) ((-308 . -23) T) ((-308 . -21) T) ((-308 . -970) T) ((-308 . -1025) T) ((-308 . -1060) T) ((-308 . -663) T) ((-308 . -961) T) ((-308 . -312) T) ((-308 . -1133) T) ((-308 . -832) T) ((-308 . -495) T) ((-308 . -146) T) ((-308 . -654) 51907) ((-308 . -582) 51859) ((-308 . -38) 51824) ((-308 . -391) T) ((-308 . -258) T) ((-308 . -82) 51755) ((-308 . -963) 51707) ((-308 . -968) 51659) ((-308 . -246) T) ((-308 . -201) T) ((-308 . -344) 51613) ((-308 . -118) 51567) ((-308 . -950) 51551) ((-308 . -1186) 51535) ((-308 . -1197) 51519) ((-304 . -280) 51503) ((-304 . -190) 51482) ((-304 . -186) 51455) ((-304 . -189) 51434) ((-304 . -319) 51413) ((-304 . -1065) 51392) ((-304 . -299) 51371) ((-304 . -120) 51350) ((-304 . -555) 51287) ((-304 . -590) 51239) ((-304 . -588) 51176) ((-304 . 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50361) ((-303 . -1013) T) ((-303 . -23) T) ((-303 . -21) T) ((-303 . -970) T) ((-303 . -1025) T) ((-303 . -1060) T) ((-303 . -663) T) ((-303 . -961) T) ((-303 . -312) T) ((-303 . -1133) T) ((-303 . -832) T) ((-303 . -495) T) ((-303 . -146) T) ((-303 . -654) 50313) ((-303 . -582) 50265) ((-303 . -38) 50230) ((-303 . -391) T) ((-303 . -258) T) ((-303 . -82) 50161) ((-303 . -963) 50113) ((-303 . -968) 50065) ((-303 . -246) T) ((-303 . -201) T) ((-303 . -344) 50019) ((-303 . -118) 49973) ((-303 . -950) 49957) ((-303 . -1186) 49941) ((-303 . -1197) 49925) ((-302 . -280) 49909) ((-302 . -190) 49888) ((-302 . -186) 49861) ((-302 . -189) 49840) ((-302 . -319) 49819) ((-302 . -1065) 49798) ((-302 . -299) 49777) ((-302 . -120) 49756) ((-302 . -555) 49693) ((-302 . -590) 49645) ((-302 . -588) 49582) ((-302 . -104) T) ((-302 . -25) T) ((-302 . -72) T) ((-302 . -13) T) ((-302 . -1128) T) ((-302 . -552) 49564) ((-302 . -1013) T) ((-302 . -23) T) ((-302 . -21) T) ((-302 . -970) T) ((-302 . -1025) T) 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. -495) T) ((-301 . -146) T) ((-301 . -654) 48806) ((-301 . -582) 48751) ((-301 . -38) 48716) ((-301 . -391) T) ((-301 . -258) T) ((-301 . -82) 48633) ((-301 . -963) 48578) ((-301 . -968) 48523) ((-301 . -246) T) ((-301 . -201) T) ((-301 . -344) T) ((-301 . -118) T) ((-301 . -950) 48500) ((-301 . -1186) 48477) ((-301 . -1197) 48454) ((-295 . -280) 48438) ((-295 . -190) 48417) ((-295 . -186) 48390) ((-295 . -189) 48369) ((-295 . -319) 48348) ((-295 . -1065) 48327) ((-295 . -299) 48306) ((-295 . -120) 48285) ((-295 . -555) 48222) ((-295 . -590) 48174) ((-295 . -588) 48111) ((-295 . -104) T) ((-295 . -25) T) ((-295 . -72) T) ((-295 . -13) T) ((-295 . -1128) T) ((-295 . -552) 48093) ((-295 . -1013) T) ((-295 . -23) T) ((-295 . -21) T) ((-295 . -970) T) ((-295 . -1025) T) ((-295 . -1060) T) ((-295 . -663) T) ((-295 . -961) T) ((-295 . -312) T) ((-295 . -1133) T) ((-295 . -832) T) ((-295 . -495) T) ((-295 . -146) T) ((-295 . -654) 48045) ((-295 . -582) 47997) ((-295 . -38) 47962) ((-295 . 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. -23) T) ((-177 . -1013) T) ((-177 . -552) 16389) ((-177 . -1128) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -950) 16366) ((-176 . -214) 16350) ((-176 . -1034) 16334) ((-176 . -76) 16318) ((-176 . -34) T) ((-176 . -13) T) ((-176 . -1128) T) ((-176 . -72) 16272) ((-176 . -552) 16207) ((-176 . -260) 16145) ((-176 . -455) 16078) ((-176 . -1013) 16056) ((-176 . -428) 16040) ((-176 . -908) 16024) ((-172 . -995) T) ((-172 . -429) 16005) ((-172 . -552) 15971) ((-172 . -555) 15952) ((-172 . -1013) T) ((-172 . -1128) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -904) 15934) ((-171 . -1065) T) ((-171 . -555) 15884) ((-171 . -950) 15844) ((-171 . -553) 15774) ((-171 . -933) T) ((-171 . -821) NIL) ((-171 . -794) 15756) ((-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) 15738) ((-171 . -342) 15720) ((-171 . -580) 15702) ((-171 . -328) 15684) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -455) NIL) ((-171 . -288) 15666) ((-171 . -201) T) ((-171 . -82) 15593) ((-171 . -963) 15543) ((-171 . -968) 15493) ((-171 . -246) T) ((-171 . -654) 15443) ((-171 . -582) 15393) ((-171 . -590) 15343) ((-171 . -588) 15293) ((-171 . -38) 15243) ((-171 . -258) T) ((-171 . -391) T) ((-171 . -146) T) ((-171 . -495) T) ((-171 . -832) T) ((-171 . -1133) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15230) ((-171 . -189) T) ((-171 . -225) 15212) ((-171 . -806) NIL) ((-171 . -811) NIL) ((-171 . -809) NIL) ((-171 . -184) 15194) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1128) T) ((-171 . -552) 15136) ((-171 . -1013) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -961) T) ((-171 . -663) T) ((-171 . -1060) T) ((-171 . -1025) T) ((-171 . -970) T) ((-168 . -752) T) ((-168 . -759) T) ((-168 . -756) T) ((-168 . -1013) T) ((-168 . -552) 15118) ((-168 . -1128) T) 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-429) 10756) ((-135 . -552) 10722) ((-135 . -555) 10703) ((-135 . -1013) T) ((-135 . -1128) T) ((-135 . -13) T) ((-135 . -72) T) ((-135 . -64) T) ((-134 . -1013) T) ((-134 . -552) 10685) ((-134 . -1128) T) ((-134 . -13) T) ((-134 . -72) T) ((-130 . -25) T) ((-130 . -72) T) ((-130 . -13) T) ((-130 . -1128) T) ((-130 . -552) 10667) ((-130 . -1013) T) ((-129 . -995) T) ((-129 . -429) 10648) ((-129 . -552) 10614) ((-129 . -555) 10595) ((-129 . -1013) T) ((-129 . -1128) T) ((-129 . -13) T) ((-129 . -72) T) ((-129 . -64) T) ((-127 . -995) T) ((-127 . -429) 10576) ((-127 . -552) 10542) ((-127 . -555) 10523) ((-127 . -1013) T) ((-127 . -1128) T) ((-127 . -13) T) ((-127 . -72) T) ((-127 . -64) T) ((-125 . -961) T) ((-125 . -663) T) ((-125 . -1060) T) ((-125 . -1025) T) ((-125 . -970) T) ((-125 . -21) T) ((-125 . -588) 10482) ((-125 . -23) T) ((-125 . -1013) T) ((-125 . -552) 10464) ((-125 . -1128) T) ((-125 . -13) T) ((-125 . -72) T) ((-125 . -25) T) ((-125 . -104) T) ((-125 . -590) 10438) 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. -553) NIL) ((-102 . -428) 9347) ((-102 . -1013) T) ((-102 . -455) NIL) ((-102 . -260) NIL) ((-102 . -552) 9291) ((-102 . -72) T) ((-102 . -1128) T) ((-102 . -13) T) ((-102 . -34) T) ((-102 . -124) 9273) ((-102 . -756) T) ((-102 . -759) T) ((-102 . -323) 9255) ((-101 . -752) T) ((-101 . -759) T) ((-101 . -756) T) ((-101 . -1013) T) ((-101 . -552) 9237) ((-101 . -1128) T) ((-101 . -13) T) ((-101 . -72) T) ((-101 . -319) T) ((-101 . -604) T) ((-100 . -98) 9221) ((-100 . -923) 9205) ((-100 . -34) T) ((-100 . -13) T) ((-100 . -1128) T) ((-100 . -72) 9159) ((-100 . -552) 9094) ((-100 . -260) 9032) ((-100 . -455) 8965) ((-100 . -1013) 8943) ((-100 . -428) 8927) ((-100 . -92) 8911) ((-99 . -98) 8895) ((-99 . -923) 8879) ((-99 . -34) T) ((-99 . -13) T) ((-99 . -1128) T) ((-99 . -72) 8833) ((-99 . -552) 8768) ((-99 . -260) 8706) ((-99 . -455) 8639) ((-99 . -1013) 8617) ((-99 . -428) 8601) ((-99 . -92) 8585) ((-94 . -98) 8569) ((-94 . -923) 8553) ((-94 . -34) T) ((-94 . -13) T) ((-94 . -1128) T) ((-94 . -72) 8507) ((-94 . -552) 8442) ((-94 . -260) 8380) ((-94 . -455) 8313) ((-94 . -1013) 8291) ((-94 . -428) 8275) ((-94 . -92) 8259) ((-90 . -904) 8237) ((-90 . -1065) NIL) ((-90 . -950) 8215) ((-90 . -555) 8146) ((-90 . -553) NIL) ((-90 . -933) NIL) ((-90 . -821) NIL) ((-90 . -794) 8124) ((-90 . -755) NIL) ((-90 . -721) NIL) ((-90 . -718) NIL) ((-90 . -759) NIL) ((-90 . -756) NIL) ((-90 . -716) NIL) ((-90 . -714) NIL) ((-90 . -740) NIL) ((-90 . -796) NIL) ((-90 . -342) 8102) ((-90 . -580) 8080) ((-90 . -590) 8026) ((-90 . -328) 8004) ((-90 . -241) 7938) ((-90 . -260) 7885) ((-90 . -455) 7755) ((-90 . -288) 7733) ((-90 . -201) T) ((-90 . -82) 7652) ((-90 . -963) 7598) ((-90 . -968) 7544) ((-90 . -246) T) ((-90 . -654) 7490) ((-90 . -582) 7436) ((-90 . -588) 7367) ((-90 . -38) 7313) ((-90 . -258) T) ((-90 . -391) T) ((-90 . -146) T) ((-90 . -495) T) ((-90 . -832) T) ((-90 . -1133) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7291) ((-90 . -806) NIL) ((-90 . -811) NIL) ((-90 . -809) NIL) ((-90 . -184) 7269) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1128) T) ((-90 . -552) 7251) ((-90 . -1013) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -961) T) ((-90 . -663) T) ((-90 . -1060) T) ((-90 . -1025) T) ((-90 . -970) T) ((-89 . -779) 7235) ((-89 . -832) T) ((-89 . -495) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -555) 7207) ((-89 . -654) 7194) ((-89 . -582) 7181) ((-89 . -968) 7168) ((-89 . -963) 7155) ((-89 . -82) 7140) ((-89 . -38) 7127) ((-89 . -391) T) ((-89 . -258) T) ((-89 . -961) T) ((-89 . -663) T) ((-89 . -1060) T) ((-89 . -1025) T) ((-89 . -970) T) ((-89 . -21) T) ((-89 . -588) 7099) ((-89 . -23) T) ((-89 . -1013) T) ((-89 . -552) 7081) ((-89 . -1128) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -590) 7068) ((-89 . -120) T) ((-86 . -756) T) ((-86 . -552) 7050) ((-86 . -1013) T) ((-86 . -72) T) ((-86 . -13) T) 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((-77 . -755) T) ((-77 . -721) T) ((-77 . -718) T) ((-77 . -759) T) ((-77 . -756) T) ((-77 . -716) T) ((-77 . -714) T) ((-77 . -740) T) ((-77 . -796) 6485) ((-77 . -342) 6467) ((-77 . -580) 6449) ((-77 . -328) 6431) ((-77 . -241) NIL) ((-77 . -260) NIL) ((-77 . -455) NIL) ((-77 . -288) 6413) ((-77 . -201) T) ((-77 . -82) 6340) ((-77 . -963) 6290) ((-77 . -968) 6240) ((-77 . -246) T) ((-77 . -654) 6190) ((-77 . -582) 6140) ((-77 . -590) 6090) ((-77 . -588) 6040) ((-77 . -38) 5990) ((-77 . -258) T) ((-77 . -391) T) ((-77 . -146) T) ((-77 . -495) T) ((-77 . -832) T) ((-77 . -1133) T) ((-77 . -312) T) ((-77 . -190) T) ((-77 . -186) 5977) ((-77 . -189) T) ((-77 . -225) 5959) ((-77 . -806) NIL) ((-77 . -811) NIL) ((-77 . -809) NIL) ((-77 . -184) 5941) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1128) T) ((-77 . -552) 5884) ((-77 . -1013) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -961) T) ((-77 . -663) T) ((-77 . -1060) T) ((-77 . -1025) T) ((-77 . -970) T) ((-73 . -98) 5868) ((-73 . -923) 5852) ((-73 . -34) T) ((-73 . -13) T) ((-73 . -1128) T) ((-73 . -72) 5806) ((-73 . -552) 5741) ((-73 . -260) 5679) ((-73 . -455) 5612) ((-73 . -1013) 5590) ((-73 . -428) 5574) ((-73 . -92) 5558) ((-69 . -412) T) ((-69 . -1025) T) ((-69 . -72) T) ((-69 . -13) T) ((-69 . -1128) T) ((-69 . -552) 5540) ((-69 . -1013) T) ((-69 . -663) T) ((-69 . -241) 5519) ((-67 . -995) T) ((-67 . -429) 5500) ((-67 . -552) 5466) ((-67 . -555) 5447) ((-67 . -1013) T) ((-67 . -1128) T) ((-67 . -13) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1034) 5431) ((-62 . -428) 5415) ((-62 . -1013) 5393) ((-62 . -455) 5326) ((-62 . -260) 5264) ((-62 . -552) 5199) ((-62 . -72) 5153) ((-62 . -1128) T) ((-62 . -13) T) ((-62 . -34) T) ((-62 . -76) 5137) ((-60 . -57) 5099) ((-60 . -34) T) ((-60 . -13) T) ((-60 . -1128) T) ((-60 . -72) 5053) ((-60 . -552) 4988) ((-60 . -260) 4926) ((-60 . -455) 4859) ((-60 . -1013) 4837) ((-60 . -428) 4821) ((-58 . -19) 4805) ((-58 . -593) 4789) ((-58 . -243) 4766) ((-58 . -241) 4718) ((-58 . -538) 4695) ((-58 . -553) 4656) ((-58 . -428) 4640) ((-58 . -1013) 4593) ((-58 . -455) 4526) ((-58 . -260) 4464) ((-58 . -552) 4379) ((-58 . -72) 4313) ((-58 . -1128) T) ((-58 . -13) T) ((-58 . -34) T) ((-58 . -124) 4297) ((-58 . -756) 4276) ((-58 . -759) 4255) ((-58 . -323) 4239) ((-55 . -1013) T) ((-55 . -552) 4221) ((-55 . -1128) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -950) 4203) ((-55 . -555) 4185) ((-51 . -1013) T) ((-51 . -552) 4167) ((-51 . -1128) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -560) 4151) ((-50 . -555) 4120) ((-50 . -590) 4094) ((-50 . -588) 4053) ((-50 . -970) T) ((-50 . -1025) T) ((-50 . -1060) T) ((-50 . -663) T) ((-50 . -961) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1013) T) ((-50 . -552) 4035) ((-50 . -1128) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -950) 4019) ((-49 . -1013) T) ((-49 . -552) 4001) ((-49 . -1128) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -254) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1128) T) ((-48 . -552) 3983) ((-48 . -1013) T) ((-48 . -555) 3884) ((-48 . -950) 3827) ((-48 . -455) 3793) ((-48 . -260) 3780) ((-48 . -27) T) ((-48 . -915) T) ((-48 . -201) T) ((-48 . -82) 3729) ((-48 . -963) 3694) ((-48 . -968) 3659) ((-48 . -246) T) ((-48 . -654) 3624) ((-48 . -582) 3589) ((-48 . -590) 3539) ((-48 . -588) 3489) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -961) T) ((-48 . -663) T) ((-48 . -1060) T) ((-48 . -1025) T) ((-48 . -970) T) ((-48 . -38) 3454) ((-48 . -258) T) ((-48 . -391) T) ((-48 . -146) T) ((-48 . -495) T) ((-48 . -832) T) ((-48 . -1133) T) ((-48 . -312) T) ((-48 . -580) 3414) ((-48 . -933) T) ((-48 . -553) 3359) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3346) ((-48 . -189) T) ((-45 . -36) 3325) ((-45 . -538) 3248) ((-45 . -260) 3046) ((-45 . -455) 2798) ((-45 . -428) 2733) ((-45 . -241) 2631) ((-45 . -243) 2554) ((-45 . -549) 2533) ((-45 . -193) 2481) ((-45 . -76) 2429) ((-45 . -183) 2377) ((-45 . -1106) 2356) ((-45 . -237) 2304) ((-45 . -124) 2252) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1128) T) ((-45 . -72) T) ((-45 . -552) 2234) ((-45 . -1013) T) ((-45 . -553) NIL) ((-45 . -593) 2182) ((-45 . -323) 2130) ((-45 . -759) NIL) ((-45 . -756) NIL) ((-45 . -1063) 2078) ((-45 . -923) 2026) ((-45 . -1167) 1974) ((-45 . -608) 1922) ((-44 . -360) 1906) ((-44 . -683) 1890) ((-44 . -657) T) ((-44 . -685) T) ((-44 . -82) 1869) ((-44 . -963) 1853) ((-44 . -968) 1837) ((-44 . -21) T) ((-44 . -588) 1780) ((-44 . -23) T) ((-44 . -1013) T) ((-44 . -552) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -104) T) ((-44 . -590) 1720) ((-44 . -582) 1704) ((-44 . -654) 1688) ((-44 . -316) 1672) ((-44 . -1128) T) ((-44 . -13) T) ((-44 . -241) 1649) ((-40 . -291) 1623) ((-40 . -146) T) ((-40 . -555) 1553) ((-40 . -970) T) ((-40 . -1025) T) ((-40 . -1060) T) ((-40 . -663) T) ((-40 . -961) T) ((-40 . -590) 1455) ((-40 . -588) 1385) ((-40 . -104) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -13) T) ((-40 . -1128) T) ((-40 . -552) 1367) ((-40 . -1013) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -968) 1312) ((-40 . -963) 1257) ((-40 . -82) 1174) ((-40 . -553) 1158) ((-40 . -184) 1135) ((-40 . -809) 1087) ((-40 . -811) 999) ((-40 . -806) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -312) T) ((-40 . -1133) T) ((-40 . -832) T) ((-40 . -495) T) ((-40 . -654) 677) ((-40 . -582) 622) ((-40 . -38) 567) ((-40 . -391) T) ((-40 . -258) T) ((-40 . -246) T) ((-40 . -201) T) ((-40 . -319) NIL) ((-40 . -299) NIL) ((-40 . -1065) NIL) ((-40 . -118) 539) ((-40 . -344) NIL) ((-40 . -352) 511) ((-40 . -120) 483) ((-40 . -321) 455) ((-40 . -328) 432) ((-40 . -580) 366) ((-40 . -354) 343) ((-40 . -950) 220) ((-40 . -661) 192) ((-31 . -995) T) ((-31 . -429) 173) ((-31 . -552) 139) ((-31 . -555) 120) ((-31 . -1013) T) ((-31 . -1128) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -866) T) ((-30 . -552) 102) ((0 . |EnumerationCategory|) T) ((0 . -552) 84) ((0 . -1013) T) ((0 . -72) T) ((0 . -1128) T) ((-2 . |RecordCategory|) T) ((-2 . -552) 66) ((-2 . -1013) T) ((-2 . -72) T) ((-2 . -1128) T) ((-3 . |UnionCategory|) T) ((-3 . -552) 48) ((-3 . -1013) T) ((-3 . -72) T) ((-3 . -1128) T) ((-1 . -1013) T) ((-1 . -552) 30) ((-1 . -1128) T) ((-1 . -13) T) ((-1 . -72) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index c13a83a2..469090b4 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3577545197)            
-(3996 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3577666330)            
+(3997 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -98,19 +98,20 @@
  |FiniteFieldPolynomialPackage| |FiniteFieldPolynomialPackage2|
  |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension|
  |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |File| |FileCategory|
- |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite&|
- |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregate&|
- |FiniteLinearAggregate| |FiniteLinearAggregateFunctions2| |FreeLieAlgebra|
- |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&|
- |FullyLinearlyExplicitRingOver| |Float| |FloatingComplexPackage|
- |FloatingRealPackage| |FreeModule| |FreeModule1| |FreeModuleCat|
- |FreeMonoidCategory| |FreeMonoid| |FileName| |FileNameCategory|
- |FreeNilpotentLie| |FindOrderFinite| |FullPartialFractionExpansion|
- |FullyPatternMatchable| |FieldOfPrimeCharacteristic&|
- |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem|
- |Factored| |FactoredFunctions2| |Fraction| |FractionFunctions2|
- |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo|
- |FractionalIdeal| |FractionalIdealFunctions2| |FramedModule|
+ |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra|
+ |FiniteAggregate| |Finite&| |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra|
+ |FiniteLinearAggregate&| |FiniteLinearAggregate|
+ |FiniteLinearAggregateFunctions2| |FreeLieAlgebra| |FiniteLinearAggregateSort|
+ |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |Float|
+ |FloatingComplexPackage| |FloatingRealPackage| |FreeModule| |FreeModule1|
+ |FreeModuleCat| |FreeMonoidCategory| |FreeMonoid| |FileName|
+ |FileNameCategory| |FreeNilpotentLie| |FindOrderFinite|
+ |FullPartialFractionExpansion| |FullyPatternMatchable|
+ |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic|
+ |FloatingPointSystem&| |FloatingPointSystem| |Factored| |FactoredFunctions2|
+ |Fraction| |FractionFunctions2| |FramedAlgebra&| |FramedAlgebra|
+ |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdeal|
+ |FractionalIdealFunctions2| |FramedModule|
  |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&|
  |FramedNonAssociativeAlgebra| |FactoredFunctionUtilities| |FunctionSpace&|
  |FunctionSpace| |FunctionSpaceFunctions2|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index e427ef94..ec690a56 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4039 +1,4044 @@
 
-(2809135 . 3577545205)       
-((-1730 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1728 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3786 ((|#2| $ (-483) |#2|) NIL T ELT) ((|#2| $ (-1144 (-483)) |#2|) 44 T ELT)) (-2296 (($ $) 80 T ELT)) (-3840 ((|#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)) (-3417 (((-483) (-1 (-85) |#2|) $) 27 T ELT) (((-483) |#2| $) NIL T ELT) (((-483) |#2| $ (-483)) 96 T ELT)) (-2888 (((-582 |#2|) $) 13 T ELT)) (-3516 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1947 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3956 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2303 (($ |#2| $ (-483)) NIL T ELT) (($ $ $ (-483)) 67 T ELT)) (-1352 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1945 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3798 ((|#2| $ (-483) |#2|) NIL T ELT) ((|#2| $ (-483)) NIL T ELT) (($ $ (-1144 (-483))) 66 T ELT)) (-2304 (($ $ (-483)) 76 T ELT) (($ $ (-1144 (-483))) 75 T ELT)) (-1944 (((-693) (-1 (-85) |#2|) $) 34 T ELT) (((-693) |#2| $) NIL T ELT)) (-1729 (($ $ $ (-483)) 69 T ELT)) (-3398 (($ $) 68 T ELT)) (-3528 (($ (-582 |#2|)) 73 T ELT)) (-3800 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-582 $)) 85 T ELT)) (-3944 (((-771) $) 92 T ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3055 (((-85) $ $) 95 T ELT)) (-2684 (((-85) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -7 (-15 -3055 ((-85) |#1| |#1|)) (-15 -3944 ((-771) |#1|)) (-15 -2684 ((-85) |#1| |#1|)) (-15 -1728 (|#1| |#1|)) (-15 -1728 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2296 (|#1| |#1|)) (-15 -1729 (|#1| |#1| |#1| (-483))) (-15 -1730 ((-85) |#1|)) (-15 -3516 (|#1| |#1| |#1|)) (-15 -3417 ((-483) |#2| |#1| (-483))) (-15 -3417 ((-483) |#2| |#1|)) (-15 -3417 ((-483) (-1 (-85) |#2|) |#1|)) (-15 -1730 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3516 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -3786 (|#2| |#1| (-1144 (-483)) |#2|)) (-15 -2303 (|#1| |#1| |#1| (-483))) (-15 -2303 (|#1| |#2| |#1| (-483))) (-15 -2304 (|#1| |#1| (-1144 (-483)))) (-15 -2304 (|#1| |#1| (-483))) (-15 -3956 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3800 (|#1| (-582 |#1|))) (-15 -3800 (|#1| |#1| |#1|)) (-15 -3800 (|#1| |#2| |#1|)) (-15 -3800 (|#1| |#1| |#2|)) (-15 -3798 (|#1| |#1| (-1144 (-483)))) (-15 -3528 (|#1| (-582 |#2|))) (-15 -1352 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -3840 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3840 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3840 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3798 (|#2| |#1| (-483))) (-15 -3798 (|#2| |#1| (-483) |#2|)) (-15 -3786 (|#2| |#1| (-483) |#2|)) (-15 -1944 ((-693) |#2| |#1|)) (-15 -2888 ((-582 |#2|) |#1|)) (-15 -1944 ((-693) (-1 (-85) |#2|) |#1|)) (-15 -1945 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1946 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1947 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3956 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3398 (|#1| |#1|))) (-19 |#2|) (-1127)) (T -18)) 
+(2811729 . 3577666338)       
+((-1731 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1729 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3787 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-1145 (-484)) |#2|) 44 T ELT)) (-2297 (($ $) 80 T ELT)) (-3841 ((|#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)) (-3418 (((-484) (-1 (-85) |#2|) $) 27 T ELT) (((-484) |#2| $) NIL T ELT) (((-484) |#2| $ (-484)) 96 T ELT)) (-2889 (((-583 |#2|) $) 13 T ELT)) (-3517 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1948 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3957 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2304 (($ |#2| $ (-484)) NIL T ELT) (($ $ $ (-484)) 67 T ELT)) (-1353 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3799 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-484)) NIL T ELT) (($ $ (-1145 (-484))) 66 T ELT)) (-2305 (($ $ (-484)) 76 T ELT) (($ $ (-1145 (-484))) 75 T ELT)) (-1945 (((-694) (-1 (-85) |#2|) $) 34 T ELT) (((-694) |#2| $) NIL T ELT)) (-1730 (($ $ $ (-484)) 69 T ELT)) (-3399 (($ $) 68 T ELT)) (-3529 (($ (-583 |#2|)) 73 T ELT)) (-3801 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-583 $)) 85 T ELT)) (-3945 (((-772) $) 92 T ELT)) (-1947 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3056 (((-85) $ $) 95 T ELT)) (-2685 (((-85) $ $) 99 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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 (((-38 |#1|) (-113) (-146)) (T -38)) 
 NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-554 (-483)) . T) ((-554 |#1|) . T) ((-551 (-771)) . T) ((-13) . T) ((-587 (-483)) . T) ((-587 |#1|) . T) ((-587 $) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-581 |#1|) . T) ((-653 |#1|) . T) ((-662) . T) ((-962 |#1|) . T) ((-967 |#1|) . T) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T)) 
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-NIL 
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 (((-64) (-113)) (T -64)) 
 NIL 
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 NIL 
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 NIL 
 (((-68) (-113)) (T -68)) 
 NIL 
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-NIL 
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 (((-146) (-113)) (T -146)) 
 NIL 
-(-13 (-960) (-82 $ $) (-10 -7 (-6 (-3995 "*")))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-554 (-483)) . T) ((-551 (-771)) . T) ((-13) . T) ((-587 (-483)) . T) ((-587 $) . T) ((-589 $) . T) ((-662) . T) ((-962 $) . T) ((-967 $) . T) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T)) 
-((-1698 (($ $) 6 T ELT))) 
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-NIL 
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-NIL 
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+NIL 
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 NIL 
 (-13 (-193 |t#1|)) 
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-NIL 
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-((-2668 ((|#2| $) 9 T ELT))) 
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-NIL 
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-(((-13) . T) ((-1127) . T)) 
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-(((-187 |#1|) (-113) (-960)) (T -187)) 
-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-551 (-771)) . T) ((-186 $) . T) ((-189) . T) ((-13) . T) ((-587 (-483)) . T) ((-587 |#1|) . T) ((-589 |#1|) . T) ((-581 |#1|) |has| |#1| (-146)) ((-653 |#1|) |has| |#1| (-146)) ((-962 |#1|) . T) ((-967 |#1|) . T) ((-1012) . T) ((-1127) . T)) 
-((-3756 (($ $) NIL T ELT) (($ $ (-693)) 9 T ELT)) (-2668 (($ $) NIL T ELT) (($ $ (-693)) 11 T ELT))) 
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-NIL 
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+NIL 
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 (((-190) (-113)) (T -190)) 
 NIL 
-(-13 (-960) (-189)) 
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 (((-191) (-113)) (T -191)) 
 NIL 
-(-13 (-715) (-1059)) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-551 (-771)) . T) ((-13) . T) ((-662) . T) ((-715) . T) ((-717) . T) ((-755) . T) ((-758) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T)) 
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-NIL 
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(-961))) ELT) (($ $ (-583 (-1089))) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-1089)) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-961)) ELT) (($ $ (-1 |#2| |#2|) (-694)) NIL (|has| |#2| (-961)) ELT)) (-1945 (((-694) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3994)) ELT) (((-694) |#2| $) NIL (-12 (|has| $ (-6 -3994)) (|has| |#2| (-1013))) ELT)) (-3399 (($ $) NIL T ELT)) (-3945 (((-1178 |#2|) $) 9 T ELT) (($ (-484)) NIL (OR (-12 (|has| |#2| (-950 (-484))) (|has| |#2| (-1013))) (|has| |#2| (-961))) ELT) (($ (-349 (-484))) NIL (-12 (|has| |#2| (-950 (-349 (-484)))) (|has| |#2| (-1013))) ELT) (($ |#2|) 12 (|has| |#2| (-1013)) ELT) (((-772) $) NIL (|has| |#2| (-552 (-772))) ELT)) (-3126 (((-694)) NIL (|has| |#2| (-961)) CONST)) (-1264 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-1947 (((-85) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3994)) ELT)) (-3125 (((-85) $ $) NIL (|has| |#2| (-961)) ELT)) (-2660 (($) 37 (|has| |#2| (-23)) CONST)) (-2666 (($) 41 (|has| |#2| (-961)) CONST)) (-2669 (($ $ (-694)) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) ELT) (($ $) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) ELT) (($ $ (-583 (-1089)) (-583 (-694))) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-1089) (-694)) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-583 (-1089))) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-1089)) NIL (-12 (|has| |#2| (-811 (-1089))) (|has| |#2| (-961))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-961)) ELT) (($ $ (-1 |#2| |#2|) (-694)) NIL (|has| |#2| (-961)) ELT)) (-2566 (((-85) $ $) NIL (|has| |#2| (-756)) ELT)) (-2567 (((-85) $ $) NIL (|has| |#2| (-756)) ELT)) (-3056 (((-85) $ $) 28 (|has| |#2| (-72)) ELT)) (-2684 (((-85) $ $) NIL (|has| |#2| (-756)) ELT)) (-2685 (((-85) $ $) 67 (|has| |#2| (-756)) ELT)) (-3948 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3836 (($ $ $) NIL (|has| |#2| (-21)) ELT) 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+(((-197 |#1| |#2|) (-196 |#1| |#2|) (-694) (-1128)) (T -197)) 
+NIL 
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+((-3957 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-197 *5 *6)) (-14 *5 (-694)) (-4 *6 (-1128)) (-4 *7 (-1128)) (-5 *2 (-197 *5 *7)) (-5 *1 (-198 *5 *6 *7)))) (-3841 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-197 *5 *6)) (-14 *5 (-694)) (-4 *6 (-1128)) (-4 *2 (-1128)) (-5 *1 (-198 *5 *6 *2)))) (-3840 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-197 *6 *7)) (-14 *6 (-694)) (-4 *7 (-1128)) (-4 *5 (-1128)) (-5 *2 (-197 *6 *5)) (-5 *1 (-198 *6 *7 *5))))) 
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+NIL 
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 (((-201) (-113)) (T -201)) 
-((** (*1 *1 *1 *2) (-12 (-4 *1 (-201)) (-5 *2 (-483)))) (-2483 (*1 *1 *1) (-4 *1 (-201)))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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ELT) (($ $ (-1 |#1| |#1|) (-694)) NIL T ELT) (($ $ (-1089)) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-583 (-1089))) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-1089) (-694)) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-583 (-1089)) (-583 (-694))) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-694)) NIL (|has| |#1| (-189)) ELT)) (-1488 (((-583 |#2|) $) NIL T ELT)) (-3947 (((-469 |#3|) $) NIL T ELT) (((-694) $ |#3|) NIL T ELT) (((-583 (-694)) $ (-583 |#3|)) NIL T ELT) (((-694) $ |#2|) NIL T ELT)) (-3971 (((-800 (-329)) $) NIL (-12 (|has| |#1| (-553 (-800 (-329)))) (|has| |#3| (-553 (-800 (-329))))) 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)) (-2817 ((|#1| $) NIL (|has| |#1| (-391)) ELT) (($ $ |#3|) NIL (|has| |#1| (-391)) ELT)) (-2703 (((-3 (-1178 $) #1#) (-630 $)) NIL (-12 (|has| $ (-118)) (|has| |#1| (-821))) ELT)) (-3945 (((-772) $) NIL T ELT) (($ (-484)) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ (-1038 |#1| |#2|)) 32 T ELT) (($ (-349 (-484))) NIL (OR (|has| |#1| (-38 (-349 (-484)))) (|has| |#1| (-950 (-349 (-484))))) ELT) (($ $) NIL (|has| |#1| (-495)) ELT)) (-3816 (((-583 |#1|) $) NIL T ELT)) (-3676 ((|#1| $ (-469 |#3|)) NIL T ELT) (($ $ |#3| (-694)) NIL T ELT) (($ $ (-583 |#3|) (-583 (-694))) NIL T ELT)) (-2702 (((-632 $) $) NIL (OR (-12 (|has| $ (-118)) (|has| |#1| (-821))) (|has| |#1| (-118))) ELT)) (-3126 (((-694)) NIL T CONST)) (-1622 (($ $ $ (-694)) NIL (|has| |#1| (-146)) ELT)) (-1264 (((-85) $ $) NIL T ELT)) (-2062 (((-85) $ $) NIL (|has| |#1| (-495)) ELT)) (-3125 (((-85) $ $) NIL T ELT)) (-2660 (($) NIL T CONST)) (-2666 (($) NIL T CONST)) (-2669 (($ $ (-583 |#3|) (-583 (-694))) NIL T ELT) (($ $ |#3| (-694)) NIL T ELT) (($ $ (-583 |#3|)) NIL T ELT) (($ $ |#3|) NIL T ELT) (($ $ (-1 |#1| |#1|)) NIL T ELT) (($ $ (-1 |#1| |#1|) (-694)) NIL T ELT) (($ $ (-1089)) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-583 (-1089))) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-1089) (-694)) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $ (-583 (-1089)) (-583 (-694))) NIL (|has| |#1| (-811 (-1089))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-694)) NIL (|has| |#1| (-189)) ELT)) (-3056 (((-85) $ $) NIL T ELT)) (-3948 (($ $ |#1|) NIL (|has| |#1| (-312)) ELT)) (-3836 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3838 (($ $ $) NIL T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) NIL T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-349 (-484))) NIL (|has| |#1| (-38 (-349 (-484)))) ELT) (($ (-349 (-484)) $) NIL (|has| |#1| (-38 (-349 (-484)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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+NIL 
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+NIL 
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 ((** (($ $ $) 10 T ELT))) 
 (((-238 |#1|) (-10 -7 (-15 ** (|#1| |#1| |#1|))) (-239)) (T -238)) 
 NIL 
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-NIL 
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+NIL 
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+NIL 
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 (((-246) (-113)) (T -246)) 
 NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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(($ (-349 (-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) (-829)) (T -308)) 
-NIL 
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-((-2567 (((-85) $ $) NIL T ELT)) (-3135 (((-693) $) NIL T ELT)) (-3722 (($) NIL T CONST)) (-3156 (((-3 |#1| #1="failed") $) NIL T ELT)) (-3155 ((|#1| $) NIL T ELT)) (-3465 (((-3 $ #1#) $) NIL T ELT)) (-2409 (((-85) $) 17 T ELT)) (-2298 ((|#1| $ (-483)) NIL T ELT)) (-2299 (((-483) $ (-483)) NIL T ELT)) (-2289 (($ (-1 |#1| |#1|) $) 34 T ELT)) (-2290 (($ (-1 (-483) (-483)) $) 26 T ELT)) (-3241 (((-1071) $) NIL T ELT)) (-2483 (($ $) 28 T ELT)) (-3242 (((-1032) $) NIL T ELT)) (-1777 (((-582 (-2 (|:| |gen| |#1|) (|:| -3941 (-483)))) $) 30 T ELT)) (-3008 (($ $ $) NIL T ELT)) (-2434 (($ $ $) NIL T ELT)) (-3944 (((-771) $) 40 T ELT) (($ |#1|) NIL T ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-2665 (($) 7 T CONST)) (-3055 (((-85) $ $) NIL T ELT)) (-3947 (($ $ $) NIL T ELT)) (** (($ $ (-829)) NIL T ELT) (($ $ (-693)) NIL T ELT) (($ $ (-483)) NIL T ELT) (($ |#1| (-483)) 19 T ELT)) (* (($ $ $) 53 T ELT) (($ |#1| $) 23 T ELT) (($ $ |#1|) 21 T ELT))) 
-(((-310 |#1|) (-13 (-411) (-949 |#1|) (-10 -8 (-15 * ($ |#1| $)) (-15 * ($ $ |#1|)) (-15 ** ($ |#1| (-483))) (-15 -3135 ((-693) $)) (-15 -2299 ((-483) $ (-483))) (-15 -2298 (|#1| $ (-483))) (-15 -2290 ($ (-1 (-483) (-483)) $)) (-15 -2289 ($ (-1 |#1| |#1|) $)) (-15 -1777 ((-582 (-2 (|:| |gen| |#1|) (|:| -3941 (-483)))) $)))) (-1012)) (T -310)) 
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-((-2063 (((-2 (|:| -1770 $) (|:| -3980 $) (|:| |associate| $)) $) 13 T ELT)) (-2062 (($ $) 14 T ELT)) (-3969 (((-346 $) $) 31 T ELT)) (-3721 (((-85) $) 27 T ELT)) (-2483 (($ $) 19 T ELT)) (-3143 (($ $ $) 22 T ELT) (($ (-582 $)) NIL T ELT)) (-3730 (((-346 $) $) 32 T ELT)) (-3464 (((-3 $ "failed") $ $) 21 T ELT)) (-1605 (((-693) $) 25 T ELT)) (-2878 (((-2 (|:| -1971 $) (|:| -2901 $)) $ $) 36 T ELT)) (-2061 (((-85) $ $) 16 T ELT)) (-3947 (($ $ $) 34 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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-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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-((-3625 (*1 *1) (-5 *1 (-415)))) 
-((-2567 (((-85) $ $) NIL T ELT)) (-3526 (((-1047) $) 12 T ELT)) (-3527 (((-1047) $) 10 T ELT)) (-3241 (((-1071) $) NIL T ELT)) (-3242 (((-1032) $) NIL T ELT)) (-3944 (((-771) $) 18 T ELT) (($ (-1093)) NIL T ELT) (((-1093) $) NIL T ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-3055 (((-85) $ $) NIL T ELT))) 
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-((-3527 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-416)))) (-3526 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-416))))) 
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(|:| |entry| |#2|)) (-1012))) ELT) (($ (-1 (-85) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3993)) ELT)) (-3840 (((-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| $ (-6 -3993)) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (((-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) NIL (|has| $ (-6 -3993)) ELT) (((-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3993)) ELT)) (-1574 ((|#2| $ |#1| |#2|) NIL (|has| $ (-6 -3994)) ELT)) (-3111 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|#2|))))) NIL (-12 (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (($ $ (-249 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (($ $ (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (($ $ (-582 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) (-582 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (($ $ (-582 |#2|) (-582 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ELT) (($ $ (-249 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ELT) (($ $ (-582 (-249 |#2|))) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1012))) ELT)) (-1220 (((-85) $ $) NIL T ELT)) (-2201 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3993)) (|has| |#2| (-1012))) ELT)) (-2204 (((-582 |#2|) $) NIL T ELT)) (-3401 (((-85) $) NIL T ELT)) (-3563 (($) 19 T ELT)) (-3798 ((|#2| $ |#1|) NIL T ELT) ((|#2| $ |#1| |#2|) NIL T ELT)) (-1464 (($) NIL T ELT) (($ (-582 (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-1944 (((-693) (-1 (-85) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-6 -3993)) ELT) (((-693) (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) $) NIL (-12 (|has| $ (-6 -3993)) (|has| (-2 (|:| -3858 |#1|) (|:| |entry| |#2|)) (-1012))) ELT) (((-693) |#2| $) NIL (-12 (|has| $ (-6 -3993)) (|has| |#2| (-1012))) ELT) (((-693) (-1 (-85) |#2|) $) NIL (|has| $ (-6 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-(((-417 |#1| |#2| |#3|) (-13 (-1105 |#1| |#2|) (-10 -7 (-6 -3993))) (-1012) (-1012) (-1071)) (T -417)) 
-NIL 
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ELT)) (-2816 ((|#2| $) NIL (|has| |#2| (-390)) ELT) (($ $ (-772 |#1|)) NIL (|has| |#2| (-390)) ELT)) (-2702 (((-3 (-1177 $) #1#) (-629 $)) NIL (-12 (|has| $ (-118)) (|has| |#2| (-820))) ELT)) (-3944 (((-771) $) NIL T ELT) (($ (-483)) NIL T ELT) (($ |#2|) NIL T ELT) (($ (-772 |#1|)) NIL T ELT) (($ (-348 (-483))) NIL (OR (|has| |#2| (-38 (-348 (-483)))) (|has| |#2| (-949 (-348 (-483))))) ELT) (($ $) NIL (|has| |#2| (-494)) ELT)) (-3815 (((-582 |#2|) $) NIL T ELT)) (-3675 ((|#2| $ (-420 (-3955 |#1|) (-693))) NIL T ELT) (($ $ (-772 |#1|) (-693)) NIL T ELT) (($ $ (-582 (-772 |#1|)) (-582 (-693))) NIL T ELT)) (-2701 (((-631 $) $) NIL (OR (-12 (|has| $ (-118)) (|has| |#2| (-820))) (|has| |#2| (-118))) ELT)) (-3125 (((-693)) NIL T CONST)) (-1621 (($ $ $ (-693)) NIL (|has| |#2| (-146)) ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-2061 (((-85) $ $) NIL (|has| |#2| (-494)) ELT)) (-3124 (((-85) $ $) NIL T ELT)) (-2659 (($) NIL T CONST)) (-2665 (($) NIL T CONST)) (-2668 (($ $ (-582 (-772 |#1|)) (-582 (-693))) NIL T ELT) (($ $ (-772 |#1|) (-693)) NIL T ELT) (($ $ (-582 (-772 |#1|))) NIL T ELT) (($ $ (-772 |#1|)) NIL T ELT)) (-3055 (((-85) $ $) NIL T ELT)) (-3947 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3835 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3837 (($ $ $) NIL T ELT)) (** (($ $ (-829)) NIL T ELT) (($ $ (-693)) NIL T ELT)) (* (($ (-829) $) NIL T ELT) (($ (-693) $) NIL T ELT) (($ (-483) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-348 (-483))) NIL (|has| |#2| (-38 (-348 (-483)))) ELT) (($ (-348 (-483)) $) NIL (|has| |#2| (-38 (-348 (-483)))) ELT) (($ |#2| $) NIL T ELT) (($ $ |#2|) NIL T ELT))) 
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-((-1935 (*1 *1 *1 *2) (-12 (-5 *2 (-582 (-483))) (-5 *1 (-419 *3 *4)) (-14 *3 (-582 (-1088))) (-4 *4 (-960))))) 
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(((-2 (|:| |mat| (-629 (-483))) (|:| |vec| (-1177 (-483)))) (-629 $) (-1177 $)) NIL (-12 (|has| |#2| (-579 (-483))) (|has| |#2| (-960))) ELT) (((-2 (|:| |mat| (-629 |#2|)) (|:| |vec| (-1177 |#2|))) (-629 $) (-1177 $)) NIL (|has| |#2| (-960)) ELT) (((-629 |#2|) (-629 $)) NIL (|has| |#2| (-960)) ELT)) (-3465 (((-3 $ #1#) $) NIL (|has| |#2| (-960)) ELT)) (-2993 (($) NIL (|has| |#2| (-318)) ELT)) (-1574 ((|#2| $ (-483) |#2|) NIL (|has| $ (-6 -3994)) ELT)) (-3111 ((|#2| $ (-483)) 11 T ELT)) (-3185 (((-85) $) NIL (|has| |#2| (-716)) ELT)) (-2888 (((-582 |#2|) $) NIL (|has| $ (-6 -3993)) ELT)) (-1212 (((-85) $ $) NIL (|has| |#2| (-23)) ELT)) (-2409 (((-85) $) NIL (|has| |#2| (-960)) ELT)) (-2199 (((-483) $) NIL (|has| (-483) (-755)) ELT)) (-2530 (($ $ $) NIL (|has| |#2| (-755)) ELT)) (-2607 (((-582 |#2|) $) NIL (|has| $ (-6 -3993)) ELT)) (-3244 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3993)) (|has| |#2| (-1012))) ELT)) (-2200 (((-483) $) NIL (|has| (-483) (-755)) ELT)) (-2856 (($ $ $) NIL 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(|has| |#2| (-960))) ELT) (($ $ (-582 (-1088))) NIL (-12 (|has| |#2| (-810 (-1088))) (|has| |#2| (-960))) ELT) (($ $ (-1088)) NIL (-12 (|has| |#2| (-810 (-1088))) (|has| |#2| (-960))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-960)) ELT) (($ $ (-1 |#2| |#2|) (-693)) NIL (|has| |#2| (-960)) ELT)) (-1944 (((-693) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3993)) ELT) (((-693) |#2| $) NIL (-12 (|has| $ (-6 -3993)) (|has| |#2| (-1012))) ELT)) (-3398 (($ $) NIL T ELT)) (-3944 (((-1177 |#2|) $) NIL T ELT) (($ (-483)) NIL (OR (-12 (|has| |#2| (-949 (-483))) (|has| |#2| (-1012))) (|has| |#2| (-960))) ELT) (($ (-348 (-483))) NIL (-12 (|has| |#2| (-949 (-348 (-483)))) (|has| |#2| (-1012))) ELT) (($ |#2|) NIL (|has| |#2| (-1012)) ELT) (((-771) $) NIL (|has| |#2| (-551 (-771))) ELT)) (-3125 (((-693)) NIL (|has| |#2| (-960)) CONST)) (-1263 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3993)) ELT)) (-3124 (((-85) $ $) NIL (|has| |#2| (-960)) ELT)) (-2659 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|#2| (-21)) ELT) (($ $) NIL (|has| |#2| (-21)) ELT)) (-3837 (($ $ $) NIL (|has| |#2| (-25)) ELT)) (** (($ $ (-693)) NIL (|has| |#2| (-960)) ELT) (($ $ (-829)) NIL (|has| |#2| (-960)) ELT)) (* (($ $ $) NIL (|has| |#2| (-960)) ELT) (($ $ |#2|) NIL (|has| |#2| (-662)) ELT) (($ |#2| $) NIL (|has| |#2| (-662)) ELT) (($ (-483) $) NIL (|has| |#2| (-21)) ELT) (($ (-693) $) NIL (|has| |#2| (-23)) ELT) (($ (-829) $) NIL (|has| |#2| (-25)) ELT)) (-3955 (((-693) $) NIL (|has| $ (-6 -3993)) ELT))) 
-(((-420 |#1| |#2|) (-196 |#1| |#2|) (-693) (-716)) (T -420)) 
-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-457) (-13 (-994) (-10 -8 (-15 -3920 ((-1047) $)) (-15 -1990 ((-1047) $)) (-15 -1989 ((-1047) $))))) (T -457)) 
-((-3920 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-457)))) (-1990 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-457)))) (-1989 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-457))))) 
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-NIL 
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-NIL 
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+(((-318 |#1|) (-10 -7 (-15 -2994 (|#1|))) (-319)) (T -318)) 
+NIL 
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+NIL 
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+NIL 
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+NIL 
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+((-1890 (($ $ $) 14 T ELT) (($ (-583 $)) 21 T ELT)) (-2708 (((-1084 $) (-1084 $) (-1084 $)) 45 T ELT)) (-3144 (($ $ $) NIL T ELT) (($ (-583 $)) 22 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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-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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+(((-740) (-113)) (T -740)) 
+NIL 
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 (((-754) (-113)) (T -754)) 
 NIL 
-(-13 (-713) (-120) (-662)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-554 (-483)) . T) ((-551 (-771)) . T) ((-13) . T) ((-587 (-483)) . T) ((-587 $) . T) ((-589 $) . T) ((-662) . T) ((-713) . T) ((-715) . T) ((-717) . T) ((-720) . T) ((-755) . T) ((-758) . T) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T)) 
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 (((-755) (-113)) (T -755)) 
 NIL 
-(-13 (-1012) (-758)) 
-(((-72) . T) ((-551 (-771)) . T) ((-13) . T) ((-758) . T) ((-1012) . T) ((-1127) . T)) 
-((-2567 (((-85) $ $) NIL T ELT)) (-2530 (($ $ $) NIL T ELT)) (-2856 (($ $ $) NIL T ELT)) (-3944 (($ |#1|) 10 T ELT) ((|#1| $) 9 T ELT) (((-771) $) 15 (|has| |#1| (-551 (-771))) ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-2565 (((-85) $ $) NIL T ELT)) (-2566 (((-85) $ $) NIL T ELT)) (-3055 (((-85) $ $) NIL T ELT)) (-2683 (((-85) $ $) NIL T ELT)) (-2684 (((-85) $ $) 12 T ELT))) 
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-NIL 
-((-2530 (($ $ $) 16 T ELT)) (-2856 (($ $ $) 15 T ELT)) (-1263 (((-85) $ $) 17 T ELT)) (-2565 (((-85) $ $) 12 T ELT)) (-2566 (((-85) $ $) 9 T ELT)) (-3055 (((-85) $ $) 14 T ELT)) (-2683 (((-85) $ $) 11 T ELT))) 
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-NIL 
-((-2567 (((-85) $ $) 7 T ELT)) (-2530 (($ $ $) 10 T ELT)) (-2856 (($ $ $) 11 T ELT)) (-1263 (((-85) $ $) 6 T ELT)) (-2565 (((-85) $ $) 12 T ELT)) (-2566 (((-85) $ $) 14 T ELT)) (-3055 (((-85) $ $) 8 T ELT)) (-2683 (((-85) $ $) 13 T ELT)) (-2684 (((-85) $ $) 15 T ELT))) 
-(((-758) (-113)) (T -758)) 
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-(((-72) . T) ((-13) . T) ((-1127) . T)) 
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-NIL 
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-(((-765) (-113)) (T -765)) 
-NIL 
-(-13 (-755) (-1024)) 
-(((-72) . T) ((-551 (-771)) . T) ((-13) . T) ((-755) . T) ((-758) . T) ((-1024) . T) ((-1012) . T) ((-1127) . T)) 
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-(((-766) (-13 (-755) (-10 -8 (-15 -3944 ($ (-483))) (-15 -3400 ((-483) $))))) (T -766)) 
-((-3944 (*1 *1 *2) (-12 (-5 *2 (-483)) (-5 *1 (-766)))) (-3400 (*1 *2 *1) (-12 (-5 *2 (-483)) (-5 *1 (-766))))) 
-((-2552 (((-1183) (-582 (-51))) 23 T ELT)) (-3458 (((-1183) (-1071) (-771)) 13 T ELT) (((-1183) (-771)) 8 T ELT) (((-1183) (-1071)) 10 T ELT))) 
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-NIL 
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+(-13 (-714) (-120) (-663)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-555 (-484)) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-714) . T) ((-716) . T) ((-718) . T) ((-721) . T) ((-756) . T) ((-759) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T)) 
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+(((-756) (-113)) (T -756)) 
+NIL 
+(-13 (-1013) (-759)) 
+(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-759) . T) ((-1013) . T) ((-1128) . T)) 
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+NIL 
+((-2531 (($ $ $) 16 T ELT)) (-2857 (($ $ $) 15 T ELT)) (-1264 (((-85) $ $) 17 T ELT)) (-2566 (((-85) $ $) 12 T ELT)) (-2567 (((-85) $ $) 9 T ELT)) (-3056 (((-85) $ $) 14 T ELT)) (-2684 (((-85) $ $) 11 T ELT))) 
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+NIL 
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+(((-72) . T) ((-13) . T) ((-1128) . T)) 
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+NIL 
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+(((-761 |#1|) (-113) (-961)) (T -761)) 
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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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+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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|bas| $) (|:| -3323 (-583 |#4|))) #1#) (-583 |#4|) (-1 (-85) |#4|) (-1 (-85) |#4| |#4|)) 113 T ELT)) (-3689 (((-85) $ (-1 (-85) |#4| (-583 |#4|))) 103 T ELT)) (-3189 (((-583 $) |#4| $) 128 T ELT) (((-583 $) |#4| (-583 $)) 127 T ELT) (((-583 $) (-583 |#4|) $) 126 T ELT) (((-583 $) (-583 |#4|) (-583 $)) 125 T ELT)) (-1947 (((-85) (-1 (-85) |#4|) $) 50 (|has| $ (-6 -3994)) ELT)) (-3679 (((-583 |#3|) $) 86 T ELT)) (-3196 (((-85) |#4| $) 142 T ELT)) (-3932 (((-85) |#3| $) 85 T ELT)) (-3056 (((-85) $ $) 8 T ELT)) (-3956 (((-694) $) 47 (|has| $ (-6 -3994)) ELT))) 
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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))) ((-428 |#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) ((-1020 |#1| |#2| |#3| |#4|) . T) ((-1123 |#1| |#2| |#3| |#4|) . T) ((-1128) . T)) 
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NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-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)) (-3956 (((-694) $) NIL (|has| $ (-6 -3994)) ELT))) 
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+NIL 
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 NIL 
 (-13) 
 (((-13) . T)) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-483)) . T) ((-25) . T) ((-38 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-348 (-483)))) ((-66) |has| |#1| (-38 (-348 (-483)))) ((-72) . T) ((-82 (-348 (-483)) (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-494)) (|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| (-739))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-554 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-554 (-483)) . T) ((-554 (-1088)) -12 (|has| |#1| (-312)) (|has| |#2| (-949 (-1088)))) ((-554 |#1|) |has| |#1| (-146)) ((-554 |#2|) . 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T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-483) (-1024)) ((-246) OR (|has| |#1| (-494)) (|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)) ((-327 |#2|) |has| |#1| (-312)) ((-341 |#2|) |has| |#1| (-312)) ((-390) |has| |#1| (-312)) ((-431) |has| |#1| (-38 (-348 (-483)))) ((-454 (-1088) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-454 (-1088) |#2|))) ((-454 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-494) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-13) . T) ((-587 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-587 (-483)) . T) ((-587 |#1|) . T) ((-587 |#2|) |has| |#1| (-312)) ((-587 $) . T) ((-589 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-589 (-483)) -12 (|has| |#1| (-312)) (|has| |#2| (-579 (-483)))) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-581 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-581 |#1|) |has| |#1| (-146)) ((-581 |#2|) |has| |#1| (-312)) ((-581 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-579 (-483)) -12 (|has| |#1| (-312)) (|has| |#2| (-579 (-483)))) ((-579 |#2|) |has| |#1| (-312)) ((-653 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-653 |#1|) |has| |#1| (-146)) ((-653 |#2|) |has| |#1| (-312)) ((-653 $) OR (|has| |#1| (-494)) (|has| |#1| (-312))) ((-662) . 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T) ((-831) |has| |#1| (-312)) ((-903 |#2|) |has| |#1| (-312)) ((-914) |has| |#1| (-38 (-348 (-483)))) ((-932) -12 (|has| |#1| (-312)) (|has| |#2| (-932))) ((-949 (-348 (-483))) -12 (|has| |#1| (-312)) (|has| |#2| (-949 (-483)))) ((-949 (-483)) -12 (|has| |#1| (-312)) (|has| |#2| (-949 (-483)))) ((-949 (-1088)) -12 (|has| |#1| (-312)) (|has| |#2| (-949 (-1088)))) ((-949 |#2|) . T) ((-962 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-962 |#1|) . T) ((-962 |#2|) |has| |#1| (-312)) ((-962 $) OR (|has| |#1| (-494)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-967 (-348 (-483))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-483))))) ((-967 |#1|) . T) ((-967 |#2|) |has| |#1| (-312)) ((-967 $) OR (|has| |#1| (-494)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . 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-NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-693)) . T) ((-25) . T) ((-38 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-494)) ((-35) |has| |#1| (-38 (-348 (-483)))) ((-66) |has| |#1| (-38 (-348 (-483)))) ((-72) . T) ((-82 (-348 (-483)) (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-554 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-554 (-483)) . T) ((-554 |#1|) |has| |#1| (-146)) ((-554 $) |has| |#1| (-494)) ((-551 (-771)) . T) ((-146) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-693) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-693) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-693) |#1|))) ((-239) |has| |#1| (-38 (-348 (-483)))) ((-241 (-693) |#1|) . T) ((-241 $ $) |has| (-693) (-1024)) ((-246) |has| |#1| (-494)) ((-431) |has| |#1| (-38 (-348 (-483)))) ((-494) |has| |#1| (-494)) ((-13) . T) ((-587 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-587 (-483)) . T) ((-587 |#1|) . T) ((-587 $) . T) ((-589 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-589 |#1|) . T) ((-589 $) . T) ((-581 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-581 |#1|) |has| |#1| (-146)) ((-581 $) |has| |#1| (-494)) ((-653 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-653 |#1|) |has| |#1| (-146)) ((-653 $) |has| |#1| (-494)) ((-662) . T) ((-805 $ (-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|)))) ((-808 (-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|)))) ((-810 (-1088)) -12 (|has| |#1| (-808 (-1088))) (|has| |#1| (-15 * (|#1| (-693) |#1|)))) ((-885 |#1| (-693) (-993)) . T) ((-914) |has| |#1| (-38 (-348 (-483)))) ((-962 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-962 |#1|) . T) ((-962 $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-967 (-348 (-483))) |has| |#1| (-38 (-348 (-483)))) ((-967 |#1|) . T) ((-967 $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-960) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1113) |has| |#1| (-38 (-348 (-483)))) ((-1116) |has| |#1| (-38 (-348 (-483)))) ((-1127) . T) ((-1156 |#1| (-693)) . T)) 
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-NIL 
-(((-1173) (-113)) (T -1173)) 
-NIL 
-(-13 (-10 -7 (-6 -2286))) 
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-NIL 
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-NIL 
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-NIL 
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(-258) (-120) (-932))) (-5 *2 (-582 (-2 (|:| -1745 (-1083 *5)) (|:| -3223 (-582 (-856 *5)))))) (-5 *1 (-1205 *5 *6 *7)) (-5 *3 (-582 (-856 *5))) (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088))))) (-3966 (*1 *2 *3) (-12 (-5 *3 (-957 *4 *5)) (-4 *4 (-13 (-754) (-258) (-120) (-932))) (-14 *5 (-582 (-1088))) (-5 *2 (-582 (-2 (|:| -1745 (-1083 *4)) (|:| -3223 (-582 (-856 *4)))))) (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-582 (-1088))))) (-3965 (*1 *2 *3) (-12 (-5 *3 (-582 (-856 *4))) (-4 *4 (-13 (-754) (-258) (-120) (-932))) (-5 *2 (-582 (-957 *4 *5))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-582 (-1088))) (-14 *6 (-582 (-1088))))) (-3965 (*1 *2 *3 *4) (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-754) (-258) (-120) (-932))) (-5 *2 (-582 (-957 *5 *6))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088))))) (-3965 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-754) (-258) (-120) (-932))) (-5 *2 (-582 (-957 *5 *6))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))) 
-((-3973 (((-3 (-1177 (-348 (-483))) #1="failed") (-1177 |#1|) |#1|) 21 T ELT)) (-3971 (((-85) (-1177 |#1|)) 12 T ELT)) (-3972 (((-3 (-1177 (-483)) #1#) (-1177 |#1|)) 16 T ELT))) 
-(((-1206 |#1|) (-10 -7 (-15 -3971 ((-85) (-1177 |#1|))) (-15 -3972 ((-3 (-1177 (-483)) #1="failed") (-1177 |#1|))) (-15 -3973 ((-3 (-1177 (-348 (-483))) #1#) (-1177 |#1|) |#1|))) (-13 (-960) (-579 (-483)))) (T -1206)) 
-((-3973 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) (-5 *2 (-1177 (-348 (-483)))) (-5 *1 (-1206 *4)))) (-3972 (*1 *2 *3) (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) (-5 *2 (-1177 (-483))) (-5 *1 (-1206 *4)))) (-3971 (*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) (-5 *2 (-85)) (-5 *1 (-1206 *4))))) 
-((-2567 (((-85) $ $) NIL T ELT)) (-3187 (((-85) $) 12 T ELT)) (-1310 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3135 (((-693)) 9 T ELT)) (-3722 (($) NIL T CONST)) (-3465 (((-3 $ #1#) $) 57 T ELT)) (-2993 (($) 46 T ELT)) (-1212 (((-85) $ $) NIL T ELT)) (-2409 (((-85) $) 38 T ELT)) (-3443 (((-631 $) $) 36 T ELT)) (-2009 (((-829) $) 14 T ELT)) (-3241 (((-1071) $) NIL T ELT)) (-3444 (($) 26 T CONST)) (-2399 (($ (-829)) 47 T ELT)) (-3242 (((-1032) $) NIL T ELT)) (-3970 (((-483) $) 16 T ELT)) (-3944 (((-771) $) 21 T ELT) (($ (-483)) 18 T ELT)) (-3125 (((-693)) 10 T CONST)) (-1263 (((-85) $ $) 59 T ELT)) (-3124 (((-85) $ $) NIL T ELT)) (-2659 (($) 23 T CONST)) (-2665 (($) 25 T CONST)) (-3055 (((-85) $ $) 31 T ELT)) (-3835 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3837 (($ $ $) 29 T ELT)) (** (($ $ (-829)) NIL T ELT) (($ $ (-693)) 52 T ELT)) (* (($ (-829) $) NIL T ELT) (($ (-693) $) NIL T ELT) (($ (-483) $) 41 T ELT) (($ $ $) 40 T ELT))) 
-(((-1207 |#1|) (-13 (-146) (-318) (-552 (-483)) (-1064)) (-829)) (T -1207)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-((-3 2809120 2809125 2809130 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2809105 2809110 2809115 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2809090 2809095 2809100 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2809075 2809080 2809085 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1207 2808054 2808993 2809070 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1206 2807269 2807448 2807667 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1205 2798428 2800297 2802231 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1204 2797816 2797969 2798158 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1203 2797278 2797581 2797694 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1202 2794838 2796740 2796943 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1201 2791602 2793255 2793826 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1200 2788859 2790589 2790643 "XPOLYC" 2790928 XPOLYC (NIL T T) -9 NIL 2791041 NIL) (-1199 2786378 2788363 2788566 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1198 2782626 2785237 2785625 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1197 2777473 2779106 2779160 "XFALG" 2781305 XFALG (NIL T T) -9 NIL 2782089 NIL) (-1196 2772629 2775362 2775404 "XF" 2776022 XF (NIL T) -9 NIL 2776418 NIL) (-1195 2772347 2772457 2772624 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1194 2771574 2771696 2771900 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1193 2769316 2771474 2771569 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1192 2767897 2768692 2768734 "XALG" 2768739 XALG (NIL T) -9 NIL 2768848 NIL) (-1191 2761454 2766307 2766785 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1190 2759697 2760699 2761020 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1189 2759296 2759568 2759637 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1188 2758783 2759086 2759179 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1187 2757860 2758070 2758365 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1186 2756156 2756619 2757081 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1185 2755045 2755630 2755672 "VSPACE" 2755808 VSPACE (NIL T) -9 NIL 2755882 NIL) (-1184 2754916 2754949 2755040 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1183 2754759 2754813 2754881 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1182 2751742 2752537 2753274 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1181 2742840 2745441 2747614 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1180 2736417 2738308 2739887 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1179 2734901 2735296 2735702 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1178 2733728 2734009 2734325 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1177 2728844 2733555 2733647 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1176 2721946 2726554 2726597 "VECTCAT" 2727585 VECTCAT (NIL T) -9 NIL 2728169 NIL) (-1175 2721225 2721551 2721941 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1174 2720719 2720961 2721081 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1173 2720652 2720657 2720687 "UTYPE" 2720692 UTYPE (NIL) -9 NIL NIL NIL) (-1172 2719639 2719815 2720076 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1171 2717490 2717998 2718522 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1170 2707372 2713342 2713384 "UTSCAT" 2714482 UTSCAT (NIL T) -9 NIL 2715239 NIL) (-1169 2705437 2706380 2707367 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1168 2705111 2705160 2705291 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1167 2696822 2703307 2703786 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2690817 2693630 2693673 "URAGG" 2695743 URAGG (NIL T) -9 NIL 2696465 NIL) (-1165 2688832 2689794 2690812 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1164 2684539 2687808 2688270 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1163 2676968 2684463 2684534 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1162 2665619 2673106 2673167 "UPXSCCA" 2673735 UPXSCCA (NIL T T) -9 NIL 2673967 NIL) (-1161 2665340 2665442 2665614 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1160 2653892 2661104 2661146 "UPXSCAT" 2661786 UPXSCAT (NIL T) -9 NIL 2662394 NIL) (-1159 2653405 2653490 2653667 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1158 2645091 2652996 2653258 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1157 2643986 2644256 2644606 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1156 2636689 2640174 2640228 "UPSCAT" 2641297 UPSCAT (NIL T T) -9 NIL 2642061 NIL) (-1155 2636109 2636361 2636684 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1154 2635783 2635832 2635963 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1153 2619913 2628867 2628909 "UPOLYC" 2630987 UPOLYC (NIL T) -9 NIL 2632207 NIL) (-1152 2613968 2616816 2619908 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1151 2613404 2613529 2613692 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1150 2613038 2613125 2613264 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1149 2611851 2612118 2612422 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1148 2611184 2611314 2611499 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1147 2610776 2610851 2610998 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1146 2601540 2610542 2610670 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1145 2600902 2601039 2601244 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1144 2599503 2600350 2600626 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1143 2598732 2598929 2599154 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1142 2585542 2598656 2598727 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1141 2565348 2578583 2578644 "ULSCCAT" 2579275 ULSCCAT (NIL T T) -9 NIL 2579562 NIL) (-1140 2564683 2564969 2565343 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1139 2553055 2560189 2560231 "ULSCAT" 2561084 ULSCAT (NIL T) -9 NIL 2561814 NIL) (-1138 2552568 2552653 2552830 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1137 2534685 2552067 2552308 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1136 2533719 2534412 2534526 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2534637) (-1135 2532752 2533445 2533559 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2533670) (-1134 2531785 2532478 2532592 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2532703) (-1133 2530818 2531511 2531625 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2531736) (-1132 2528825 2530046 2530076 "UFD" 2530287 UFD (NIL) -9 NIL 2530400 NIL) (-1131 2528669 2528726 2528820 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1130 2527921 2528128 2528344 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1129 2526141 2526594 2527059 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1128 2525866 2526106 2526136 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1127 2525804 2525809 2525839 "TYPE" 2525844 TYPE (NIL) -9 NIL 2525851 NIL) (-1126 2524963 2525183 2525423 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1125 2524141 2524572 2524807 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1124 2522295 2522868 2523407 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1123 2521329 2521565 2521801 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1122 2509683 2514151 2514247 "TSETCAT" 2519462 TSETCAT (NIL T T T T) -9 NIL 2520974 NIL) (-1121 2506020 2507836 2509678 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1120 2500412 2505246 2505528 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1119 2495749 2496762 2497691 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1118 2495246 2495321 2495484 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1117 2493322 2493612 2493967 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1116 2492806 2492955 2492985 "TRIGCAT" 2493198 TRIGCAT (NIL) -9 NIL NIL NIL) (-1115 2492557 2492660 2492801 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1114 2489553 2491666 2491944 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1113 2488659 2489355 2489385 "TRANFUN" 2489420 TRANFUN (NIL) -9 NIL 2489486 NIL) (-1112 2488123 2488374 2488654 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1111 2487960 2487998 2488059 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1110 2487417 2487548 2487699 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1109 2486158 2486815 2487051 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1108 2485970 2486007 2486079 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1107 2484184 2484830 2485259 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1106 2482564 2482901 2483223 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1105 2473622 2480365 2480421 "TBAGG" 2480823 TBAGG (NIL T T) -9 NIL 2481036 NIL) (-1104 2470153 2471845 2473617 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1103 2469630 2469755 2469900 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1102 2469140 2469460 2469550 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1101 2468637 2468754 2468892 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1100 2461724 2468539 2468632 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1099 2457477 2458772 2460017 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1098 2456846 2457005 2457186 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1097 2454000 2454753 2455536 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1096 2453774 2453964 2453995 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1095 2452728 2453413 2453539 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2453725) (-1094 2451992 2452540 2452619 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2452679) (-1093 2448815 2449974 2450674 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1092 2446498 2447181 2447815 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1091 2442576 2443622 2444599 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1090 2439675 2442231 2442460 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1089 2439271 2439358 2439480 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1088 2435895 2437369 2438188 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1087 2428855 2435092 2435385 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2420541 2428446 2428708 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1085 2419820 2419959 2420176 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1084 2419504 2419569 2419680 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1083 2410227 2419216 2419341 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1082 2408957 2409255 2409610 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1081 2408362 2408440 2408631 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1080 2390514 2407861 2408102 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1079 2390113 2390385 2390454 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1078 2389449 2389730 2389870 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1077 2384051 2385310 2386263 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1076 2383583 2383683 2383847 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1075 2378694 2379976 2381123 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1074 2373152 2374623 2375934 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1073 2366067 2368131 2369922 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1072 2358897 2365979 2366062 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1071 2353591 2358611 2358726 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1070 2353178 2353261 2353405 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1069 2352329 2352530 2352765 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1068 2352069 2352127 2352220 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1067 2344807 2350274 2350880 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1066 2343983 2344188 2344419 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1065 2343228 2343599 2343746 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1064 2342716 2342958 2342988 "STEP" 2343082 STEP (NIL) -9 NIL 2343153 NIL) (-1063 2335819 2342634 2342711 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1062 2330034 2334617 2334660 "STAGG" 2335087 STAGG (NIL T) -9 NIL 2335261 NIL) (-1061 2328413 2329161 2330029 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1060 2326570 2328240 2328332 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1059 2325850 2326389 2326419 "SRING" 2326424 SRING (NIL) -9 NIL 2326444 NIL) (-1058 2318472 2324388 2324827 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2312246 2313685 2315189 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2304671 2309582 2309612 "SRAGG" 2310911 SRAGG (NIL) -9 NIL 2311515 NIL) (-1055 2303968 2304288 2304666 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1054 2298023 2303290 2303713 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1053 2292236 2295405 2296127 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1052 2288665 2289484 2290121 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1051 2287640 2287945 2287975 "SPFCAT" 2288419 SPFCAT (NIL) -9 NIL NIL NIL) (-1050 2286577 2286829 2287093 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1049 2277335 2279609 2279639 "SPADXPT" 2284276 SPADXPT (NIL) -9 NIL 2286400 NIL) (-1048 2277137 2277183 2277252 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1047 2274793 2277101 2277132 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1046 2266467 2268556 2268598 "SPACEC" 2272913 SPACEC (NIL T) -9 NIL 2274718 NIL) (-1045 2264296 2266414 2266462 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1044 2263229 2263418 2263707 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1043 2261633 2261966 2262377 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1042 2260898 2261132 2261393 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1041 2257078 2258038 2259033 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1040 2253436 2254135 2254864 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1039 2247222 2252776 2252872 "SNTSCAT" 2252877 SNTSCAT (NIL T T T T) -9 NIL 2252947 NIL) (-1038 2241043 2245863 2246253 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1037 2234815 2240962 2241038 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1036 2233247 2233578 2233976 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1035 2224852 2229831 2229933 "SMATCAT" 2231276 SMATCAT (NIL NIL T T T) -9 NIL 2231824 NIL) (-1034 2222693 2223677 2224847 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1033 2220285 2221899 2221942 "SKAGG" 2222203 SKAGG (NIL T) -9 NIL 2222337 NIL) (-1032 2216331 2220105 2220216 "SINT" NIL SINT (NIL) -8 NIL NIL 2220257) (-1031 2216141 2216185 2216251 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1030 2215216 2215448 2215716 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1029 2214220 2214382 2214658 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1028 2213566 2213906 2214029 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1027 2212912 2213219 2213359 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1026 2211023 2211515 2212021 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1025 2204463 2210942 2211018 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1024 2203966 2204203 2204233 "SGROUP" 2204326 SGROUP (NIL) -9 NIL 2204388 NIL) (-1023 2203856 2203888 2203961 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1022 2203494 2203534 2203575 "SGPOPC" 2203580 SGPOPC (NIL T) -9 NIL 2203781 NIL) (-1021 2203028 2203305 2203411 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1020 2200451 2201220 2201942 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1019 2194336 2199890 2199986 "SFRTCAT" 2199991 SFRTCAT (NIL T T T T) -9 NIL 2200029 NIL) (-1018 2188728 2189841 2190968 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1017 2182904 2184065 2185229 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1016 2181876 2182778 2182899 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1015 2177484 2178379 2178474 "SEXCAT" 2181087 SEXCAT (NIL T T T T T) -9 NIL 2181638 NIL) (-1014 2176457 2177411 2177479 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1013 2174848 2175433 2175735 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1012 2174371 2174556 2174586 "SETCAT" 2174703 SETCAT (NIL) -9 NIL 2174787 NIL) (-1011 2174203 2174267 2174366 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1010 2170426 2172657 2172700 "SETAGG" 2173568 SETAGG (NIL T) -9 NIL 2173906 NIL) (-1009 2170032 2170184 2170421 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1008 2166986 2169979 2170027 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1007 2166452 2166762 2166862 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1006 2165579 2165945 2166006 "SEGXCAT" 2166292 SEGXCAT (NIL T T) -9 NIL 2166412 NIL) (-1005 2164504 2164772 2164815 "SEGCAT" 2165337 SEGCAT (NIL T) -9 NIL 2165558 NIL) (-1004 2164184 2164249 2164362 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1003 2163250 2163720 2163928 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1002 2162828 2163107 2163183 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1001 2162193 2162329 2162533 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1000 2161259 2162006 2162188 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-999 2160514 2161209 2161254 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-998 2152051 2160385 2160509 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-997 2150911 2151201 2151518 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-996 2150217 2150429 2150617 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-995 2149567 2149724 2149900 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-994 2149140 2149371 2149399 "SASTCAT" 2149404 SASTCAT (NIL) -9 NIL 2149417 NIL) (-993 2148607 2149032 2149106 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-992 2148210 2148251 2148422 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-991 2147841 2147882 2148039 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-990 2140922 2147758 2147836 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-989 2139572 2139901 2140297 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-988 2138333 2138694 2138994 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-987 2137957 2138178 2138259 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-986 2135417 2136051 2136504 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-985 2135256 2135289 2135357 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-984 2134747 2135050 2135141 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-983 2130375 2131243 2132154 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-982 2119194 2124748 2124842 "RSETCAT" 2128898 RSETCAT (NIL T T T T) -9 NIL 2129986 NIL) (-981 2117732 2118374 2119189 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-980 2111506 2112951 2114458 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-979 2109388 2109945 2110017 "RRCC" 2111090 RRCC (NIL T T) -9 NIL 2111431 NIL) (-978 2108913 2109112 2109383 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-977 2108383 2108693 2108791 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-976 2080935 2091648 2091712 "RPOLCAT" 2102186 RPOLCAT (NIL T T T) -9 NIL 2105331 NIL) (-975 2075034 2077857 2080930 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-974 2071201 2074782 2074920 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-973 2069529 2070268 2070524 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-972 2065172 2067984 2068012 "RNS" 2068274 RNS (NIL) -9 NIL 2068526 NIL) (-971 2064075 2064562 2065099 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-970 2063193 2063594 2063794 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-969 2062331 2062893 2062921 "RNG" 2062981 RNG (NIL) -9 NIL 2063035 NIL) (-968 2062220 2062254 2062326 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-967 2061482 2061987 2062027 "RMODULE" 2062032 RMODULE (NIL T) -9 NIL 2062058 NIL) (-966 2060421 2060527 2060857 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-965 2057267 2060011 2060304 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-964 2049916 2052408 2052520 "RMATCAT" 2055825 RMATCAT (NIL NIL NIL T T T) -9 NIL 2056802 NIL) (-963 2049433 2049612 2049911 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-962 2049001 2049212 2049253 "RLINSET" 2049314 RLINSET (NIL T) -9 NIL 2049358 NIL) (-961 2048646 2048727 2048853 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-960 2047492 2048223 2048251 "RING" 2048306 RING (NIL) -9 NIL 2048398 NIL) (-959 2047337 2047393 2047487 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-958 2046391 2046658 2046914 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-957 2037378 2046019 2046220 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-956 2036603 2037114 2037153 "RGBCSPC" 2037210 RGBCSPC (NIL T) -9 NIL 2037261 NIL) (-955 2035637 2036123 2036162 "RGBCMDL" 2036390 RGBCMDL (NIL T) -9 NIL 2036504 NIL) (-954 2035349 2035418 2035519 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-953 2035112 2035153 2035248 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-952 2033536 2033966 2034346 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-951 2031123 2031791 2032459 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-950 2030673 2030771 2030931 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-949 2030295 2030393 2030434 "RETRACT" 2030565 RETRACT (NIL T) -9 NIL 2030652 NIL) (-948 2030175 2030206 2030290 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-947 2029777 2030049 2030116 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-946 2028257 2029148 2029345 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-945 2027948 2028009 2028105 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-944 2027691 2027732 2027837 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-943 2027426 2027467 2027576 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-942 2022497 2023948 2025163 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-941 2019596 2020354 2021162 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-940 2017565 2018187 2018787 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-939 2010200 2016116 2016552 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-938 2009512 2009792 2009941 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-937 2008997 2009112 2009277 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-936 2004590 2008400 2008621 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-935 2003822 2004021 2004234 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-934 2001112 2001950 2002832 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-933 1997694 1998730 1999789 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-932 1997530 1997583 1997611 "REAL" 1997616 REAL (NIL) -9 NIL 1997651 NIL) (-931 1997020 1997324 1997415 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-930 1996500 1996578 1996783 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-929 1995733 1995925 1996136 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-928 1994621 1994918 1995285 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-927 1992888 1993358 1993891 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-926 1991810 1992087 1992474 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-925 1990637 1990946 1991365 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-924 1983985 1987497 1987525 "RCFIELD" 1988802 RCFIELD (NIL) -9 NIL 1989532 NIL) (-923 1982603 1983215 1983912 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-922 1978803 1980695 1980736 "RCAGG" 1981803 RCAGG (NIL T) -9 NIL 1982264 NIL) (-921 1978530 1978640 1978798 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-920 1977975 1978104 1978265 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-919 1977592 1977671 1977790 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-918 1977007 1977157 1977307 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-917 1976789 1976839 1976910 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-916 1969231 1975907 1976215 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-915 1958933 1969098 1969226 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-914 1958567 1958660 1958688 "RADCAT" 1958845 RADCAT (NIL) -9 NIL NIL NIL) (-913 1958405 1958465 1958562 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-912 1956505 1958236 1958325 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-911 1956186 1956235 1956362 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-910 1948473 1952557 1952597 "QUATCAT" 1953375 QUATCAT (NIL T) -9 NIL 1954139 NIL) (-909 1945723 1947003 1948379 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-908 1941563 1945673 1945718 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-907 1938950 1940617 1940658 "QUAGG" 1941033 QUAGG (NIL T) -9 NIL 1941207 NIL) (-906 1938552 1938824 1938891 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-905 1937558 1938188 1938351 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-904 1937239 1937288 1937415 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-903 1926839 1933008 1933048 "QFCAT" 1933706 QFCAT (NIL T) -9 NIL 1934699 NIL) (-902 1923723 1925162 1926745 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-901 1923269 1923403 1923533 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-900 1917465 1918626 1919788 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-899 1916884 1917064 1917296 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-898 1914706 1915234 1915657 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-897 1913605 1913847 1914164 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-896 1911966 1912164 1912517 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-895 1907722 1908938 1908979 "PTRANFN" 1910863 PTRANFN (NIL T) -9 NIL NIL NIL) (-894 1906369 1906714 1907035 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-893 1906062 1906125 1906232 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-892 1900135 1904858 1904898 "PTCAT" 1905190 PTCAT (NIL T) -9 NIL 1905343 NIL) (-891 1899828 1899869 1899993 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-890 1898707 1899023 1899357 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-889 1887586 1890147 1892456 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-888 1880493 1883389 1883483 "PSETCAT" 1886457 PSETCAT (NIL T T T T) -9 NIL 1887264 NIL) (-887 1878943 1879677 1880488 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-886 1878262 1878457 1878485 "PSCURVE" 1878753 PSCURVE (NIL) -9 NIL 1878920 NIL) (-885 1873864 1875684 1875748 "PSCAT" 1876583 PSCAT (NIL T T T) -9 NIL 1876822 NIL) (-884 1873178 1873460 1873859 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-883 1871575 1872490 1872753 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-882 1871066 1871369 1871460 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-881 1862086 1864508 1866696 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-880 1859829 1861406 1861446 "PRQAGG" 1861629 PRQAGG (NIL T) -9 NIL 1861730 NIL) (-879 1859002 1859448 1859476 "PROPLOG" 1859615 PROPLOG (NIL) -9 NIL 1859729 NIL) (-878 1858677 1858740 1858863 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-877 1858113 1858252 1858424 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-876 1856361 1857124 1857421 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-875 1855913 1856045 1856173 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-874 1850354 1854853 1855673 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-873 1850183 1850221 1850280 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-872 1849622 1849762 1849913 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-871 1848090 1848509 1848975 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-870 1847807 1847868 1847896 "PRIMCAT" 1848020 PRIMCAT (NIL) -9 NIL NIL NIL) (-869 1846978 1847174 1847402 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-868 1842859 1846928 1846973 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-867 1842558 1842620 1842731 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-866 1839694 1842207 1842440 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-865 1839145 1839302 1839330 "PPCURVE" 1839535 PPCURVE (NIL) -9 NIL 1839671 NIL) (-864 1838758 1839003 1839086 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-863 1836514 1836935 1837527 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-862 1835957 1836021 1836254 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-861 1832677 1833163 1833774 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-860 1818268 1824397 1824461 "POLYCAT" 1827946 POLYCAT (NIL T T T) -9 NIL 1829823 NIL) (-859 1813778 1815925 1818263 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-858 1813435 1813509 1813628 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-857 1813128 1813191 1813298 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-856 1806491 1812861 1813020 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-855 1805378 1805641 1805917 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-854 1803982 1804295 1804625 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-853 1799144 1803932 1803977 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-852 1797632 1798043 1798418 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-851 1796389 1796698 1797094 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-850 1796060 1796144 1796261 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-849 1795639 1795714 1795888 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-848 1795125 1795221 1795381 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-847 1794597 1794717 1794871 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-846 1793492 1793710 1794087 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-845 1793103 1793188 1793340 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-844 1792654 1792736 1792917 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-843 1792346 1792427 1792540 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-842 1791859 1791934 1792142 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-841 1791207 1791335 1791537 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-840 1790569 1790703 1790866 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-839 1789873 1790055 1790236 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-838 1789596 1789670 1789764 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-837 1786164 1787353 1788269 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-836 1785248 1785449 1785684 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-835 1780813 1782197 1783339 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-834 1760734 1765621 1770468 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-833 1760474 1760527 1760630 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-832 1759915 1760049 1760229 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-831 1757924 1759145 1759173 "PID" 1759370 PID (NIL) -9 NIL 1759497 NIL) (-830 1757712 1757755 1757830 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-829 1756899 1757559 1757646 "PI" NIL PI (NIL) -8 NIL NIL 1757686) (-828 1756351 1756502 1756678 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-827 1752679 1753637 1754542 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-826 1751043 1751332 1751698 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-825 1750485 1750600 1750761 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-824 1747026 1749354 1749707 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-823 1745632 1745912 1746237 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-822 1744397 1744651 1744999 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-821 1743107 1743334 1743686 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-820 1740117 1741677 1741705 "PFECAT" 1742298 PFECAT (NIL) -9 NIL 1742675 NIL) (-819 1739740 1739905 1740112 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-818 1738564 1738846 1739147 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-817 1736746 1737133 1737563 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-816 1732716 1736672 1736741 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-815 1728619 1729766 1730633 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-814 1726551 1727640 1727681 "PERMCAT" 1728080 PERMCAT (NIL T) -9 NIL 1728377 NIL) (-813 1726247 1726294 1726417 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-812 1722696 1724377 1725022 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-811 1720161 1722451 1722572 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-810 1719030 1719293 1719334 "PDSPC" 1719867 PDSPC (NIL T) -9 NIL 1720112 NIL) (-809 1718397 1718663 1719025 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-808 1717032 1718025 1718066 "PDRING" 1718071 PDRING (NIL T) -9 NIL 1718098 NIL) (-807 1715742 1716531 1716584 "PDMOD" 1716589 PDMOD (NIL T T) -9 NIL 1716692 NIL) (-806 1714835 1715047 1715296 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-805 1714440 1714507 1714561 "PDDOM" 1714726 PDDOM (NIL T T) -9 NIL 1714806 NIL) (-804 1714292 1714328 1714435 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-803 1714078 1714117 1714206 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-802 1712395 1713149 1713448 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-801 1712084 1712147 1712256 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-800 1710222 1710652 1711103 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-799 1703842 1705671 1706963 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-798 1703473 1703546 1703678 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-797 1701175 1701855 1702336 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-796 1699379 1699807 1700210 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-795 1698825 1699073 1699114 "PATMAB" 1699221 PATMAB (NIL T) -9 NIL 1699304 NIL) (-794 1697472 1697876 1698133 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-793 1697010 1697141 1697182 "PATAB" 1697187 PATAB (NIL T) -9 NIL 1697359 NIL) (-792 1695553 1695990 1696413 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-791 1695231 1695306 1695408 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-790 1694920 1694983 1695092 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-789 1694725 1694771 1694838 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-788 1694403 1694478 1694580 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-787 1694092 1694155 1694264 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-786 1693783 1693853 1693950 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-785 1693472 1693535 1693644 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-784 1692633 1693012 1693191 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-783 1692240 1692338 1692457 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-782 1691208 1691633 1691852 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-781 1689873 1690527 1690887 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-780 1682963 1689277 1689471 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-779 1675384 1682461 1682645 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-778 1672109 1674024 1674064 "PADICCT" 1674645 PADICCT (NIL NIL) -9 NIL 1674927 NIL) (-777 1670099 1672059 1672104 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-776 1669261 1669471 1669737 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-775 1668603 1668746 1668950 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-774 1666984 1668011 1668289 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-773 1666508 1666767 1666864 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-772 1665567 1666245 1666417 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-771 1655989 1658858 1661057 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-770 1655381 1655695 1655821 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-769 1654658 1654853 1654881 "OUTBCON" 1655199 OUTBCON (NIL) -9 NIL 1655365 NIL) (-768 1654366 1654496 1654653 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-767 1653747 1653892 1654053 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-766 1653118 1653545 1653634 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-765 1652533 1652948 1652976 "OSGROUP" 1652981 OSGROUP (NIL) -9 NIL 1653003 NIL) (-764 1651497 1651758 1652043 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-763 1648766 1651372 1651492 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-762 1645907 1648517 1648643 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-761 1643925 1644453 1645013 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-760 1637267 1639807 1639847 "OREPCAT" 1642168 OREPCAT (NIL T) -9 NIL 1643270 NIL) (-759 1635293 1636227 1637262 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-758 1634490 1634761 1634789 "ORDTYPE" 1635094 ORDTYPE (NIL) -9 NIL 1635252 NIL) (-757 1634024 1634235 1634485 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-756 1633486 1633862 1634019 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-755 1632980 1633343 1633371 "ORDSET" 1633376 ORDSET (NIL) -9 NIL 1633398 NIL) (-754 1631545 1632567 1632595 "ORDRING" 1632600 ORDRING (NIL) -9 NIL 1632628 NIL) (-753 1630793 1631350 1631378 "ORDMON" 1631383 ORDMON (NIL) -9 NIL 1631404 NIL) (-752 1630097 1630259 1630451 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-751 1629308 1629816 1629844 "ORDFIN" 1629909 ORDFIN (NIL) -9 NIL 1629983 NIL) (-750 1628702 1628841 1629027 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-749 1625377 1627670 1628076 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-748 1624784 1625139 1625244 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-747 1624592 1624637 1624703 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-746 1623893 1624169 1624210 "OPERCAT" 1624421 OPERCAT (NIL T) -9 NIL 1624517 NIL) (-745 1623705 1623772 1623888 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-744 1621071 1622507 1623003 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-743 1620492 1620619 1620793 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-742 1617393 1619631 1619997 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-741 1614024 1616823 1616863 "OMSAGG" 1616924 OMSAGG (NIL T) -9 NIL 1616988 NIL) (-740 1612436 1613695 1613863 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-739 1610632 1611873 1611901 "OINTDOM" 1611906 OINTDOM (NIL) -9 NIL 1611927 NIL) (-738 1608062 1609634 1609963 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-737 1607316 1608012 1608057 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-736 1604518 1607157 1607311 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-735 1596055 1604389 1604513 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-734 1589466 1595946 1596050 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-733 1588438 1588675 1588948 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-732 1586072 1586742 1587446 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-731 1581849 1582809 1583832 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-730 1581357 1581445 1581639 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-729 1578806 1579388 1580061 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-728 1576201 1576709 1577305 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-727 1573198 1573737 1574383 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-726 1572553 1572661 1572919 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-725 1571711 1571836 1572057 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-724 1567995 1568791 1569704 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-723 1567435 1567530 1567752 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-722 1567116 1567165 1567292 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-721 1563719 1566915 1567034 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-720 1562879 1563501 1563529 "OCAMON" 1563534 OCAMON (NIL) -9 NIL 1563555 NIL) (-719 1557091 1559905 1559945 "OC" 1561040 OC (NIL T) -9 NIL 1561896 NIL) (-718 1555091 1556017 1556997 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-717 1554507 1554925 1554953 "OASGP" 1554958 OASGP (NIL) -9 NIL 1554978 NIL) (-716 1553570 1554219 1554247 "OAMONS" 1554287 OAMONS (NIL) -9 NIL 1554330 NIL) (-715 1552715 1553296 1553324 "OAMON" 1553381 OAMON (NIL) -9 NIL 1553432 NIL) (-714 1552611 1552643 1552710 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-713 1551362 1552136 1552164 "OAGROUP" 1552310 OAGROUP (NIL) -9 NIL 1552402 NIL) (-712 1551153 1551240 1551357 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-711 1550893 1550949 1551037 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-710 1545955 1547518 1549045 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-709 1542650 1543684 1544719 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-708 1541760 1541993 1542211 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-707 1530621 1533649 1536097 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-706 1524508 1530062 1530156 "NTSCAT" 1530161 NTSCAT (NIL T T T T) -9 NIL 1530199 NIL) (-705 1523849 1524028 1524221 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-704 1523542 1523605 1523712 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-703 1511209 1521162 1521972 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-702 1500218 1511074 1511204 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-701 1498938 1499263 1499620 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-700 1497774 1498038 1498396 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-699 1496941 1497074 1497290 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-698 1495259 1495578 1495984 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-697 1494972 1495006 1495130 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-696 1494791 1494826 1494895 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-695 1494567 1494757 1494786 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-694 1494131 1494198 1494375 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-693 1492417 1493494 1493749 "NNI" NIL NNI (NIL) -8 NIL NIL 1494096) (-692 1491145 1491482 1491846 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-691 1490122 1490374 1490676 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-690 1489209 1489774 1489815 "NETCLT" 1489986 NETCLT (NIL T) -9 NIL 1490067 NIL) (-689 1488113 1488380 1488661 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-688 1487912 1487955 1488030 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-687 1486443 1486831 1487251 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-686 1485076 1486042 1486070 "NASRING" 1486180 NASRING (NIL) -9 NIL 1486260 NIL) (-685 1484921 1484977 1485071 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-684 1483850 1484528 1484556 "NARNG" 1484673 NARNG (NIL) -9 NIL 1484764 NIL) (-683 1483626 1483711 1483845 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-682 1482392 1483146 1483186 "NAALG" 1483265 NAALG (NIL T) -9 NIL 1483326 NIL) (-681 1482262 1482297 1482387 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-680 1477241 1478426 1479612 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-679 1476636 1476723 1476907 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-678 1468646 1473140 1473192 "MTSCAT" 1474252 MTSCAT (NIL T T) -9 NIL 1474766 NIL) (-677 1468412 1468472 1468564 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-676 1468238 1468277 1468337 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-675 1465100 1467789 1467830 "MSETAGG" 1467835 MSETAGG (NIL T) -9 NIL 1467869 NIL) (-674 1461237 1464146 1464464 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-673 1457511 1459334 1460074 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-672 1457148 1457221 1457350 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-671 1456801 1456842 1456986 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-670 1454666 1455003 1455434 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-669 1448064 1454565 1454661 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-668 1447589 1447630 1447838 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-667 1447148 1447197 1447380 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1446422 1446515 1446734 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-665 1445039 1445400 1445790 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-664 1444560 1444627 1444666 "MONOPC" 1444726 MONOPC (NIL T) -9 NIL 1444945 NIL) (-663 1444011 1444347 1444475 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-662 1443153 1443532 1443560 "MONOID" 1443778 MONOID (NIL) -9 NIL 1443922 NIL) (-661 1442812 1442962 1443148 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-660 1431750 1438620 1438679 "MONOGEN" 1439353 MONOGEN (NIL T T) -9 NIL 1439809 NIL) (-659 1429762 1430648 1431631 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-658 1428476 1429020 1429048 "MONADWU" 1429439 MONADWU (NIL) -9 NIL 1429674 NIL) (-657 1428024 1428224 1428471 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-656 1427301 1427602 1427630 "MONAD" 1427837 MONAD (NIL) -9 NIL 1427949 NIL) (-655 1427068 1427164 1427296 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-654 1425458 1426228 1426507 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-653 1424592 1425119 1425159 "MODULE" 1425164 MODULE (NIL T) -9 NIL 1425202 NIL) (-652 1424271 1424397 1424587 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-651 1421982 1422868 1423182 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-650 1419161 1420578 1421091 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-649 1417795 1418369 1418645 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-648 1407014 1416460 1416873 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-647 1403970 1406014 1406283 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-646 1403054 1403421 1403611 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-645 1402623 1402672 1402851 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-644 1400448 1401444 1401484 "MLO" 1401901 MLO (NIL T) -9 NIL 1402141 NIL) (-643 1398329 1398856 1399451 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-642 1397797 1397893 1398047 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-641 1397467 1397543 1397666 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-640 1396679 1396865 1397093 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-639 1396172 1396288 1396444 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-638 1395544 1395658 1395843 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-637 1394571 1394844 1395121 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-636 1394004 1394092 1394263 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-635 1391162 1392041 1392920 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-634 1389829 1390177 1390530 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-633 1386486 1388953 1388994 "MDAGG" 1389251 MDAGG (NIL T) -9 NIL 1389396 NIL) (-632 1385760 1385924 1386124 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-631 1384838 1385124 1385354 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-630 1382935 1383512 1384073 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-629 1378688 1382525 1382772 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-628 1375037 1375806 1376540 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-627 1373790 1373959 1374288 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-626 1363306 1366914 1366990 "MATCAT" 1371978 MATCAT (NIL T T T) -9 NIL 1373424 NIL) (-625 1360587 1361893 1363301 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-624 1358988 1359348 1359732 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-623 1358121 1358318 1358540 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-622 1356872 1357198 1357525 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-621 1356034 1356436 1356612 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-620 1355703 1355767 1355890 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-619 1355351 1355424 1355538 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-618 1354886 1355001 1355143 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-617 1353095 1353863 1354164 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-616 1352589 1352891 1352981 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-615 1346098 1350904 1350945 "LZSTAGG" 1351722 LZSTAGG (NIL T) -9 NIL 1352012 NIL) (-614 1343217 1344651 1346093 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-613 1340604 1341570 1342053 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-612 1340185 1340464 1340538 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-611 1332349 1340046 1340180 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-610 1331712 1331857 1332085 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-609 1329196 1329894 1330606 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-608 1327308 1327631 1328079 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-607 1320477 1326395 1326436 "LSAGG" 1326498 LSAGG (NIL T) -9 NIL 1326576 NIL) (-606 1318171 1319270 1320472 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-605 1315651 1317520 1317769 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-604 1315318 1315409 1315532 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-603 1314989 1315068 1315096 "LOGIC" 1315207 LOGIC (NIL) -9 NIL 1315289 NIL) (-602 1314884 1314913 1314984 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-601 1314203 1314361 1314554 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-600 1312988 1313237 1313588 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-599 1308810 1311609 1311649 "LODOCAT" 1312081 LODOCAT (NIL T) -9 NIL 1312292 NIL) (-598 1308603 1308679 1308805 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-597 1305603 1308480 1308598 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-596 1302701 1305553 1305598 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-595 1299788 1302631 1302696 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-594 1298841 1299016 1299318 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-593 1296973 1298103 1298356 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-592 1292068 1295132 1295173 "LNAGG" 1296035 LNAGG (NIL T) -9 NIL 1296470 NIL) (-591 1291455 1291722 1292063 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-590 1288027 1288968 1289605 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-589 1287289 1287794 1287834 "LMODULE" 1287839 LMODULE (NIL T) -9 NIL 1287865 NIL) (-588 1284468 1287026 1287148 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-587 1284036 1284247 1284288 "LLINSET" 1284349 LLINSET (NIL T) -9 NIL 1284393 NIL) (-586 1283712 1283972 1284031 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-585 1283311 1283391 1283530 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-584 1281762 1282110 1282509 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-583 1280933 1281129 1281357 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-582 1273979 1280189 1280443 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-581 1273556 1273789 1273830 "LINSET" 1273835 LINSET (NIL T) -9 NIL 1273868 NIL) (-580 1272457 1273179 1273346 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-579 1270723 1271478 1271518 "LINEXP" 1272004 LINEXP (NIL T) -9 NIL 1272277 NIL) (-578 1269345 1270332 1270513 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-577 1268172 1268444 1268746 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-576 1267385 1267974 1268084 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-575 1264935 1265657 1266407 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-574 1263565 1263862 1264253 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-573 1262358 1262960 1263000 "LIECAT" 1263140 LIECAT (NIL T) -9 NIL 1263291 NIL) (-572 1262232 1262265 1262353 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-571 1256488 1261922 1262150 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-570 1248837 1256164 1256320 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-569 1245289 1246238 1247173 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-568 1243913 1244821 1244849 "LFCAT" 1245056 LFCAT (NIL) -9 NIL 1245195 NIL) (-567 1242152 1242482 1242827 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-566 1239669 1240334 1241015 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-565 1236681 1237659 1238162 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-564 1236172 1236475 1236566 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-563 1234879 1235203 1235603 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-562 1234145 1234230 1234456 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-561 1229148 1232713 1233249 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-560 1228773 1228823 1228983 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-559 1227544 1228317 1228357 "LALG" 1228418 LALG (NIL T) -9 NIL 1228476 NIL) (-558 1227327 1227404 1227539 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-557 1225180 1226595 1226846 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-556 1225009 1225039 1225080 "KVTFROM" 1225142 KVTFROM (NIL T) -9 NIL NIL NIL) (-555 1223825 1224540 1224729 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-554 1223654 1223684 1223725 "KRCFROM" 1223787 KRCFROM (NIL T) -9 NIL NIL NIL) (-553 1222756 1222953 1223248 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-552 1222585 1222615 1222656 "KONVERT" 1222718 KONVERT (NIL T) -9 NIL NIL NIL) (-551 1222414 1222444 1222485 "KOERCE" 1222547 KOERCE (NIL T) -9 NIL NIL NIL) (-550 1221984 1222077 1222209 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-549 1220037 1220931 1221303 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-548 1213214 1218229 1218283 "KDAGG" 1218659 KDAGG (NIL T T) -9 NIL 1218866 NIL) (-547 1212862 1213004 1213209 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-546 1205692 1212643 1212800 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-545 1205342 1205624 1205687 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-544 1204312 1204811 1205060 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-543 1203438 1203887 1204092 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-542 1202302 1202794 1203094 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-541 1201584 1201983 1202144 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-540 1201294 1201530 1201579 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-539 1195549 1200984 1201212 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-538 1194967 1195300 1195420 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-537 1191129 1193144 1193198 "IXAGG" 1194125 IXAGG (NIL T T) -9 NIL 1194582 NIL) (-536 1190335 1190706 1191124 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-535 1189302 1189577 1189840 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-534 1187964 1188171 1188464 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-533 1186915 1187137 1187420 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-532 1186590 1186653 1186776 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-531 1185852 1186224 1186398 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-530 1183828 1185128 1185402 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-529 1173376 1179145 1180302 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-528 1172621 1172773 1173009 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-527 1172112 1172415 1172506 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-526 1171405 1171496 1171709 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-525 1170537 1170762 1171002 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-524 1168950 1169331 1169759 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-523 1168735 1168779 1168855 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-522 1167585 1167882 1168177 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-521 1166858 1167209 1167360 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-520 1166061 1166192 1166405 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-519 1164216 1164713 1165257 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-518 1161297 1162565 1163254 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-517 1161122 1161162 1161222 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-516 1157120 1161048 1161117 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-515 1155123 1157059 1157115 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-514 1154494 1154793 1154923 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-513 1153947 1154235 1154367 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-512 1153028 1153653 1153779 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-511 1152438 1152932 1152960 "IOBCON" 1152965 IOBCON (NIL) -9 NIL 1152986 NIL) (-510 1152009 1152073 1152255 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-509 1144053 1146424 1148749 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-508 1141164 1141947 1142811 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-507 1140841 1140938 1141055 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-506 1138283 1140777 1140836 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-505 1136395 1136924 1137491 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-504 1135897 1136011 1136151 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-503 1134281 1134687 1135149 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-502 1132060 1132654 1133265 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-501 1129433 1130043 1130763 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-500 1128837 1128995 1129203 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-499 1128356 1128442 1128630 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-498 1126561 1127082 1127539 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-497 1119643 1121296 1123025 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-496 1119009 1119171 1119344 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-495 1116882 1117346 1117890 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-494 1115008 1115958 1115986 "INTDOM" 1116285 INTDOM (NIL) -9 NIL 1116490 NIL) (-493 1114561 1114763 1115003 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-492 1110368 1112840 1112894 "INTCAT" 1113690 INTCAT (NIL T) -9 NIL 1114006 NIL) (-491 1109933 1110053 1110180 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-490 1108773 1108945 1109251 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-489 1108346 1108442 1108599 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-488 1101386 1108201 1108341 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-487 1100684 1101239 1101304 "INT8" NIL INT8 (NIL) -8 NIL NIL 1101338) (-486 1099981 1100536 1100601 "INT64" NIL INT64 (NIL) -8 NIL NIL 1100635) (-485 1099278 1099833 1099898 "INT32" NIL INT32 (NIL) -8 NIL NIL 1099932) (-484 1098575 1099130 1099195 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099229) (-483 1095038 1098494 1098570 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-482 1089095 1092578 1092606 "INS" 1093536 INS (NIL) -9 NIL 1094195 NIL) (-481 1087157 1088075 1089022 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-480 1086216 1086439 1086714 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-479 1085430 1085571 1085768 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-478 1084420 1084561 1084798 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-477 1083572 1083736 1083996 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-476 1082852 1082967 1083155 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-475 1081591 1081860 1082184 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-474 1080871 1081012 1081195 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-473 1080534 1080606 1080704 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-472 1077612 1079098 1079621 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-471 1077211 1077318 1077432 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-470 1076367 1077012 1077113 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-469 1075217 1075485 1075806 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-468 1074207 1075147 1075212 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-467 1073832 1073912 1074029 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-466 1072746 1073291 1073495 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-465 1068841 1069896 1070839 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-464 1067695 1068018 1068046 "INBCON" 1068559 INBCON (NIL) -9 NIL 1068825 NIL) (-463 1067149 1067414 1067690 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-462 1066643 1066945 1067035 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-461 1066100 1066409 1066514 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-460 1064940 1065079 1065394 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1063364 1063631 1063968 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1058207 1063295 1063359 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1057587 1057921 1058036 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1052394 1057025 1057211 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1051424 1052316 1052389 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1050996 1051073 1051127 "IEVALAB" 1051334 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1050751 1050831 1050991 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050136 1050363 1050520 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049129 1050056 1050131 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048192 1049049 1049124 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047274 1047921 1048058 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1045637 1046208 1046259 "IDPC" 1046765 IDPC (NIL T T) -9 NIL 1047078 NIL) (-447 1044925 1045559 1045632 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044095 1044847 1044920 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1043788 1044001 1044061 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1043492 1043532 1043571 "IDEMOPC" 1043576 IDEMOPC (NIL T) -9 NIL 1043713 NIL) (-443 1040563 1041444 1042336 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034189 1035466 1036505 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1033451 1033581 1033780 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1032624 1033123 1033261 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031013 1031344 1031735 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1026782 1030969 1031008 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024040 1024664 1025359 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022266 1022746 1023279 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020095 1022172 1022261 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-434 1015956 1020033 1020090 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1009535 1014920 1015388 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009103 1009166 1009339 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1008595 1008744 1008772 "HYPCAT" 1008979 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008251 1008404 1008590 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1007864 1008109 1008192 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1007697 1007746 1007787 "HOMOTOP" 1007792 HOMOTOP (NIL T) -9 NIL 1007825 NIL) (-427 1004265 1005639 1005680 "HOAGG" 1006655 HOAGG (NIL T) -9 NIL 1007376 NIL) (-426 1003271 1003741 1004260 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 996471 1002996 1003144 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 995406 995664 995927 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 994341 995271 995401 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 992535 994174 994262 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 991850 992202 992335 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 985304 991783 991845 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 978443 985040 985191 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 977896 978053 978216 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 970979 977787 977891 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 970470 970773 970864 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968020 970257 970436 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 963413 967903 968015 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 956499 963310 963408 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 948436 955868 956123 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 947460 947969 947997 "GROUP" 948200 GROUP (NIL) -9 NIL 948334 NIL) (-410 947003 947204 947455 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 945675 946014 946401 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 944497 944854 944905 "GRMOD" 945434 GRMOD (NIL T T) -9 NIL 945600 NIL) (-407 944316 944364 944492 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 940439 941650 942650 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939161 939485 939800 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 938714 938842 938983 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 937787 938286 938337 "GRALG" 938490 GRALG (NIL T T) -9 NIL 938580 NIL) (-402 937506 937607 937782 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934223 937188 937364 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 933636 933699 933956 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 929490 930386 930911 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 928665 928867 929105 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 923668 924595 925614 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 923416 923473 923562 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 922898 922987 923152 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 922407 922448 922661 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921208 921491 921795 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 914483 920898 921059 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904266 909273 910377 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 902318 903421 903449 "GCDDOM" 903704 GCDDOM (NIL) -9 NIL 903861 NIL) (-389 901941 902098 902313 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 892734 895204 897592 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 890869 891194 891612 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 889810 889999 890266 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 888681 888888 889192 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888144 888286 888434 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 886756 887104 887417 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 885301 885622 885944 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 882927 883283 883688 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876179 877840 879418 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 875831 876052 876120 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 875455 875676 875757 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 873552 874235 874695 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872145 872452 872844 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 870800 871159 871483 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870103 870227 870414 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869077 869343 869690 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 866735 867265 867747 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 866318 866378 866547 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 864618 865532 865835 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 863766 863900 864123 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 862937 863098 863325 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 858920 861871 861912 "FSAGG" 862282 FSAGG (NIL T) -9 NIL 862541 NIL) (-366 857274 858033 858825 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855230 855526 856070 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854277 854459 854759 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 853958 854007 854134 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834114 843615 843656 "FS" 847526 FS (NIL T) -9 NIL 849804 NIL) (-361 826345 829838 833817 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 825879 826006 826158 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 820402 823560 823600 "FRNAALG" 824920 FRNAALG (NIL T) -9 NIL 825518 NIL) (-358 817143 818394 819652 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 816824 816873 817000 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 815311 815868 816162 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 814597 814690 814977 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 812431 813197 813513 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 811540 811983 812024 "FRETRCT" 812029 FRETRCT (NIL T) -9 NIL 812200 NIL) (-352 810913 811191 811535 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 807657 809177 809236 "FRAMALG" 810118 FRAMALG (NIL T T) -9 NIL 810410 NIL) (-350 806253 806804 807434 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 805946 806009 806116 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 799587 805751 805941 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799280 799343 799450 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 791588 796159 797487 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 785366 788869 788897 "FPS" 790016 FPS (NIL) -9 NIL 790572 NIL) (-344 784923 785056 785220 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 781733 783776 783804 "FPC" 784029 FPC (NIL) -9 NIL 784171 NIL) (-342 781579 781631 781728 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 780356 781065 781106 "FPATMAB" 781111 FPATMAB (NIL T) -9 NIL 781263 NIL) (-340 778786 779382 779729 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 778361 778419 778592 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 776864 777759 777933 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 775479 775984 776012 "FNCAT" 776469 FNCAT (NIL) -9 NIL 776726 NIL) (-336 774936 775446 775474 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 773523 774885 774931 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770111 771469 771510 "FMONCAT" 772727 FMONCAT (NIL T) -9 NIL 773331 NIL) (-333 766969 768047 768100 "FMCAT" 769281 FMCAT (NIL T T) -9 NIL 769773 NIL) (-332 765669 766792 766891 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 764717 765517 765664 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 762904 763356 763850 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 760839 761375 761953 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754225 759176 759790 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 752706 753807 753847 "FLINEXP" 753852 FLINEXP (NIL T) -9 NIL 753945 NIL) (-326 752115 752374 752701 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 751330 751489 751710 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748213 749292 749344 "FLALG" 750571 FLALG (NIL T T) -9 NIL 751038 NIL) (-323 747384 747545 747772 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 740793 744803 744844 "FLAGG" 746099 FLAGG (NIL T) -9 NIL 746744 NIL) (-321 739901 740305 740788 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 736462 737726 737785 "FINRALG" 738913 FINRALG (NIL T T) -9 NIL 739421 NIL) (-319 735853 736118 736457 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735151 735447 735475 "FINITE" 735671 FINITE (NIL) -9 NIL 735778 NIL) (-317 735059 735085 735146 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727020 729611 729651 "FINAALG" 733303 FINAALG (NIL T) -9 NIL 734741 NIL) (-315 723287 724532 725655 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 721839 722258 722312 "FILECAT" 722996 FILECAT (NIL T T) -9 NIL 723212 NIL) (-313 721190 721664 721767 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 718438 720316 720344 "FIELD" 720384 FIELD (NIL) -9 NIL 720464 NIL) (-311 717463 717924 718433 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 715467 716413 716759 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 714710 714891 715110 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 709980 714648 714705 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 709642 709709 709844 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709182 709224 709433 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 705862 706739 707516 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701146 705794 705857 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 695825 700635 700825 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 690306 695106 695364 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 684513 689757 689968 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 683536 683746 684061 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 678976 681681 681709 "FFIELDC" 682328 FFIELDC (NIL) -9 NIL 682703 NIL) (-298 678045 678485 678971 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 677660 677718 677842 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 675804 676327 676844 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 670898 675603 675704 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 665998 670687 670794 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 660664 665789 665897 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660118 660167 660402 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 638693 649727 649813 "FFCAT" 654963 FFCAT (NIL T T T) -9 NIL 656399 NIL) (-290 634933 636159 637465 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 629776 634864 634928 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 628668 629137 629178 "FEVALAB" 629262 FEVALAB (NIL T) -9 NIL 629523 NIL) (-287 628073 628325 628663 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 624900 625811 625926 "FDIVCAT" 627493 FDIVCAT (NIL T T T T) -9 NIL 627929 NIL) (-285 624694 624726 624895 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624001 624094 624371 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 622487 623485 623688 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 621580 621964 622166 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 620702 621191 621331 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612289 616932 616972 "FAXF" 618773 FAXF (NIL T) -9 NIL 619463 NIL) (-279 610205 611009 611824 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605069 609727 609901 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 599527 601950 602002 "FAMR" 603013 FAMR (NIL T T) -9 NIL 603472 NIL) (-276 598726 599091 599522 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 597747 598668 598721 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 595341 596220 596273 "FAMONC" 597214 FAMONC (NIL T T) -9 NIL 597599 NIL) (-273 593897 595199 595336 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 591977 592338 592740 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591254 591451 591673 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583114 590701 590900 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581133 581703 582289 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578035 578677 579397 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573192 573899 574704 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 572881 572944 573053 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 557674 571930 572356 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548201 556994 557282 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 547695 547997 548087 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 547471 547661 547690 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547160 547228 547341 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 546677 546819 546860 "EVALAB" 547030 EVALAB (NIL T) -9 NIL 547134 NIL) (-259 546305 546451 546672 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 543348 544943 544971 "EUCDOM" 545525 EUCDOM (NIL) -9 NIL 545874 NIL) (-257 542275 542768 543343 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542000 542056 542156 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 541688 541752 541861 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 535459 537359 537387 "ES" 540129 ES (NIL) -9 NIL 541513 NIL) (-253 531974 533506 535298 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 531322 531475 531651 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524411 531226 531317 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524100 524163 524272 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 517727 520852 522285 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514030 515126 516219 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 512859 513209 513514 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 511744 512475 512503 "ENTIRER" 512508 ENTIRER (NIL) -9 NIL 512552 NIL) (-245 511633 511667 511739 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508266 510063 510412 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507358 507569 507623 "ELTAGG" 508003 ELTAGG (NIL T T) -9 NIL 508214 NIL) (-242 507138 507212 507353 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 506884 506919 506973 "ELTAB" 507057 ELTAB (NIL T T) -9 NIL 507109 NIL) (-240 506135 506305 506504 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 505859 505933 505961 "ELEMFUN" 506066 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 505759 505786 505854 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500305 503800 503841 "ELAGG" 504778 ELAGG (NIL T) -9 NIL 505238 NIL) (-236 499103 499641 500300 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498521 498688 498844 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497434 497753 498032 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 490827 492825 493652 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 484806 486802 487612 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482620 483026 483497 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473620 475533 477074 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 472733 473234 473383 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471431 472105 472145 "DVARCAT" 472428 DVARCAT (NIL T) -9 NIL 472568 NIL) (-227 470850 471114 471426 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 462917 470718 470845 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461255 462046 462087 "DSEXT" 462450 DSEXT (NIL T) -9 NIL 462744 NIL) (-224 460060 460584 461250 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 459784 459849 459947 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 455935 457151 458282 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451581 452936 454000 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450256 450617 451003 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 449942 450001 450119 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 448917 449215 449505 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448502 448577 448727 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 440915 443027 445142 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436432 437451 438530 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433027 435096 435137 "DQAGG" 435766 DQAGG (NIL T) -9 NIL 436039 NIL) (-213 419570 427210 427292 "DPOLCAT" 429129 DPOLCAT (NIL T T T T) -9 NIL 429672 NIL) (-212 415978 417626 419565 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 408983 415876 415973 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 401897 408812 408978 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 401490 401750 401839 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 400904 401352 401432 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400190 400515 400666 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393329 399926 400077 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391078 392395 392435 "DMEXT" 392440 DMEXT (NIL T) -9 NIL 392615 NIL) (-204 390734 390796 390940 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384059 390219 390409 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 380725 382882 382923 "DLAGG" 383473 DLAGG (NIL T) -9 NIL 383702 NIL) (-201 379076 379947 379975 "DIVRING" 380067 DIVRING (NIL) -9 NIL 380150 NIL) (-200 378527 378771 379071 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 376955 377372 377778 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 375992 376213 376478 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 369466 375924 375987 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 357786 364246 364299 "DIRPCAT" 364555 DIRPCAT (NIL NIL T) -9 NIL 365428 NIL) (-195 355792 356562 357449 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355239 355405 355591 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 351785 354125 354166 "DIOPS" 354598 DIOPS (NIL T) -9 NIL 354824 NIL) (-192 351445 351589 351780 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 350452 351198 351226 "DIOID" 351231 DIOID (NIL) -9 NIL 351253 NIL) (-190 349280 350109 350137 "DIFRING" 350142 DIFRING (NIL) -9 NIL 350163 NIL) (-189 348916 349014 349042 "DIFFSPC" 349161 DIFFSPC (NIL) -9 NIL 349236 NIL) (-188 348657 348759 348911 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 347560 348185 348225 "DIFFMOD" 348230 DIFFMOD (NIL T) -9 NIL 348327 NIL) (-186 347244 347301 347342 "DIFFDOM" 347463 DIFFDOM (NIL T) -9 NIL 347531 NIL) (-185 347125 347155 347239 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 344798 346319 346359 "DIFEXT" 346364 DIFEXT (NIL T) -9 NIL 346516 NIL) (-183 341959 344299 344340 "DIAGG" 344345 DIAGG (NIL T) -9 NIL 344365 NIL) (-182 341515 341705 341954 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 336708 340705 340982 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333166 334219 335229 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 327716 332320 332647 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326282 326574 326949 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 323402 324654 325050 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321122 323233 323322 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 320505 320650 320832 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 317823 318547 319347 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 315932 316390 316952 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 315315 315648 315762 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 308515 315040 315188 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 306435 306945 307449 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306074 306123 306274 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 305333 305895 305986 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 303357 303799 304159 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 302649 302938 303084 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302100 302246 302398 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 299462 300255 300982 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 298901 299047 299218 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 296973 297284 297651 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 296530 296785 296886 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 295731 296114 296142 "CTORCAT" 296323 CTORCAT (NIL) -9 NIL 296435 NIL) (-159 295434 295568 295726 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 294927 295184 295292 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 294343 294774 294847 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 293802 293919 294072 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290196 290952 291707 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 289687 289990 290081 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 288906 289115 289343 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 288410 288515 288719 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288163 288197 288303 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285102 285864 286582 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 284621 284763 284902 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 280514 283084 283576 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 280388 280415 280443 "CONDUIT" 280480 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279267 279998 280026 "COMRING" 280031 COMRING (NIL) -9 NIL 280081 NIL) (-145 278432 278799 278977 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278128 278169 278297 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 277821 277884 277991 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 266663 277771 277816 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266124 266263 266423 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 265877 265918 266016 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 247308 259558 259598 "COMPCAT" 260599 COMPCAT (NIL T) -9 NIL 261941 NIL) (-138 239846 243359 246952 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 239605 239639 239741 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 239435 239474 239532 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239016 239295 239369 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 238593 238834 238921 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 237788 238036 238064 "COMBOPC" 238402 COMBOPC (NIL) -9 NIL 238577 NIL) (-132 236852 237104 237346 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 233784 234468 235091 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 232664 233115 233350 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232155 232458 232549 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 231842 231895 232020 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 231312 231622 231720 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 227832 228902 229982 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226127 227112 227350 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222239 224247 224288 "CLAGG" 225214 CLAGG (NIL T) -9 NIL 225747 NIL) (-123 221132 221659 222234 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220761 220852 220992 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218698 219205 219753 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217659 218390 218418 "CHARZ" 218423 CHARZ (NIL) -9 NIL 218437 NIL) (-119 217453 217499 217577 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 216292 217055 217083 "CHARNZ" 217144 CHARNZ (NIL) -9 NIL 217192 NIL) (-117 213770 214867 215390 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213478 213557 213585 "CFCAT" 213696 CFCAT (NIL) -9 NIL NIL NIL) (-115 212821 212950 213132 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208810 212234 212514 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208188 208375 208552 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207716 208135 208183 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207189 207498 207595 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206680 206983 207074 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205929 206089 206310 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202029 203286 203994 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200395 201426 201677 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199976 200255 200329 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199410 199663 199691 "CACHSET" 199823 CACHSET (NIL) -9 NIL 199901 NIL) (-104 198762 199177 199205 "CABMON" 199255 CABMON (NIL) -9 NIL 199311 NIL) (-103 198292 198556 198666 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193515 197949 198121 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192485 193189 193324 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193487) (-100 189956 192252 192358 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187387 189699 189818 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184627 186831 186870 "BTCAT" 186937 BTCAT (NIL T) -9 NIL 187013 NIL) (-97 184378 184476 184622 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179488 183609 183635 "BTAGG" 183746 BTAGG (NIL) -9 NIL 183854 NIL) (-95 179119 179280 179483 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176181 178589 178801 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175451 175603 175781 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 171984 174157 174196 "BRAGG" 174837 BRAGG (NIL T) -9 NIL 175094 NIL) (-91 170939 171434 171979 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 163473 170444 170625 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 161465 163425 163468 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161198 161234 161345 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 159437 159870 160318 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 155403 156819 157709 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154279 155170 155292 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 153865 154022 154048 "BOOLE" 154156 BOOLE (NIL) -9 NIL 154237 NIL) (-83 153658 153739 153860 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 152796 153323 153373 "BMODULE" 153378 BMODULE (NIL T T) -9 NIL 153442 NIL) (-81 148413 152653 152722 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148226 148266 148305 "BINOPC" 148310 BINOPC (NIL T) -9 NIL 148355 NIL) (-79 147768 148041 148143 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147289 147433 147571 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 140495 147019 147164 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138229 139724 139763 "BGAGG" 140019 BGAGG (NIL T) -9 NIL 140156 NIL) (-75 138098 138136 138224 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 136949 137150 137435 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 133587 136107 136434 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133172 133265 133291 "BASTYPE" 133462 BASTYPE (NIL) -9 NIL 133558 NIL) (-71 132942 133038 133167 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 132457 132545 132695 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 131356 132031 132216 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131082 131087 131113 "ATTREG" 131118 ATTREG (NIL) -9 NIL NIL NIL) (-67 130687 130959 131024 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130187 130336 130362 "ATRIG" 130563 ATRIG (NIL) -9 NIL NIL NIL) (-65 130042 130095 130182 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 129612 129843 129869 "ASTCAT" 129874 ASTCAT (NIL) -9 NIL 129904 NIL) (-63 129411 129488 129607 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 127570 129244 129332 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 126377 126690 127055 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124184 126307 126372 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 123375 123566 123787 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 118962 123106 123220 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113256 115307 115382 "ARR2CAT" 117894 ARR2CAT (NIL T T T) -9 NIL 118623 NIL) (-56 112217 112699 113251 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111585 111956 112078 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110517 110685 110981 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110218 110272 110390 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109601 109747 109903 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 109006 109296 109416 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106574 107735 108058 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106099 106359 106455 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99794 105161 105603 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95328 96991 97041 "AMR" 97779 AMR (NIL T T) -9 NIL 98376 NIL) (-46 94682 94962 95323 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77862 94616 94677 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74265 77538 77707 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71275 71935 72542 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70654 70767 70951 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67066 67691 68283 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56555 66759 66909 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55872 56026 56204 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54585 55380 55418 "ALGEBRA" 55423 ALGEBRA (NIL T) -9 NIL 55463 NIL) (-37 54371 54448 54580 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34368 51577 51629 "ALAGG" 51767 ALAGG (NIL T T) -9 NIL 51932 NIL) (-35 33868 34017 34043 "AHYP" 34244 AHYP (NIL) -9 NIL NIL NIL) (-34 33164 33345 33371 "AGG" 33652 AGG (NIL) -9 NIL 33839 NIL) (-33 32953 33040 33159 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31092 31552 31952 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30587 30890 30979 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29957 30252 30408 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17515 26794 26832 "ACFS" 27439 ACFS (NIL T) -9 NIL 27678 NIL) (-28 16138 16748 17510 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11690 14069 14095 "ACF" 14974 ACF (NIL) -9 NIL 15386 NIL) (-26 10786 11192 11685 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10288 10528 10554 "ABELSG" 10646 ABELSG (NIL) -9 NIL 10711 NIL) (-24 10186 10217 10283 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9341 9715 9741 "ABELMON" 9966 ABELMON (NIL) -9 NIL 10099 NIL) (-22 9023 9163 9336 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8235 8718 8744 "ABELGRP" 8816 ABELGRP (NIL) -9 NIL 8891 NIL) (-20 7788 7984 8230 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 7046 7085 "A1AGG" 7090 A1AGG (NIL T) -9 NIL 7130 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
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+(((-1129) (-995)) (T -1129)) 
+NIL 
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+(((-1132 |#1|) (-10 -7 (-15 -3774 (|#1| |#1|)) (-15 -3722 ((-85) |#1|))) (-1133)) (T -1132)) 
+NIL 
+((-2568 (((-85) $ $) 7 T ELT)) (-3188 (((-85) $) 22 T ELT)) (-2064 (((-2 (|:| -1771 $) (|:| -3981 $) (|:| |associate| $)) $) 55 T ELT)) (-2063 (($ $) 54 T ELT)) (-2061 (((-85) $) 52 T ELT)) (-1311 (((-3 $ "failed") $ $) 26 T ELT)) (-3774 (($ $) 66 T ELT)) (-3970 (((-347 $) $) 67 T ELT)) (-3723 (($) 23 T CONST)) (-3466 (((-3 $ "failed") $) 42 T ELT)) (-3722 (((-85) $) 68 T ELT)) (-1213 (((-85) $ $) 20 T ELT)) (-2410 (((-85) $) 44 T ELT)) (-1890 (($ $ $) 60 T ELT) (($ (-583 $)) 59 T ELT)) (-3242 (((-1072) $) 11 T ELT)) (-3243 (((-1033) $) 12 T ELT)) (-2708 (((-1084 $) (-1084 $) (-1084 $)) 58 T ELT)) (-3144 (($ $ $) 62 T ELT) (($ (-583 $)) 61 T ELT)) (-3731 (((-347 $) $) 65 T ELT)) (-3465 (((-3 $ "failed") $ $) 56 T ELT)) (-3945 (((-772) $) 13 T ELT) (($ (-484)) 41 T ELT) (($ $) 57 T ELT)) (-3126 (((-694)) 40 T CONST)) (-1264 (((-85) $ $) 6 T ELT)) (-2062 (((-85) $ $) 53 T ELT)) (-3125 (((-85) $ $) 33 T ELT)) (-2660 (($) 24 T CONST)) (-2666 (($) 45 T CONST)) (-3056 (((-85) $ $) 8 T ELT)) (-3836 (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (-3838 (($ $ $) 18 T ELT)) (** (($ $ (-830)) 35 T ELT) (($ $ (-694)) 43 T ELT)) (* (($ (-830) $) 17 T ELT) (($ (-694) $) 21 T ELT) (($ (-484) $) 30 T ELT) (($ $ $) 34 T ELT))) 
+(((-1133) (-113)) (T -1133)) 
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+(-13 (-391) (-10 -8 (-15 -3722 ((-85) $)) (-15 -3970 ((-347 $) $)) (-15 -3774 ($ $)) (-15 -3731 ((-347 $) $)))) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 $) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-555 (-484)) . T) ((-555 $) . T) ((-552 (-772)) . T) ((-146) . T) ((-246) . T) ((-391) . T) ((-495) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-582 $) . T) ((-654 $) . T) ((-663) . T) ((-963 $) . T) ((-968 $) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T)) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| (-484)) . T) ((-25) . T) ((-38 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-349 (-484)))) ((-66) |has| |#1| (-38 (-349 (-484)))) ((-72) . T) ((-82 (-349 (-484)) (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-495)) (|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| (-740))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-555 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-555 (-484)) . T) ((-555 (-1089)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1089)))) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . T) ((-555 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-553 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-329)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-473)) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-473)))) ((-553 (-800 (-329))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-329))))) ((-553 (-800 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-484))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-484) |#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| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-484) |#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 (-349 (-484)))) ((-241 (-484) |#1|) . 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)) ((-328 |#2|) |has| |#1| (-312)) ((-342 |#2|) |has| |#1| (-312)) ((-391) |has| |#1| (-312)) ((-432) |has| |#1| (-38 (-349 (-484)))) ((-455 (-1089) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-455 (-1089) |#2|))) ((-455 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-588 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 |#2|) |has| |#1| (-312)) ((-588 $) . T) ((-590 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-590 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-582 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-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 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-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 $ (-1089)) OR (-12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1089)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1089))))) ((-809 (-1089)) OR (-12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1089))))) ((-811 (-1089)) OR (-12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1089)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1089))))) ((-796 (-329)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-329)))) ((-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 (-349 (-484)))) ((-933) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-950 (-349 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-1089)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1089)))) ((-950 |#2|) . T) ((-963 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-484))))) ((-963 |#1|) . T) ((-963 |#2|) |has| |#1| (-312)) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-968 (-349 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-349 (-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) ((-1060) . T) ((-1013) . T) ((-1065) -12 (|has| |#1| (-312)) (|has| |#2| (-1065))) ((-1114) |has| |#1| (-38 (-349 (-484)))) ((-1117) |has| |#1| (-38 (-349 (-484)))) ((-1128) . T) ((-1133) |has| |#1| (-312)) ((-1140 |#1|) . T) ((-1157 |#1| (-484)) . T)) 
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+NIL 
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+((-3817 (*1 *1 *2) (-12 (-5 *2 (-1068 (-2 (|:| |k| (-694)) (|:| |c| *3)))) (-4 *3 (-961)) (-4 *1 (-1171 *3)))) (-3816 (*1 *2 *1) (-12 (-4 *1 (-1171 *3)) (-4 *3 (-961)) (-5 *2 (-1068 *3)))) (-3817 (*1 *1 *2) (-12 (-5 *2 (-1068 *3)) (-4 *3 (-961)) (-4 *1 (-1171 *3)))) (-3815 (*1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-961)))) (-3814 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-484))) (-4 *1 (-1171 *3)) (-4 *3 (-961)))) (-3813 (*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1171 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (-3813 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1171 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-961)) (-4 *2 (-312)))) (-3811 (*1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-961)) (-4 *2 (-38 (-349 (-484)))))) (-3811 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1089)) (-4 *1 (-1171 *3)) (-4 *3 (-961)) (-12 (-4 *3 (-29 (-484))) (-4 *3 (-871)) (-4 *3 (-1114)) (-4 *3 (-38 (-349 (-484)))))) (-12 (-5 *2 (-1089)) (-4 *1 (-1171 *3)) (-4 *3 (-961)) (-12 (|has| *3 (-15 -3081 ((-583 *2) *3))) (|has| *3 (-15 -3811 (*3 *3 *2))) (-4 *3 (-38 (-349 (-484))))))))) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| (-694)) . T) ((-25) . T) ((-38 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-35) |has| |#1| (-38 (-349 (-484)))) ((-66) |has| |#1| (-38 (-349 (-484)))) ((-72) . T) ((-82 (-349 (-484)) (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-349 (-484))) |has| |#1| (-38 (-349 (-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 (-349 (-484)))) ((-241 (-694) |#1|) . T) ((-241 $ $) |has| (-694) (-1025)) ((-246) |has| |#1| (-495)) ((-432) |has| |#1| (-38 (-349 (-484)))) ((-495) |has| |#1| (-495)) ((-13) . T) ((-588 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) |has| |#1| (-495)) ((-654 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) |has| |#1| (-495)) ((-663) . T) ((-806 $ (-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-809 (-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-811 (-1089)) -12 (|has| |#1| (-809 (-1089))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-886 |#1| (-694) (-994)) . T) ((-915) |has| |#1| (-38 (-349 (-484)))) ((-963 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-968 (-349 (-484))) |has| |#1| (-38 (-349 (-484)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1114) |has| |#1| (-38 (-349 (-484)))) ((-1117) |has| |#1| (-38 (-349 (-484)))) ((-1128) . T) ((-1157 |#1| (-694)) . T)) 
+((-3820 (((-1 (-1068 |#1|) (-583 (-1068 |#1|))) (-1 |#2| (-583 |#2|))) 24 T ELT)) (-3819 (((-1 (-1068 |#1|) (-1068 |#1|) (-1068 |#1|)) (-1 |#2| |#2| |#2|)) 16 T ELT)) (-3818 (((-1 (-1068 |#1|) (-1068 |#1|)) (-1 |#2| |#2|)) 13 T ELT)) (-3823 ((|#2| (-1 |#2| |#2| |#2|) |#1| |#1|) 48 T ELT)) (-3822 ((|#2| (-1 |#2| |#2|) |#1|) 46 T ELT)) (-3824 ((|#2| (-1 |#2| (-583 |#2|)) (-583 |#1|)) 60 T ELT)) (-3825 (((-583 |#2|) (-583 |#1|) (-583 (-1 |#2| (-583 |#2|)))) 66 T ELT)) (-3821 ((|#2| |#2| |#2|) 43 T ELT))) 
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+((-3827 ((|#2| |#4| (-694)) 31 T ELT)) (-3826 ((|#4| |#2|) 26 T ELT)) (-3829 ((|#4| (-349 |#2|)) 49 (|has| |#1| (-495)) ELT)) (-3828 (((-1 |#4| (-583 |#4|)) |#3|) 43 T ELT))) 
+(((-1173 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3826 (|#4| |#2|)) (-15 -3827 (|#2| |#4| (-694))) (-15 -3828 ((-1 |#4| (-583 |#4|)) |#3|)) (IF (|has| |#1| (-495)) (-15 -3829 (|#4| (-349 |#2|))) |%noBranch|)) (-961) (-1154 |#1|) (-600 |#2|) (-1171 |#1|)) (T -1173)) 
+((-3829 (*1 *2 *3) (-12 (-5 *3 (-349 *5)) (-4 *5 (-1154 *4)) (-4 *4 (-495)) (-4 *4 (-961)) (-4 *2 (-1171 *4)) (-5 *1 (-1173 *4 *5 *6 *2)) (-4 *6 (-600 *5)))) (-3828 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *5 (-1154 *4)) (-5 *2 (-1 *6 (-583 *6))) (-5 *1 (-1173 *4 *5 *3 *6)) (-4 *3 (-600 *5)) (-4 *6 (-1171 *4)))) (-3827 (*1 *2 *3 *4) (-12 (-5 *4 (-694)) (-4 *5 (-961)) (-4 *2 (-1154 *5)) (-5 *1 (-1173 *5 *2 *6 *3)) (-4 *6 (-600 *2)) (-4 *3 (-1171 *5)))) (-3826 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *3 (-1154 *4)) (-4 *2 (-1171 *4)) (-5 *1 (-1173 *4 *3 *5 *2)) (-4 *5 (-600 *3))))) 
+NIL 
+(((-1174) (-113)) (T -1174)) 
+NIL 
+(-13 (-10 -7 (-6 -2287))) 
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+(((-1175 |#1|) (-13 (-1013) (-552 (-1089)) (-10 -8 (-15 -3945 ((-1089) $)) (-15 -3830 ((-1089))))) (-1089)) (T -1175)) 
+((-3945 (*1 *2 *1) (-12 (-5 *2 (-1089)) (-5 *1 (-1175 *3)) (-14 *3 *2))) (-3830 (*1 *2) (-12 (-5 *2 (-1089)) (-5 *1 (-1175 *3)) (-14 *3 *2)))) 
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+NIL 
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*6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))) 
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+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2811714 2811719 2811724 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2811699 2811704 2811709 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2811684 2811689 2811694 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2811669 2811674 2811679 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1208 2810648 2811587 2811664 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1207 2809863 2810042 2810261 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1206 2801022 2802891 2804825 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1205 2800410 2800563 2800752 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1204 2799872 2800175 2800288 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1203 2797432 2799334 2799537 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1202 2794196 2795849 2796420 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1201 2791453 2793183 2793237 "XPOLYC" 2793522 XPOLYC (NIL T T) -9 NIL 2793635 NIL) (-1200 2788972 2790957 2791160 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1199 2785220 2787831 2788219 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1198 2780067 2781700 2781754 "XFALG" 2783899 XFALG (NIL T T) -9 NIL 2784683 NIL) (-1197 2775223 2777956 2777998 "XF" 2778616 XF (NIL T) -9 NIL 2779012 NIL) (-1196 2774941 2775051 2775218 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1195 2774168 2774290 2774494 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1194 2771910 2774068 2774163 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1193 2770491 2771286 2771328 "XALG" 2771333 XALG (NIL T) -9 NIL 2771442 NIL) (-1192 2764048 2768901 2769379 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1191 2762291 2763293 2763614 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1190 2761890 2762162 2762231 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1189 2761377 2761680 2761773 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1188 2760454 2760664 2760959 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1187 2758750 2759213 2759675 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1186 2757639 2758224 2758266 "VSPACE" 2758402 VSPACE (NIL T) -9 NIL 2758476 NIL) (-1185 2757510 2757543 2757634 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1184 2757353 2757407 2757475 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1183 2754336 2755131 2755868 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1182 2745434 2748035 2750208 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1181 2739011 2740902 2742481 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1180 2737495 2737890 2738296 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1179 2736322 2736603 2736919 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1178 2731438 2736149 2736241 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1177 2724540 2729148 2729191 "VECTCAT" 2730179 VECTCAT (NIL T) -9 NIL 2730763 NIL) (-1176 2723819 2724145 2724535 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1175 2723313 2723555 2723675 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1174 2723246 2723251 2723281 "UTYPE" 2723286 UTYPE (NIL) -9 NIL NIL NIL) (-1173 2722233 2722409 2722670 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1172 2720084 2720592 2721116 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1171 2709966 2715936 2715978 "UTSCAT" 2717076 UTSCAT (NIL T) -9 NIL 2717833 NIL) (-1170 2708031 2708974 2709961 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1169 2707705 2707754 2707885 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1168 2699416 2705901 2706380 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2693411 2696224 2696267 "URAGG" 2698337 URAGG (NIL T) -9 NIL 2699059 NIL) (-1166 2691426 2692388 2693406 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1165 2687133 2690402 2690864 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1164 2679562 2687057 2687128 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1163 2668213 2675700 2675761 "UPXSCCA" 2676329 UPXSCCA (NIL T T) -9 NIL 2676561 NIL) (-1162 2667934 2668036 2668208 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1161 2656486 2663698 2663740 "UPXSCAT" 2664380 UPXSCAT (NIL T) -9 NIL 2664988 NIL) (-1160 2655999 2656084 2656261 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1159 2647685 2655590 2655852 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2646580 2646850 2647200 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1157 2639283 2642768 2642822 "UPSCAT" 2643891 UPSCAT (NIL T T) -9 NIL 2644655 NIL) (-1156 2638703 2638955 2639278 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1155 2638377 2638426 2638557 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1154 2622507 2631461 2631503 "UPOLYC" 2633581 UPOLYC (NIL T) -9 NIL 2634801 NIL) (-1153 2616562 2619410 2622502 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1152 2615998 2616123 2616286 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1151 2615632 2615719 2615858 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1150 2614445 2614712 2615016 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1149 2613778 2613908 2614093 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1148 2613370 2613445 2613592 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1147 2604134 2613136 2613264 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1146 2603496 2603633 2603838 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1145 2602097 2602944 2603220 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1144 2601326 2601523 2601748 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1143 2588136 2601250 2601321 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1142 2567942 2581177 2581238 "ULSCCAT" 2581869 ULSCCAT (NIL T T) -9 NIL 2582156 NIL) (-1141 2567277 2567563 2567937 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1140 2555649 2562783 2562825 "ULSCAT" 2563678 ULSCAT (NIL T) -9 NIL 2564408 NIL) (-1139 2555162 2555247 2555424 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1138 2537279 2554661 2554902 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1137 2536313 2537006 2537120 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2537231) (-1136 2535346 2536039 2536153 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2536264) (-1135 2534379 2535072 2535186 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2535297) (-1134 2533412 2534105 2534219 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2534330) (-1133 2531419 2532640 2532670 "UFD" 2532881 UFD (NIL) -9 NIL 2532994 NIL) (-1132 2531263 2531320 2531414 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1131 2530515 2530722 2530938 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1130 2528735 2529188 2529653 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1129 2528460 2528700 2528730 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1128 2528398 2528403 2528433 "TYPE" 2528438 TYPE (NIL) -9 NIL 2528445 NIL) (-1127 2527557 2527777 2528017 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1126 2526735 2527166 2527401 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1125 2524889 2525462 2526001 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1124 2523923 2524159 2524395 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1123 2512277 2516745 2516841 "TSETCAT" 2522056 TSETCAT (NIL T T T T) -9 NIL 2523568 NIL) (-1122 2508614 2510430 2512272 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1121 2503006 2507840 2508122 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1120 2498343 2499356 2500285 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1119 2497840 2497915 2498078 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1118 2495916 2496206 2496561 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1117 2495400 2495549 2495579 "TRIGCAT" 2495792 TRIGCAT (NIL) -9 NIL NIL NIL) (-1116 2495151 2495254 2495395 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1115 2492147 2494260 2494538 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1114 2491253 2491949 2491979 "TRANFUN" 2492014 TRANFUN (NIL) -9 NIL 2492080 NIL) (-1113 2490717 2490968 2491248 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1112 2490554 2490592 2490653 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1111 2490011 2490142 2490293 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1110 2488752 2489409 2489645 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1109 2488564 2488601 2488673 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1108 2486778 2487424 2487853 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1107 2485158 2485495 2485817 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1106 2476216 2482959 2483015 "TBAGG" 2483417 TBAGG (NIL T T) -9 NIL 2483630 NIL) (-1105 2472747 2474439 2476211 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1104 2472224 2472349 2472494 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1103 2471734 2472054 2472144 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1102 2471231 2471348 2471486 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1101 2464318 2471133 2471226 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1100 2460071 2461366 2462611 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1099 2459440 2459599 2459780 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1098 2456594 2457347 2458130 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1097 2456368 2456558 2456589 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1096 2455322 2456007 2456133 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2456319) (-1095 2454586 2455134 2455213 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2455273) (-1094 2451409 2452568 2453268 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1093 2449092 2449775 2450409 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1092 2445170 2446216 2447193 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1091 2442269 2444825 2445054 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1090 2441865 2441952 2442074 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1089 2438489 2439963 2440782 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1088 2431449 2437686 2437979 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2423135 2431040 2431302 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2422414 2422553 2422770 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1085 2422098 2422163 2422274 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1084 2412821 2421810 2421935 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1083 2411551 2411849 2412204 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1082 2410956 2411034 2411225 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1081 2393108 2410455 2410696 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1080 2392707 2392979 2393048 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1079 2392043 2392324 2392464 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1078 2386645 2387904 2388857 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1077 2386177 2386277 2386441 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1076 2381288 2382570 2383717 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1075 2375746 2377217 2378528 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1074 2368661 2370725 2372516 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1073 2361491 2368573 2368656 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1072 2356185 2361205 2361320 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1071 2355772 2355855 2355999 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1070 2354923 2355124 2355359 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1069 2354663 2354721 2354814 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1068 2347401 2352868 2353474 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1067 2346577 2346782 2347013 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1066 2345822 2346193 2346340 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1065 2345310 2345552 2345582 "STEP" 2345676 STEP (NIL) -9 NIL 2345747 NIL) (-1064 2338413 2345228 2345305 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1063 2332628 2337211 2337254 "STAGG" 2337681 STAGG (NIL T) -9 NIL 2337855 NIL) (-1062 2331007 2331755 2332623 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1061 2329164 2330834 2330926 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1060 2328444 2328983 2329013 "SRING" 2329018 SRING (NIL) -9 NIL 2329038 NIL) (-1059 2321066 2326982 2327421 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2314840 2316279 2317783 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1057 2307265 2312176 2312206 "SRAGG" 2313505 SRAGG (NIL) -9 NIL 2314109 NIL) (-1056 2306562 2306882 2307260 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1055 2300617 2305884 2306307 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1054 2294830 2297999 2298721 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1053 2291259 2292078 2292715 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1052 2290234 2290539 2290569 "SPFCAT" 2291013 SPFCAT (NIL) -9 NIL NIL NIL) (-1051 2289171 2289423 2289687 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1050 2279929 2282203 2282233 "SPADXPT" 2286870 SPADXPT (NIL) -9 NIL 2288994 NIL) (-1049 2279731 2279777 2279846 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1048 2277387 2279695 2279726 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1047 2269061 2271150 2271192 "SPACEC" 2275507 SPACEC (NIL T) -9 NIL 2277312 NIL) (-1046 2266890 2269008 2269056 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1045 2265823 2266012 2266301 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1044 2264227 2264560 2264971 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1043 2263492 2263726 2263987 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1042 2259672 2260632 2261627 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1041 2256030 2256729 2257458 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1040 2249816 2255370 2255466 "SNTSCAT" 2255471 SNTSCAT (NIL T T T T) -9 NIL 2255541 NIL) (-1039 2243637 2248457 2248847 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1038 2237409 2243556 2243632 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1037 2235841 2236172 2236570 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1036 2227446 2232425 2232527 "SMATCAT" 2233870 SMATCAT (NIL NIL T T T) -9 NIL 2234418 NIL) (-1035 2225287 2226271 2227441 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1034 2222879 2224493 2224536 "SKAGG" 2224797 SKAGG (NIL T) -9 NIL 2224931 NIL) (-1033 2218925 2222699 2222810 "SINT" NIL SINT (NIL) -8 NIL NIL 2222851) (-1032 2218735 2218779 2218845 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2217810 2218042 2218310 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2216814 2216976 2217252 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2216160 2216500 2216623 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2215506 2215813 2215953 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2213617 2214109 2214615 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2207057 2213536 2213612 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2206560 2206797 2206827 "SGROUP" 2206920 SGROUP (NIL) -9 NIL 2206982 NIL) (-1024 2206450 2206482 2206555 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2206088 2206128 2206169 "SGPOPC" 2206174 SGPOPC (NIL T) -9 NIL 2206375 NIL) (-1022 2205622 2205899 2206005 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2203045 2203814 2204536 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2196930 2202484 2202580 "SFRTCAT" 2202585 SFRTCAT (NIL T T T T) -9 NIL 2202623 NIL) (-1019 2191322 2192435 2193562 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2185498 2186659 2187823 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2184470 2185372 2185493 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2180078 2180973 2181068 "SEXCAT" 2183681 SEXCAT (NIL T T T T T) -9 NIL 2184232 NIL) (-1015 2179051 2180005 2180073 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2177442 2178027 2178329 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2176965 2177150 2177180 "SETCAT" 2177297 SETCAT (NIL) -9 NIL 2177381 NIL) (-1012 2176797 2176861 2176960 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2173020 2175251 2175294 "SETAGG" 2176162 SETAGG (NIL T) -9 NIL 2176500 NIL) (-1010 2172626 2172778 2173015 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2169580 2172573 2172621 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2169046 2169356 2169456 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2168173 2168539 2168600 "SEGXCAT" 2168886 SEGXCAT (NIL T T) -9 NIL 2169006 NIL) (-1006 2167098 2167366 2167409 "SEGCAT" 2167931 SEGCAT (NIL T) -9 NIL 2168152 NIL) (-1005 2166778 2166843 2166956 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2165844 2166314 2166522 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2165422 2165701 2165777 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2164787 2164923 2165127 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2163853 2164600 2164782 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2163106 2163801 2163848 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2154593 2162975 2163101 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2153453 2153743 2154060 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2152759 2152971 2153159 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2152109 2152266 2152442 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2151682 2151913 2151941 "SASTCAT" 2151946 SASTCAT (NIL) -9 NIL 2151959 NIL) (-994 2151149 2151574 2151648 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2150752 2150793 2150964 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2150383 2150424 2150581 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2143464 2150300 2150378 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2142114 2142443 2142839 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2140875 2141236 2141536 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2140499 2140720 2140801 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2137959 2138593 2139046 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2137798 2137831 2137899 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2137289 2137592 2137683 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2132917 2133785 2134696 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2121736 2127290 2127384 "RSETCAT" 2131440 RSETCAT (NIL T T T T) -9 NIL 2132528 NIL) (-982 2120274 2120916 2121731 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2114048 2115493 2117000 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2111930 2112487 2112559 "RRCC" 2113632 RRCC (NIL T T) -9 NIL 2113973 NIL) (-979 2111455 2111654 2111925 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2110925 2111235 2111333 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2083477 2094190 2094254 "RPOLCAT" 2104728 RPOLCAT (NIL T T T) -9 NIL 2107873 NIL) (-976 2077576 2080399 2083472 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2073743 2077324 2077462 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2072071 2072810 2073066 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2067714 2070526 2070554 "RNS" 2070816 RNS (NIL) -9 NIL 2071068 NIL) (-972 2066617 2067104 2067641 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2065735 2066136 2066336 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2064873 2065435 2065463 "RNG" 2065523 RNG (NIL) -9 NIL 2065577 NIL) (-969 2064762 2064796 2064868 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-968 2064024 2064529 2064569 "RMODULE" 2064574 RMODULE (NIL T) -9 NIL 2064600 NIL) (-967 2062963 2063069 2063399 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2059809 2062553 2062846 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2052458 2054950 2055062 "RMATCAT" 2058367 RMATCAT (NIL NIL NIL T T T) -9 NIL 2059344 NIL) (-964 2051975 2052154 2052453 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2051543 2051754 2051795 "RLINSET" 2051856 RLINSET (NIL T) -9 NIL 2051900 NIL) (-962 2051188 2051269 2051395 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2050034 2050765 2050793 "RING" 2050848 RING (NIL) -9 NIL 2050940 NIL) (-960 2049879 2049935 2050029 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2048933 2049200 2049456 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2039920 2048561 2048762 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2039145 2039656 2039695 "RGBCSPC" 2039752 RGBCSPC (NIL T) -9 NIL 2039803 NIL) (-956 2038179 2038665 2038704 "RGBCMDL" 2038932 RGBCMDL (NIL T) -9 NIL 2039046 NIL) (-955 2037891 2037960 2038061 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2037654 2037695 2037790 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2036078 2036508 2036888 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2033665 2034333 2035001 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2033215 2033313 2033473 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2032837 2032935 2032976 "RETRACT" 2033107 RETRACT (NIL T) -9 NIL 2033194 NIL) (-949 2032717 2032748 2032832 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2032319 2032591 2032658 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2030799 2031690 2031887 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2030490 2030551 2030647 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2030233 2030274 2030379 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2029968 2030009 2030118 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2025039 2026490 2027705 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2022138 2022896 2023704 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2020107 2020729 2021329 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 2012742 2018658 2019094 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 2012054 2012334 2012483 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 2011539 2011654 2011819 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 2007132 2010942 2011163 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 2006364 2006563 2006776 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 2003654 2004492 2005374 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 2000236 2001272 2002331 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 2000072 2000125 2000153 "REAL" 2000158 REAL (NIL) -9 NIL 2000193 NIL) (-932 1999562 1999866 1999957 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 1999042 1999120 1999325 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 1998275 1998467 1998678 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 1997163 1997460 1997827 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1995430 1995900 1996433 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1994352 1994629 1995016 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1993179 1993488 1993907 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1986527 1990039 1990067 "RCFIELD" 1991344 RCFIELD (NIL) -9 NIL 1992074 NIL) (-924 1985145 1985757 1986454 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1981345 1983237 1983278 "RCAGG" 1984345 RCAGG (NIL T) -9 NIL 1984806 NIL) (-922 1981072 1981182 1981340 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1980517 1980646 1980807 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1980134 1980213 1980332 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1979549 1979699 1979849 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1979331 1979381 1979452 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1971773 1978449 1978757 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1961475 1971640 1971768 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1961109 1961202 1961230 "RADCAT" 1961387 RADCAT (NIL) -9 NIL NIL NIL) (-914 1960947 1961007 1961104 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1959047 1960778 1960867 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1958728 1958777 1958904 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1951015 1955099 1955139 "QUATCAT" 1955917 QUATCAT (NIL T) -9 NIL 1956681 NIL) (-910 1948265 1949545 1950921 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1944105 1948215 1948260 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1941492 1943159 1943200 "QUAGG" 1943575 QUAGG (NIL T) -9 NIL 1943749 NIL) (-907 1941094 1941366 1941433 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1940100 1940730 1940893 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1939781 1939830 1939957 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1929381 1935550 1935590 "QFCAT" 1936248 QFCAT (NIL T) -9 NIL 1937241 NIL) (-903 1926265 1927704 1929287 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1925811 1925945 1926075 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1920007 1921168 1922330 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1919426 1919606 1919838 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1917248 1917776 1918199 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1916147 1916389 1916706 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1914508 1914706 1915059 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1910264 1911480 1911521 "PTRANFN" 1913405 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1908911 1909256 1909577 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1908604 1908667 1908774 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1902677 1907400 1907440 "PTCAT" 1907732 PTCAT (NIL T) -9 NIL 1907885 NIL) (-892 1902370 1902411 1902535 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1901249 1901565 1901899 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1890128 1892689 1894998 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1883035 1885931 1886025 "PSETCAT" 1888999 PSETCAT (NIL T T T T) -9 NIL 1889806 NIL) (-888 1881485 1882219 1883030 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1880804 1880999 1881027 "PSCURVE" 1881295 PSCURVE (NIL) -9 NIL 1881462 NIL) (-886 1876406 1878226 1878290 "PSCAT" 1879125 PSCAT (NIL T T T) -9 NIL 1879364 NIL) (-885 1875720 1876002 1876401 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1874117 1875032 1875295 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1873608 1873911 1874002 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1864628 1867050 1869238 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1862371 1863948 1863988 "PRQAGG" 1864171 PRQAGG (NIL T) -9 NIL 1864272 NIL) (-880 1861544 1861990 1862018 "PROPLOG" 1862157 PROPLOG (NIL) -9 NIL 1862271 NIL) (-879 1861219 1861282 1861405 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1860655 1860794 1860966 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1858903 1859666 1859963 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1858455 1858587 1858715 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1852896 1857395 1858215 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1852725 1852763 1852822 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1852164 1852304 1852455 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1850632 1851051 1851517 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1850349 1850410 1850438 "PRIMCAT" 1850562 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1849520 1849716 1849944 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1845401 1849470 1849515 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1845100 1845162 1845273 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1842236 1844749 1844982 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1841687 1841844 1841872 "PPCURVE" 1842077 PPCURVE (NIL) -9 NIL 1842213 NIL) (-865 1841300 1841545 1841628 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1839056 1839477 1840069 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1838499 1838563 1838796 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1835219 1835705 1836316 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1820810 1826939 1827003 "POLYCAT" 1830488 POLYCAT (NIL T T T) -9 NIL 1832365 NIL) (-860 1816320 1818467 1820805 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1815977 1816051 1816170 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1815670 1815733 1815840 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1809033 1815403 1815562 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1807920 1808183 1808459 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1806524 1806837 1807167 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1801686 1806474 1806519 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1800174 1800585 1800960 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1798931 1799240 1799636 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1798602 1798686 1798803 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1798181 1798256 1798430 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1797667 1797763 1797923 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1797139 1797259 1797413 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1796034 1796252 1796629 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1795645 1795730 1795882 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1795196 1795278 1795459 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1794888 1794969 1795082 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1794401 1794476 1794684 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1793749 1793877 1794079 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1793111 1793245 1793408 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1792415 1792597 1792778 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1792138 1792212 1792306 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1788706 1789895 1790811 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1787790 1787991 1788226 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1783355 1784739 1785881 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1763276 1768163 1773010 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1763016 1763069 1763172 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1762457 1762591 1762771 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1760466 1761687 1761715 "PID" 1761912 PID (NIL) -9 NIL 1762039 NIL) (-831 1760254 1760297 1760372 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1759441 1760101 1760188 "PI" NIL PI (NIL) -8 NIL NIL 1760228) (-829 1758893 1759044 1759220 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1755221 1756179 1757084 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1753585 1753874 1754240 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1753027 1753142 1753303 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1749568 1751896 1752249 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1748174 1748454 1748779 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1746939 1747193 1747541 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1745649 1745876 1746228 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1742659 1744219 1744247 "PFECAT" 1744840 PFECAT (NIL) -9 NIL 1745217 NIL) (-820 1742282 1742447 1742654 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1741106 1741388 1741689 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1739288 1739675 1740105 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1735258 1739214 1739283 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1731161 1732308 1733175 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1729093 1730182 1730223 "PERMCAT" 1730622 PERMCAT (NIL T) -9 NIL 1730919 NIL) (-814 1728789 1728836 1728959 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1725238 1726919 1727564 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1722703 1724993 1725114 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1721572 1721835 1721876 "PDSPC" 1722409 PDSPC (NIL T) -9 NIL 1722654 NIL) (-810 1720939 1721205 1721567 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1719574 1720567 1720608 "PDRING" 1720613 PDRING (NIL T) -9 NIL 1720640 NIL) (-808 1718284 1719073 1719126 "PDMOD" 1719131 PDMOD (NIL T T) -9 NIL 1719234 NIL) (-807 1717377 1717589 1717838 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1716982 1717049 1717103 "PDDOM" 1717268 PDDOM (NIL T T) -9 NIL 1717348 NIL) (-805 1716834 1716870 1716977 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1716620 1716659 1716748 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1714937 1715691 1715990 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1714626 1714689 1714798 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1712764 1713194 1713645 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1706384 1708213 1709505 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1706015 1706088 1706220 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1703717 1704397 1704878 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1701921 1702349 1702752 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1701367 1701615 1701656 "PATMAB" 1701763 PATMAB (NIL T) -9 NIL 1701846 NIL) (-795 1700014 1700418 1700675 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1699552 1699683 1699724 "PATAB" 1699729 PATAB (NIL T) -9 NIL 1699901 NIL) (-793 1698095 1698532 1698955 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1697773 1697848 1697950 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1697462 1697525 1697634 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1697267 1697313 1697380 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1696945 1697020 1697122 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1696634 1696697 1696806 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1696325 1696395 1696492 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1696014 1696077 1696186 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1695175 1695554 1695733 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1694782 1694880 1694999 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1693750 1694175 1694394 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1692415 1693069 1693429 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1685505 1691819 1692013 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1677926 1685003 1685187 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1674651 1676566 1676606 "PADICCT" 1677187 PADICCT (NIL NIL) -9 NIL 1677469 NIL) (-778 1672641 1674601 1674646 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1671803 1672013 1672279 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1671145 1671288 1671492 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1669526 1670553 1670831 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1669050 1669309 1669406 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1668109 1668787 1668959 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1658531 1661400 1663599 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1657923 1658237 1658363 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1657200 1657395 1657423 "OUTBCON" 1657741 OUTBCON (NIL) -9 NIL 1657907 NIL) (-769 1656908 1657038 1657195 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1656289 1656434 1656595 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1655660 1656087 1656176 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1655075 1655490 1655518 "OSGROUP" 1655523 OSGROUP (NIL) -9 NIL 1655545 NIL) (-765 1654039 1654300 1654585 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1651308 1653914 1654034 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1648449 1651059 1651185 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1646467 1646995 1647555 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1639809 1642349 1642389 "OREPCAT" 1644710 OREPCAT (NIL T) -9 NIL 1645812 NIL) (-760 1637835 1638769 1639804 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1637032 1637303 1637331 "ORDTYPE" 1637636 ORDTYPE (NIL) -9 NIL 1637794 NIL) (-758 1636566 1636777 1637027 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1636028 1636404 1636561 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1635522 1635885 1635913 "ORDSET" 1635918 ORDSET (NIL) -9 NIL 1635940 NIL) (-755 1634087 1635109 1635137 "ORDRING" 1635142 ORDRING (NIL) -9 NIL 1635170 NIL) (-754 1633335 1633892 1633920 "ORDMON" 1633925 ORDMON (NIL) -9 NIL 1633946 NIL) (-753 1632639 1632801 1632993 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1631850 1632358 1632386 "ORDFIN" 1632451 ORDFIN (NIL) -9 NIL 1632525 NIL) (-751 1631244 1631383 1631569 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1627919 1630212 1630618 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1627326 1627681 1627786 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1627134 1627179 1627245 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1626435 1626711 1626752 "OPERCAT" 1626963 OPERCAT (NIL T) -9 NIL 1627059 NIL) (-746 1626247 1626314 1626430 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1623613 1625049 1625545 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1623034 1623161 1623335 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1619935 1622173 1622539 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1616566 1619365 1619405 "OMSAGG" 1619466 OMSAGG (NIL T) -9 NIL 1619530 NIL) (-741 1614978 1616237 1616405 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1613174 1614415 1614443 "OINTDOM" 1614448 OINTDOM (NIL) -9 NIL 1614469 NIL) (-739 1610604 1612176 1612505 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1609858 1610554 1610599 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1607060 1609699 1609853 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1598597 1606931 1607055 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1592008 1598488 1598592 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1590980 1591217 1591490 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1588614 1589284 1589988 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1584391 1585351 1586374 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1583899 1583987 1584181 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1581348 1581930 1582603 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1578743 1579251 1579847 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1575740 1576279 1576925 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1575095 1575203 1575461 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1574253 1574378 1574599 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1570537 1571333 1572246 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1569977 1570072 1570294 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1569658 1569707 1569834 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1566261 1569457 1569576 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1565421 1566043 1566071 "OCAMON" 1566076 OCAMON (NIL) -9 NIL 1566097 NIL) (-720 1559633 1562447 1562487 "OC" 1563582 OC (NIL T) -9 NIL 1564438 NIL) (-719 1557633 1558559 1559539 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1557049 1557467 1557495 "OASGP" 1557500 OASGP (NIL) -9 NIL 1557520 NIL) (-717 1556112 1556761 1556789 "OAMONS" 1556829 OAMONS (NIL) -9 NIL 1556872 NIL) (-716 1555257 1555838 1555866 "OAMON" 1555923 OAMON (NIL) -9 NIL 1555974 NIL) (-715 1555153 1555185 1555252 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1553904 1554678 1554706 "OAGROUP" 1554852 OAGROUP (NIL) -9 NIL 1554944 NIL) (-713 1553695 1553782 1553899 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1553435 1553491 1553579 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1548497 1550060 1551587 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1545192 1546226 1547261 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1544302 1544535 1544753 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1533163 1536191 1538639 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1527050 1532604 1532698 "NTSCAT" 1532703 NTSCAT (NIL T T T T) -9 NIL 1532741 NIL) (-706 1526391 1526570 1526763 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1526084 1526147 1526254 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1513751 1523704 1524514 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1502760 1513616 1513746 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1501480 1501805 1502162 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1500316 1500580 1500938 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1499483 1499616 1499832 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1497801 1498120 1498526 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1497514 1497548 1497672 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1497333 1497368 1497437 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1497109 1497299 1497328 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1496673 1496740 1496917 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1494959 1496036 1496291 "NNI" NIL NNI (NIL) -8 NIL NIL 1496638) (-693 1493687 1494024 1494388 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1492664 1492916 1493218 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1491751 1492316 1492357 "NETCLT" 1492528 NETCLT (NIL T) -9 NIL 1492609 NIL) (-690 1490655 1490922 1491203 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1490454 1490497 1490572 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1488985 1489373 1489793 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1487618 1488584 1488612 "NASRING" 1488722 NASRING (NIL) -9 NIL 1488802 NIL) (-686 1487463 1487519 1487613 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1486392 1487070 1487098 "NARNG" 1487215 NARNG (NIL) -9 NIL 1487306 NIL) (-684 1486168 1486253 1486387 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1484934 1485688 1485728 "NAALG" 1485807 NAALG (NIL T) -9 NIL 1485868 NIL) (-682 1484804 1484839 1484929 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1479783 1480968 1482154 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1479178 1479265 1479449 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1471188 1475682 1475734 "MTSCAT" 1476794 MTSCAT (NIL T T) -9 NIL 1477308 NIL) (-678 1470954 1471014 1471106 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1470780 1470819 1470879 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1467642 1470331 1470372 "MSETAGG" 1470377 MSETAGG (NIL T) -9 NIL 1470411 NIL) (-675 1463779 1466688 1467006 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1460053 1461876 1462616 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1459690 1459763 1459892 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1459343 1459384 1459528 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1457208 1457545 1457976 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1450606 1457107 1457203 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1450131 1450172 1450380 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1449690 1449739 1449922 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1448964 1449057 1449276 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1447581 1447942 1448332 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1447102 1447169 1447208 "MONOPC" 1447268 MONOPC (NIL T) -9 NIL 1447487 NIL) (-664 1446553 1446889 1447017 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1445695 1446074 1446102 "MONOID" 1446320 MONOID (NIL) -9 NIL 1446464 NIL) (-662 1445354 1445504 1445690 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1434292 1441162 1441221 "MONOGEN" 1441895 MONOGEN (NIL T T) -9 NIL 1442351 NIL) (-660 1432304 1433190 1434173 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1431018 1431562 1431590 "MONADWU" 1431981 MONADWU (NIL) -9 NIL 1432216 NIL) (-658 1430566 1430766 1431013 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1429843 1430144 1430172 "MONAD" 1430379 MONAD (NIL) -9 NIL 1430491 NIL) (-656 1429610 1429706 1429838 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1428000 1428770 1429049 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1427134 1427661 1427701 "MODULE" 1427706 MODULE (NIL T) -9 NIL 1427744 NIL) (-653 1426813 1426939 1427129 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1424524 1425410 1425724 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1421703 1423120 1423633 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1420337 1420911 1421187 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1409556 1419002 1419415 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1406512 1408556 1408825 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1405596 1405963 1406153 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1405165 1405214 1405393 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1402990 1403986 1404026 "MLO" 1404443 MLO (NIL T) -9 NIL 1404683 NIL) (-644 1400871 1401398 1401993 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1400339 1400435 1400589 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1400009 1400085 1400208 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1399221 1399407 1399635 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1398714 1398830 1398986 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1398086 1398200 1398385 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1397113 1397386 1397663 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1396546 1396634 1396805 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1393704 1394583 1395462 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1392371 1392719 1393072 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1389028 1391495 1391536 "MDAGG" 1391793 MDAGG (NIL T) -9 NIL 1391938 NIL) (-633 1388302 1388466 1388666 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1387380 1387666 1387896 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1385477 1386054 1386615 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1381230 1385067 1385314 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1377579 1378348 1379082 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1376332 1376501 1376830 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1365848 1369456 1369532 "MATCAT" 1374520 MATCAT (NIL T T T) -9 NIL 1375966 NIL) (-626 1363129 1364435 1365843 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1361530 1361890 1362274 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1360663 1360860 1361082 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1359414 1359740 1360067 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1358576 1358978 1359154 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1358245 1358309 1358432 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1357893 1357966 1358080 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1357428 1357543 1357685 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1355637 1356405 1356706 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1355131 1355433 1355523 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1348640 1353446 1353487 "LZSTAGG" 1354264 LZSTAGG (NIL T) -9 NIL 1354554 NIL) (-615 1345759 1347193 1348635 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1343146 1344112 1344595 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1342727 1343006 1343080 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1334891 1342588 1342722 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1334254 1334399 1334627 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1331738 1332436 1333148 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1329850 1330173 1330621 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1323019 1328937 1328978 "LSAGG" 1329040 LSAGG (NIL T) -9 NIL 1329118 NIL) (-607 1320713 1321812 1323014 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1318193 1320062 1320311 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1317860 1317951 1318074 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1317531 1317610 1317638 "LOGIC" 1317749 LOGIC (NIL) -9 NIL 1317831 NIL) (-603 1317426 1317455 1317526 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1316745 1316903 1317096 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1315530 1315779 1316130 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1311352 1314151 1314191 "LODOCAT" 1314623 LODOCAT (NIL T) -9 NIL 1314834 NIL) (-599 1311145 1311221 1311347 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1308145 1311022 1311140 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1305243 1308095 1308140 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1302330 1305173 1305238 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1301383 1301558 1301860 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1299515 1300645 1300898 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1294610 1297674 1297715 "LNAGG" 1298577 LNAGG (NIL T) -9 NIL 1299012 NIL) (-592 1293997 1294264 1294605 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1290569 1291510 1292147 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1289831 1290336 1290376 "LMODULE" 1290381 LMODULE (NIL T) -9 NIL 1290407 NIL) (-589 1287010 1289568 1289690 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1286578 1286789 1286830 "LLINSET" 1286891 LLINSET (NIL T) -9 NIL 1286935 NIL) (-587 1286254 1286514 1286573 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1285853 1285933 1286072 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1284304 1284652 1285051 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1283475 1283671 1283899 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1276521 1282731 1282985 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1276098 1276331 1276372 "LINSET" 1276377 LINSET (NIL T) -9 NIL 1276410 NIL) (-581 1274999 1275721 1275888 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1273265 1274020 1274060 "LINEXP" 1274546 LINEXP (NIL T) -9 NIL 1274819 NIL) (-579 1271887 1272874 1273055 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1270714 1270986 1271288 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1269927 1270516 1270626 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1267477 1268199 1268949 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1266107 1266404 1266795 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1264900 1265502 1265542 "LIECAT" 1265682 LIECAT (NIL T) -9 NIL 1265833 NIL) (-573 1264774 1264807 1264895 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1259030 1264464 1264692 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1251379 1258706 1258862 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1247831 1248780 1249715 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1246455 1247363 1247391 "LFCAT" 1247598 LFCAT (NIL) -9 NIL 1247737 NIL) (-568 1244694 1245024 1245369 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1242211 1242876 1243557 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1239223 1240201 1240704 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1238714 1239017 1239108 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1237421 1237745 1238145 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1236687 1236772 1236998 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1231690 1235255 1235791 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1231315 1231365 1231525 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1230086 1230859 1230899 "LALG" 1230960 LALG (NIL T) -9 NIL 1231018 NIL) (-559 1229869 1229946 1230081 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1227722 1229137 1229388 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1227551 1227581 1227622 "KVTFROM" 1227684 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1226367 1227082 1227271 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1226196 1226226 1226267 "KRCFROM" 1226329 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1225298 1225495 1225790 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1225127 1225157 1225198 "KONVERT" 1225260 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1224956 1224986 1225027 "KOERCE" 1225089 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1224526 1224619 1224751 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1222579 1223473 1223845 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1215756 1220771 1220825 "KDAGG" 1221201 KDAGG (NIL T T) -9 NIL 1221408 NIL) (-548 1215404 1215546 1215751 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1208234 1215185 1215342 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1207884 1208166 1208229 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1206854 1207353 1207602 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1205980 1206429 1206634 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1204844 1205336 1205636 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1204126 1204525 1204686 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1203836 1204072 1204121 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1198091 1203526 1203754 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1197509 1197842 1197962 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1193671 1195686 1195740 "IXAGG" 1196667 IXAGG (NIL T T) -9 NIL 1197124 NIL) (-537 1192877 1193248 1193666 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1191844 1192119 1192382 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1190506 1190713 1191006 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1189457 1189679 1189962 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1189132 1189195 1189318 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1188394 1188766 1188940 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1186370 1187670 1187944 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1175918 1181687 1182844 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1175163 1175315 1175551 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1174654 1174957 1175048 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1173947 1174038 1174251 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1173079 1173304 1173544 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1171492 1171873 1172301 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1171277 1171321 1171397 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1170127 1170424 1170719 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1169400 1169751 1169902 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1168603 1168734 1168947 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1166758 1167255 1167799 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1163839 1165107 1165796 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1163664 1163704 1163764 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1159662 1163590 1163659 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1157665 1159601 1159657 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1157036 1157335 1157465 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1156489 1156777 1156909 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1155570 1156195 1156321 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1154980 1155474 1155502 "IOBCON" 1155507 IOBCON (NIL) -9 NIL 1155528 NIL) (-511 1154551 1154615 1154797 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1146595 1148966 1151291 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1143706 1144489 1145353 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1143383 1143480 1143597 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1140825 1143319 1143378 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1138937 1139466 1140033 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1138439 1138553 1138693 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1136823 1137229 1137691 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1134602 1135196 1135807 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1131975 1132585 1133305 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1131379 1131537 1131745 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1130898 1130984 1131172 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1129103 1129624 1130081 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1122185 1123838 1125567 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1121551 1121713 1121886 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1119424 1119888 1120432 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1117550 1118500 1118528 "INTDOM" 1118827 INTDOM (NIL) -9 NIL 1119032 NIL) (-494 1117103 1117305 1117545 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1112910 1115382 1115436 "INTCAT" 1116232 INTCAT (NIL T) -9 NIL 1116548 NIL) (-492 1112475 1112595 1112722 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1111315 1111487 1111793 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1110888 1110984 1111141 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1103928 1110743 1110883 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1103226 1103781 1103846 "INT8" NIL INT8 (NIL) -8 NIL NIL 1103880) (-487 1102523 1103078 1103143 "INT64" NIL INT64 (NIL) -8 NIL NIL 1103177) (-486 1101820 1102375 1102440 "INT32" NIL INT32 (NIL) -8 NIL NIL 1102474) (-485 1101117 1101672 1101737 "INT16" NIL INT16 (NIL) -8 NIL NIL 1101771) (-484 1097580 1101036 1101112 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1091637 1095120 1095148 "INS" 1096078 INS (NIL) -9 NIL 1096737 NIL) (-482 1089699 1090617 1091564 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1088758 1088981 1089256 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1087972 1088113 1088310 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1086962 1087103 1087340 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1086114 1086278 1086538 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1085394 1085509 1085697 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1084133 1084402 1084726 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1083413 1083554 1083737 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1083076 1083148 1083246 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1080154 1081640 1082163 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1079753 1079860 1079974 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1078909 1079554 1079655 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1077759 1078027 1078348 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1076749 1077689 1077754 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1076374 1076454 1076571 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1075288 1075833 1076037 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1071383 1072438 1073381 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1070237 1070560 1070588 "INBCON" 1071101 INBCON (NIL) -9 NIL 1071367 NIL) (-464 1069691 1069956 1070232 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1069185 1069487 1069577 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1068642 1068951 1069056 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1067482 1067621 1067936 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1065906 1066173 1066510 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1060749 1065837 1065901 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-458 1060129 1060463 1060578 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-457 1054936 1059567 1059753 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-456 1053966 1054858 1054931 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-455 1053538 1053615 1053669 "IEVALAB" 1053876 IEVALAB (NIL T T) -9 NIL NIL NIL) (-454 1053293 1053373 1053533 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-453 1052678 1052905 1053062 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-452 1051671 1052598 1052673 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-451 1050734 1051591 1051666 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-450 1049816 1050463 1050600 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-449 1048179 1048750 1048801 "IDPC" 1049307 IDPC (NIL T T) -9 NIL 1049620 NIL) (-448 1047467 1048101 1048174 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-447 1046637 1047389 1047462 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-446 1046330 1046543 1046603 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-445 1046034 1046074 1046113 "IDEMOPC" 1046118 IDEMOPC (NIL T) -9 NIL 1046255 NIL) (-444 1043105 1043986 1044878 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-443 1036731 1038008 1039047 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-442 1035993 1036123 1036322 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-441 1035166 1035665 1035803 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-440 1033555 1033886 1034277 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-439 1029324 1033511 1033550 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-438 1026582 1027206 1027901 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-437 1024808 1025288 1025821 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-436 1022637 1024714 1024803 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-435 1018498 1022575 1022632 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-434 1012077 1017462 1017930 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-433 1011645 1011708 1011881 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-432 1011137 1011286 1011314 "HYPCAT" 1011521 HYPCAT (NIL) -9 NIL NIL NIL) (-431 1010793 1010946 1011132 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-430 1010406 1010651 1010734 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-429 1010239 1010288 1010329 "HOMOTOP" 1010334 HOMOTOP (NIL T) -9 NIL 1010367 NIL) (-428 1006807 1008181 1008222 "HOAGG" 1009197 HOAGG (NIL T) -9 NIL 1009918 NIL) (-427 1005813 1006283 1006802 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-426 999013 1005538 1005686 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-425 997948 998206 998469 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-424 996883 997813 997943 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-423 995077 996716 996804 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-422 994392 994744 994877 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-421 987846 994325 994387 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-420 980985 987582 987733 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-419 980438 980595 980758 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-418 973521 980329 980433 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-417 973012 973315 973406 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-416 970562 972799 972978 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-415 965955 970445 970557 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-414 959041 965852 965950 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-413 950978 958410 958665 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-412 950002 950511 950539 "GROUP" 950742 GROUP (NIL) -9 NIL 950876 NIL) (-411 949545 949746 949997 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-410 948217 948556 948943 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-409 947039 947396 947447 "GRMOD" 947976 GRMOD (NIL T T) -9 NIL 948142 NIL) (-408 946858 946906 947034 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-407 942981 944192 945192 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-406 941703 942027 942342 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-405 941256 941384 941525 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-404 940329 940828 940879 "GRALG" 941032 GRALG (NIL T T) -9 NIL 941122 NIL) (-403 940048 940149 940324 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-402 936765 939730 939906 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-401 936178 936241 936498 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-400 932032 932928 933453 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-399 931207 931409 931647 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-398 926210 927137 928156 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-397 925958 926015 926104 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-396 925440 925529 925694 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-395 924949 924990 925203 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-394 923750 924033 924337 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-393 917025 923440 923601 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-392 906808 911815 912919 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-391 904860 905963 905991 "GCDDOM" 906246 GCDDOM (NIL) -9 NIL 906403 NIL) (-390 904483 904640 904855 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-389 895276 897746 900134 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-388 893411 893736 894154 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-387 892352 892541 892808 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-386 891223 891430 891734 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-385 890686 890828 890976 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-384 889298 889646 889959 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-383 887843 888164 888486 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-382 885469 885825 886230 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-381 878721 880382 881960 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-380 878373 878594 878662 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-379 877997 878218 878299 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-378 876094 876777 877237 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-377 874687 874994 875386 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-376 873342 873701 874025 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-375 872645 872769 872956 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-374 871619 871885 872232 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-373 869277 869807 870289 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-372 868860 868920 869089 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-371 867160 868074 868377 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-370 866308 866442 866665 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-369 865479 865640 865867 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-368 861462 864413 864454 "FSAGG" 864824 FSAGG (NIL T) -9 NIL 865083 NIL) (-367 859816 860575 861367 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-366 857772 858068 858612 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-365 856819 857001 857301 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-364 856500 856549 856676 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-363 836656 846157 846198 "FS" 850068 FS (NIL T) -9 NIL 852346 NIL) (-362 828887 832380 836359 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-361 828421 828548 828700 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-360 822944 826102 826142 "FRNAALG" 827462 FRNAALG (NIL T) -9 NIL 828060 NIL) (-359 819685 820936 822194 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-358 819366 819415 819542 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-357 817853 818410 818704 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-356 817139 817232 817519 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 814973 815739 816055 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-354 814082 814525 814566 "FRETRCT" 814571 FRETRCT (NIL T) -9 NIL 814742 NIL) (-353 813455 813733 814077 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-352 810199 811719 811778 "FRAMALG" 812660 FRAMALG (NIL T T) -9 NIL 812952 NIL) (-351 808795 809346 809976 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-350 808488 808551 808658 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-349 802129 808293 808483 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-348 801822 801885 801992 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-347 794130 798701 800029 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-346 787908 791411 791439 "FPS" 792558 FPS (NIL) -9 NIL 793114 NIL) (-345 787465 787598 787762 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-344 784275 786318 786346 "FPC" 786571 FPC (NIL) -9 NIL 786713 NIL) (-343 784121 784173 784270 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-342 782898 783607 783648 "FPATMAB" 783653 FPATMAB (NIL T) -9 NIL 783805 NIL) (-341 781328 781924 782271 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-340 780903 780961 781134 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-339 779406 780301 780475 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-338 778021 778526 778554 "FNCAT" 779011 FNCAT (NIL) -9 NIL 779268 NIL) (-337 777478 777988 778016 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-336 776065 777427 777473 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-335 772653 774011 774052 "FMONCAT" 775269 FMONCAT (NIL T) -9 NIL 775873 NIL) (-334 769511 770589 770642 "FMCAT" 771823 FMCAT (NIL T T) -9 NIL 772315 NIL) (-333 768211 769334 769433 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-332 767259 768059 768206 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-331 765446 765898 766392 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-330 763381 763917 764495 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-329 756767 761718 762332 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-328 755248 756349 756389 "FLINEXP" 756394 FLINEXP (NIL T) -9 NIL 756487 NIL) (-327 754657 754916 755243 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-326 753872 754031 754252 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-325 750755 751834 751886 "FLALG" 753113 FLALG (NIL T T) -9 NIL 753580 NIL) (-324 749926 750087 750314 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-323 743335 747345 747386 "FLAGG" 748641 FLAGG (NIL T) -9 NIL 749286 NIL) (-322 742443 742847 743330 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-321 739004 740268 740327 "FINRALG" 741455 FINRALG (NIL T T) -9 NIL 741963 NIL) (-320 738395 738660 738999 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-319 737693 737989 738017 "FINITE" 738213 FINITE (NIL) -9 NIL 738320 NIL) (-318 737601 737627 737688 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-317 735059 736284 736325 "FINAGG" 736959 FINAGG (NIL T) -9 NIL 737262 NIL) (-316 727020 729611 729651 "FINAALG" 733303 FINAALG (NIL T) -9 NIL 734741 NIL) (-315 723287 724532 725655 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 721839 722258 722312 "FILECAT" 722996 FILECAT (NIL T T) -9 NIL 723212 NIL) (-313 721190 721664 721767 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 718438 720316 720344 "FIELD" 720384 FIELD (NIL) -9 NIL 720464 NIL) (-311 717463 717924 718433 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 715467 716413 716759 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 714710 714891 715110 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 709980 714648 714705 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 709642 709709 709844 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709182 709224 709433 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 705862 706739 707516 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701146 705794 705857 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 695825 700635 700825 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 690306 695106 695364 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 684513 689757 689968 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 683536 683746 684061 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 678976 681681 681709 "FFIELDC" 682328 FFIELDC (NIL) -9 NIL 682703 NIL) (-298 678045 678485 678971 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 677660 677718 677842 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 675804 676327 676844 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 670898 675603 675704 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 665998 670687 670794 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 660664 665789 665897 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660118 660167 660402 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 638693 649727 649813 "FFCAT" 654963 FFCAT (NIL T T T) -9 NIL 656399 NIL) (-290 634933 636159 637465 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 629776 634864 634928 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 628668 629137 629178 "FEVALAB" 629262 FEVALAB (NIL T) -9 NIL 629523 NIL) (-287 628073 628325 628663 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 624900 625811 625926 "FDIVCAT" 627493 FDIVCAT (NIL T T T T) -9 NIL 627929 NIL) (-285 624694 624726 624895 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624001 624094 624371 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 622487 623485 623688 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 621580 621964 622166 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 620702 621191 621331 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612289 616932 616972 "FAXF" 618773 FAXF (NIL T) -9 NIL 619463 NIL) (-279 610205 611009 611824 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605069 609727 609901 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 599527 601950 602002 "FAMR" 603013 FAMR (NIL T T) -9 NIL 603472 NIL) (-276 598726 599091 599522 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 597747 598668 598721 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 595341 596220 596273 "FAMONC" 597214 FAMONC (NIL T T) -9 NIL 597599 NIL) (-273 593897 595199 595336 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 591977 592338 592740 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591254 591451 591673 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583114 590701 590900 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581133 581703 582289 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578035 578677 579397 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573192 573899 574704 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 572881 572944 573053 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 557674 571930 572356 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548201 556994 557282 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 547695 547997 548087 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 547471 547661 547690 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547160 547228 547341 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 546677 546819 546860 "EVALAB" 547030 EVALAB (NIL T) -9 NIL 547134 NIL) (-259 546305 546451 546672 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 543348 544943 544971 "EUCDOM" 545525 EUCDOM (NIL) -9 NIL 545874 NIL) (-257 542275 542768 543343 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542000 542056 542156 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 541688 541752 541861 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 535459 537359 537387 "ES" 540129 ES (NIL) -9 NIL 541513 NIL) (-253 531974 533506 535298 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 531322 531475 531651 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524411 531226 531317 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524100 524163 524272 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 517727 520852 522285 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514030 515126 516219 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 512859 513209 513514 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 511744 512475 512503 "ENTIRER" 512508 ENTIRER (NIL) -9 NIL 512552 NIL) (-245 511633 511667 511739 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508266 510063 510412 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507358 507569 507623 "ELTAGG" 508003 ELTAGG (NIL T T) -9 NIL 508214 NIL) (-242 507138 507212 507353 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 506884 506919 506973 "ELTAB" 507057 ELTAB (NIL T T) -9 NIL 507109 NIL) (-240 506135 506305 506504 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 505859 505933 505961 "ELEMFUN" 506066 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 505759 505786 505854 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500305 503800 503841 "ELAGG" 504778 ELAGG (NIL T) -9 NIL 505238 NIL) (-236 499103 499641 500300 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498521 498688 498844 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497434 497753 498032 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 490827 492825 493652 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 484806 486802 487612 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482620 483026 483497 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473620 475533 477074 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 472733 473234 473383 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471431 472105 472145 "DVARCAT" 472428 DVARCAT (NIL T) -9 NIL 472568 NIL) (-227 470850 471114 471426 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 462917 470718 470845 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461255 462046 462087 "DSEXT" 462450 DSEXT (NIL T) -9 NIL 462744 NIL) (-224 460060 460584 461250 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 459784 459849 459947 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 455935 457151 458282 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451581 452936 454000 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450256 450617 451003 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 449942 450001 450119 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 448917 449215 449505 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448502 448577 448727 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 440915 443027 445142 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436432 437451 438530 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433027 435096 435137 "DQAGG" 435766 DQAGG (NIL T) -9 NIL 436039 NIL) (-213 419570 427210 427292 "DPOLCAT" 429129 DPOLCAT (NIL T T T T) -9 NIL 429672 NIL) (-212 415978 417626 419565 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 408983 415876 415973 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 401897 408812 408978 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 401490 401750 401839 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 400904 401352 401432 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400190 400515 400666 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393329 399926 400077 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391078 392395 392435 "DMEXT" 392440 DMEXT (NIL T) -9 NIL 392615 NIL) (-204 390734 390796 390940 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384059 390219 390409 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 380725 382882 382923 "DLAGG" 383473 DLAGG (NIL T) -9 NIL 383702 NIL) (-201 379076 379947 379975 "DIVRING" 380067 DIVRING (NIL) -9 NIL 380150 NIL) (-200 378527 378771 379071 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 376955 377372 377778 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 375992 376213 376478 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 369466 375924 375987 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 357786 364246 364299 "DIRPCAT" 364555 DIRPCAT (NIL NIL T) -9 NIL 365428 NIL) (-195 355792 356562 357449 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355239 355405 355591 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 351785 354125 354166 "DIOPS" 354598 DIOPS (NIL T) -9 NIL 354824 NIL) (-192 351445 351589 351780 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 350452 351198 351226 "DIOID" 351231 DIOID (NIL) -9 NIL 351253 NIL) (-190 349280 350109 350137 "DIFRING" 350142 DIFRING (NIL) -9 NIL 350163 NIL) (-189 348916 349014 349042 "DIFFSPC" 349161 DIFFSPC (NIL) -9 NIL 349236 NIL) (-188 348657 348759 348911 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 347560 348185 348225 "DIFFMOD" 348230 DIFFMOD (NIL T) -9 NIL 348327 NIL) (-186 347244 347301 347342 "DIFFDOM" 347463 DIFFDOM (NIL T) -9 NIL 347531 NIL) (-185 347125 347155 347239 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 344798 346319 346359 "DIFEXT" 346364 DIFEXT (NIL T) -9 NIL 346516 NIL) (-183 341959 344299 344340 "DIAGG" 344345 DIAGG (NIL T) -9 NIL 344365 NIL) (-182 341515 341705 341954 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 336708 340705 340982 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333166 334219 335229 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 327716 332320 332647 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326282 326574 326949 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 323402 324654 325050 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321122 323233 323322 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 320505 320650 320832 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 317823 318547 319347 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 315932 316390 316952 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 315315 315648 315762 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 308515 315040 315188 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 306435 306945 307449 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306074 306123 306274 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 305333 305895 305986 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 303357 303799 304159 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 302649 302938 303084 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302100 302246 302398 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 299462 300255 300982 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 298901 299047 299218 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 296973 297284 297651 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 296530 296785 296886 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 295731 296114 296142 "CTORCAT" 296323 CTORCAT (NIL) -9 NIL 296435 NIL) (-159 295434 295568 295726 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 294927 295184 295292 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 294343 294774 294847 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 293802 293919 294072 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290196 290952 291707 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 289687 289990 290081 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 288906 289115 289343 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 288410 288515 288719 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288163 288197 288303 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285102 285864 286582 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 284621 284763 284902 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 280514 283084 283576 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 280388 280415 280443 "CONDUIT" 280480 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279267 279998 280026 "COMRING" 280031 COMRING (NIL) -9 NIL 280081 NIL) (-145 278432 278799 278977 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278128 278169 278297 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 277821 277884 277991 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 266663 277771 277816 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266124 266263 266423 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 265877 265918 266016 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 247308 259558 259598 "COMPCAT" 260599 COMPCAT (NIL T) -9 NIL 261941 NIL) (-138 239846 243359 246952 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 239605 239639 239741 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 239435 239474 239532 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239016 239295 239369 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 238593 238834 238921 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 237788 238036 238064 "COMBOPC" 238402 COMBOPC (NIL) -9 NIL 238577 NIL) (-132 236852 237104 237346 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 233784 234468 235091 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 232664 233115 233350 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232155 232458 232549 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 231842 231895 232020 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 231312 231622 231720 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 227832 228902 229982 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226127 227112 227350 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222239 224247 224288 "CLAGG" 225214 CLAGG (NIL T) -9 NIL 225747 NIL) (-123 221132 221659 222234 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220761 220852 220992 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218698 219205 219753 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217659 218390 218418 "CHARZ" 218423 CHARZ (NIL) -9 NIL 218437 NIL) (-119 217453 217499 217577 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 216292 217055 217083 "CHARNZ" 217144 CHARNZ (NIL) -9 NIL 217192 NIL) (-117 213770 214867 215390 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213478 213557 213585 "CFCAT" 213696 CFCAT (NIL) -9 NIL NIL NIL) (-115 212821 212950 213132 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208810 212234 212514 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208188 208375 208552 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207716 208135 208183 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207189 207498 207595 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206680 206983 207074 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205929 206089 206310 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202029 203286 203994 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200395 201426 201677 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199976 200255 200329 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199410 199663 199691 "CACHSET" 199823 CACHSET (NIL) -9 NIL 199901 NIL) (-104 198762 199177 199205 "CABMON" 199255 CABMON (NIL) -9 NIL 199311 NIL) (-103 198292 198556 198666 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193515 197949 198121 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192485 193189 193324 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193487) (-100 189956 192252 192358 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187387 189699 189818 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184627 186831 186870 "BTCAT" 186937 BTCAT (NIL T) -9 NIL 187013 NIL) (-97 184378 184476 184622 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179488 183609 183635 "BTAGG" 183746 BTAGG (NIL) -9 NIL 183854 NIL) (-95 179119 179280 179483 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176181 178589 178801 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175451 175603 175781 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 171984 174157 174196 "BRAGG" 174837 BRAGG (NIL T) -9 NIL 175094 NIL) (-91 170939 171434 171979 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 163473 170444 170625 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 161465 163425 163468 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161198 161234 161345 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 159437 159870 160318 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 155403 156819 157709 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154279 155170 155292 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 153865 154022 154048 "BOOLE" 154156 BOOLE (NIL) -9 NIL 154237 NIL) (-83 153658 153739 153860 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 152796 153323 153373 "BMODULE" 153378 BMODULE (NIL T T) -9 NIL 153442 NIL) (-81 148413 152653 152722 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148226 148266 148305 "BINOPC" 148310 BINOPC (NIL T) -9 NIL 148355 NIL) (-79 147768 148041 148143 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147289 147433 147571 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 140495 147019 147164 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138229 139724 139763 "BGAGG" 140019 BGAGG (NIL T) -9 NIL 140156 NIL) (-75 138098 138136 138224 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 136949 137150 137435 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 133587 136107 136434 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133172 133265 133291 "BASTYPE" 133462 BASTYPE (NIL) -9 NIL 133558 NIL) (-71 132942 133038 133167 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 132457 132545 132695 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 131356 132031 132216 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131082 131087 131113 "ATTREG" 131118 ATTREG (NIL) -9 NIL NIL NIL) (-67 130687 130959 131024 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130187 130336 130362 "ATRIG" 130563 ATRIG (NIL) -9 NIL NIL NIL) (-65 130042 130095 130182 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 129612 129843 129869 "ASTCAT" 129874 ASTCAT (NIL) -9 NIL 129904 NIL) (-63 129411 129488 129607 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 127570 129244 129332 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 126377 126690 127055 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124184 126307 126372 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 123375 123566 123787 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 118962 123106 123220 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113256 115307 115382 "ARR2CAT" 117894 ARR2CAT (NIL T T T) -9 NIL 118623 NIL) (-56 112217 112699 113251 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111585 111956 112078 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110517 110685 110981 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110218 110272 110390 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109601 109747 109903 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 109006 109296 109416 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106574 107735 108058 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106099 106359 106455 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99794 105161 105603 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95328 96991 97041 "AMR" 97779 AMR (NIL T T) -9 NIL 98376 NIL) (-46 94682 94962 95323 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77862 94616 94677 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74265 77538 77707 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71275 71935 72542 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70654 70767 70951 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67066 67691 68283 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56555 66759 66909 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55872 56026 56204 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54585 55380 55418 "ALGEBRA" 55423 ALGEBRA (NIL T) -9 NIL 55463 NIL) (-37 54371 54448 54580 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34368 51577 51629 "ALAGG" 51767 ALAGG (NIL T T) -9 NIL 51932 NIL) (-35 33868 34017 34043 "AHYP" 34244 AHYP (NIL) -9 NIL NIL NIL) (-34 33164 33345 33371 "AGG" 33652 AGG (NIL) -9 NIL 33839 NIL) (-33 32953 33040 33159 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31092 31552 31952 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30587 30890 30979 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29957 30252 30408 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17515 26794 26832 "ACFS" 27439 ACFS (NIL T) -9 NIL 27678 NIL) (-28 16138 16748 17510 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11690 14069 14095 "ACF" 14974 ACF (NIL) -9 NIL 15386 NIL) (-26 10786 11192 11685 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10288 10528 10554 "ABELSG" 10646 ABELSG (NIL) -9 NIL 10711 NIL) (-24 10186 10217 10283 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9341 9715 9741 "ABELMON" 9966 ABELMON (NIL) -9 NIL 10099 NIL) (-22 9023 9163 9336 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8235 8718 8744 "ABELGRP" 8816 ABELGRP (NIL) -9 NIL 8891 NIL) (-20 7788 7984 8230 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 7046 7085 "A1AGG" 7090 A1AGG (NIL T) -9 NIL 7130 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index d43080c9..b908f729 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,793 +1,794 @@
 
-(630940 . 3577545199)        
+(631546 . 3577666331)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483))))
-   (-5 *2 (-1177 (-348 (-483)))) (-5 *1 (-1206 *4))))) 
+  (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
+   (-5 *2 (-1178 (-349 (-484)))) (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483))))
-   (-5 *2 (-1177 (-483))) (-5 *1 (-1206 *4))))) 
+  (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
+   (-5 *2 (-1178 (-484))) (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-960) (-579 (-483)))) (-5 *2 (-85))
-   (-5 *1 (-1206 *4))))) 
+  (-12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-85))
+   (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-552 *2) (-146))) (-5 *2 (-799 *4)) (-5 *1 (-144 *4 *5 *3))
-   (-4 *4 (-1012)) (-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 (-1177 *3)) (-4 *3 (-146)) (-4 *1 (-351 *3 *4))
-   (-4 *4 (-1153 *3))))
+  (-12 (-5 *2 (-1178 *3)) (-4 *3 (-146)) (-4 *1 (-352 *3 *4))
+   (-4 *4 (-1154 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-351 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1153 *3))
-   (-5 *2 (-1177 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1177 *3)) (-4 *3 (-146)) (-4 *1 (-359 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-359 *3)) (-4 *3 (-146)) (-5 *2 (-1177 *3))))
+  (-12 (-4 *1 (-352 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1154 *3))
+   (-5 *2 (-1178 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-146)) (-4 *1 (-360 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-360 *3)) (-4 *3 (-146)) (-5 *2 (-1178 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-346 *1)) (-4 *1 (-362 *3)) (-4 *3 (-494)) (-4 *3 (-1012))))
+  (-12 (-5 *2 (-347 *1)) (-4 *1 (-363 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-582 *6)) (-4 *6 (-976 *3 *4 *5)) (-4 *3 (-960)) (-4 *4 (-716))
-   (-4 *5 (-755)) (-5 *1 (-401 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1014)) (-5 *1 (-472))))
- ((*1 *2 *1) (-12 (-4 *1 (-552 *2)) (-4 *2 (-1127))))
- ((*1 *1 *2) (-12 (-4 *1 (-556 *2)) (-4 *2 (-1127))))
- ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-660 *3 *2)) (-4 *2 (-1153 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-582 (-799 *3))) (-5 *1 (-799 *3)) (-4 *3 (-1012))))
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717))
+   (-4 *5 (-756)) (-5 *1 (-402 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-473))))
+ ((*1 *2 *1) (-12 (-4 *1 (-553 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *2) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-661 *3 *2)) (-4 *2 (-1154 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-856 *3)) (-4 *3 (-960)) (-4 *1 (-976 *3 *4 *5))
-   (-4 *5 (-552 (-1088))) (-4 *4 (-716)) (-4 *5 (-755))))
+  (-12 (-5 *2 (-857 *3)) (-4 *3 (-961)) (-4 *1 (-977 *3 *4 *5))
+   (-4 *5 (-553 (-1089))) (-4 *4 (-717)) (-4 *5 (-756))))
  ((*1 *1 *2)
   (OR
-   (-12 (-5 *2 (-856 (-483))) (-4 *1 (-976 *3 *4 *5))
-    (-12 (-2559 (-4 *3 (-38 (-348 (-483))))) (-4 *3 (-38 (-483)))
-     (-4 *5 (-552 (-1088))))
-    (-4 *3 (-960)) (-4 *4 (-716)) (-4 *5 (-755)))
-   (-12 (-5 *2 (-856 (-483))) (-4 *1 (-976 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-348 (-483)))) (-4 *5 (-552 (-1088)))) (-4 *3 (-960))
-    (-4 *4 (-716)) (-4 *5 (-755)))))
+   (-12 (-5 *2 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
+    (-12 (-2560 (-4 *3 (-38 (-349 (-484))))) (-4 *3 (-38 (-484)))
+     (-4 *5 (-553 (-1089))))
+    (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756)))
+   (-12 (-5 *2 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
+    (-12 (-4 *3 (-38 (-349 (-484)))) (-4 *5 (-553 (-1089)))) (-4 *3 (-961))
+    (-4 *4 (-717)) (-4 *5 (-756)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-856 (-348 (-483)))) (-4 *1 (-976 *3 *4 *5))
-   (-4 *3 (-38 (-348 (-483)))) (-4 *5 (-552 (-1088))) (-4 *3 (-960))
-   (-4 *4 (-716)) (-4 *5 (-755))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-582 *7)) (|:| -1598 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-716)) (-4 *6 (-755)) (-5 *2 (-1071))
-   (-5 *1 (-980 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-582 *7)) (|:| -1598 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-1019 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-716)) (-4 *6 (-755)) (-5 *2 (-1071))
-   (-5 *1 (-1057 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1014)) (-5 *1 (-1093))))
- ((*1 *2 *1) (-12 (-5 *2 (-1014)) (-5 *1 (-1093))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-771)) (-5 *3 (-483)) (-5 *1 (-1107))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-771)) (-5 *3 (-483)) (-5 *1 (-1107))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-702 *4 (-772 *5))) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *5 (-582 (-1088))) (-5 *2 (-702 *4 (-772 *6))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *6 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-856 *4)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-856 (-936 (-348 *4)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-582 (-1088))) (-14 *6 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-702 *4 (-772 *6))) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *6 (-582 (-1088))) (-5 *2 (-856 (-936 (-348 *4))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *4)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-1083 (-936 (-348 *4)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-582 (-1088))) (-14 *6 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1058 *4 (-468 (-772 *6)) (-772 *6) (-702 *4 (-772 *6))))
-   (-4 *4 (-13 (-754) (-258) (-120) (-932))) (-14 *6 (-582 (-1088)))
-   (-5 *2 (-582 (-702 *4 (-772 *6)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-582 (-1088)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-346 *3)) (-5 *1 (-496 *3)) (-4 *3 (-482))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-258)) (-5 *2 (-346 *3))
-   (-5 *1 (-680 *4 *5 *6 *3)) (-4 *3 (-860 *6 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-258)) (-4 *7 (-860 *6 *4 *5))
-   (-5 *2 (-346 (-1083 *7))) (-5 *1 (-680 *4 *5 *6 *7)) (-5 *3 (-1083 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-390)) (-4 *3 (-960)) (-4 *4 (-716)) (-4 *5 (-755))
-   (-5 *2 (-346 *1)) (-4 *1 (-860 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-755)) (-4 *5 (-716)) (-4 *6 (-390)) (-5 *2 (-346 *3))
-   (-5 *1 (-891 *4 *5 *6 *3)) (-4 *3 (-860 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-390)) (-4 *7 (-860 *6 *4 *5))
-   (-5 *2 (-346 (-1083 (-348 *7)))) (-5 *1 (-1085 *4 *5 *6 *7))
-   (-5 *3 (-1083 (-348 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-346 *1)) (-4 *1 (-1132))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-494)) (-5 *2 (-346 *3)) (-5 *1 (-1157 *4 *3))
-   (-4 *3 (-13 (-1153 *4) (-494) (-10 -8 (-15 -3143 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-957 *4 *5)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *5 (-582 (-1088)))
-   (-5 *2 (-582 (-1058 *4 (-468 (-772 *6)) (-772 *6) (-702 *4 (-772 *6)))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-582 (-1088)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-957 *4 *5)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *5 (-582 (-1088))) (-5 *2 (-582 (-582 (-936 (-348 *4)))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-582 (-1088)))))
+  (-12 (-5 *2 (-857 (-349 (-484)))) (-4 *1 (-977 *3 *4 *5))
+   (-4 *3 (-38 (-349 (-484)))) (-4 *5 (-553 (-1089))) (-4 *3 (-961))
+   (-4 *4 (-717)) (-4 *5 (-756))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1599 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-391))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1072))
+   (-5 *1 (-981 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1599 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-1020 *4 *5 *6 *7)) (-4 *4 (-391))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1072))
+   (-5 *1 (-1058 *4 *5 *6 *7 *8))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-1094))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1015)) (-5 *1 (-1094))))
+ ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1108))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1108))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-703 *4 (-773 *5))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1089))) (-5 *2 (-703 *4 (-773 *6))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *6 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-857 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-857 (-937 (-349 *4)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-583 (-1089))) (-14 *6 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-703 *4 (-773 *6))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *6 (-583 (-1089))) (-5 *2 (-857 (-937 (-349 *4))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *5 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1084 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-1084 (-937 (-349 *4)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-583 (-1089))) (-14 *6 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1059 *4 (-469 (-773 *6)) (-773 *6) (-703 *4 (-773 *6))))
+   (-4 *4 (-13 (-755) (-258) (-120) (-933))) (-14 *6 (-583 (-1089)))
+   (-5 *2 (-583 (-703 *4 (-773 *6)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-583 (-1089)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-347 *3)) (-5 *1 (-497 *3)) (-4 *3 (-483))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-258)) (-5 *2 (-347 *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 (-347 (-1084 *7))) (-5 *1 (-681 *4 *5 *6 *7)) (-5 *3 (-1084 *7))))
+ ((*1 *2 *1)
+  (-12 (-4 *3 (-391)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-5 *2 (-347 *1)) (-4 *1 (-861 *3 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-756)) (-4 *5 (-717)) (-4 *6 (-391)) (-5 *2 (-347 *3))
+   (-5 *1 (-892 *4 *5 *6 *3)) (-4 *3 (-861 *6 *5 *4))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-391)) (-4 *7 (-861 *6 *4 *5))
+   (-5 *2 (-347 (-1084 (-349 *7)))) (-5 *1 (-1086 *4 *5 *6 *7))
+   (-5 *3 (-1084 (-349 *7)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-347 *1)) (-4 *1 (-1133))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-495)) (-5 *2 (-347 *3)) (-5 *1 (-1158 *4 *3))
+   (-4 *3 (-13 (-1154 *4) (-495) (-10 -8 (-15 -3144 ($ $ $)))))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1089)))
+   (-5 *2 (-583 (-1059 *4 (-469 (-773 *6)) (-773 *6) (-703 *4 (-773 *6)))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-583 (-1089)))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1089))) (-5 *2 (-583 (-583 (-937 (-349 *4)))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-583 (-1089)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85))
-   (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *5))))) (-5 *1 (-1205 *5 *6 *7))
-   (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85))
-   (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *5))))) (-5 *1 (-1205 *5 *6 *7))
-   (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-582 (-856 *4))) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *4))))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-582 (-1088))) (-14 *6 (-582 (-1088)))))) 
+  (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85))
+   (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *5))))) (-5 *1 (-1206 *5 *6 *7))
+   (-14 *6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85))
+   (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *5))))) (-5 *1 (-1206 *5 *6 *7))
+   (-14 *6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-583 (-857 *4))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *4))))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-583 (-1089))) (-14 *6 (-583 (-1089)))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-582 (-856 (-483)))) (-5 *4 (-582 (-1088)))
-   (-5 *2 (-582 (-582 (-328)))) (-5 *1 (-935)) (-5 *5 (-328))))
+  (-12 (-5 *3 (-583 (-857 (-484)))) (-5 *4 (-583 (-1089)))
+   (-5 *2 (-583 (-583 (-329)))) (-5 *1 (-936)) (-5 *5 (-329))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-957 *4 *5)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *5 (-582 (-1088))) (-5 *2 (-582 (-582 (-936 (-348 *4)))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-582 (-1088)))))
+  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1089))) (-5 *2 (-583 (-583 (-937 (-349 *4)))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-583 (-1089)))))
  ((*1 *2 *3 *4 *4 *4)
-  (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85))
-   (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *5))))) (-5 *1 (-1205 *5 *6 *7))
-   (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))
+  (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85))
+   (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *5))))) (-5 *1 (-1206 *5 *6 *7))
+   (-14 *6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85))
-   (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *5))))) (-5 *1 (-1205 *5 *6 *7))
-   (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))
- ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-856 *5))) (-5 *4 (-85))
-   (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *5))))) (-5 *1 (-1205 *5 *6 *7))
-   (-14 *6 (-582 (-1088))) (-14 *7 (-582 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-582 (-856 *4))) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-582 (-936 (-348 *4))))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-582 (-1088))) (-14 *6 (-582 (-1088)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-957 *4 *5)) (-4 *4 (-13 (-754) (-258) (-120) (-932)))
-   (-14 *5 (-582 (-1088)))
-   (-5 *2 (-582 (-2 (|:| -1745 (-1083 *4)) (|:| -3223 (-582 (-856 *4))))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-582 (-1088)))))
+  (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85))
+   (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *5))))) (-5 *1 (-1206 *5 *6 *7))
+   (-14 *6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))
+ ((*1 *2 *3 *4)
+  (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85))
+   (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *5))))) (-5 *1 (-1206 *5 *6 *7))
+   (-14 *6 (-583 (-1089))) (-14 *7 (-583 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-583 (-857 *4))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-583 (-937 (-349 *4))))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-583 (-1089))) (-14 *6 (-583 (-1089)))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1089)))
+   (-5 *2 (-583 (-2 (|:| -1746 (-1084 *4)) (|:| -3224 (-583 (-857 *4))))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-583 (-1089)))))
  ((*1 *2 *3 *4 *4 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-754) (-258) (-120) (-932)))
-   (-5 *2 (-582 (-2 (|:| -1745 (-1083 *5)) (|:| -3223 (-582 (-856 *5))))))
-   (-5 *1 (-1205 *5 *6 *7)) (-5 *3 (-582 (-856 *5))) (-14 *6 (-582 (-1088)))
-   (-14 *7 (-582 (-1088)))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-583 (-2 (|:| -1746 (-1084 *5)) (|:| -3224 (-583 (-857 *5))))))
+   (-5 *1 (-1206 *5 *6 *7)) (-5 *3 (-583 (-857 *5))) (-14 *6 (-583 (-1089)))
+   (-14 *7 (-583 (-1089)))))
  ((*1 *2 *3 *4 *4)
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@@ -796,11150 +797,11161 @@
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   (-12
    (-5 *2
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 (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21)))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *1)
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    (-5 *2
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+    (-3 (|:| |f1| (-750 *3)) (|:| |f2| (-583 (-750 *3)))
      (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")))
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+  (-12 (-5 *2 (-2 (|:| -3228 (-583 (-1089))) (|:| -3229 (-583 (-1089)))))
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+(((*1 *2 *3) (-12 (-5 *3 (-583 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-583 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131))))) 
 (((*1 *2 *1 *3)
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 (((*1 *2 *1 *3)
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 (((*1 *2)
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 (((*1 *2 *3)
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+ ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1124 *3)) (-4 *3 (-887))))) 
 (((*1 *2 *1)
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 (((*1 *2 *3 *4 *5)
   (|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9))
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-   (-4 *1 (-1122 *5 *6 *7 *8))))) 
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-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-582 *6))))) 
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    (-5 *2 (-85))))
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    (-5 *2 (-85))))
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 (((*1 *2 *1)
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-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-85))))
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-   (-4 *3 (-976 *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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    (-5 *2 (-85))))
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-   (-4 *3 (-976 *4 *5 *6)) (-5 *2 (-85))))) 
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+   (-4 *3 (-977 *4 *5 *6)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *3)
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-   (-5 *1 (-1057 *7 *8 *9 *10 *11))))) 
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-   (-4 *5 (-1153 (-348 *4))) (-4 *6 (-291 *3 *4 *5))
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    (-5 *2
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-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-582 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-582 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-582 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-483)) (-5 *1 (-1020))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1177 (-483))) (-5 *3 (-483)) (-5 *1 (-1020))))
+  (-12 (-4 *4 (-740)) (-14 *5 (-1089)) (-5 *2 (-583 (-1147 *5 *4)))
+   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1147 *5 *4))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1022 *3))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-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 (-1178 (-484))) (-5 *3 (-484)) (-5 *1 (-1021))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-1177 (-483))) (-5 *3 (-582 (-483))) (-5 *4 (-483))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-1178 (-484))) (-5 *3 (-583 (-484))) (-5 *4 (-484))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-582 (-483))) (-5 *3 (-582 (-829))) (-5 *4 (-85))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-583 (-830))) (-5 *4 (-85))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-629 (-483))) (-5 *3 (-582 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-630 (-484))) (-5 *3 (-583 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-829))) (-5 *4 (-582 (-483))) (-5 *2 (-629 (-483)))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-583 (-830))) (-5 *4 (-583 (-484))) (-5 *2 (-630 (-484)))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-582 (-829))) (-5 *2 (-582 (-629 (-483)))) (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-583 (-830))) (-5 *2 (-583 (-630 (-484)))) (-5 *1 (-1021))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-582 (-483))) (-5 *3 (-629 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-630 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-582 (-483))) (-5 *2 (-629 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-583 (-484))) (-5 *2 (-630 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| *3) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-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 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-85)) (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))
+  (-12 (-4 *5 (-391)) (-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 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-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 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-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 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| *3) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| *3) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1599 *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 (-390)) (-4 *7 (-716)) (-4 *8 (-755))
-   (-4 *3 (-976 *6 *7 *8)) (-5 *2 (-582 (-2 (|:| |val| *3) (|:| -1598 *4))))
-   (-5 *1 (-1018 *6 *7 *8 *3 *4)) (-4 *4 (-982 *6 *7 *8 *3))))
+  (-12 (-5 *5 (-85)) (-4 *6 (-391)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *3 (-977 *6 *7 *8)) (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1599 *4))))
+   (-5 *1 (-1019 *6 *7 *8 *3 *4)) (-4 *4 (-983 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-582 (-2 (|:| |val| (-582 *8)) (|:| -1598 *9)))) (-5 *5 (-85))
-   (-4 *8 (-976 *6 *7 *4)) (-4 *9 (-982 *6 *7 *4 *8)) (-4 *6 (-390))
-   (-4 *7 (-716)) (-4 *4 (-755))
-   (-5 *2 (-582 (-2 (|:| |val| *8) (|:| -1598 *9))))
-   (-5 *1 (-1018 *6 *7 *4 *8 *9))))) 
+  (-12 (-5 *3 (-583 (-2 (|:| |val| (-583 *8)) (|:| -1599 *9)))) (-5 *5 (-85))
+   (-4 *8 (-977 *6 *7 *4)) (-4 *9 (-983 *6 *7 *4 *8)) (-4 *6 (-391))
+   (-4 *7 (-717)) (-4 *4 (-756))
+   (-5 *2 (-583 (-2 (|:| |val| *8) (|:| -1599 *9))))
+   (-5 *1 (-1019 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-390)) (-4 *6 (-716)) (-4 *7 (-755)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-582 (-2 (|:| |val| (-582 *3)) (|:| -1598 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-391)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-583 *3)) (|:| -1599 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-983 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-983 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-983 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-390)) (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-983 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-390)) (-4 *7 (-716)) (-4 *8 (-755))
-   (-4 *9 (-976 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3265 (-582 *9)) (|:| -1598 *4) (|:| |ineq| (-582 *9))))
-   (-5 *1 (-900 *6 *7 *8 *9 *4)) (-5 *3 (-582 *9)) (-4 *4 (-982 *6 *7 *8 *9))))
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-391)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *9 (-977 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3266 (-583 *9)) (|:| -1599 *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 (-390)) (-4 *7 (-716)) (-4 *8 (-755))
-   (-4 *9 (-976 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3265 (-582 *9)) (|:| -1598 *4) (|:| |ineq| (-582 *9))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *4)) (-5 *3 (-582 *9))
-   (-4 *4 (-982 *6 *7 *8 *9))))) 
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-391)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *9 (-977 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3266 (-583 *9)) (|:| -1599 *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 (-582 *10)) (-5 *5 (-85)) (-4 *10 (-982 *6 *7 *8 *9))
-   (-4 *6 (-390)) (-4 *7 (-716)) (-4 *8 (-755)) (-4 *9 (-976 *6 *7 *8))
+  (-12 (-5 *4 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
+   (-4 *6 (-391)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
    (-5 *2
-    (-582 (-2 (|:| -3265 (-582 *9)) (|:| -1598 *10) (|:| |ineq| (-582 *9)))))
-   (-5 *1 (-900 *6 *7 *8 *9 *10)) (-5 *3 (-582 *9))))
+    (-583 (-2 (|:| -3266 (-583 *9)) (|:| -1599 *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 (-582 *10)) (-5 *5 (-85)) (-4 *10 (-982 *6 *7 *8 *9))
-   (-4 *6 (-390)) (-4 *7 (-716)) (-4 *8 (-755)) (-4 *9 (-976 *6 *7 *8))
+  (-12 (-5 *4 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
+   (-4 *6 (-391)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
    (-5 *2
-    (-582 (-2 (|:| -3265 (-582 *9)) (|:| -1598 *10) (|:| |ineq| (-582 *9)))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *10)) (-5 *3 (-582 *9))))) 
+    (-583 (-2 (|:| -3266 (-583 *9)) (|:| -1599 *10) (|:| |ineq| (-583 *9)))))
+   (-5 *1 (-1018 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-582 (-2 (|:| |val| (-582 *6)) (|:| -1598 *7))))
-   (-4 *6 (-976 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-716)) (-4 *5 (-755)) (-5 *1 (-900 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1599 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-901 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-582 (-2 (|:| |val| (-582 *6)) (|:| -1598 *7))))
-   (-4 *6 (-976 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-716)) (-4 *5 (-755)) (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1599 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-582 *7)) (|:| -1598 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-716)) (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1599 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-391))
+   (-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| (-582 *7)) (|:| -1598 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-390))
-   (-4 *5 (-716)) (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1599 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-391))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-582 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-900 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-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 (-582 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-391)) (-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 (-582 *3)) (-4 *3 (-982 *5 *6 *7 *8)) (-4 *5 (-390))
-   (-4 *6 (-716)) (-4 *7 (-755)) (-4 *8 (-976 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-900 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-391))
+   (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-391)) (-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 (-582 *3)) (-4 *3 (-982 *5 *6 *7 *8)) (-4 *5 (-390))
-   (-4 *6 (-716)) (-4 *7 (-755)) (-4 *8 (-976 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1017 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-391))
+   (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *3))
-   (-4 *3 (-982 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-391)) (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3))
-   (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-391)) (-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 (-582 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-716))
-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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 (-582 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-716))
-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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 (-582 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-390)) (-4 *5 (-716))
-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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)
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-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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)
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-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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)
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-   (-4 *6 (-755)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-391)) (-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)
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-   (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-391)) (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-391)) (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-391)) (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-391)) (-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 (-582 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-390))
-   (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-900 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-901 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
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-   (-4 *4 (-716)) (-4 *5 (-755)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-391))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
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-   (-5 *2 (-85)) (-5 *1 (-900 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-391)) (-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 (-390)) (-4 *5 (-716)) (-4 *6 (-755)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-391)) (-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)
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-   (-5 *2 (-1183)) (-5 *1 (-900 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-901 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
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-   (-5 *2 (-1183)) (-5 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-391)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-900 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-390)) (-4 *5 (-716)) (-4 *6 (-755))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-985))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-391)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
+(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-986))))
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-799 *3)) (-4 *3 (-1012))))
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
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- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-504 *3)) (-4 *3 (-949 (-483)))))
+  (-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 (-376))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-505 *3)) (-4 *3 (-950 (-484)))))
  ((*1 *2 *1)
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-582 (-2 (|:| -3858 (-1088)) (|:| |entry| *4))))
-   (-5 *1 (-797 *3 *4)) (-4 *3 (-1012)) (-4 *4 (-1012))))
+  (-12 (-5 *2 (-583 (-2 (|:| -3859 (-1089)) (|:| |entry| *4))))
+   (-5 *1 (-798 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))
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-   (-4 *7 (-1012)) (-5 *2 (-582 *1)) (-4 *1 (-1015 *3 *4 *5 *6 *7))))) 
+  (-12 (-4 *3 (-1013)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
+   (-4 *7 (-1013)) (-5 *2 (-583 *1)) (-4 *1 (-1016 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
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+  (-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))))
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-483)) (-5 *3 (-829)) (-4 *1 (-345))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-483)) (-4 *1 (-345))))
+  (-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 (-346))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-484)) (-4 *1 (-346))))
  ((*1 *2 *1)
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-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *2 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *2)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
+  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *2)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
 (((*1 *1 *1)
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   (-12 (-4 *4 (-13 (-258) (-120)))
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   (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120)))
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 (((*1 *2 *3 *3 *4)
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 (((*1 *1 *1)
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 (((*1 *1 *1)
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+(((*1 *2) (-12 (-5 *2 (-329)) (-5 *1 (-953))))) 
+(((*1 *2) (-12 (-5 *2 (-329)) (-5 *1 (-953))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1083 (-348 (-1083 *2)))) (-5 *4 (-549 *2))
-   (-4 *2 (-13 (-362 *5) (-27) (-1113)))
-   (-4 *5 (-13 (-390) (-949 (-483)) (-120) (-579 (-483))))
-   (-5 *1 (-497 *5 *2 *6)) (-4 *6 (-1012))))
+  (-12 (-5 *3 (-1084 (-349 (-1084 *2)))) (-5 *4 (-550 *2))
+   (-4 *2 (-13 (-363 *5) (-27) (-1114)))
+   (-4 *5 (-13 (-391) (-950 (-484)) (-120) (-580 (-484))))
+   (-5 *1 (-498 *5 *2 *6)) (-4 *6 (-1013))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1083 *1)) (-4 *1 (-860 *4 *5 *3)) (-4 *4 (-960)) (-4 *5 (-716))
-   (-4 *3 (-755))))
+  (-12 (-5 *2 (-1084 *1)) (-4 *1 (-861 *4 *5 *3)) (-4 *4 (-961)) (-4 *5 (-717))
+   (-4 *3 (-756))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1083 *4)) (-4 *4 (-960)) (-4 *1 (-860 *4 *5 *3)) (-4 *5 (-716))
-   (-4 *3 (-755))))
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+   (-4 *3 (-756))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-348 (-1083 *2))) (-4 *5 (-716)) (-4 *4 (-755)) (-4 *6 (-960))
+  (-12 (-5 *3 (-349 (-1084 *2))) (-4 *5 (-717)) (-4 *4 (-756)) (-4 *6 (-961))
    (-4 *2
     (-13 (-312)
-     (-10 -8 (-15 -3944 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))
-   (-5 *1 (-861 *5 *4 *6 *7 *2)) (-4 *7 (-860 *6 *5 *4))))
+     (-10 -8 (-15 -3945 ($ *7)) (-15 -2998 (*7 $)) (-15 -2997 (*7 $)))))
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  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-348 (-1083 (-348 (-856 *5))))) (-5 *4 (-1088))
-   (-5 *2 (-348 (-856 *5))) (-5 *1 (-951 *5)) (-4 *5 (-494))))) 
+  (-12 (-5 *3 (-349 (-1084 (-349 (-857 *5))))) (-5 *4 (-1089))
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 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-549 *1)) (-4 *1 (-362 *4)) (-4 *4 (-1012)) (-4 *4 (-494))
-   (-5 *2 (-348 (-1083 *1)))))
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-  (-12 (-5 *4 (-549 *3)) (-4 *3 (-13 (-362 *6) (-27) (-1113)))
-   (-4 *6 (-13 (-390) (-949 (-483)) (-120) (-579 (-483))))
-   (-5 *2 (-1083 (-348 (-1083 *3)))) (-5 *1 (-497 *6 *3 *7)) (-5 *5 (-1083 *3))
-   (-4 *7 (-1012))))
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+   (-4 *6 (-13 (-391) (-950 (-484)) (-120) (-580 (-484))))
+   (-5 *2 (-1084 (-349 (-1084 *3)))) (-5 *1 (-498 *6 *3 *7)) (-5 *5 (-1084 *3))
+   (-4 *7 (-1013))))
  ((*1 *2 *3 *4)
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-   (-5 *2 (-1146 *5 (-856 *6))) (-5 *1 (-858 *5 *6)) (-5 *3 (-856 *6))))
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  ((*1 *2 *1)
-  (-12 (-4 *1 (-860 *3 *4 *5)) (-4 *3 (-960)) (-4 *4 (-716)) (-4 *5 (-755))
-   (-5 *2 (-1083 *3))))
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  ((*1 *2 *1 *3)
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-   (-4 *1 (-860 *4 *5 *3))))
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  ((*1 *2 *3 *4)
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-   (-5 *2 (-348 (-1083 *3))) (-5 *1 (-861 *5 *4 *6 *7 *3))
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    (-4 *3
     (-13 (-312)
-     (-10 -8 (-15 -3944 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))))
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  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-1083 *3))
+  (-12 (-5 *2 (-1084 *3))
    (-4 *3
     (-13 (-312)
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-   (-5 *1 (-861 *5 *4 *6 *7 *3))))
+     (-10 -8 (-15 -3945 ($ *7)) (-15 -2998 (*7 $)) (-15 -2997 (*7 $)))))
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-   (-5 *1 (-951 *5)) (-5 *3 (-348 (-856 *5)))))) 
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 (((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-860 *3 *4 *2)) (-4 *3 (-960)) (-4 *4 (-716))
-   (-4 *2 (-755))))
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  ((*1 *2 *3)
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-   (-4 *2 (-755)) (-5 *1 (-861 *4 *2 *5 *6 *3))
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    (-4 *3
     (-13 (-312)
-     (-10 -8 (-15 -3944 ($ *6)) (-15 -2997 (*6 $)) (-15 -2996 (*6 $)))))))
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  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-348 (-856 *4))) (-4 *4 (-494)) (-5 *2 (-1088))
-   (-5 *1 (-951 *4))))) 
+  (|partial| -12 (-5 *3 (-349 (-857 *4))) (-4 *4 (-495)) (-5 *2 (-1089))
+   (-5 *1 (-952 *4))))) 
 (((*1 *2 *3)
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-   (-4 *6 (-960)) (-5 *2 (-582 *5)) (-5 *1 (-272 *4 *5 *6 *7))))
- ((*1 *2 *1) (-12 (-4 *1 (-362 *3)) (-4 *3 (-1012)) (-5 *2 (-582 (-1088)))))
- ((*1 *2 *1) (-12 (-5 *2 (-582 (-799 *3))) (-5 *1 (-799 *3)) (-4 *3 (-1012))))
+  (-12 (-5 *3 (-1084 *7)) (-4 *7 (-861 *6 *4 *5)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-4 *6 (-961)) (-5 *2 (-583 *5)) (-5 *1 (-272 *4 *5 *6 *7))))
+ ((*1 *2 *1) (-12 (-4 *1 (-363 *3)) (-4 *3 (-1013)) (-5 *2 (-583 (-1089)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
  ((*1 *2 *1)
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-   (-5 *2 (-582 *5))))
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+   (-5 *2 (-583 *5))))
  ((*1 *2 *3)
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-   (-5 *2 (-582 *5)) (-5 *1 (-861 *4 *5 *6 *7 *3))
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    (-4 *3
     (-13 (-312)
-     (-10 -8 (-15 -3944 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))))
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  ((*1 *2 *1)
-  (-12 (-4 *1 (-885 *3 *4 *5)) (-4 *3 (-960)) (-4 *4 (-715)) (-4 *5 (-755))
-   (-5 *2 (-582 *5))))
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  ((*1 *2 *1)
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-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-582 *5))))
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  ((*1 *2 *3)
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-   (-5 *1 (-951 *4))))) 
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+   (-5 *1 (-952 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-856 *6))) (-5 *4 (-582 (-1088)))
-   (-4 *6 (-13 (-494) (-949 *5))) (-4 *5 (-494))
-   (-5 *2 (-582 (-582 (-249 (-348 (-856 *6)))))) (-5 *1 (-950 *5 *6))))) 
+  (-12 (-5 *3 (-583 (-857 *6))) (-5 *4 (-583 (-1089)))
+   (-4 *6 (-13 (-495) (-950 *5))) (-4 *5 (-495))
+   (-5 *2 (-583 (-583 (-249 (-349 (-857 *6)))))) (-5 *1 (-951 *5 *6))))) 
 (((*1 *2 *3 *4)
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-   (-4 *5 (-13 (-390) (-949 (-483)) (-120) (-579 (-483))))
-   (-5 *2 (-1083 (-348 (-1083 *6)))) (-5 *1 (-497 *5 *6 *7)) (-5 *3 (-1083 *6))
-   (-4 *7 (-1012))))
- ((*1 *2 *1) (-12 (-4 *2 (-1153 *3)) (-5 *1 (-648 *3 *2)) (-4 *3 (-960))))
- ((*1 *2 *1) (-12 (-4 *1 (-660 *3 *2)) (-4 *3 (-146)) (-4 *2 (-1153 *3))))
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+   (-5 *2 (-1084 (-349 (-1084 *6)))) (-5 *1 (-498 *5 *6 *7)) (-5 *3 (-1084 *6))
+   (-4 *7 (-1013))))
+ ((*1 *2 *1) (-12 (-4 *2 (-1154 *3)) (-5 *1 (-649 *3 *2)) (-4 *3 (-961))))
+ ((*1 *2 *1) (-12 (-4 *1 (-661 *3 *2)) (-4 *3 (-146)) (-4 *2 (-1154 *3))))
  ((*1 *2 *3 *4 *4 *5 *6 *7 *8)
-  (|partial| -12 (-5 *4 (-1083 *11)) (-5 *6 (-582 *10)) (-5 *7 (-582 (-693)))
-   (-5 *8 (-582 *11)) (-4 *10 (-755)) (-4 *11 (-258)) (-4 *9 (-716))
-   (-4 *5 (-860 *11 *9 *10)) (-5 *2 (-582 (-1083 *5)))
-   (-5 *1 (-680 *9 *10 *11 *5)) (-5 *3 (-1083 *5))))
+  (|partial| -12 (-5 *4 (-1084 *11)) (-5 *6 (-583 *10)) (-5 *7 (-583 (-694)))
+   (-5 *8 (-583 *11)) (-4 *10 (-756)) (-4 *11 (-258)) (-4 *9 (-717))
+   (-4 *5 (-861 *11 *9 *10)) (-5 *2 (-583 (-1084 *5)))
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  ((*1 *2 *1)
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-   (-4 *4 (-716)) (-4 *5 (-755)) (-14 *6 (-582 *2))))) 
+  (-12 (-4 *2 (-861 *3 *4 *5)) (-5 *1 (-947 *3 *4 *5 *2 *6)) (-4 *3 (-312))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-14 *6 (-583 *2))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-829)) (-5 *1 (-944 *2))
-   (-4 *2 (-13 (-1012) (-10 -8 (-15 * ($ $ $)))))))) 
+  (-12 (-5 *3 (-830)) (-5 *1 (-945 *2))
+   (-4 *2 (-13 (-1013) (-10 -8 (-15 * ($ $ $)))))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-829)) (-5 *1 (-943 *2))
-   (-4 *2 (-13 (-1012) (-10 -8 (-15 -3837 ($ $ $)))))))) 
+  (-12 (-5 *3 (-830)) (-5 *1 (-944 *2))
+   (-4 *2 (-13 (-1013) (-10 -8 (-15 -3838 ($ $ $)))))))) 
 (((*1 *2 *3 *4)
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-   (-5 *1 (-942 *5)) (-4 *5 (-312)) (-4 *5 (-318)) (-4 *5 (-960))))) 
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+   (-5 *1 (-943 *5)) (-4 *5 (-312)) (-4 *5 (-319)) (-4 *5 (-961))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-85)) (-5 *5 (-483)) (-4 *6 (-312)) (-4 *6 (-318))
-   (-4 *6 (-960)) (-5 *2 (-582 (-582 (-629 *6)))) (-5 *1 (-942 *6))
-   (-5 *3 (-582 (-629 *6)))))
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+   (-4 *6 (-961)) (-5 *2 (-583 (-583 (-630 *6)))) (-5 *1 (-943 *6))
+   (-5 *3 (-583 (-630 *6)))))
  ((*1 *2 *3)
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-   (-5 *2 (-582 (-582 (-629 *4)))) (-5 *1 (-942 *4)) (-5 *3 (-582 (-629 *4)))))
+  (-12 (-4 *4 (-312)) (-4 *4 (-319)) (-4 *4 (-961))
+   (-5 *2 (-583 (-583 (-630 *4)))) (-5 *1 (-943 *4)) (-5 *3 (-583 (-630 *4)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-312)) (-4 *5 (-318)) (-4 *5 (-960))
-   (-5 *2 (-582 (-582 (-629 *5)))) (-5 *1 (-942 *5)) (-5 *3 (-582 (-629 *5)))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-312)) (-4 *5 (-319)) (-4 *5 (-961))
+   (-5 *2 (-583 (-583 (-630 *5)))) (-5 *1 (-943 *5)) (-5 *3 (-583 (-630 *5)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-829)) (-4 *5 (-312)) (-4 *5 (-318)) (-4 *5 (-960))
-   (-5 *2 (-582 (-582 (-629 *5)))) (-5 *1 (-942 *5)) (-5 *3 (-582 (-629 *5)))))) 
+  (-12 (-5 *4 (-830)) (-4 *5 (-312)) (-4 *5 (-319)) (-4 *5 (-961))
+   (-5 *2 (-583 (-583 (-630 *5)))) (-5 *1 (-943 *5)) (-5 *3 (-583 (-630 *5)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-629 *5))) (-5 *4 (-483)) (-4 *5 (-312)) (-4 *5 (-960))
-   (-5 *2 (-85)) (-5 *1 (-942 *5))))
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  ((*1 *2 *3)
-  (-12 (-5 *3 (-582 (-629 *4))) (-4 *4 (-312)) (-4 *4 (-960)) (-5 *2 (-85))
-   (-5 *1 (-942 *4))))) 
+  (-12 (-5 *3 (-583 (-630 *4))) (-4 *4 (-312)) (-4 *4 (-961)) (-5 *2 (-85))
+   (-5 *1 (-943 *4))))) 
 (((*1 *2 *3 *3 *4 *5)
-  (-12 (-5 *3 (-582 (-629 *6))) (-5 *4 (-85)) (-5 *5 (-483)) (-5 *2 (-629 *6))
-   (-5 *1 (-942 *6)) (-4 *6 (-312)) (-4 *6 (-960))))
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  ((*1 *2 *3 *3)
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-   (-4 *4 (-312)) (-4 *4 (-960))))
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+   (-4 *4 (-312)) (-4 *4 (-961))))
  ((*1 *2 *3 *3 *4)
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-   (-5 *1 (-942 *5)) (-4 *5 (-312)) (-4 *5 (-960))))) 
+  (-12 (-5 *3 (-583 (-630 *5))) (-5 *4 (-484)) (-5 *2 (-630 *5))
+   (-5 *1 (-943 *5)) (-4 *5 (-312)) (-4 *5 (-961))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-629 *5))) (-5 *4 (-1177 *5)) (-4 *5 (-258))
-   (-4 *5 (-960)) (-5 *2 (-629 *5)) (-5 *1 (-942 *5))))) 
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+   (-4 *5 (-961)) (-5 *2 (-630 *5)) (-5 *1 (-943 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-582 (-629 *5))) (-4 *5 (-258)) (-4 *5 (-960))
-   (-5 *2 (-1177 (-1177 *5))) (-5 *1 (-942 *5)) (-5 *4 (-1177 *5))))) 
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+   (-5 *2 (-1178 (-1178 *5))) (-5 *1 (-943 *5)) (-5 *4 (-1178 *5))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-582 (-629 *4))) (-5 *2 (-629 *4)) (-4 *4 (-960))
-   (-5 *1 (-942 *4))))) 
+  (-12 (-5 *3 (-583 (-630 *4))) (-5 *2 (-630 *4)) (-4 *4 (-961))
+   (-5 *1 (-943 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 (-1177 *4))) (-4 *4 (-960)) (-5 *2 (-629 *4))
-   (-5 *1 (-942 *4))))) 
+  (-12 (-5 *3 (-1178 (-1178 *4))) (-4 *4 (-961)) (-5 *2 (-630 *4))
+   (-5 *1 (-943 *4))))) 
 (((*1 *2 *3 *4)
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-   (-4 *5 (-960))))
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+   (-4 *5 (-961))))
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-   (-4 *4 (-960))))
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+   (-4 *4 (-961))))
  ((*1 *2 *3 *4)
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-   (-5 *1 (-941 *5)) (-4 *5 (-960))))
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  ((*1 *2 *3)
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+(((*1 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-942 *3))))
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- ((*1 *2 *2) (-12 (-5 *2 (-582 (-629 *3))) (-4 *3 (-960)) (-5 *1 (-941 *3))))) 
+  (-12 (-5 *2 (-583 (-630 *3))) (-4 *3 (-961)) (-5 *1 (-942 *3))))
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+ ((*1 *2 *2) (-12 (-5 *2 (-583 (-630 *3))) (-4 *3 (-961)) (-5 *1 (-942 *3))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-629 *4)) (-5 *3 (-829)) (-4 *4 (-960)) (-5 *1 (-941 *4))))
+  (-12 (-5 *2 (-630 *4)) (-5 *3 (-830)) (-4 *4 (-961)) (-5 *1 (-942 *4))))
  ((*1 *2 *2 *3)
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 (((*1 *2 *2 *3)
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-  (-12 (-5 *2 (-582 (-582 (-853 (-179))))) (-5 *3 (-582 (-782)))
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 (((*1 *2 *3)
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 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
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 (((*1 *2 *1)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4 *5)
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-   (-5 *1 (-393 *4 *3)) (-4 *3 (-1153 *4))))) 
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 (((*1 *2 *3 *4 *5)
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 (((*1 *2 *3 *4)
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 (((*1 *2)
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 (((*1 *1 *2 *3)
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       (|:| |polj| *6))))
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 (((*1 *2 *3)
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-   (-5 *1 (-388 *5 *6 *7 *3))))) 
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       (|:| |polj| *6))))
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       (|:| |polj| *6))))
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 (((*1 *2 *3 *2)
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       (|:| |polj| *3))))
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+  (-12 (-4 *4 (-391)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85))
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+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7)
      (|:| |polj| *7)))
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-   (-5 *2 (-85)) (-5 *1 (-388 *4 *5 *6 *7))))) 
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-   (-5 *3 (-582 *7))))
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@@ -11984,1176 +11996,1176 @@
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+  (-12 (-5 *3 (-830)) (-5 *2 (-1084 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-829)) (-5 *2 (-1083 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-829)) (-5 *2 (-1083 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-829)) (-5 *2 (-1083 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
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 (((*1 *2 *3)
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-(((*1 *2 *2) (-12 (-5 *2 (-829)) (-5 *1 (-305 *3)) (-4 *3 (-299))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-829)) (-5 *1 (-305 *3)) (-4 *3 (-299))))) 
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+(((*1 *2 *2) (-12 (-5 *2 (-830)) (-5 *1 (-305 *3)) (-4 *3 (-299))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-830)) (-5 *1 (-305 *3)) (-4 *3 (-299))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-299)) (-5 *2 (-85))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *4)) (-4 *4 (-299)) (-5 *2 (-85)) (-5 *1 (-305 *4))))) 
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 (((*1 *2)
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+  (-12 (-5 *2 (-1178 (-583 (-2 (|:| -3401 *3) (|:| -2400 (-1033))))))
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 (((*1 *2)
-  (-12 (-5 *2 (-629 (-816 *3))) (-5 *1 (-301 *3 *4)) (-14 *3 (-829))
-   (-14 *4 (-829))))
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+   (-14 *4 (-830))))
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-  (-12 (-5 *2 (-629 *3)) (-5 *1 (-302 *3 *4)) (-4 *3 (-299))
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-    (-3 (-1083 *3) (-1177 (-582 (-2 (|:| -3400 *3) (|:| -2399 (-1032)))))))))
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  ((*1 *2)
-  (-12 (-5 *2 (-629 *3)) (-5 *1 (-303 *3 *4)) (-4 *3 (-299)) (-14 *4 (-829))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 (-582 (-2 (|:| -3400 *4) (|:| -2399 (-1032))))))
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  ((*1 *2)
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  ((*1 *2)
-  (-12 (-5 *2 (-693)) (-5 *1 (-302 *3 *4)) (-4 *3 (-299))
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-    (-3 (-1083 *3) (-1177 (-582 (-2 (|:| -3400 *3) (|:| -2399 (-1032)))))))))
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 (((*1 *2)
   (-12 (-4 *1 (-299))
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 (((*1 *1) (-4 *1 (-299)))) 
 (((*1 *2)
   (-12 (-4 *1 (-299)) (-5 *2 (-3 "prime" "polynomial" "normal" "cyclic"))))) 
 (((*1 *2 *3)
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+  (-12 (-5 *3 (-830))
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 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-829))
-   (-5 *2 (-1177 (-582 (-2 (|:| -3400 *4) (|:| -2399 (-1032))))))
+  (|partial| -12 (-5 *3 (-830))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *4)) (-4 *4 (-299))
-   (-5 *2 (-1177 (-582 (-2 (|:| -3400 *4) (|:| -2399 (-1032))))))
+  (-12 (-5 *3 (-1084 *4)) (-4 *4 (-299))
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    (-5 *1 (-296 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *4)) (-4 *4 (-299)) (-5 *2 (-868 (-1032)))
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    (-5 *1 (-296 *4))))) 
 (((*1 *2)
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-   (-14 *4 (-829))))
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  ((*1 *2)
-  (-12 (-5 *2 (-868 (-1032))) (-5 *1 (-294 *3 *4)) (-4 *3 (-299))
-   (-14 *4 (-1083 *3))))
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+   (-14 *4 (-1084 *3))))
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-   (-14 *4 (-829))))) 
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+   (-14 *4 (-830))))) 
 (((*1 *2)
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-   (-5 *2 (-693)) (-5 *1 (-290 *3 *4 *5 *6)) (-4 *3 (-291 *4 *5 *6))))
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+   (-5 *2 (-694)) (-5 *1 (-290 *3 *4 *5 *6)) (-4 *3 (-291 *4 *5 *6))))
  ((*1 *2)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-693))))) 
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 (((*1 *2)
-  (-12 (-4 *4 (-1132)) (-4 *5 (-1153 *4)) (-4 *6 (-1153 (-348 *5)))
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    (-5 *2 (-85)) (-5 *1 (-290 *3 *4 *5 *6)) (-4 *3 (-291 *4 *5 *6))))
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-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2 *3 *3)
-  (-12 (-4 *3 (-1132)) (-4 *5 (-1153 *3)) (-4 *6 (-1153 (-348 *5)))
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    (-5 *2 (-85)) (-5 *1 (-290 *4 *3 *5 *6)) (-4 *4 (-291 *3 *5 *6))))
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-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
+   (-4 *5 (-1154 (-349 *4))) (-5 *2 (-85))))) 
 (((*1 *2 *3)
-  (-12 (-4 *1 (-291 *4 *3 *5)) (-4 *4 (-1132)) (-4 *3 (-1153 *4))
-   (-4 *5 (-1153 (-348 *3))) (-5 *2 (-85))))
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2 *3)
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-   (-4 *5 (-1153 (-348 *3))) (-5 *2 (-85))))
+  (-12 (-4 *1 (-291 *4 *3 *5)) (-4 *4 (-1133)) (-4 *3 (-1154 *4))
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  ((*1 *2 *3)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
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 (((*1 *2 *3)
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-   (-4 *5 (-1153 (-348 *3))) (-5 *2 (-85))))
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  ((*1 *2 *3)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
+   (-4 *5 (-1154 (-349 *4))) (-5 *2 (-85))))) 
 (((*1 *2)
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-   (-5 *2 (-1177 *1)) (-4 *1 (-291 *3 *4 *5))))) 
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 (((*1 *2 *1)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
+   (-4 *5 (-1154 (-349 *4))) (-5 *2 (-85))))) 
 (((*1 *2 *1 *3)
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-   (-4 *5 (-1153 (-348 *3))) (-5 *2 (-85))))
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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 (((*1 *2 *2)
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-   (-4 *4 (-1153 *3)) (-4 *5 (-1153 (-348 *4)))))) 
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 (((*1 *2 *2)
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-   (-4 *4 (-1153 *3)) (-4 *5 (-1153 (-348 *4)))))) 
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 (((*1 *2 *2)
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-   (-4 *4 (-1153 *3)) (-4 *5 (-1153 (-348 *4)))))) 
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 (((*1 *2)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-629 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
+   (-4 *5 (-1154 (-349 *4))) (-5 *2 (-630 (-349 *4)))))) 
 (((*1 *2)
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-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-629 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-629 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
-   (-4 *5 (-1153 (-348 *4))) (-5 *2 (-629 (-348 *4)))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1133)) (-4 *4 (-1154 *3))
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-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
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+   (-5 *2 (-2 (|:| |num| (-1178 *4)) (|:| |den| *4)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1132)) (-4 *4 (-1153 *3))
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-   (-5 *2 (-2 (|:| |num| (-1177 *4)) (|:| |den| *4)))))) 
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+   (-5 *2 (-2 (|:| |num| (-1178 *4)) (|:| |den| *4)))))) 
 (((*1 *1 *2 *3)
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-   (-4 *1 (-291 *4 *3 *5)) (-4 *5 (-1153 (-348 *3)))))) 
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 (((*1 *2 *3)
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-   (-5 *2 (-2 (|:| |num| (-629 *5)) (|:| |den| *5)))))) 
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+   (-4 *5 (-1154 *4)) (-4 *6 (-1154 (-349 *5)))
+   (-5 *2 (-2 (|:| |num| (-630 *5)) (|:| |den| *5)))))) 
 (((*1 *2 *3)
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-   (-4 *3 (-13 (-312) (-1113) (-914)))))
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+   (-4 *3 (-13 (-312) (-1114) (-915)))))
  ((*1 *2)
-  (|partial| -12 (-4 *4 (-1132)) (-4 *5 (-1153 (-348 *2))) (-4 *2 (-1153 *4))
+  (|partial| -12 (-4 *4 (-1133)) (-4 *5 (-1154 (-349 *2))) (-4 *2 (-1154 *4))
    (-5 *1 (-290 *3 *4 *2 *5)) (-4 *3 (-291 *4 *2 *5))))
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-  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1132))
-   (-4 *4 (-1153 (-348 *2))) (-4 *2 (-1153 *3))))) 
+  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1133))
+   (-4 *4 (-1154 (-349 *2))) (-4 *2 (-1154 *3))))) 
 (((*1 *2)
-  (|partial| -12 (-4 *4 (-1132)) (-4 *5 (-1153 (-348 *2))) (-4 *2 (-1153 *4))
+  (|partial| -12 (-4 *4 (-1133)) (-4 *5 (-1154 (-349 *2))) (-4 *2 (-1154 *4))
    (-5 *1 (-290 *3 *4 *2 *5)) (-4 *3 (-291 *4 *2 *5))))
  ((*1 *2)
-  (|partial| -12 (-4 *1 (-291 *3 *2 *4)) (-4 *3 (-1132))
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-   (-5 *2 (-582 (-856 *4)))))) 
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    (-4 *6 (-291 *2 *4 *5))))
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 (((*1 *2 *3)
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 (((*1 *2 *3) (-12 (-5 *2 (-1 (-179) (-179))) (-5 *1 (-269)) (-5 *3 (-179))))) 
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    (-4 *1 (-258))))
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-  (|partial| -12 (-5 *3 (-582 (-221))) (-5 *4 (-1088)) (-5 *2 (-51))
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-835))
+  (-12 (-5 *3 (-836))
    (-5 *2
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-     (|:| |xValues| (-1000 (-179))) (|:| |yValues| (-1000 (-179)))))
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-  (-12 (-5 *3 (-835)) (-5 *4 (-348 (-483)))
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    (-5 *2
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   (-12
    (-5 *2
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 (((*1 *2 *3 *4)
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 (((*1 *2 *2) (-12 (-5 *2 (-179)) (-5 *1 (-218))))) 
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+  (-12 (-5 *3 (-1089)) (-4 *4 (-495)) (-5 *2 (-583 *1)) (-4 *1 (-29 *4))))
+ ((*1 *2 *1) (-12 (-4 *3 (-495)) (-5 *2 (-583 *1)) (-4 *1 (-29 *3))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-23)) (-5 *2 (-85))))) 
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\ No newline at end of file
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+ (-3951 . 31402) (-3952 . 31107) (-3953 . 30759) (-3954 . 30593)
+ (-3955 . 30427) (-3956 . 29945) (-3957 . 16071) (-3958 . 14964) (* . 10917)
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+ (-3965 . 9140) (-3966 . 8513) (-3967 . 7240) (-3968 . 5996) (-3969 . 5127)
+ (-3970 . 3864) (-3971 . 420) (-3972 . 306) (-3973 . 173) (-3974 . 30)) 
\ No newline at end of file