Update cached database

5 files changed, 27060 insertions, 27040 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 21253206..53ab59f1 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2267485 . 3485510916)       
+(2268331 . 3485633349)       
 (-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."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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},{}...,{}\\spad{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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . 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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4451 . T) (-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4447 . T) (-4452 . T) (-4446 . T)) 
+((-4453 . T) (-4451 . T) (-4450 . T) ((-4458 "*") . T) (-4449 . T) (-4454 . T) (-4448 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -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 \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -1384) 
+(-32 R -1386) 
 ((|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| (LIST (QUOTE -1049) (QUOTE (-572))))) 
+((|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) 
 (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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 -4454))) 
+((|HasAttribute| |#1| (QUOTE -4456))) 
 (-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 \\%")) (|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.")) (|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} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\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}."))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . 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"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . 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 a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -1384 UP UPUP -1929) 
+(-40 -1386 UP UPUP -3201) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-2813 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-2813 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-2813 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) 
-(-41 R -1384) 
+((-4449 |has| (-417 |#2|) (-372)) (-4454 |has| (-417 |#2|) (-372)) (-4448 |has| (-417 |#2|) (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2818 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2818 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2818 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2818 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) 
+(-41 R -1386) 
 ((|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}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'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 (-460))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -438) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -440) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -103,34 +103,34 @@ NIL
 (-43 R A) 
 ((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-313)))) 
+((|HasCategory| |#1| (QUOTE (-315)))) 
 (-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."))) 
-((-4451 |has| |#1| (-564)) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) 
+((-4453 |has| |#1| (-566)) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) 
 (-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."))) 
-((-4454 . T) (-4455 . T)) 
-((-2813 (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|))))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|))))))) 
+((-4456 . T) (-4457 . T)) 
+((-2818 (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|))))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|))))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370)))) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| $ (QUOTE (-1060))) (|HasCategory| $ (LIST (QUOTE -1049) (QUOTE (-572))))) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| $ (QUOTE (-1062))) (|HasCategory| $ (LIST (QUOTE -1051) (QUOTE (-574))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
 (-51 S) 
 ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) 
@@ -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 -1384) 
+(-54 |Base| R -1386) 
 ((|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},{}...,{}\\spad{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},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,7 +158,7 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'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"))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
 (-58 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),...]}."))) 
@@ -166,65 +166,65 @@ NIL
 NIL 
 (-59 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}"))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-61 -2030) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-61 -2032) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-62 -2030) 
+(-62 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-63 -2030) 
+(-63 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-64 -2030) 
+(-64 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-65 -2030) 
+(-65 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -2030) 
+(-66 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-67 -2030) 
+(-67 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-68 -2030) 
+(-68 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -2030) 
+(-69 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-70 -2030) 
+(-70 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-71 -2030) 
+(-71 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-72 -2030) 
+(-72 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-73 -2030) 
+(-73 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-74 -2030) 
+(-74 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
@@ -236,66 +236,66 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-77 -2030) 
+(-77 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-78 -2030) 
+(-78 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -2030) 
+(-79 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -2030) 
+(-80 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -2030) 
+(-81 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-82 -2030) 
+(-82 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -2030) 
+(-83 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -2030) 
+(-84 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -2030) 
+(-85 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -2030) 
+(-86 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -2030) 
+(-87 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-88 -2030) 
+(-88 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-89 -2030) 
+(-89 -2032) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
 (-90 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}\\spad{'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 (-370)))) 
+((|HasCategory| |#1| (QUOTE (-372)))) 
 (-91 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}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -318,15 +318,15 @@ NIL
 NIL 
 (-97) 
 ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) 
-((-4454 . T)) 
+((-4456 . T)) 
 NIL 
 (-98) 
 ((|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."))) 
-((-4454 . T) ((-4456 "*") . T) (-4455 . T) (-4451 . T) (-4449 . T) (-4448 . T) (-4447 . T) (-4452 . T) (-4446 . T) (-4445 . T) (-4444 . T) (-4443 . T) (-4442 . T) (-4450 . T) (-4453 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4441 . T)) 
+((-4456 . T) ((-4458 "*") . T) (-4457 . T) (-4453 . T) (-4451 . T) (-4450 . T) (-4449 . T) (-4454 . T) (-4448 . T) (-4447 . T) (-4446 . T) (-4445 . T) (-4444 . T) (-4452 . T) (-4455 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4443 . T)) 
 NIL 
 (-99 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}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
 (-100 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}."))) 
@@ -342,15 +342,15 @@ NIL
 NIL 
 (-103 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 \\spad{pl} and \\spad{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{:=} \\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 \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-104 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 (-4456 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4458 "*")))) 
 (-105) 
 ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) 
-((-4454 . T)) 
+((-4456 . T)) 
 NIL 
 (-106 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."))) 
@@ -358,23 +358,23 @@ NIL
 NIL 
 (-107 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."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
 (-108) 
 ((|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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-574) (QUOTE (-920))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1035))) (|HasCategory| (-574) (QUOTE (-830))) (-2818 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1165))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (|HasCategory| (-574) (QUOTE (-146))))) 
 (-109) 
 ((|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 \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
 NIL 
 (-110) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1111))) (|HasCategory| (-112) (LIST (QUOTE -315) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-112) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-112) (QUOTE (-1111))) (|HasCategory| (-112) (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1113))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1113))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-111 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}"))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
 (-112) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) 
@@ -392,22 +392,22 @@ NIL
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
 NIL 
 NIL 
-(-116 -1384 UP) 
+(-116 -1386 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 
 (-117 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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}."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-118 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-117 |#1|) (QUOTE (-918))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-117 |#1|) (QUOTE (-1033))) (|HasCategory| (-117 |#1|) (QUOTE (-828))) (-2813 (|HasCategory| (-117 |#1|) (QUOTE (-828))) (|HasCategory| (-117 |#1|) (QUOTE (-858)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-1163))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-313))) (|HasCategory| (-117 |#1|) (QUOTE (-553))) (|HasCategory| (-117 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-918)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-117 |#1|) (QUOTE (-920))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-117 |#1|) (QUOTE (-1035))) (|HasCategory| (-117 |#1|) (QUOTE (-830))) (-2818 (|HasCategory| (-117 |#1|) (QUOTE (-830))) (|HasCategory| (-117 |#1|) (QUOTE (-860)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-1165))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -524) (QUOTE (-1190)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-315))) (|HasCategory| (-117 |#1|) (QUOTE (-555))) (|HasCategory| (-117 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-920)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
 (-119 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4455))) 
+((|HasAttribute| |#1| (QUOTE -4457))) 
 (-120 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 
@@ -418,15 +418,15 @@ NIL
 NIL 
 (-122 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"))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-123 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-124) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
 (-125 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -434,20 +434,20 @@ NIL
 NIL 
 (-126 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-128 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."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-129) 
 ((|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 \\spad{`n'}. The array can then store up to \\spad{`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 \\spad{`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."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130)))))) (-2813 (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-130) (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111)))) (|HasCategory| (-130) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-130) (QUOTE (-1111))) (|HasCategory| (-130) (LIST (QUOTE -315) (QUOTE (-130)))))) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1113))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) (-2818 (-12 (|HasCategory| (-130) (QUOTE (-1113))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1113)))) (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1113))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-130) (QUOTE (-1113))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) 
 (-130) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) 
 NIL 
@@ -470,13 +470,13 @@ NIL
 NIL 
 (-135) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4456 "*") . T)) 
+(((-4458 "*") . T)) 
 NIL 
-(-136 |minix| -4127 S T$) 
+(-136 |minix| -4129 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -4127 R) 
+(-137 |minix| -4129 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
@@ -498,8 +498,8 @@ NIL
 NIL 
 (-142) 
 ((|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}."))) 
-((-4454 . T) (-4444 . T) (-4455 . T)) 
-((-2813 (-12 (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-375))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) 
+((-4456 . T) (-4446 . T) (-4457 . T)) 
+((-2818 (-12 (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) 
 (-143 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}\\spad{'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}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -514,7 +514,7 @@ NIL
 NIL 
 (-146) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
 (-147 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 \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) 
@@ -522,9 +522,9 @@ NIL
 NIL 
 (-148) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-149 -1384 UP UPUP) 
+(-149 -1386 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 
@@ -535,14 +535,14 @@ NIL
 (-151 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasAttribute| |#1| (QUOTE -4454))) 
+((|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasAttribute| |#1| (QUOTE -4456))) 
 (-152 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|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{==} [\\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 
 (-153 |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."))) 
-((-4449 . T) (-4448 . T) (-4451 . T)) 
+((-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
 (-154) 
 ((|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."))) 
@@ -564,7 +564,7 @@ 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 
-(-159 R -1384) 
+(-159 R -1386) 
 ((|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})\\spad{/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.} \\spad{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.} \\spad{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.} \\spad{n!/}(\\spad{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 
@@ -595,10 +595,10 @@ NIL
 (-166 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 (-918))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-564)))) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1216))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-1035))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasAttribute| |#2| (QUOTE -4455)) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566)))) 
 (-167 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})"))) 
-((-4447 -2813 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-3559 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 -2818 (|has| |#1| (-566)) (-12 (|has| |#1| (-315)) (|has| |#1| (-920)))) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4452 |has| |#1| (-6 -4452)) (-4455 |has| |#1| (-6 -4455)) (-3562 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-168 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."))) 
@@ -614,8 +614,8 @@ NIL
 NIL 
 (-171 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}."))) 
-((-4447 -2813 (|has| |#1| (-564)) (-12 (|has| |#1| (-313)) (|has| |#1| (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4450 |has| |#1| (-6 -4450)) (-4453 |has| |#1| (-6 -4453)) (-3559 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-836)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1214)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-918))))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-1071))) (-12 (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-1214)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-237))) (-12 (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4453)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-356))))) 
+((-4449 -2818 (|has| |#1| (-566)) (-12 (|has| |#1| (-315)) (|has| |#1| (-920)))) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4452 |has| |#1| (-6 -4452)) (-4455 |has| |#1| (-6 -4455)) (-3562 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-377)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1035)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1216)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-920))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-920)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-920))))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1216)))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (QUOTE (-1035))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-1073))) (-12 (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-1216)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-372)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#1| (QUOTE -4455)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190))))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-358))))) 
 (-172 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -626,7 +626,7 @@ NIL
 NIL 
 (-174) 
 ((|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."))) 
-(((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-175) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -634,7 +634,7 @@ NIL
 NIL 
 (-176 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) 
-(((-4456 "*") . T) (-4447 . T) (-4452 . T) (-4446 . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") . T) (-4449 . T) (-4454 . T) (-4448 . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-177) 
 ((|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|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -651,7 +651,7 @@ NIL
 (-180 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| (-961 |#2|) (LIST (QUOTE -895) (|devaluate| |#1|)))) 
+((|HasCategory| (-963 |#2|) (LIST (QUOTE -897) (|devaluate| |#1|)))) 
 (-181 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)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -688,7 +688,7 @@ NIL
 ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-190 R -1384) 
+(-190 R -1386) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -796,23 +796,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-217 -1384 UP UPUP R) 
+(-217 -1386 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 
-(-218 -1384 FP) 
+(-218 -1386 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 \\spad{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 
 (-219) 
 ((|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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-574) (QUOTE (-920))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1035))) (|HasCategory| (-574) (QUOTE (-830))) (-2818 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1165))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (|HasCategory| (-574) (QUOTE (-146))))) 
 (-220) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-221 R -1384) 
+(-221 R -1386) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -826,19 +826,19 @@ NIL
 NIL 
 (-224 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-225 |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}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-226 R -1384) 
+(-226 R -1386) 
 ((|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 
 (-227) 
 ((|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.")) (|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}."))) 
-((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-3551 . T) (-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 (-228) 
 ((|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)}.}"))) 
@@ -846,23 +846,23 @@ NIL
 NIL 
 (-229 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}"))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4458 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-230 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 
 (-231 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."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
 (-232 S R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) 
+((|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239)))) 
 (-233 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
 (-234 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -873,4296 +873,4304 @@ NIL
 NIL 
 NIL 
 (-236 S) 
-((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}."))) 
+((|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}."))) 
 NIL 
 NIL 
 (-237) 
+((|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}."))) 
+NIL 
+NIL 
+(-238 S) 
+((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}."))) 
+NIL 
+NIL 
+(-239) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-238 A S) 
+(-240 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 -4454))) 
-(-239 S) 
+((|HasAttribute| |#1| (QUOTE -4456))) 
+(-241 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}."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
-(-240) 
+(-242) 
 ((|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 
-(-241 S -4127 R) 
+(-243 S -4129 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|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 (-370))) (|HasCategory| |#3| (QUOTE (-801))) (|HasCategory| |#3| (QUOTE (-856))) (|HasAttribute| |#3| (QUOTE -4451)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-734))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1060))) (|HasCategory| |#3| (QUOTE (-1111)))) 
-(-242 -4127 R) 
+((|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-858))) (|HasAttribute| |#3| (QUOTE -4453)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (QUOTE (-1113)))) 
+(-244 -4129 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#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}.")) (|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"))) 
-((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) 
+((-4450 |has| |#2| (-1062)) (-4451 |has| |#2| (-1062)) (-4453 |has| |#2| (-6 -4453)) ((-4458 "*") |has| |#2| (-174)) (-4456 . T)) 
 NIL 
-(-243 -4127 A B) 
+(-245 -4129 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 
-(-244 -4127 R) 
+(-246 -4129 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."))) 
-((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (-2813 (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1060)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-370))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) 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(|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-370))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1060)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-370))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1060)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-370))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1060)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1060)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#2| (LIST (QUOTE 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(QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-801)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-856)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1060)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1111))))) (-2813 (-12 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1060))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))))) (|HasCategory| (-572) (QUOTE (-858))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1060)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188))))) (-2813 (|HasCategory| |#2| (QUOTE (-1060))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1111)))) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))))) 
-(-245) 
+((-4450 |has| |#2| (-1062)) (-4451 |has| |#2| (-1062)) (-4453 |has| |#2| (-6 -4453)) ((-4458 "*") |has| |#2| (-174)) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE 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+(-247) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
 NIL 
-(-246 S) 
+(-248 S) 
 ((|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}."))) 
 NIL 
 NIL 
-(-247) 
+(-249) 
 ((|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}."))) 
-((-4447 . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-248 S) 
+(-250 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."))) 
 NIL 
 NIL 
-(-249 S) 
+(-251 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}"))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-250 M) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-252 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\\spad{'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 
-(-251 |vl| R) 
+(-253 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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-(-252) 
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+(-254) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|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 \\spad{`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 \\spad{`d'}."))) 
 NIL 
 NIL 
-(-253) 
+(-255) 
 ((|constructor| (NIL "This domain provides representations for domains constructors.")) (|functorData| (((|FunctorData|) $) "\\spad{functorData x} returns the functor data associated with the domain constructor \\spad{x}."))) 
 NIL 
 NIL 
-(-254) 
+(-256) 
 ((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
 NIL 
 NIL 
-(-255 |n| R M S) 
+(-257 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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+(-259 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} \\spad{:=} 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 
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-(-258 R S V E) 
+((|HasCategory| |#2| (QUOTE (-239)))) 
+(-260 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} \\spad{:=} 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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-259 S) 
+(-261 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}."))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
-(-260) 
+(-262) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,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)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,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)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,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)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,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)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(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)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,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)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,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)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),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)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,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)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
 NIL 
 NIL 
-(-261 R |Ex|) 
+(-263 R |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,y) = g(x,y),x,y,l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) 
 NIL 
 NIL 
-(-262) 
+(-264) 
 ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,rRange,iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f, -2..2, -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,rRange,iRange,arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f, 0.3..3, 0..2*\\%pi, false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) 
 NIL 
 NIL 
-(-263 R) 
+(-265 R) 
 ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) 
 NIL 
 NIL 
-(-264 |Ex|) 
+(-266 |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."))) 
 NIL 
 NIL 
-(-265) 
+(-267) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,lz,l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly,lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) 
 NIL 
 NIL 
-(-266) 
+(-268) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) 
 NIL 
 NIL 
-(-267 S) 
+(-269 S) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) 
 NIL 
 NIL 
-(-268) 
+(-270) 
 ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) 
 NIL 
 NIL 
-(-269 R S V) 
+(-271 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"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
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-(-270 A S) 
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+(-272 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.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|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 
 NIL 
-(-271 S) 
+(-273 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.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
 NIL 
-(-272) 
+(-274) 
 ((|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\axiom{\\spad{l}}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}."))) 
 NIL 
 NIL 
-(-273) 
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 ((|constructor| (NIL "\\axiomType{e04dgfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04DGF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04DGF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-274) 
+(-276) 
 ((|constructor| (NIL "\\axiomType{e04fdfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04FDF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04FDF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-275) 
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 ((|constructor| (NIL "\\axiomType{e04gcfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04GCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04GCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-276) 
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 ((|constructor| (NIL "\\axiomType{e04jafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04JAF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04JAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-277) 
+(-279) 
 ((|constructor| (NIL "\\axiomType{e04mbfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04MBF,{} an optimization routine for Linear functions. The function \\axiomFun{measure} measures the usefulness of the routine E04MBF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-278) 
+(-280) 
 ((|constructor| (NIL "\\axiomType{e04nafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04NAF,{} an optimization routine for Quadratic functions. The function \\axiomFun{measure} measures the usefulness of the routine E04NAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-279) 
+(-281) 
 ((|constructor| (NIL "\\axiomType{e04ucfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04UCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04UCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}."))) 
 NIL 
 NIL 
-(-280) 
+(-282) 
 ((|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|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'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 
-(-281 R -1384) 
+(-283 R -1386) 
 ((|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 
-(-282 R -1384) 
+(-284 R -1386) 
 ((|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 
-(-283 |Coef| UTS ULS) 
+(-285 |Coef| UTS ULS) 
 ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-370)))) 
-(-284 |Coef| ULS UPXS EFULS) 
+((|HasCategory| |#1| (QUOTE (-372)))) 
+(-286 |Coef| ULS UPXS EFULS) 
 ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-370)))) 
-(-285) 
+((|HasCategory| |#1| (QUOTE (-372)))) 
+(-287) 
 ((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) 
 NIL 
 NIL 
-(-286) 
+(-288) 
 ((|environment| (((|Environment|) $) "\\spad{environment(x)} returns the environment of the elaboration \\spad{x}.")) (|typeForm| (((|InternalTypeForm|) $) "\\spad{typeForm(x)} returns the type form of the elaboration \\spad{x}.")) (|irForm| (((|InternalRepresentationForm|) $) "\\spad{irForm(x)} returns the internal representation form of the elaboration \\spad{x}.")) (|elaboration| (($ (|InternalRepresentationForm|) (|InternalTypeForm|) (|Environment|)) "\\spad{elaboration(ir,ty,env)} construct an elaboration object for for the internal representation form \\spad{ir},{} with type \\spad{ty},{} and environment \\spad{env}."))) 
 NIL 
 NIL 
-(-287 A S) 
+(-289 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 (-858))) (|HasCategory| |#2| (QUOTE (-1111)))) 
-(-288 S) 
+((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113)))) 
+(-290 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}."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
-(-289 S) 
+(-291 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-290) 
+(-292) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-291 |Coef| UTS) 
+(-293 |Coef| UTS) 
 ((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) 
 NIL 
 NIL 
-(-292 S T$) 
+(-294 S T$) 
 ((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) 
 NIL 
 NIL 
-(-293 S |Dom| |Im|) 
+(-295 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 -4455))) 
-(-294 |Dom| |Im|) 
+((|HasAttribute| |#1| (QUOTE -4457))) 
+(-296 |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 
-(-295 S R |Mod| -3104 -1767 |exactQuo|) 
+(-297 S R |Mod| -2348 -2130 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-296) 
+(-298) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-4447 . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-297) 
+(-299) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
 NIL 
 NIL 
-(-298 R) 
+(-300 R) 
 ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,m,k,g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) 
 NIL 
 NIL 
-(-299 S R) 
+(-301 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 
-(-300 S) 
+(-302 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| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and 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."))) 
-((-4451 -2813 (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4448 |has| |#1| (-1060)) (-4449 |has| |#1| (-1060))) 
-((|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1060)))) (-2813 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-734)))) (|HasCategory| |#1| (QUOTE (-481))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2813 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1123)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-308))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-481)))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734)))) (-2813 (|HasCategory| |#1| (QUOTE (-481))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-734)))) 
-(-301 |Key| |Entry|) 
+((-4453 -2818 (|has| |#1| (-1062)) (|has| |#1| (-483))) (-4450 |has| |#1| (-1062)) (-4451 |has| |#1| (-1062))) 
+((|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1062)))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-1062)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1062)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1062)))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1062)))) (-2818 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736)))) (|HasCategory| |#1| (QUOTE (-483))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1113)))) (-2818 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-310))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483)))) (-2818 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736)))) (-2818 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-1062)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-736)))) 
+(-303 |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."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-302) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-304) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
 NIL 
-(-303 -1384 S) 
+(-305 -1386 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 
-(-304 E -1384) 
+(-306 E -1386) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\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 
-(-305 A B) 
+(-307 A B) 
 ((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]"))) 
 NIL 
 NIL 
-(-306) 
+(-308) 
 ((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,var,range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,vars,range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,var,range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}"))) 
 NIL 
 NIL 
-(-307 S) 
+(-309 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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|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| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1060)))) 
-(-308) 
+((|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1062)))) 
+(-310) 
 ((|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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|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 
-(-309 R1) 
+(-311 R1) 
 ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}"))) 
 NIL 
 NIL 
-(-310 R1 R2) 
+(-312 R1 R2) 
 ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}"))) 
 NIL 
 NIL 
-(-311) 
+(-313) 
 ((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}"))) 
 NIL 
 NIL 
-(-312 S) 
+(-314 S) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
 NIL 
 NIL 
-(-313) 
+(-315) 
 ((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-314 S R) 
+(-316 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-315 R) 
+(-317 R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} 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 
-(-316 -1384) 
+(-318 -1386) 
 ((|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 
-(-317) 
+(-319) 
 ((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) 
 NIL 
 NIL 
-(-318) 
+(-320) 
 ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) 
 NIL 
 NIL 
-(-319 R FE |var| |cen|) 
+(-321 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
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-(-320 R S) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
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+(-322 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
 NIL 
-(-321 R FE) 
+(-323 R FE) 
 ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) 
 NIL 
 NIL 
-(-322 R) 
+(-324 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."))) 
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-(-323 R -1384) 
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+(-325 R -1386) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'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 
-(-324) 
+(-326) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) 
 NIL 
 NIL 
-(-325 FE |var| |cen|) 
+(-327 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
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+(-328 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},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between \\spad{-k} and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}."))) 
 NIL 
 NIL 
-(-328 S) 
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 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) 
-((-4449 . T) (-4448 . T)) 
-((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-800)))) 
-(-329 S E) 
+((-4451 . T) (-4450 . T)) 
+((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-802)))) 
+(-331 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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}\\spad{'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) 
 NIL 
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+((|HasCategory| (-781) (QUOTE (-802)))) 
+(-333 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 \\spad{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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-332 R E) 
+((|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-334 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 \\spad{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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-333 S) 
+(-335 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."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-334 S -1384) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-336 S -1386) 
 ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-375)))) 
-(-335 -1384) 
+((|HasCategory| |#2| (QUOTE (-377)))) 
+(-337 -1386) 
 ((|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})\\spad{\\$}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})\\spad{\\$}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**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{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},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-336) 
+(-338) 
 ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) 
 NIL 
 NIL 
-(-337 E) 
+(-339 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"))) 
 NIL 
 NIL 
-(-338) 
+(-340) 
 ((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,b,d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,p,q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,p)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-339) 
+(-341) 
 ((|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 
-(-340 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+(-342 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|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 
-(-341 S -1384 UP UPUP R) 
+(-343 S -1386 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 
-(-342 -1384 UP UPUP R) 
+(-344 -1386 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 \\spad{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 \\spad{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 
-(-343 -1384 UP UPUP R) 
+(-345 -1386 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
-(-344 S R) 
+(-346 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) 
-(-345 R) 
+((|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+(-347 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
-(-346 |basicSymbols| |subscriptedSymbols| R) 
+(-348 |basicSymbols| |subscriptedSymbols| R) 
 ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#3| (LIST (QUOTE -1049) (QUOTE (-386)))) (|HasCategory| $ (QUOTE (-1060))) (|HasCategory| $ (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-347 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-388)))) (|HasCategory| $ (QUOTE (-1062))) (|HasCategory| $ (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-349 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-348 S -1384 UP UPUP) 
+(-350 S -1386 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 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 (-375))) (|HasCategory| |#2| (QUOTE (-370)))) 
-(-349 -1384 UP UPUP) 
+((|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-372)))) 
+(-351 -1386 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 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."))) 
-((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 |has| (-417 |#2|) (-372)) (-4454 |has| (-417 |#2|) (-372)) (-4448 |has| (-417 |#2|) (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-350 |p| |extdeg|) 
+(-352 |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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) 
-(-351 GF |defpol|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| (-921 |#1|) (QUOTE (-146))) (|HasCategory| (-921 |#1|) (QUOTE (-377)))) (|HasCategory| (-921 |#1|) (QUOTE (-148))) (|HasCategory| (-921 |#1|) (QUOTE (-377))) (|HasCategory| (-921 |#1|) (QUOTE (-146)))) 
+(-353 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-352 GF |extdeg|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-354 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-353 GF) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-355 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
 NIL 
-(-354 F1 GF F2) 
+(-356 F1 GF F2) 
 ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) 
 NIL 
 NIL 
-(-355 S) 
+(-357 S) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
 NIL 
 NIL 
-(-356) 
+(-358) 
 ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-357 R UP -1384) 
+(-359 R UP -1386) 
 ((|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 
-(-358 |p| |extdeg|) 
+(-360 |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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) 
-(-359 GF |uni|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| (-921 |#1|) (QUOTE (-146))) (|HasCategory| (-921 |#1|) (QUOTE (-377)))) (|HasCategory| (-921 |#1|) (QUOTE (-148))) (|HasCategory| (-921 |#1|) (QUOTE (-377))) (|HasCategory| (-921 |#1|) (QUOTE (-146)))) 
+(-361 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-360 GF |extdeg|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-362 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-361 |p| |n|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-363 |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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| (-919 |#1|) (QUOTE (-146))) (|HasCategory| (-919 |#1|) (QUOTE (-375)))) (|HasCategory| (-919 |#1|) (QUOTE (-148))) (|HasCategory| (-919 |#1|) (QUOTE (-375))) (|HasCategory| (-919 |#1|) (QUOTE (-146)))) 
-(-362 GF |defpol|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| (-921 |#1|) (QUOTE (-146))) (|HasCategory| (-921 |#1|) (QUOTE (-377)))) (|HasCategory| (-921 |#1|) (QUOTE (-148))) (|HasCategory| (-921 |#1|) (QUOTE (-377))) (|HasCategory| (-921 |#1|) (QUOTE (-146)))) 
+(-364 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-363 -1384 GF) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-365 -1386 GF) 
 ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{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 
-(-364 GF) 
+(-366 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(\\spad{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(\\spad{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(\\spad{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(\\spad{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(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{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 
-(-365 -1384 FP FPP) 
+(-367 -1386 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}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-366 GF |n|) 
+(-368 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-367 R |ls|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-369 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{\\spad{ls}}."))) 
 NIL 
 NIL 
-(-368 S) 
+(-370 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-369 S) 
+(-371 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
 NIL 
 NIL 
-(-370) 
+(-372) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-371 |Name| S) 
+(-373 |Name| S) 
 ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) 
 NIL 
 NIL 
-(-372 S) 
+(-374 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
 NIL 
 NIL 
-(-373 S R) 
+(-375 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\\spad{'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\\spad{'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\\spad{'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(\\spad{\"*\"})} 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\\spad{'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\\spad{'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\\spad{'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\\spad{'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 (-564)))) 
-(-374 R) 
+((|HasCategory| |#2| (QUOTE (-566)))) 
+(-376 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\\spad{'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\\spad{'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\\spad{'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(\\spad{\"*\"})} 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\\spad{'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\\spad{'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\\spad{'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\\spad{'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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4451 |has| |#1| (-564)) (-4449 . T) (-4448 . T)) 
+((-4453 |has| |#1| (-566)) (-4451 . T) (-4450 . T)) 
 NIL 
-(-375) 
+(-377) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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 
-(-376 S R UP) 
+(-378 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 ( \\spad{Tr}(\\spad{vi} * \\spad{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}\\spad{'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 (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-370)))) 
-(-377 R UP) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-372)))) 
+(-379 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 ( \\spad{Tr}(\\spad{vi} * \\spad{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}\\spad{'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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-378 S A R B) 
+(-380 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-379 A S) 
+(-381 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{>=} \\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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4455)) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111)))) 
-(-380 S) 
+((|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113)))) 
+(-382 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{>=} \\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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4454 . T)) 
+((-4456 . T)) 
 NIL 
-(-381 |VarSet| R) 
+(-383 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#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) (-4449 . T) (-4448 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4451 . T) (-4450 . T)) 
 NIL 
-(-382 S V) 
+(-384 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 
-(-383 S R) 
+(-385 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| (LIST (QUOTE -647) (QUOTE (-572))))) 
-(-384 R) 
+((|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) 
+(-386 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 
-(-385 |Par|) 
+(-387 |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 \\spad{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 
-(-386) 
+(-388) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4437 . T) (-4445 . T) (-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4439 . T) (-4447 . T) (-3551 . T) (-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-387 |Par|) 
+(-389 |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 \\spad{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 
-(-388 R S) 
+(-390 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.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174)))) 
-(-389 R |Basis|) 
+(-391 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.\\spad{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}."))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-390) 
+(-392) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
 NIL 
 NIL 
-(-391) 
+(-393) 
 ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-392 R S) 
+(-394 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."))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174)))) 
-(-393 S) 
+(-395 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
 NIL 
-(-394 S) 
+(-396 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-858)))) 
-(-395) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-397) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-396) 
+(-398) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
 NIL 
-(-397) 
+(-399) 
 ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|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 
-(-398 |n| |class| R) 
+(-400 |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"))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-399) 
+(-401) 
 ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) 
 NIL 
 NIL 
-(-400 -1384 UP UPUP R) 
+(-402 -1386 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 
-(-401 S) 
+(-403 S) 
 ((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format."))) 
 NIL 
 NIL 
-(-402) 
+(-404) 
 ((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula 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 \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the 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 formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to SCRIPT formula 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 
-(-403) 
+(-405) 
 ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) 
 NIL 
 NIL 
-(-404) 
+(-406) 
 ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-405) 
+(-407) 
 ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-406 -2030 |returnType| -1563 |symbols|) 
+(-408 -2032 |returnType| -1565 |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-407 -1384 UP) 
+(-409 -1386 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
-(-408 R) 
+(-410 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
 NIL 
 NIL 
-(-409 S) 
+(-411 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
 NIL 
 NIL 
-(-410) 
+(-412) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-411 S) 
+(-413 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\\spad{'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\\spad{'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 -4437)) (|HasAttribute| |#1| (QUOTE -4445))) 
-(-412) 
+((|HasAttribute| |#1| (QUOTE -4439)) (|HasAttribute| |#1| (QUOTE -4447))) 
+(-414) 
 ((|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(\\spad{\"+\"}) 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\\spad{'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\\spad{'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\"."))) 
-((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-3551 . T) (-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-413 R S) 
+(-415 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 
-(-414 A B) 
+(-416 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 
-(-415 S) 
+(-417 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 \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-4441 -12 (|has| |#1| (-6 -4452)) (|has| |#1| (-460)) (|has| |#1| (-6 -4441))) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
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-(-416 S R UP) 
+((-4443 -12 (|has| |#1| (-6 -4454)) (|has| |#1| (-462)) (|has| |#1| (-6 -4443))) (-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
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+(-418 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{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},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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 
-(-417 R UP) 
+(-419 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{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},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'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."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-418 A S) 
+(-420 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\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-419 S) 
+((|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-421 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\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-420 R1 F1 U1 A1 R2 F2 U2 A2) 
+(-422 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 
-(-421 R -1384 UP A) 
+(-423 R -1386 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)}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-422 R -1384 UP A |ibasis|) 
+(-424 R -1386 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (LIST (QUOTE -1049) (|devaluate| |#2|)))) 
-(-423 AR R AS S) 
+((|HasCategory| |#4| (LIST (QUOTE -1051) (|devaluate| |#2|)))) 
+(-425 AR R AS S) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
 NIL 
-(-424 S R) 
+(-426 S R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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\\spad{'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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-370)))) 
-(-425 R) 
+((|HasCategory| |#2| (QUOTE (-372)))) 
+(-427 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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\\spad{'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."))) 
-((-4451 |has| |#1| (-564)) (-4449 . T) (-4448 . T)) 
+((-4453 |has| |#1| (-566)) (-4451 . T) (-4450 . T)) 
 NIL 
-(-426 R) 
+(-428 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 \\spad{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| "nil" "sqfr" "irred" "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| "nil" "sqfr" "irred" "prime") $ (|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| "nil" "sqfr" "irred" "prime")) (|:| |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| "nil" "sqfr" "irred" "prime")) (|:| |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."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -315) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1233))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -292) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-460)))) 
-(-427 R) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -317) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1235))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-1235)))) (|HasCategory| |#1| (QUOTE (-1035))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-462)))) 
+(-429 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 
-(-428 R FE |x| |cen|) 
+(-430 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\\spad{'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\\spad{'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 
-(-429 R A S B) 
+(-431 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\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 
-(-430 R FE |Expon| UPS TRAN |x|) 
+(-432 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\\spad{'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\\spad{'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\\spad{'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| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) 
 NIL 
 NIL 
-(-431 S A R B) 
+(-433 S A R B) 
 ((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-432 A S) 
+(-434 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 (-858))) (|HasCategory| |#2| (QUOTE (-375)))) 
-(-433 S) 
+((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-377)))) 
+(-435 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4454 . T) (-4444 . T) (-4455 . T)) 
+((-4456 . T) (-4446 . T) (-4457 . T)) 
 NIL 
-(-434 R -1384) 
+(-436 R -1386) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
-(-435 R E) 
+(-437 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) 
-((-4441 -12 (|has| |#1| (-6 -4441)) (|has| |#2| (-6 -4441))) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#2| (QUOTE -4441)))) 
-(-436 R -1384) 
+((-4443 -12 (|has| |#1| (-6 -4443)) (|has| |#2| (-6 -4443))) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4443)) (|HasAttribute| |#2| (QUOTE -4443)))) 
+(-438 R -1386) 
 ((|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 
-(-437 S R) 
+(-439 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|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}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'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| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-481))) (|HasCategory| |#2| (QUOTE (-1123))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) 
-(-438 R) 
+((|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) 
+(-440 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|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}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'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}."))) 
-((-4451 -2813 (|has| |#1| (-1060)) (|has| |#1| (-481))) (-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) ((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-564)) (-4446 |has| |#1| (-564))) 
+((-4453 -2818 (|has| |#1| (-1062)) (|has| |#1| (-483))) (-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) ((-4458 "*") |has| |#1| (-566)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-566)) (-4448 |has| |#1| (-566))) 
 NIL 
-(-439 R -1384) 
+(-441 R -1386) 
 ((|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 
-(-440 R -1384) 
+(-442 R -1386) 
 ((|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 a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve 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)))) 
-(-441 R -1384) 
+(-443 R -1386) 
 ((|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 
-(-442) 
+(-444) 
 ((|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 
-(-443 R -1384 UP) 
+(-445 R -1386 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| (LIST (QUOTE -1049) (QUOTE (-48))))) 
-(-444) 
+((|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-48))))) 
+(-446) 
 ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) 
 NIL 
 NIL 
-(-445) 
+(-447) 
 ((|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| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|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| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
 NIL 
-(-446 |f|) 
+(-448 |f|) 
 ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-447) 
+(-449) 
 ((|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|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) 
 NIL 
 NIL 
-(-448) 
+(-450) 
 ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) 
 NIL 
 NIL 
-(-449) 
+(-451) 
 ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) 
 NIL 
 NIL 
-(-450 UP) 
+(-452 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\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'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\\spad{'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 
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-(-451 R UP -1384) 
+(-453 R UP -1386) 
 ((|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 \\spad{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\\spad{'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\\spad{'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\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'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 
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-(-452 R UP) 
+(-454 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)."))) 
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-(-453 R) 
+(-455 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 (-412)))) 
-(-454) 
+((|HasCategory| |#1| (QUOTE (-414)))) 
+(-456) 
 ((|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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-(-455 |Dom| |Expon| |VarSet| |Dpol|) 
+(-457 |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 
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-(-456 |Dom| |Expon| |VarSet| |Dpol|) 
+(-458 |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\\spad{'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\\spad{'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 
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-(-457 |Dom| |Expon| |VarSet| |Dpol|) 
+(-459 |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 
-(-458 |Dom| |Expon| |VarSet| |Dpol|) 
+(-460 |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 (-370)))) 
-(-459 S) 
+((|HasCategory| |#1| (QUOTE (-372)))) 
+(-461 S) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-460) 
+(-462) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-461 R |n| |ls| |gamma|) 
+(-463 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"))) 
-((-4451 |has| (-415 (-961 |#1|)) (-564)) (-4449 . T) (-4448 . T)) 
-((|HasCategory| (-415 (-961 |#1|)) (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| (-415 (-961 |#1|)) (QUOTE (-564)))) 
-(-462 |vl| R E) 
+((-4453 |has| (-417 (-963 |#1|)) (-566)) (-4451 . T) (-4450 . T)) 
+((|HasCategory| (-417 (-963 |#1|)) (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-417 (-963 |#1|)) (QUOTE (-566)))) 
+(-464 |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"))) 
-(((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
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-(-463 R BP) 
+(((-4458 "*") |has| |#2| (-174)) (-4449 |has| |#2| (-566)) (-4454 |has| |#2| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
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+(-465 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\\spad{'s} conditional."))) 
 NIL 
 NIL 
-(-464 OV E S R P) 
+(-466 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 
-(-465 E OV R P) 
+(-467 E OV R P) 
 ((|constructor| (NIL "This package provides operations for \\spad{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 \\spad{GCD} of \\spad{p} and \\spad{q}"))) 
 NIL 
 NIL 
-(-466 R) 
+(-468 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 
-(-467 R FE) 
+(-469 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 
-(-468 RP TP) 
+(-470 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 
-(-469 |vl| R IS E |ff| P) 
+(-471 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-470 E V R P Q) 
+(-472 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
 NIL 
 NIL 
-(-471 R E |VarSet| P) 
+(-473 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#4| (LIST (QUOTE -315) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#4| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-472 S R E) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-474 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} 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 
-(-473 R E) 
+(-475 R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} 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 
-(-474) 
+(-476) 
 ((|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(\\spad{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 
-(-475) 
+(-477) 
 ((|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 
-(-476) 
+(-478) 
 ((|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},{}\\spad{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.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\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 
-(-477 S R E) 
+(-479 S R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-478 R E) 
+(-480 R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-479 |lv| -1384 R) 
+(-481 |lv| -1386 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
-(-480 S) 
+(-482 S) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
 NIL 
 NIL 
-(-481) 
+(-483) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-482 |Coef| |var| |cen|) 
+(-484 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) 
-(-483 |Key| |Entry| |Tbl| |dent|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+(-485 |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."))) 
-((-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111)))) 
-(-484 R E V P) 
+((-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113)))) 
+(-486 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)}"))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#4| (LIST (QUOTE -315) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#4| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-485) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-487) 
 ((|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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-486) 
+(-488) 
 ((|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 
-(-487 |Key| |Entry| |hashfn|) 
+(-489 |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."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-488) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-490) 
 ((|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\\spad{'s} book Lie Groups \\spad{--} 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{<=} \\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 
-(-489 |vl| R) 
+(-491 |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"))) 
-(((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
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-(-490 -4127 S) 
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+(-492 -4129 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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-(-491) 
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(|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1062)))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190))))) (-2818 (|HasCategory| |#2| (QUOTE (-1062))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1113)))) (|HasAttribute| |#2| (QUOTE -4453)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) 
+(-493) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`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 
-(-492 S) 
+(-494 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}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-493 -1384 UP UPUP R) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-495 -1386 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}\\spad{'s} are integers and the \\spad{P}\\spad{'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 
-(-494 BP) 
+(-496 BP) 
 ((|constructor| (NIL "This package provides the functions for the heuristic integer \\spad{gcd}. Geddes\\spad{'s} algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,..,ak])} = \\spad{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])} = \\spad{gcd} and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,..fk])} = \\spad{gcd} and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,..,fk])} = \\spad{gcd} of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,..,fk])} = \\spad{gcd} of the polynomials \\spad{fi}."))) 
 NIL 
 NIL 
-(-495) 
+(-497) 
 ((|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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) 
-(-496 A S) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-574) (QUOTE (-920))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1035))) (|HasCategory| (-574) (QUOTE (-830))) (-2818 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1165))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (|HasCategory| (-574) (QUOTE (-146))))) 
+(-498 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 -4454)) (|HasAttribute| |#1| (QUOTE -4455)) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-497 S) 
+((|HasAttribute| |#1| (QUOTE -4456)) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-499 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
 NIL 
-(-498 S) 
+(-500 S) 
 ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) 
 NIL 
 NIL 
-(-499) 
+(-501) 
 ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) 
 NIL 
 NIL 
-(-500 S) 
+(-502 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-501) 
+(-503) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-502 -1384 UP |AlExt| |AlPol|) 
+(-504 -1386 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
-(-503) 
+(-505) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| $ (QUOTE (-1060))) (|HasCategory| $ (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-504 S |mn|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| $ (QUOTE (-1062))) (|HasCategory| $ (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-506 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-505 R |mnRow| |mnCol|) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-507 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-506 K R UP) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-508 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 
-(-507 R UP -1384) 
+(-509 R UP -1386) 
 ((|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 \\spad{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-508 |mn|) 
+(-510 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| (-112) (QUOTE (-1111))) (|HasCategory| (-112) (LIST (QUOTE -315) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-112) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-112) (QUOTE (-1111))) (|HasCategory| (-112) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-509 K R UP L) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| (-112) (QUOTE (-1113))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1113))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-511 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 
-(-510) 
+(-512) 
 ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{\\spad{s}} into an \\axiom{IndexCard}. Warning: if \\axiom{\\spad{s}} is not of the right format then an error will occur when using it.")) (|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 
-(-511 R Q A B) 
+(-513 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}\\spad{'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}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
 NIL 
-(-512 -1384 |Expon| |VarSet| |DPoly|) 
+(-514 -1386 |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| (LIST (QUOTE -622) (QUOTE (-1188))))) 
-(-513 |vl| |nv|) 
+((|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-1190))))) 
+(-515 |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 
-(-514) 
+(-516) 
 ((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-515 A S) 
+(-517 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 
 NIL 
-(-516 A S) 
+(-518 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 
 NIL 
-(-517 A S) 
+(-519 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-518 A S) 
+(-520 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-519 A S) 
+(-521 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
 NIL 
-(-520 A S) 
+(-522 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) 
 NIL 
 NIL 
-(-521 S A B) 
+(-523 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|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 
-(-522 A B) 
+(-524 A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} 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 
-(-523 S E |un|) 
+(-525 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-800)))) 
-(-524 S |mn|) 
+((|HasCategory| |#2| (QUOTE (-802)))) 
+(-526 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} 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}"))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-525) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-527) 
 ((|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 
-(-526 |p| |n|) 
+(-528 |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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| (-589 |#1|) (QUOTE (-146))) (|HasCategory| (-589 |#1|) (QUOTE (-375)))) (|HasCategory| (-589 |#1|) (QUOTE (-148))) (|HasCategory| (-589 |#1|) (QUOTE (-375))) (|HasCategory| (-589 |#1|) (QUOTE (-146)))) 
-(-527 R |mnRow| |mnCol| |Row| |Col|) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((-2818 (|HasCategory| (-591 |#1|) (QUOTE (-146))) (|HasCategory| (-591 |#1|) (QUOTE (-377)))) (|HasCategory| (-591 |#1|) (QUOTE (-148))) (|HasCategory| (-591 |#1|) (QUOTE (-377))) (|HasCategory| (-591 |#1|) (QUOTE (-146)))) 
+(-529 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-528 S |mn|) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-530 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-529 R |Row| |Col| M) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-531 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,{} \\spad{m*h} and \\spad{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 -4455))) 
-(-530 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasAttribute| |#3| (QUOTE -4457))) 
+(-532 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 -4455))) 
-(-531 R |mnRow| |mnCol|) 
+((|HasAttribute| |#7| (QUOTE -4457))) 
+(-533 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-532) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4458 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-534) 
 ((|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 
-(-533) 
+(-535) 
 ((|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 
-(-534 S) 
+(-536 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a 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 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 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 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 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 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 
-(-535) 
+(-537) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a 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 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 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 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 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 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 
-(-536 GF) 
+(-538 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{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{\\spad{**}}{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 \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{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 \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{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 \\spad{GF}."))) 
 NIL 
 NIL 
-(-537) 
+(-539) 
 ((|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 \\spad{`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 \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) 
 NIL 
 NIL 
-(-538 R) 
+(-540 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} \\spad{:=} 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} \\spad{:=} increment()} then \\spad{f x} is \\spad{x+1}."))) 
 NIL 
 NIL 
-(-539 |Varset|) 
+(-541 |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 
 NIL 
-(-540 K -1384 |Par|) 
+(-542 K -1386 |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 \\spad{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 
-(-541) 
+(-543) 
 NIL 
 NIL 
 NIL 
-(-542) 
+(-544) 
 ((|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 
-(-543 R) 
+(-545 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 
-(-544) 
+(-546) 
 ((|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}\\spad{'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 
-(-545 |Coef| UTS) 
+(-547 |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 
-(-546 K -1384 |Par|) 
+(-548 K -1386 |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 
-(-547 R BP |pMod| |nextMod|) 
+(-549 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 \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) 
 NIL 
 NIL 
-(-548 OV E R P) 
+(-550 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 
-(-549 K UP |Coef| UTS) 
+(-551 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 
-(-550 |Coef| UTS) 
+(-552 |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 
-(-551 R UP) 
+(-553 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-552 S) 
+(-554 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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-553) 
+(-555) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-4452 . T) (-4453 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4454 . T) (-4455 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-554) 
+(-556) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-555) 
+(-557) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-556) 
+(-558) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-557) 
+(-559) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-558 |Key| |Entry| |addDom|) 
+(-560 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-559 R -1384) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-561 R -1386) 
 ((|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 
-(-560 R0 -1384 UP UPUP R) 
+(-562 R0 -1386 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 
-(-561) 
+(-563) 
 ((|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 
-(-562 R) 
+(-564 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{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-3548 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-3551 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-563 S) 
+(-565 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 
-(-564) 
+(-566) 
 ((|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."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-565 R -1384) 
+(-567 R -1386) 
 ((|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|)) "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},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'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}\\spad{'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|)) "failed") |#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 
-(-566 I) 
+(-568 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\\spad{'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 
-(-567) 
+(-569) 
 ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) 
 NIL 
 NIL 
-(-568 R -1384 L) 
+(-570 R -1386 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| "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| "failed")) (|:| |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| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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|))))) "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}\\spad{'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|))))) "failed") |#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}\\spad{'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|)) "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|)) "failed") |#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 -664) (|devaluate| |#2|)))) 
-(-569) 
+((|HasCategory| |#3| (LIST (QUOTE -666) (|devaluate| |#2|)))) 
+(-571) 
 ((|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 
-(-570 -1384 UP UPUP R) 
+(-572 -1386 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 
-(-571 -1384 UP) 
+(-573 -1386 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 
-(-572) 
+(-574) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-4436 . T) (-4442 . T) (-4446 . T) (-4441 . T) (-4452 . T) (-4453 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4438 . T) (-4444 . T) (-4448 . T) (-4443 . T) (-4454 . T) (-4455 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-573) 
+(-575) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) 
 NIL 
 NIL 
-(-574 R -1384 L) 
+(-576 R -1386 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| "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| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#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}\\spad{'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 -664) (|devaluate| |#2|)))) 
-(-575 R -1384) 
+((|HasCategory| |#3| (LIST (QUOTE -666) (|devaluate| |#2|)))) 
+(-577 R -1386) 
 ((|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| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1150)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-637))))) 
-(-576 -1384 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1152)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-639))))) 
+(-578 -1386 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}\\spad{'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 
-(-577 S) 
+(-579 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 
-(-578 -1384) 
+(-580 -1386) 
 ((|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}\\spad{'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 
-(-579 R) 
+(-581 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."))) 
-((-3548 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-3551 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-580) 
+(-582) 
 ((|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}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-581 R -1384) 
+(-583 R -1386) 
 ((|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| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-290))) (|HasCategory| |#2| (QUOTE (-637))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-290)))) (|HasCategory| |#1| (QUOTE (-564)))) 
-(-582 -1384 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-292))) (|HasCategory| |#2| (QUOTE (-639))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190))))) (-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-292)))) (|HasCategory| |#1| (QUOTE (-566)))) 
+(-584 -1386 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|)) "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|)) "failed") |#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|)) "failed") |#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|)) "failed") |#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 
-(-583 R -1384) 
+(-585 R -1386) 
 ((|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 
-(-584) 
+(-586) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-585) 
+(-587) 
 ((|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|) $) "\\spad{isOpen?(f)} holds if \\spad{`f'} is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by \\spad{`f'} as a binary file."))) 
 NIL 
 NIL 
-(-586) 
+(-588) 
 ((|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 
-(-587) 
+(-589) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet IP4 addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the IP4 address of host \\spad{`h'}.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address \\spad{`x'}.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-588 |p| |unBalanced?|) 
+(-590 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-589 |p|) 
+(-591 |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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-375)))) 
-(-590) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-377)))) 
+(-592) 
 ((|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 
-(-591 R -1384) 
+(-593 R -1386) 
 ((|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},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-592 E -1384) 
+(-594 E -1386) 
 ((|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 
-(-593) 
+(-595) 
 ((|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 
-(-594 -1384) 
+(-596 -1386) 
 ((|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 \\spad{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}."))) 
-((-4449 . T) (-4448 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-1188))))) 
-(-595 I) 
+((-4451 . T) (-4450 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-1190))))) 
+(-597 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 
-(-596 GF) 
+(-598 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 
-(-597 R) 
+(-599 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},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-148)))) 
-(-598) 
+(-600) 
 ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young\\spad{'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\\spad{'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\\spad{'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\\spad{'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 
-(-599 R E V P TS) 
+(-601 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 
-(-600) 
+(-602) 
 ((|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 
-(-601 |mn|) 
+(-603 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (-2813 (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) 
-(-602 E V R P) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (-2818 (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1113)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) 
+(-604 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 
-(-603 |Coef|) 
+(-605 |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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-572)) (|devaluate| |#1|)))) (|HasCategory| (-572) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-572)))))) 
-(-604 |Coef|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|)))) (|HasCategory| (-574) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574)))))) 
+(-606 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-4456 "*") |has| |#1| (-564)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-564)))) 
-(-605) 
+(((-4458 "*") |has| |#1| (-566)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-566)))) 
+(-607) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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 
-(-606 A B) 
+(-608 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 
-(-607 A B C) 
+(-609 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 
-(-608 R -1384 FG) 
+(-610 R -1386 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{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 
-(-609 S) 
+(-611 S) 
 ((|constructor| (NIL "\\indented{1}{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 
-(-610 R |mn|) 
+(-612 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-611 S |Index| |Entry|) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1062))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1062)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-613 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 -4455)) (|HasCategory| |#2| (QUOTE (-858))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#3| (QUOTE (-1111)))) 
-(-612 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-860))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#3| (QUOTE (-1113)))) 
+(-614 |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 
-(-613) 
+(-615) 
 ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) 
 NIL 
 NIL 
-(-614) 
+(-616) 
 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join \\spad{`x'}.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
-(-615 R A) 
+(-617 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)."))) 
-((-4451 -2813 (-2085 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) 
-((-2813 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) 
-(-616 |Entry|) 
+((-4453 -2818 (-2088 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
+((-2818 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
+(-618 |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."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-617 S |Key| |Entry|) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-619 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 
-(-618 |Key| |Entry|) 
+(-620 |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}."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
-(-619 R S) 
+(-621 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 
-(-620 S) 
+(-622 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| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) 
-(-621 S) 
+((|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) 
+(-623 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 
-(-622 S) 
+(-624 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-623 -1384 UP) 
+(-625 -1386 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-624 S) 
+(-626 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 \\spad{`s'} into an element of `\\%'."))) 
 NIL 
 NIL 
-(-625) 
+(-627) 
 ((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-626 S) 
+(-628 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) 
 NIL 
 NIL 
-(-627 S R) 
+(-629 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 
-(-628 R) 
+(-630 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."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-629 A R S) 
+(-631 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}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-856)))) 
-(-630 R -1384) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-858)))) 
+(-632 R -1386) 
 ((|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 
-(-631 R UP) 
+(-633 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"))) 
-((-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4447 . T) (-4451 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-632 R E V P TS ST) 
+((-4451 . T) (-4450 . T) ((-4458 "*") . T) (-4449 . T) (-4453 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-634 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(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) 
 NIL 
 NIL 
-(-633 OV E Z P) 
+(-635 OV E Z P) 
 ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"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 
-(-634) 
+(-636) 
 ((|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 
-(-635 |VarSet| R |Order|) 
+(-637 |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.\\spad{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(\\spad{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}}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-636 R |ls|) 
+(-638 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(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{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{\\spad{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(\\spad{lp},{} norm?)} 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{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{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(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) 
 NIL 
 NIL 
-(-637) 
+(-639) 
 ((|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 
-(-638 R -1384) 
+(-640 R -1386) 
 ((|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 
-(-639 |lv| -1384) 
+(-641 |lv| -1386) 
 ((|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 
-(-640) 
+(-642) 
 ((|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."))) 
-((-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-1170) (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 (-52))) (QUOTE (-1111)))) 
-(-641 S R) 
+((-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1172) (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 (-52))) (QUOTE (-1113)))) 
+(-643 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{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-370)))) 
-(-642 R) 
+((|HasCategory| |#2| (QUOTE (-372)))) 
+(-644 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4449 . T) (-4448 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4451 . T) (-4450 . T)) 
 NIL 
-(-643 R A) 
+(-645 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4451 -2813 (-2085 (|has| |#2| (-374 |#1|)) (|has| |#1| (-564))) (-12 (|has| |#2| (-425 |#1|)) (|has| |#1| (-564)))) (-4449 . T) (-4448 . T)) 
-((-2813 (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -425) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -374) (|devaluate| |#1|)))) 
-(-644 R FE) 
+((-4453 -2818 (-2088 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4451 . T) (-4450 . T)) 
+((-2818 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
+(-646 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|) "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|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
 NIL 
 NIL 
-(-645 R) 
+(-647 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|))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "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|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|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 
-(-646 S R) 
+(-648 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}\\spad{'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}\\spad{'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}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-2074 (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-647 R) 
+((-2077 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-649 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}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
-(-648 R) 
+(-650 R) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
-(-649 A B) 
+(-651 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 \\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}. Error: if \\spad{la} and \\spad{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 
-(-650 A B) 
+(-652 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 
-(-651 A B C) 
+(-653 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 
-(-652 S) 
+(-654 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} 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."))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-653 T$) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-655 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-654 R) 
+(-656 R) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{LeftModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
-(-655 S) 
+(-657 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-656 R) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-658 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-657 S E |un|) 
+(-659 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 
-(-658 A S) 
+(-660 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{:=} \\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{:=} \\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}) \\spad{==} 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| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4455))) 
-(-659 S) 
+((|HasAttribute| |#1| (QUOTE -4457))) 
+(-661 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{:=} \\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{:=} \\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}) \\spad{==} 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| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-660 R -1384 L) 
+(-662 R -1386 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 
-(-661 A) 
+(-663 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}}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-662 A M) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-664 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-663 S A) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-665 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-370)))) 
-(-664 A) 
+((|HasCategory| |#2| (QUOTE (-372)))) 
+(-666 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}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-665 -1384 UP) 
+(-667 -1386 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)))) 
-(-666 A -3027) 
+(-668 A -3000) 
 ((|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}}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-667 A L) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-669 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 
-(-668 S) 
+(-670 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-669) 
+(-671) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-670 M R S) 
+(-672 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}."))) 
-((-4449 . T) (-4448 . T)) 
-((|HasCategory| |#1| (QUOTE (-799)))) 
-(-671 R) 
+((-4451 . T) (-4450 . T)) 
+((|HasCategory| |#1| (QUOTE (-801)))) 
+(-673 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 
-(-672 |VarSet| R) 
+(-674 |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.\\spad{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) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-673 A S) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-675 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 
-(-674 S) 
+(-676 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}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-675 -1384) 
+(-677 -1386) 
 ((|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\\spad{'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|) "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|) "failed")) (|:| |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|) "failed")) (|:| |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|) "failed")) (|:| |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|) "failed")) (|:| |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 
-(-676 -1384 |Row| |Col| M) 
+(-678 -1386 |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| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |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| "failed")) (|:| |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 
-(-677 R E OV P) 
+(-679 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 
-(-678 |n| R) 
+(-680 |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."))) 
-((-4451 . T) (-4454 . T) (-4448 . T) (-4449 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564))) (-2813 (|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-679) 
+((-4453 . T) (-4456 . T) (-4450 . T) (-4451 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4458 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566))) (-2818 (|HasAttribute| |#2| (QUOTE (-4458 "*"))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-681) 
 ((|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 
-(-680 |VarSet|) 
+(-682 |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{<=} \\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.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-681 A S) 
+(-683 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-682 S) 
+(-684 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\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 
-(-683 R) 
+(-685 R) 
 ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) 
 NIL 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-684) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-686) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`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 
-(-685 |VarSet|) 
+(-687 |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.\\spad{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{\\spad{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 
-(-686 A) 
+(-688 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 
-(-687 A C) 
+(-689 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 
-(-688 A B C) 
+(-690 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 
-(-689) 
+(-691) 
 ((|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 \\spad{`s'}.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of \\spad{`s'}.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} \\spad{->} \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-690 A) 
+(-692 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 
-(-691 A C) 
+(-693 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 
-(-692 A B C) 
+(-694 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 
-(-693 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-695 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 
-(-694 S R |Row| |Col|) 
+(-696 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4456 "*"))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-564)))) 
-(-695 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-4458 "*"))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566)))) 
+(-697 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
-(-696 R |Row| |Col| M) 
+(-698 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 \\spad{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} \\spad{~=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} \\spad{~=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 (-370))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564)))) 
-(-697 R) 
+((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566)))) 
+(-699 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."))) 
-((-4454 . T) (-4455 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-313))) (|HasCategory| |#1| (QUOTE (-564))) (|HasAttribute| |#1| (QUOTE (-4456 "*"))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-698 R) 
+((-4456 . T) (-4457 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4458 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-700 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{**} \\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 
-(-699 T$) 
+(-701 T$) 
 ((|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 \\spad{`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 \\spad{`x'} into \\%."))) 
 NIL 
 NIL 
-(-700 S -1384 FLAF FLAS) 
+(-702 S -1386 FLAF FLAS) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) 
 NIL 
 NIL 
-(-701 R Q) 
+(-703 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 
-(-702) 
+(-704) 
 ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) 
-((-4447 . T) (-4452 |has| (-707) (-370)) (-4446 |has| (-707) (-370)) (-3559 . T) (-4453 |has| (-707) (-6 -4453)) (-4450 |has| (-707) (-6 -4450)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
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-(-703 S) 
+((-4449 . T) (-4454 |has| (-709) (-372)) (-4448 |has| (-709) (-372)) (-3562 . T) (-4455 |has| (-709) (-6 -4455)) (-4452 |has| (-709) (-6 -4452)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-709) (QUOTE (-148))) (|HasCategory| (-709) (QUOTE (-146))) (|HasCategory| (-709) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-377))) (|HasCategory| (-709) (QUOTE (-372))) (-2818 (|HasCategory| (-709) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-709) (QUOTE (-239))) (-2818 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (LIST (QUOTE -294) (QUOTE (-709)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -317) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (-2818 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-709) (QUOTE (-1035))) (|HasCategory| (-709) (QUOTE (-1216))) (-12 (|HasCategory| (-709) (QUOTE (-1015))) (|HasCategory| (-709) (QUOTE (-1216)))) (-2818 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (|HasCategory| (-709) (QUOTE (-372))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-920))))) (-2818 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (-12 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-920)))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-920))))) (|HasCategory| (-709) (QUOTE (-555))) (-12 (|HasCategory| (-709) (QUOTE (-1073))) (|HasCategory| (-709) (QUOTE (-1216)))) (|HasCategory| (-709) (QUOTE (-1073))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920))) (-2818 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (|HasCategory| (-709) (QUOTE (-372)))) (-2818 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (|HasCategory| (-709) (QUOTE (-566)))) (-12 (|HasCategory| (-709) (QUOTE (-239))) (|HasCategory| (-709) (QUOTE (-372)))) (-12 (|HasCategory| (-709) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-566))) (|HasAttribute| (-709) (QUOTE -4455)) (|HasAttribute| (-709) (QUOTE -4452)) (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (|HasCategory| (-709) (QUOTE (-146)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-920)))) (|HasCategory| (-709) (QUOTE (-358))))) 
+(-705 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}."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
-(-704 U) 
+(-706 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 \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
 NIL 
 NIL 
-(-705) 
+(-707) 
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} 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|)) "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|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-706 OV E -1384 PG) 
+(-708 OV E -1386 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 
-(-707) 
+(-709) 
 ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) 
-((-3548 . T) (-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-3551 . T) (-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-708 R) 
+(-710 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 
-(-709) 
+(-711) 
 ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) 
-((-4453 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4455 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-710 S D1 D2 I) 
+(-712 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 
-(-711 S) 
+(-713 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 
-(-712 S) 
+(-714 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 
-(-713 S T$) 
+(-715 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 part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-714 S -3608 I) 
+(-716 S -3611 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 
-(-715 E OV R P) 
+(-717 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 
-(-716 R) 
+(-718 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)}.}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-717 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-719 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 
-(-718) 
+(-720) 
 ((|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 
-(-719 R |Mod| -3104 -1767 |exactQuo|) 
+(-721 R |Mod| -2348 -2130 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-720 R |Rep|) 
+(-722 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4450 |has| |#1| (-370)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1163))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-237))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-721 IS E |ff|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4452 |has| |#1| (-372)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1165))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-723 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-722 R M) 
+(-724 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) 
+((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-723 R |Mod| -3104 -1767 |exactQuo|) 
+(-725 R |Mod| -2348 -2130 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-724 S R) 
+(-726 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-725 R) 
+(-727 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-726 -1384) 
+(-728 -1386) 
 ((|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]]}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-727 S) 
+(-729 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-728) 
+(-730) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 
-(-729 S) 
+(-731 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(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'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\\spad{'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\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|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 
-(-730) 
+(-732) 
 ((|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(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'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\\spad{'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\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|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 
-(-731 S R UP) 
+(-733 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 (-356))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-375)))) 
-(-732 R UP) 
+((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-377)))) 
+(-734 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."))) 
-((-4447 |has| |#1| (-370)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 |has| |#1| (-372)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-733 S) 
+(-735 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 
-(-734) 
+(-736) 
 ((|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 
-(-735 -1384 UP) 
+(-737 -1386 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 
-(-736 |VarSet| E1 E2 R S PR PS) 
+(-738 |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 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-737 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-739 |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 
-(-738 E OV R PPR) 
+(-740 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 
-(-739 |vl| R) 
+(-741 |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."))) 
-(((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-918))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-872 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-740 E OV R PRF) 
+(((-4458 "*") |has| |#2| (-174)) (-4449 |has| |#2| (-566)) (-4454 |has| |#2| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-920))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4454)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-742 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 
-(-741 E OV R P) 
+(-743 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 
-(-742 R S M) 
+(-744 R S M) 
 ((|constructor| (NIL "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 
-(-743 R M) 
+(-745 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}."))) 
-((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-858)))) 
-(-744 S) 
+((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-860)))) 
+(-746 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4444 . T) (-4455 . T)) 
+((-4446 . T) (-4457 . T)) 
 NIL 
-(-745 S) 
+(-747 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}."))) 
-((-4454 . T) (-4444 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-746) 
+((-4456 . T) (-4446 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-748) 
 ((|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 
-(-747 S) 
+(-749 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 
-(-748 |Coef| |Var|) 
+(-750 |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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-749 OV E R P) 
+(-751 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 
-(-750 E OV R P) 
+(-752 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 
-(-751 S R) 
+(-753 S R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{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 
-(-752 R) 
+(-754 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{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}."))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-753) 
+(-755) 
 ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) 
 NIL 
 NIL 
-(-754) 
+(-756) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{manpageXXc05}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,ldfjac,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,lwa,x,xtol,ifail,fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,b,eps,eta,ifail,f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}."))) 
 NIL 
 NIL 
-(-755) 
+(-757) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{manpageXXc06}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,n,x,ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,n,x,ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,y,ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,x,ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,n,init,x,y,trigm,trign,ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,n,init,x,y,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,n,init,x,trig,ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,n,x,y,ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,x,y,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,x,ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,x,ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}."))) 
 NIL 
 NIL 
-(-756) 
+(-758) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{manpageXXd01}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,a,b,maxcls,eps,lenwrk,mincls,wrkstr,ifail,functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,y,n,ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,a,b,maxpts,eps,lenwrk,minpts,ifail,functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,b,itype,n,gtype,ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,omega,key,epsabs,limlst,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,b,c,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,b,alfa,beta,key,epsabs,epsrel,lw,liw,ifail,g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,b,omega,key,epsabs,epsrel,lw,liw,ifail,g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,inf,epsabs,epsrel,lw,liw,ifail,f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,b,npts,points,epsabs,epsrel,lw,liw,ifail,f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,b,epsabs,epsrel,lw,liw,ifail,f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}."))) 
 NIL 
 NIL 
-(-757) 
+(-759) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{manpageXXd02}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,mnp,numbeg,nummix,tol,init,iy,ijac,lwork,liwork,np,x,y,deleps,ifail,fcn,g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,m,k,tol,maxfun,match,elam,delam,hmax,maxit,ifail,coeffn,bdyval,monit,report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,m,k,tol,maxfun,match,elam,delam,hmax,maxit,ifail,coeffn,bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains Asp12 and Asp33 are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,b,n,tol,mnp,lw,liw,c,d,gam,x,np,ifail,fcnf,fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,v,n,a,b,tol,mnp,lw,liw,x,np,ifail,fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,m,n,relabs,iw,x,y,tol,ifail,g,fcn,pederv,output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,m,n,tol,relabs,x,y,ifail,g,fcn,output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,n,irelab,hmax,x,y,tol,ifail,g,fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,m,n,irelab,x,y,tol,ifail,fcn,output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}."))) 
 NIL 
 NIL 
-(-758) 
+(-760) 
 ((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{manpageXXd03}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,xf,l,lbdcnd,bdxs,bdxf,ys,yf,m,mbdcnd,bdys,bdyf,zs,zf,n,nbdcnd,bdzs,bdzf,lambda,ldimf,mdimf,lwrk,f,ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,xmax,ymin,ymax,ngx,ngy,lda,scheme,ifail,pdef,bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,ngy,lda,maxit,acc,iout,a,rhs,ub,ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}."))) 
 NIL 
 NIL 
-(-759) 
+(-761) 
 ((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{manpageXXe01}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,x,y,f,rnw,fnodes,px,py,ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,x,y,f,nw,nq,rnw,rnq,ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,x,y,f,triang,grads,px,py,ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,x,y,f,ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,my,x,y,f,ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,x,f,d,a,b,ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,x,f,d,m,px,ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,x,f,ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,x,y,lck,lwrk,ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}."))) 
 NIL 
 NIL 
-(-760) 
+(-762) 
 ((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{manpageXXe02}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,py,lamda,mu,m,x,y,npoint,nadres,ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,la,nplus2,toler,a,b,ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,my,px,py,x,y,lamda,mu,c,lwrk,liwrk,ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,px,py,x,y,lamda,mu,c,ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,m,x,y,f,w,s,nxest,nyest,lwrk,liwrk,nx,lamda,ny,mu,wrk,ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,mx,x,my,y,f,s,nxest,nyest,lwrk,liwrk,nx,lamda,ny,mu,wrk,iwrk,ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,px,py,x,y,f,w,mu,point,npoint,nc,nws,eps,lamda,ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,m,x,y,w,s,nest,lwrk,n,lamda,ifail,wrk,iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,lamda,c,ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,lamda,c,x,left,ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,lamda,c,x,ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,ncap7,x,y,w,lamda,ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,xmin,xmax,a,ia1,la,x,ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,xmin,xmax,a,ia1,la,qatm1,iaint1,laint,ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,xmin,xmax,a,ia1,la,iadif1,ladif,ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,kplus1,nrows,xmin,xmax,x,y,w,mf,xf,yf,lyf,ip,lwrk,liwrk,ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,a,xcap,ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,kplus1,nrows,x,y,w,ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}."))) 
 NIL 
 NIL 
-(-761) 
+(-763) 
 ((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{manpageXXe04}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,m,n,fsumsq,s,lv,v,ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,nclin,ncnln,nrowa,nrowj,nrowr,a,bl,bu,liwork,lwork,sta,cra,der,fea,fun,hes,infb,infs,linf,lint,list,maji,majp,mini,minp,mon,nonf,opt,ste,stao,stac,stoo,stoc,ve,istate,cjac,clamda,r,x,ifail,confun,objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,msglvl,n,nclin,nctotl,nrowa,nrowh,ncolh,bigbnd,a,bl,bu,cvec,featol,hess,cold,lpp,orthog,liwork,lwork,x,istate,ifail,qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,msglvl,n,nclin,nctotl,nrowa,a,bl,bu,cvec,linobj,liwork,lwork,x,ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,ibound,liw,lw,bl,bu,x,ifail,funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,n,liw,lw,x,ifail,lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,n,liw,lw,x,ifail,lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,es,fu,it,lin,list,ma,op,pr,sta,sto,ve,x,ifail,objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}."))) 
 NIL 
 NIL 
-(-762) 
+(-764) 
 ((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{manpageXXf01}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,m,n,ncolq,lda,theta,a,ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,wheret,m,n,a,lda,theta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,n,lda,a,ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,m,n,ncolq,lda,zeta,a,ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,wheret,m,n,a,lda,zeta,ncolb,ldb,b,ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,n,lda,a,ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,avals,lal,nrow,ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,nz,licn,lirn,abort,avals,irn,icn,droptl,densw,ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,nz,licn,ivect,jvect,icn,ikeep,grow,eta,abort,idisp,avals,ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,nz,licn,lirn,pivot,lblock,grow,abort,a,irn,icn,ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}."))) 
 NIL 
 NIL 
-(-763) 
+(-765) 
 ((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{manpageXXf02}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldph,a,b,ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,n,lda,ncolb,ldb,wantq,ldq,wantp,ldpt,a,b,ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image,monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,k,tol,novecs,nrx,lwork,lrwork,liwork,m,noits,x,ifail,dot,image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,ia,ib,eps1,matv,iv,a,b,ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,n,alb,ub,m,iv,a,ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,iar,ai,iai,n,ivr,ivi,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,iai,n,ivr,ivi,ar,ai,ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,iai,n,ar,ai,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,n,ivr,ivi,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,n,a,ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,ib,n,iv,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,ib,n,a,b,ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,ia,n,iv,ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,n,a,ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}."))) 
 NIL 
 NIL 
-(-764) 
+(-766) 
 ((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{manpageXXf04}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,n,damp,atol,btol,conlim,itnlim,msglvl,lrwork,liwork,b,ifail,aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,al,lal,d,nrow,ir,b,nrb,iselct,nrx,ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,b,precon,shift,itnlim,msglvl,lrwork,liwork,rtol,ifail,aprod,msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,nz,avals,licn,irn,lirn,icn,wkeep,ikeep,inform,b,acc,noits,ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,n,nra,tol,lwork,a,b,ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,n,d,e,b,ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,a,licn,icn,ikeep,mtype,idisp,rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,ia,b,n,iaa,ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,b,n,a,ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,b,n,a,ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,b,ib,n,m,ic,a,ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}."))) 
 NIL 
 NIL 
-(-765) 
+(-767) 
 ((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{manpageXXf07}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,n,nrhs,a,lda,ldb,b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,n,lda,a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,n,nrhs,a,lda,ipiv,ldb,b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,n,lda,a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}."))) 
 NIL 
 NIL 
-(-766) 
+(-768) 
 ((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,y,z,r,ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,y,z,ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,y,ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,fnu,z,n,scale,ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,z,scale,ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,z,scale,ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,z,n,scale,ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,x,tol,ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}."))) 
 NIL 
 NIL 
-(-767) 
+(-769) 
 ((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}"))) 
 NIL 
 NIL 
-(-768 S) 
+(-770 S) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-769) 
+(-771) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-770 S) 
+(-772 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 
-(-771) 
+(-773) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{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 
-(-772 |Par|) 
+(-774 |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 
-(-773 -1384) 
+(-775 -1386) 
 ((|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 
-(-774 P -1384) 
+(-776 P -1386) 
 ((|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\\spad{''}."))) 
 NIL 
 NIL 
-(-775 T$) 
+(-777 T$) 
 NIL 
 NIL 
 NIL 
-(-776 UP -1384) 
+(-778 UP -1386) 
 ((|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 
-(-777) 
+(-779) 
 ((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-778 R) 
+(-780 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 
-(-779) 
+(-781) 
 ((|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."))) 
-(((-4456 "*") . T)) 
+(((-4458 "*") . T)) 
 NIL 
-(-780 R -1384) 
+(-782 R -1386) 
 ((|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 
-(-781 S) 
+(-783 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 
-(-782) 
+(-784) 
 ((|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 
-(-783 R |PolR| E |PolE|) 
+(-785 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 
-(-784 R E V P TS) 
+(-786 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{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},{}\\spad{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 
-(-785 -1384 |ExtF| |SUEx| |ExtP| |n|) 
+(-787 -1386 |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 
-(-786 BP E OV R P) 
+(-788 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 
-(-787 |Par|) 
+(-789 |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 \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable."))) 
 NIL 
 NIL 
-(-788 R |VarSet|) 
+(-790 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
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-(-789 R S) 
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+(-791 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 
-(-790 R) 
+(-792 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|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)}"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4450 |has| |#1| (-370)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
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-(-791 R) 
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+(-793 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| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) 
-(-792 R E V P) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+(-794 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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.}"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-793 S) 
+(-795 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 (-564))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (QUOTE (-174)))) 
-(-794) 
+((-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-174)))) 
+(-796) 
 ((|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 
-(-795) 
+(-797) 
 ((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-796) 
+(-798) 
 ((|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\\spad{'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| (|:| |try| (|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| (|:| |try| (|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 
-(-797) 
+(-799) 
 ((|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 
-(-798 |Curve|) 
+(-800 |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 
-(-799) 
+(-801) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-800) 
+(-802) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-801) 
+(-803) 
 ((|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| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-802) 
+(-804) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-803) 
+(-805) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-804 S R) 
+(-806 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-375)))) 
-(-805 R) 
+((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-377)))) 
+(-807 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-806 -2813 R OS S) 
+(-808 -2818 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-807 R) 
+(-809 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (-2813 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-1010 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-808) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (-2818 (|HasCategory| (-1012 |#1|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (|HasCategory| (-1012 |#1|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| (-1012 |#1|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1012 |#1|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-810) 
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-809 R -1384 L) 
+(-811 R -1386 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}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-810 R -1384) 
+(-812 R -1386) 
 ((|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| "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| "failed") (|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| "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| "failed") (|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 
-(-811) 
+(-813) 
 ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) 
 NIL 
 NIL 
-(-812 R -1384) 
+(-814 R -1386) 
 ((|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 
-(-813) 
+(-815) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) 
 NIL 
 NIL 
-(-814 -1384 UP UPUP R) 
+(-816 -1386 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 
-(-815 -1384 UP L LQ) 
+(-817 -1386 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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'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}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'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 
-(-816) 
+(-818) 
 ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-817 -1384 UP L LQ) 
+(-819 -1386 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}\\spad{'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)}\\spad{'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}\\spad{'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}\\spad{'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 \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{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 {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-818 -1384 UP) 
+(-820 -1386 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|) "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}\\spad{'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|) "failed")) (|:| |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}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-819 -1384 L UP A LO) 
+(-821 -1386 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 
-(-820 -1384 UP) 
+(-822 -1386 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}\\spad{'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 \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'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)))) 
-(-821 -1384 LO) 
+(-823 -1386 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 
-(-822 -1384 LODO) 
+(-824 -1386 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-823 -4127 S |f|) 
+(-825 -4129 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-4448 |has| |#2| (-1060)) (-4449 |has| |#2| (-1060)) (-4451 |has| |#2| (-6 -4451)) ((-4456 "*") |has| |#2| (-174)) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-801))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-856))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))))) (-2813 (-12 (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1060)))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-370))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) 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-(-824 R) 
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+(-826 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
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-(-825 |Kernels| R |var|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-828 (-1190)) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-828 (-1190)) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-828 (-1190)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-828 (-1190)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-828 (-1190)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-827 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4456 "*") |has| |#2| (-370)) (-4447 |has| |#2| (-370)) (-4452 |has| |#2| (-370)) (-4446 |has| |#2| (-370)) (-4451 . T) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#2| (QUOTE (-370)))) 
-(-826 S) 
+(((-4458 "*") |has| |#2| (-372)) (-4449 |has| |#2| (-372)) (-4454 |has| |#2| (-372)) (-4448 |has| |#2| (-372)) (-4453 . T) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#2| (QUOTE (-372)))) 
+(-828 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 
-(-827 S) 
+(-829 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}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'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 (-858)))) 
-(-828) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-830) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-829) 
+(-831) 
 ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) 
 NIL 
 NIL 
-(-830) 
+(-832) 
 ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,cd,s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,mode,enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) 
 NIL 
 NIL 
-(-831) 
+(-833) 
 ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) 
 NIL 
 NIL 
-(-832) 
+(-834) 
 ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) 
 NIL 
 NIL 
-(-833) 
+(-835) 
 ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) 
 NIL 
 NIL 
-(-834 R) 
+(-836 R) 
 ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) 
 NIL 
 NIL 
-(-835 P R) 
+(-837 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-237)))) 
-(-836) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-239)))) 
+(-838) 
 ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) 
 NIL 
 NIL 
-(-837) 
+(-839) 
 ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) 
 NIL 
 NIL 
-(-838 S) 
+(-840 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4454 . T) (-4444 . T) (-4455 . T)) 
+((-4456 . T) (-4446 . T) (-4457 . T)) 
 NIL 
-(-839) 
+(-841) 
 ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) 
 NIL 
 NIL 
-(-840 R S) 
+(-842 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 
-(-841 R) 
+(-843 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."))) 
-((-4451 |has| |#1| (-856))) 
-((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) 
-(-842 A S) 
+((-4453 |has| |#1| (-858))) 
+((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2818 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (-2818 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) 
+(-844 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 
-(-843 S) 
+(-845 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-844 R) 
+(-846 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) 
+((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-845) 
+(-847) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) 
 NIL 
 NIL 
-(-846) 
+(-848) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 \\spad{`x'}."))) 
 NIL 
 NIL 
-(-847) 
+(-849) 
 ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-848) 
+(-850) 
 ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,start,lower,cons,upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information."))) 
 NIL 
 NIL 
-(-849) 
+(-851) 
 ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-850 R S) 
+(-852 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 
-(-851 R) 
+(-853 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-4451 |has| |#1| (-856))) 
-((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-21))) (-2813 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-553)))) 
-(-852) 
+((-4453 |has| |#1| (-858))) 
+((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2818 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (-2818 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) 
+(-854) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-853 -4127 S) 
+(-855 -4129 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-854) 
+(-856) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-855 S) 
+(-857 S) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
 NIL 
 NIL 
-(-856) 
+(-858) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-857 S) 
+(-859 S) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-858) 
+(-860) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
 NIL 
 NIL 
-(-859 S R) 
+(-861 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\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 \\spad{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\\spad{''}.")) (|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\\spad{''}.")) (|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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174)))) 
-(-860 R) 
+((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-862 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\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 \\spad{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\\spad{''}.")) (|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\\spad{''}.")) (|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)}.}"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-861 R C) 
+(-863 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{''}. \\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{''}. \\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{''}. \\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{''}. \\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 (-370))) (|HasCategory| |#1| (QUOTE (-564)))) 
-(-862 R |sigma| -2073) 
+((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) 
+(-864 R |sigma| -2076) 
 ((|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."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-863 |x| R |sigma| -2073) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-865 |x| R |sigma| -2076) 
 ((|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}."))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-370)))) 
-(-864 R) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-372)))) 
+(-866 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| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) 
-(-865) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+(-867) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-866) 
+(-868) 
 ((|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 
-(-867 S) 
+(-869 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-868) 
+(-870) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`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 \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-869) 
+(-871) 
 ((|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 \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) 
 NIL 
 NIL 
-(-870) 
+(-872) 
 ((|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| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|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'''},{} \\spad{\"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 
-(-871) 
+(-873) 
 ((|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\\spad{''} 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\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-872 |VariableList|) 
+(-874 |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 
-(-873) 
+(-875) 
 ((|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 
-(-874 R |vl| |wl| |wtlevel|) 
+(-876 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: \\spad{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)"))) 
-((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-875 R PS UP) 
+((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-877 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 
-(-876 R |x| |pt|) 
+(-878 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 
-(-877 |p|) 
+(-879 |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}."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-878 |p|) 
+(-880 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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)."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-879 |p|) 
+(-881 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{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)."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-878 |#1|) (QUOTE (-918))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-148))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-878 |#1|) (QUOTE (-1033))) (|HasCategory| (-878 |#1|) (QUOTE (-828))) (-2813 (|HasCategory| (-878 |#1|) (QUOTE (-828))) (|HasCategory| (-878 |#1|) (QUOTE (-858)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-1163))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| (-878 |#1|) (QUOTE (-237))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -522) (QUOTE (-1188)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -315) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (LIST (QUOTE -292) (LIST (QUOTE -878) (|devaluate| |#1|)) (LIST (QUOTE -878) (|devaluate| |#1|)))) (|HasCategory| (-878 |#1|) (QUOTE (-313))) (|HasCategory| (-878 |#1|) (QUOTE (-553))) (|HasCategory| (-878 |#1|) (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-878 |#1|) (QUOTE (-918)))) (|HasCategory| (-878 |#1|) (QUOTE (-146))))) 
-(-880 |p| PADIC) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-880 |#1|) (QUOTE (-920))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-148))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-880 |#1|) (QUOTE (-1035))) (|HasCategory| (-880 |#1|) (QUOTE (-830))) (-2818 (|HasCategory| (-880 |#1|) (QUOTE (-830))) (|HasCategory| (-880 |#1|) (QUOTE (-860)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-1165))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-239))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -524) (QUOTE (-1190)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -880) (|devaluate| |#1|)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (QUOTE (-315))) (|HasCategory| (-880 |#1|) (QUOTE (-555))) (|HasCategory| (-880 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-920)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))))) 
+(-882 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of \\spad{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)}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-828))) (-2813 (|HasCategory| |#2| (QUOTE (-828))) (|HasCategory| |#2| (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-858))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-881 S T$) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1035))) (|HasCategory| |#2| (QUOTE (-830))) (-2818 (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1165))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-883 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 \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#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 \\spad{`s'} and \\spad{`t'}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))))) 
-(-882) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) 
+(-884) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|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\\spad{'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\\spad{'s} lowest value."))) 
 NIL 
 NIL 
-(-883) 
+(-885) 
 ((|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 
-(-884) 
+(-886) 
 ((|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 
-(-885 CF1 CF2) 
+(-887 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-886 |ComponentFunction|) 
+(-888 |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 
-(-887 CF1 CF2) 
+(-889 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-888 |ComponentFunction|) 
+(-890 |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 
-(-889) 
+(-891) 
 ((|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 
-(-890 CF1 CF2) 
+(-892 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-891 |ComponentFunction|) 
+(-893 |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 
-(-892) 
+(-894) 
 ((|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\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'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}\\spad{'s},{} and 4 \\spad{5}\\spad{'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 
-(-893 R) 
+(-895 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 
-(-894 R S L) 
+(-896 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 
-(-895 S) 
+(-897 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 
-(-896 |Base| |Subject| |Pat|) 
+(-898 |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 (-2074 (|HasCategory| |#2| (QUOTE (-1060)))) (-2074 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (-12 (|HasCategory| |#2| (QUOTE (-1060))) (-2074 (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188))))) 
-(-897 R A B) 
+((-12 (-2077 (|HasCategory| |#2| (QUOTE (-1062)))) (-2077 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (-12 (|HasCategory| |#2| (QUOTE (-1062))) (-2077 (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190))))) 
+(-899 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}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-898 R S) 
+(-900 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\\spad{'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},{}e1),{}...,{}(\\spad{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 
-(-899 R -3608) 
+(-901 R -3611) 
 ((|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 \\spad{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 
-(-900 R S) 
+(-902 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 
-(-901 R) 
+(-903 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 \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and \\spad{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 \\spad{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 \\spad{'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 
-(-902 |VarSet|) 
+(-904 |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.\\spad{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 
-(-903 UP R) 
+(-905 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-904) 
+(-906) 
 ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
 NIL 
-(-905 UP -1384) 
+(-907 UP -1386) 
 ((|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 
-(-906) 
+(-908) 
 ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) 
 NIL 
 NIL 
-(-907) 
+(-909) 
 ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-908 A S) 
+(-910 A S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#2|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-909 S) 
+(-911 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-910 S) 
+(-912 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})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-911 |n| R) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-913 |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,{} \\spad{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 \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{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 
-(-912 S) 
+(-914 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."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-913 S) 
+(-915 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-914 S) 
+(-916 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) 
-((-4451 . T)) 
-((-2813 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-858)))) 
-(-915 R E |VarSet| S) 
+((-4453 . T)) 
+((-2818 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) 
+(-917 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 
-(-916 R S) 
+(-918 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 
-(-917 S) 
+(-919 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| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" 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}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{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 (-146)))) 
-(-918) 
+(-920) 
 ((|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| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" 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}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{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}."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-919 |p|) 
+(-921 |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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-375)))) 
-(-920 R0 -1384 UP UPUP R) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-377)))) 
+(-922 R0 -1386 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 
-(-921 UP UPUP R) 
+(-923 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 
-(-922 UP UPUP) 
+(-924 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 
-(-923 R) 
+(-925 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\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} 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} \\spad{``p}-adically\\spad{''} 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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-924 R) 
+(-926 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 
-(-925 E OV R P) 
+(-927 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-926) 
+(-928) 
 ((|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\\spad{'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\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'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\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\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 
-(-927 -1384) 
+(-929 -1386) 
 ((|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 \\spad{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 
-(-928 R) 
+(-930 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 
-(-929) 
+(-931) 
 ((|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| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-930) 
+(-932) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4456 "*") . T)) 
+(((-4458 "*") . T)) 
 NIL 
-(-931 -1384 P) 
+(-933 -1386 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-932 |xx| -1384) 
+(-934 |xx| -1386) 
 ((|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 
-(-933 R |Var| |Expon| GR) 
+(-935 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{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{>=} \\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} \\spad{~=} 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{>=} \\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{>=} \\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{>=} \\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{>=} \\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{>=} \\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{>=} \\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 
-(-934 S) 
+(-936 S) 
 ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{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 
-(-935) 
+(-937) 
 ((|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 
-(-936) 
+(-938) 
 ((|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 
-(-937) 
+(-939) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-938 R -1384) 
+(-940 R -1386) 
 ((|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 \\spad{'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 
-(-939) 
+(-941) 
 ((|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 \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-940 S A B) 
+(-942 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 
-(-941 S R -1384) 
+(-943 S R -1386) 
 ((|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 
-(-942 I) 
+(-944 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 
-(-943 S E) 
+(-945 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 
-(-944 S R L) 
+(-946 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 
-(-945 S E V R P) 
+(-947 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 -895) (|devaluate| |#1|)))) 
-(-946 R -1384 -3608) 
+((|HasCategory| |#3| (LIST (QUOTE -897) (|devaluate| |#1|)))) 
+(-948 R -1386 -3611) 
 ((|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 \\spad{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 
-(-947 -3608) 
+(-949 -3611) 
 ((|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 \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-948 S R Q) 
+(-950 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 
-(-949 S) 
+(-951 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 
-(-950 S R P) 
+(-952 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 
-(-951) 
+(-953) 
 ((|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 
-(-952 R) 
+(-954 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-734))) (|HasCategory| |#1| (QUOTE (-1060))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1060)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-953 |lv| R) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1062))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1062)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-955 |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 
-(-954 |TheField| |ThePols|) 
+(-956 |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},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@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},{}\\spad{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 (-856)))) 
-(-955 R S) 
+((|HasCategory| |#1| (QUOTE (-858)))) 
+(-957 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 
-(-956 |x| R) 
+(-958 |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 
-(-957 S R E |VarSet|) 
+(-959 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 (-918))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#4| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#4| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#4| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) 
-(-958 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasAttribute| |#2| (QUOTE -4454)) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) 
+(-960 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-959 E V R P -1384) 
+(-961 E V R P -1386) 
 ((|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},{}...,{}\\spad{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 
-(-960 E |Vars| R P S) 
+(-962 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 
-(-961 R) 
+(-963 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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1188) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-962 E V R P -1384) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1190) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1190) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1190) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1190) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1190) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-964 E V R P -1386) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-460)))) 
-(-963) 
+((|HasCategory| |#3| (QUOTE (-462)))) 
+(-965) 
 ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) 
 NIL 
 NIL 
-(-964) 
+(-966) 
 ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-965 R L) 
+(-967 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-966 A B) 
+(-968 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-967 S) 
+(-969 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
-((-4455 . T) (-4454 . T)) 
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-(-968) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-970) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) 
 NIL 
 NIL 
-(-969 -1384) 
+(-971 -1386) 
 ((|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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'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}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-970 I) 
+(-972 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'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\\spad{'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 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 
-(-971) 
+(-973) 
 ((|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 
-(-972 R E) 
+(-974 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}"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4448 . T) (-4449 . T) (-4451 . T)) 
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-(-973 A B) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4450 . T) (-4451 . T) (-4453 . T)) 
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+(-975 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"))) 
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-(-974) 
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+(-976) 
 ((|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 \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-975 T$) 
+(-977 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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-976 T$) 
+(-978 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-977 S T$) 
+(-979 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-978) 
+(-980) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-979 S) 
+(-981 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
-(-980 R |polR|) 
+(-982 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{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{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.\\spad{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{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\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{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{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} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + 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{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} 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{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} 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}) \\spad{>=} 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 = \\spad{+/-} 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 \\spad{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}) \\spad{>=} 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}) \\spad{>=} 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}) \\spad{>=} 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{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} 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 (-460)))) 
-(-981) 
+((|HasCategory| |#1| (QUOTE (-462)))) 
+(-983) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-982) 
+(-984) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-983 S |Coef| |Expon| |Var|) 
+(-985 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 
-(-984 |Coef| |Expon| |Var|) 
+(-986 |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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-985) 
+(-987) 
 ((|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 \\spad{x-},{} \\spad{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 
-(-986 S R E |VarSet| P) 
+(-988 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?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{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,{}\\spad{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{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{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{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{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?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-564)))) 
-(-987 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-566)))) 
+(-989 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?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{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,{}\\spad{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{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{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{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{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?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((-4454 . T)) 
+((-4456 . T)) 
 NIL 
-(-988 R E V P) 
+(-990 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(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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 \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{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(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{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},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{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(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{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(\\spad{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(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{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?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{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 \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{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(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-313)))) (|HasCategory| |#1| (QUOTE (-460)))) 
-(-989 K) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-315)))) (|HasCategory| |#1| (QUOTE (-462)))) 
+(-991 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
 NIL 
 NIL 
-(-990 |VarSet| E RC P) 
+(-992 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
 NIL 
 NIL 
-(-991 R) 
+(-993 R) 
 ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-992 R1 R2) 
+(-994 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-993 R) 
+(-995 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
 NIL 
 NIL 
-(-994 K) 
+(-996 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-995 R E OV PPR) 
+(-997 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-996 K R UP -1384) 
+(-998 K R UP -1386) 
 ((|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 
-(-997 |vl| |nv|) 
+(-999 |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 
-(-998 R |Var| |Expon| |Dpoly|) 
+(-1000 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\\spad{'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|) "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\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|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} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-313))))) 
-(-999 R E V P TS) 
+((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-315))))) 
+(-1001 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,{}\\spad{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(\\spad{lp},{}\\spad{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?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{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?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{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{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{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 
-(-1000) 
+(-1002) 
 ((|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 
-(-1001 A B R S) 
+(-1003 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 
-(-1002 A S) 
+(-1004 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 (-918))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-313))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-828))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-1163)))) 
-(-1003 S) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1035))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1165)))) 
+(-1005 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}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1004 |n| K) 
+(-1006 |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 
-(-1005) 
+(-1007) 
 ((|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 
-(-1006 S) 
+(-1008 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\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."))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
-(-1007 S R) 
+(-1009 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 (-553))) (|HasCategory| |#2| (QUOTE (-1071))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-296)))) 
-(-1008 R) 
+((|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1073))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-298)))) 
+(-1010 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}."))) 
-((-4447 |has| |#1| (-296)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 |has| |#1| (-298)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1009 QR R QS S) 
+(-1011 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 
-(-1010 R) 
+(-1012 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.}"))) 
-((-4447 |has| |#1| (-296)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-296))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -292) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-1071))) (|HasCategory| |#1| (QUOTE (-553)))) 
-(-1011 S) 
+((-4449 |has| |#1| (-298)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1190)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1073))) (|HasCategory| |#1| (QUOTE (-555)))) 
+(-1013 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}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1012 S) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1014 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-1013) 
+(-1015) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-1014 -1384 UP UPUP |radicnd| |n|) 
+(-1016 -1386 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4447 |has| (-415 |#2|) (-370)) (-4452 |has| (-415 |#2|) (-370)) (-4446 |has| (-415 |#2|) (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-415 |#2|) (QUOTE (-146))) (|HasCategory| (-415 |#2|) (QUOTE (-148))) (|HasCategory| (-415 |#2|) (QUOTE (-356))) (-2813 (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (|HasCategory| (-415 |#2|) (QUOTE (-370))) (|HasCategory| (-415 |#2|) (QUOTE (-375))) (-2813 (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (QUOTE (-356)))) (-2813 (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-356))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 |#2|) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| (-415 |#2|) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-415 |#2|) (QUOTE (-370)))) (-12 (|HasCategory| (-415 |#2|) (QUOTE (-237))) (|HasCategory| (-415 |#2|) (QUOTE (-370))))) 
-(-1015 |bb|) 
+((-4449 |has| (-417 |#2|) (-372)) (-4454 |has| (-417 |#2|) (-372)) (-4448 |has| (-417 |#2|) (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2818 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2818 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2818 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2818 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) 
+(-1017 |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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| (-572) (QUOTE (-918))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-1188)))) (|HasCategory| (-572) (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-148))) (|HasCategory| (-572) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-1033))) (|HasCategory| (-572) (QUOTE (-828))) (-2813 (|HasCategory| (-572) (QUOTE (-828))) (|HasCategory| (-572) (QUOTE (-858)))) (|HasCategory| (-572) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-1163))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| (-572) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| (-572) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| (-572) (QUOTE (-237))) (|HasCategory| (-572) (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| (-572) (LIST (QUOTE -522) (QUOTE (-1188)) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -315) (QUOTE (-572)))) (|HasCategory| (-572) (LIST (QUOTE -292) (QUOTE (-572)) (QUOTE (-572)))) (|HasCategory| (-572) (QUOTE (-313))) (|HasCategory| (-572) (QUOTE (-553))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-572) (LIST (QUOTE -647) (QUOTE (-572)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-572) (QUOTE (-918)))) (|HasCategory| (-572) (QUOTE (-146))))) 
-(-1016) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-574) (QUOTE (-920))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-1190)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1035))) (|HasCategory| (-574) (QUOTE (-830))) (-2818 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1165))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1190)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-920)))) (|HasCategory| (-574) (QUOTE (-146))))) 
+(-1018) 
 ((|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 
-(-1017) 
+(-1019) 
 ((|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 
-(-1018 RP) 
+(-1020 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 
-(-1019 S) 
+(-1021 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 
-(-1020 A S) 
+(-1022 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{:=} \\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 -4455)) (|HasCategory| |#2| (QUOTE (-1111)))) 
-(-1021 S) 
+((|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-1113)))) 
+(-1023 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{:=} \\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 
-(-1022 S) 
+(-1024 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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (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 
-(-1023) 
+(-1025) 
 ((|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} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (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}}"))) 
-((-4447 . T) (-4452 . T) (-4446 . T) (-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4451 . T)) 
+((-4449 . T) (-4454 . T) (-4448 . T) (-4451 . T) (-4450 . T) ((-4458 "*") . T) (-4453 . T)) 
 NIL 
-(-1024 R -1384) 
+(-1026 R -1386) 
 ((|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 
-(-1025 R -1384) 
+(-1027 R -1386) 
 ((|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 
-(-1026 -1384 UP) 
+(-1028 -1386 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 
-(-1027 -1384 UP) 
+(-1029 -1386 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 
-(-1028 S) 
+(-1030 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 
-(-1029 F1 UP UPUP R F2) 
+(-1031 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 
-(-1030) 
+(-1032) 
 ((|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 
-(-1031 |Pol|) 
+(-1033 |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 
-(-1032 |Pol|) 
+(-1034 |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 
-(-1033) 
+(-1035) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-1034) 
+(-1036) 
 ((|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 
-(-1035 |TheField|) 
+(-1037 |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"))) 
-((-4447 . T) (-4452 . T) (-4446 . T) (-4449 . T) (-4448 . T) ((-4456 "*") . T) (-4451 . T)) 
-((-2813 (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| (-415 (-572)) (LIST (QUOTE -1049) (QUOTE (-572))))) 
-(-1036 -1384 L) 
+((-4449 . T) (-4454 . T) (-4448 . T) (-4451 . T) (-4450 . T) ((-4458 "*") . T) (-4453 . T)) 
+((-2818 (|HasCategory| (-417 (-574)) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1051) (QUOTE (-574))))) 
+(-1038 -1386 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 
-(-1037 S) 
+(-1039 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(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1111)))) 
-(-1038 R E V P) 
+((|HasCategory| |#1| (QUOTE (-1113)))) 
+(-1040 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#4| (LIST (QUOTE -315) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#4| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1039 R) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1041 R) 
 ((|constructor| (NIL "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{<=} \\spad{i} \\spad{<=} \\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{<=} \\spad{i} \\spad{<=} \\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 (-4456 "*")))) 
-(-1040 R) 
+((|HasAttribute| |#1| (QUOTE (-4458 "*")))) 
+(-1042 R) 
 ((|constructor| (NIL "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\\spad{'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\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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\\spad{'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 (-370))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-313)))) 
-(-1041 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-315)))) 
+(-1043 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 
-(-1042) 
+(-1044) 
 ((|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 
-(-1043 S) 
+(-1045 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 
-(-1044 S) 
+(-1046 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 
-(-1045 -1384 |Expon| |VarSet| |FPol| |LFPol|) 
+(-1047 -1386 |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"))) 
-(((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1046) 
+(-1048) 
 ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1047) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1049) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-1048 A S) 
+(-1050 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 
-(-1049 S) 
+(-1051 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 
-(-1050 Q R) 
+(-1052 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 
-(-1051) 
+(-1053) 
 ((|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 
-(-1052 UP) 
+(-1054 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 
-(-1053 R) 
+(-1055 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 
-(-1054 R) 
+(-1056 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}\\spad{'s} appearing inside the \\spad{gi}\\spad{'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}\\spad{'s} appearing inside the \\spad{gi}\\spad{'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 
-(-1055 T$) 
+(-1057 T$) 
 ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) 
 NIL 
 NIL 
-(-1056 T$) 
+(-1058 T$) 
 ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-1057 R |ls|) 
+(-1059 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{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}."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| (-788 |#1| (-872 |#2|)) (QUOTE (-1111))) (|HasCategory| (-788 |#1| (-872 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -788) (|devaluate| |#1|) (LIST (QUOTE -872) (|devaluate| |#2|)))))) (|HasCategory| (-788 |#1| (-872 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-788 |#1| (-872 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| (-872 |#2|) (QUOTE (-375))) (|HasCategory| (-788 |#1| (-872 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1058) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1113))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -790) (|devaluate| |#1|) (LIST (QUOTE -874) (|devaluate| |#2|)))))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-874 |#2|) (QUOTE (-377))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1060) 
 ((|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 
-(-1059 S) 
+(-1061 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 
-(-1060) 
+(-1062) 
 ((|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."))) 
-((-4451 . T)) 
+((-4453 . T)) 
 NIL 
-(-1061 |xx| -1384) 
+(-1063 |xx| -1386) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1062 R) 
+(-1064 R) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{RightModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
-(-1063 S |m| |n| R |Row| |Col|) 
+(-1065 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 (-313))) (|HasCategory| |#4| (QUOTE (-370))) (|HasCategory| |#4| (QUOTE (-564))) (|HasCategory| |#4| (QUOTE (-174)))) 
-(-1064 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-315))) (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (QUOTE (-566))) (|HasCategory| |#4| (QUOTE (-174)))) 
+(-1066 |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"))) 
-((-4454 . T) (-4449 . T) (-4448 . T)) 
+((-4456 . T) (-4451 . T) (-4450 . T)) 
 NIL 
-(-1065 |m| |n| R) 
+(-1067 |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}."))) 
-((-4454 . T) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#3| (QUOTE (-174))) (-2813 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -622) (QUOTE (-544)))) (-2813 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-370)))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (QUOTE (-313))) (|HasCategory| |#3| (QUOTE (-564))) (-12 (|HasCategory| |#3| (QUOTE (-1111))) (|HasCategory| |#3| (LIST (QUOTE -315) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1066 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-4456 . T) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#3| (QUOTE (-174))) (-2818 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372)))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (QUOTE (-315))) (|HasCategory| |#3| (QUOTE (-566))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1068 |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 
-(-1067 R) 
+(-1069 R) 
 ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
 NIL 
-(-1068 S T$) 
+(-1070 S T$) 
 ((|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 (-1111)))) 
-(-1069) 
+((|HasCategory| |#1| (QUOTE (-1113)))) 
+(-1071) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) 
 NIL 
 NIL 
-(-1070 S) 
+(-1072 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.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-1071) 
+(-1073) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1072 |TheField| |ThePolDom|) 
+(-1074 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-1073) 
+(-1075) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-4442 . T) (-4446 . T) (-4441 . T) (-4452 . T) (-4453 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4444 . T) (-4448 . T) (-4443 . T) (-4454 . T) (-4455 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1074) 
+(-1076) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -1907) (QUOTE (-52))))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-52) (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| (-52) (QUOTE (-1111))) (|HasCategory| (-52) (LIST (QUOTE -315) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (QUOTE (-1111))) (|HasCategory| (-1188) (QUOTE (-858))) (|HasCategory| (-52) (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-52) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1188)) (|:| -1907 (-52))) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1075 S R E V) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1190))) (LIST (QUOTE |:|) (QUOTE -1909) (QUOTE (-52))))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-52) (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1113))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (QUOTE (-1113))) (|HasCategory| (-1190) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1190)) (|:| -1909 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1077 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| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{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 \\spad{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{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)\\spad{*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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -1003) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-1188))))) 
-(-1076 R E V) 
+((|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1005) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-1190))))) 
+(-1078 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{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 \\spad{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{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)\\spad{*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)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{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}}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-1077) 
+(-1079) 
 ((|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 
-(-1078 S |TheField| |ThePols|) 
+(-1080 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 
-(-1079 |TheField| |ThePols|) 
+(-1081 |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 
-(-1080 R E V P TS) 
+(-1082 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\\spad{'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},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{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{\\spad{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 
-(-1081 S R E V P) 
+(-1083 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}{\\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1082 R E V P) 
+(-1084 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}{\\spad{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 \\spad{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 \\spad{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 \\spad{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}."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1083 R E V P TS) 
+(-1085 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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},{}\\spad{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 
-(-1084) 
+(-1086) 
 ((|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 
-(-1085) 
+(-1087) 
 ((|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 
-(-1086 |f|) 
+(-1088 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1087 |Base| R -1384) 
+(-1089 |Base| R -1386) 
 ((|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},{}...,{}\\spad{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 
-(-1088 |Base| R -1384) 
+(-1090 |Base| R -1386) 
 ((|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 
-(-1089 R |ls|) 
+(-1091 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 
-(-1090 UP SAE UPA) 
+(-1092 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 
-(-1091 R UP M) 
+(-1093 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."))) 
-((-4447 |has| |#1| (-370)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-356))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-375))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-356)))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-370))))) 
-(-1092 UP SAE UPA) 
+((-4449 |has| |#1| (-372)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-358)))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372))))) 
+(-1094 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 
-(-1093) 
+(-1095) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-1094) 
+(-1096) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1095 S) 
+(-1097 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 
-(-1096) 
+(-1098) 
 ((|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 \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`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 
-(-1097 R) 
+(-1099 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 
-(-1098 R) 
+(-1100 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"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| (-1099 (-1188)) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1099 (-1188)) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1099 (-1188)) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1099 (-1188)) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1099 (-1188)) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1099 S) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1101 (-1190)) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1101 (-1190)) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1101 (-1190)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1101 (-1190)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1101 (-1190)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1101 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 
-(-1100 R S) 
+(-1102 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 (-856)))) 
-(-1101) 
+((|HasCategory| |#1| (QUOTE (-858)))) 
+(-1103) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1102 R S) 
+(-1104 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1103 S) 
+(-1105 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1105 |#1|) (QUOTE (-1111)))) 
-(-1104 S) 
+((|HasCategory| (-1107 |#1|) (QUOTE (-1113)))) 
+(-1106 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1105 S) 
+(-1107 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1111)))) 
-(-1106 S L) 
+((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1113)))) 
+(-1108 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 
-(-1107) 
+(-1109) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1108 A S) 
+(-1110 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1109 S) 
+(-1111 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-4444 . T)) 
+((-4446 . T)) 
 NIL 
-(-1110 S) 
+(-1112 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 
-(-1111) 
+(-1113) 
 ((|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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 
-(-1112 |m| |n|) 
+(-1114 |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 \\spad{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 {a_1,{}...,{}a_m}. Error if {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| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the \\spad{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| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the \\spad{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 
-(-1113 S) 
+(-1115 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)}}"))) 
-((-4454 . T) (-4444 . T) (-4455 . T)) 
-((-2813 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|))))) 
-(-1114 |Str| |Sym| |Int| |Flt| |Expr|) 
+((-4456 . T) (-4446 . T) (-4457 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-1116 |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 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 \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{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 \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{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 \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{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|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
 NIL 
-(-1115) 
+(-1117) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1116 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1118 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1117 R FS) 
+(-1119 R FS) 
 ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) 
 NIL 
 NIL 
-(-1118 R E V P TS) 
+(-1120 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,{}\\spad{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(\\spad{lp},{}\\spad{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?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{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?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{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{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{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 
-(-1119 R E V P TS) 
+(-1121 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 \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of 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 
-(-1120 R E V P) 
+(-1122 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 \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{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.}"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1121) 
+(-1123) 
 ((|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 
-(-1122 S) 
+(-1124 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1123) 
+(-1125) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1124 |dimtot| |dim1| S) 
+(-1126 |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 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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-(-1125 R |x|) 
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(|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1062)))) (-12 (|HasCategory| |#3| (QUOTE (-1062))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-1190))))) (-2818 (|HasCategory| |#3| (QUOTE (-1062))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574)))))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -1051) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1113)))) (|HasAttribute| |#3| (QUOTE -4453)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#3| (QUOTE (-1113))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) 
+(-1127 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 \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If 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 \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If 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 (-460)))) 
-(-1126) 
+((|HasCategory| |#1| (QUOTE (-462)))) 
+(-1128) 
 ((|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 \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) 
 NIL 
 NIL 
-(-1127 R -1384) 
+(-1129 R -1386) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "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|) "failed") |#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|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1128 R) 
+(-1130 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "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|) "failed") (|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|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1129) 
+(-1131) 
 ((|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 \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) 
 NIL 
 NIL 
-(-1130) 
+(-1132) 
 ((|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 
-(-1131) 
+(-1133) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\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."))) 
-((-4442 . T) (-4446 . T) (-4441 . T) (-4452 . T) (-4453 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4444 . T) (-4448 . T) (-4443 . T) (-4454 . T) (-4455 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1132 S) 
+(-1134 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}) = \\spad{#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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4454 . T) (-4455 . T)) 
+((-4456 . T) (-4457 . T)) 
 NIL 
-(-1133 S |ndim| R |Row| |Col|) 
+(-1135 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-370))) (|HasAttribute| |#3| (QUOTE (-4456 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
-(-1134 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-372))) (|HasAttribute| |#3| (QUOTE (-4458 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) 
+(-1136 |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}\\spad{'s} on the diagonal and zeroes elsewhere."))) 
-((-4454 . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4456 . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1135 R |Row| |Col| M) 
+(-1137 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 
-(-1136 R |VarSet|) 
+(-1138 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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-918))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (|HasCategory| |#1| (QUOTE (-460))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#1| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4452)) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-918)))) (|HasCategory| |#1| (QUOTE (-146))))) 
-(-1137 |Coef| |Var| SMP) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1139 |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 \\spad{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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-1138 R E V P) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-1140 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}"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1139 UP -1384) 
+(-1141 UP -1386) 
 ((|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 
-(-1140 R) 
+(-1142 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 
-(-1141 R) 
+(-1143 R) 
 ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function 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 func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1142 R) 
+(-1144 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 
-(-1143 S A) 
+(-1145 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 (-858)))) 
-(-1144 R) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1146 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 
-(-1145 R) 
+(-1147 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 \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and 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); 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 \\spad{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 \\spad{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 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 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 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 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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1146) 
+(-1148) 
 ((|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 
-(-1147) 
+(-1149) 
 ((|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 
-(-1148) 
+(-1150) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`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 \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`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 \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`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 \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`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 \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) 
 NIL 
 NIL 
-(-1149) 
+(-1151) 
 ((|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 
-(-1150) 
+(-1152) 
 ((|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 
-(-1151 V C) 
+(-1153 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},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{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},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{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 
-(-1152 V C) 
+(-1154 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,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{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,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{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|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{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},{}\\spad{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 \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{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 \\spad{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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))) (-2813 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -315) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1151 |#1| |#2|) (QUOTE (-1111))))) (|HasCategory| (-1151 |#1| |#2|) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1153 |ndim| R) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-1153 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1153) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1153 |#1| |#2|) (QUOTE (-1113)))) (|HasCategory| (-1153 |#1| |#2|) (QUOTE (-1113))) (-2818 (|HasCategory| (-1153 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-1153 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1153) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1153 |#1| |#2|) (QUOTE (-1113))))) (|HasCategory| (-1153 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1155 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
-((-4451 . T) (-4443 |has| |#2| (-6 (-4456 "*"))) (-4454 . T) (-4448 . T) (-4449 . T)) 
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-(-1154 S) 
+((-4453 . T) (-4445 |has| |#2| (-6 (-4458 "*"))) (-4456 . T) (-4450 . T) (-4451 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4458 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-372))) (-2818 (|HasAttribute| |#2| (QUOTE (-4458 "*"))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+(-1156 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{>=} \\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{>=} \\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\",{}\\spad{\"*\"})} 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}) \\spad{==} 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1155) 
+(-1157) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{>=} \\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{>=} \\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\",{}\\spad{\"*\"})} 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}) \\spad{==} 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1156 R E V P TS) 
+(-1158 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\\spad{'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{\\spad{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 
-(-1157 R E V P) 
+(-1159 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(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{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(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{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},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#4| (LIST (QUOTE -315) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#4| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1158 S) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1160 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}."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1159 A S) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1161 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}.")) (|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 
-(-1160 S) 
+(-1162 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}.")) (|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 
-(-1161 |Key| |Ent| |dent|) 
+(-1163 |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."))) 
-((-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-858))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111)))) 
-(-1162) 
+((-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113)))) 
+(-1164) 
 ((|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 
-(-1163) 
+(-1165) 
 ((|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 infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1164 |Coef|) 
+(-1166 |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 
-(-1165 S) 
+(-1167 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 
-(-1166 A B) 
+(-1168 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 
-(-1167 A B C) 
+(-1169 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 
-(-1168 S) 
+(-1170 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."))) 
-((-4455 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1169) 
+((-4457 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1171) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1170) 
+(-1172) 
 NIL 
-((-4455 . T) (-4454 . T)) 
-((-2813 (-12 (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| (-145) (QUOTE (-858))) (|HasCategory| (-572) (QUOTE (-858))) (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -621) (QUOTE (-870)))) (-12 (|HasCategory| (-145) (QUOTE (-1111))) (|HasCategory| (-145) (LIST (QUOTE -315) (QUOTE (-145)))))) 
-(-1171 |Entry|) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1113))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) 
+(-1173 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#1|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (QUOTE (-1111))) (|HasCategory| (-1170) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 (-1170)) (|:| -1907 |#1|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1172 A) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (QUOTE (-1172))) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#1|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (QUOTE (-1113))) (|HasCategory| (-1172) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 (-1172)) (|:| -1909 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1174 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 \\spad{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 \\spad{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 (-370))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) 
-(-1173 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+(-1175 |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 
-(-1174 |Coef|) 
+(-1176 |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 
-(-1175 R UP) 
+(-1177 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 (-313)))) 
-(-1176 |n| R) 
+((|HasCategory| |#1| (QUOTE (-315)))) 
+(-1178 |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\\spad{'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\\spad{'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 
-(-1177 S1 S2) 
+(-1179 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 \\spad{s:t}"))) 
 NIL 
 NIL 
-(-1178) 
+(-1180) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1179 |Coef| |var| |cen|) 
+(-1181 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-4456 "*") -2813 (-2085 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-828))) (|has| |#1| (-174)) (-2085 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-918)))) (-4447 -2813 (-2085 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-828))) (|has| |#1| (-564)) (-2085 (|has| |#1| (-370)) (|has| (-1186 |#1| |#2| |#3|) (-918)))) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (QUOTE (-1163))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| (-1186 |#1| |#2| |#3|) (LIST (QUOTE -292) (LIST (QUOTE -1186) (|devaluate| |#1|) (|devaluate| |#2|) 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-(-1180 R -1384) 
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+(-1182 R -1386) 
 ((|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}(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 
-(-1181 R) 
+(-1183 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 
-(-1182 R S) 
+(-1184 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 
-(-1183 E OV R P) 
+(-1185 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 
-(-1184 R) 
+(-1186 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1185 |Coef| |var| |cen|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4452 |has| |#1| (-372)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-920))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1165))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4454)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-920)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(-1187 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) 
-(-1186 |Coef| |var| |cen|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+(-1188 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) 
-(-1187) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+(-1189) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-1188) 
+(-1190) 
 ((|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}([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 
-(-1189 R) 
+(-1191 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 
-(-1190 R) 
+(-1192 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-6 -4452)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (LIST (QUOTE -1049) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-460))) (-12 (|HasCategory| (-982) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasAttribute| |#1| (QUOTE -4452))) 
-(-1191) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-6 -4454)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2818 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| (-984) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasAttribute| |#1| (QUOTE -4454))) 
+(-1193) 
 ((|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| "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| "void"))) "\\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| "void"))) "\\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| "void")) $) "\\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 
-(-1192) 
+(-1194) 
 ((|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 
-(-1193) 
+(-1195) 
 ((|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 \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`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 \\spad{`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 \\spad{`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 \\spad{`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 \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1194 N) 
+(-1196 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1195 N) 
+(-1197 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| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) 
 NIL 
 NIL 
-(-1196) 
+(-1198) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1197 R) 
+(-1199 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 
-(-1198) 
+(-1200) 
 ((|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 
-(-1199 S) 
+(-1201 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 \\spad{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}{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{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 bat1 is the inverse of 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 
-(-1200 S) 
+(-1202 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 
-(-1201 |Key| |Entry|) 
+(-1203 |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}"))) 
-((-4454 . T) (-4455 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -315) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3690) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1907) (|devaluate| |#2|)))))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#2| (QUOTE (-1111)))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -622) (QUOTE (-544)))) (-12 (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#2| (QUOTE (-1111))) (-2813 (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#2| (LIST (QUOTE -621) (QUOTE (-870)))) (|HasCategory| (-2 (|:| -3690 |#1|) (|:| -1907 |#2|)) (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1202 S) 
+((-4456 . T) (-4457 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3693) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1909) (|devaluate| |#2|)))))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-1113)))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1113))) (-2818 (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3693 |#1|) (|:| -1909 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1204 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 
-(-1203 R) 
+(-1205 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 
-(-1204 S |Key| |Entry|) 
+(-1206 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{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1205 |Key| |Entry|) 
+(-1207 |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{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
-((-4455 . T)) 
+((-4457 . T)) 
 NIL 
-(-1206 |Key| |Entry|) 
+(-1208 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} 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 
-(-1207) 
+(-1209) 
 ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) 
 NIL 
 NIL 
-(-1208 S) 
+(-1210 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 
-(-1209) 
+(-1211) 
 ((|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 \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} 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 
-(-1210) 
+(-1212) 
 ((|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 
-(-1211 R) 
+(-1213 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 
-(-1212) 
+(-1214) 
 ((|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 
-(-1213 S) 
+(-1215 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1214) 
+(-1216) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1215 S) 
+(-1217 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1111))) (-2813 (-12 (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -315) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1216 S) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1113))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1218 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1217) 
+(-1219) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1218 R -1384) 
+(-1220 R -1386) 
 ((|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 
-(-1219 R |Row| |Col| M) 
+(-1221 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 
-(-1220 R -1384) 
+(-1222 R -1386) 
 ((|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 \\spad{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 \\spad{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 -622) (LIST (QUOTE -901) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -895) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -895) (|devaluate| |#1|))))) 
-(-1221 S R E V P) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -897) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -897) (|devaluate| |#1|))))) 
+(-1223 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{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 (-375)))) 
-(-1222 R E V P) 
+((|HasCategory| |#4| (QUOTE (-377)))) 
+(-1224 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} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{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|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{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{\\spad{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(\\spad{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{\\spad{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(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{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},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{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{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{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},{}\\spad{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{\\spad{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},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff 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{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{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{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{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{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1223 |Coef|) 
+(-1225 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-1224 |Curve|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-1226 |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 
-(-1225) 
+(-1227) 
 ((|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 
-(-1226 S) 
+(-1228 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'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 (-1111))) (|HasCategory| |#1| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1227 -1384) 
+((|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1229 -1386) 
 ((|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 
-(-1228) 
+(-1230) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1229) 
+(-1231) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1230 S) 
+(-1232 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 \\spad{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 \\spad{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}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{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}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-858)))) 
-(-1231) 
+((|HasCategory| |#1| (QUOTE (-860)))) 
+(-1233) 
 ((|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 
-(-1232 S) 
+(-1234 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 
-(-1233) 
+(-1235) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1234) 
+(-1236) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1235) 
+(-1237) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1236) 
+(-1238) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1237) 
+(-1239) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1238 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1240 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1239 |Coef|) 
+(-1241 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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{<=} \\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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1240 S |Coef| UTS) 
+(-1242 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 (-370)))) 
-(-1241 |Coef| UTS) 
+((|HasCategory| |#2| (QUOTE (-372)))) 
+(-1243 |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)}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1242 |Coef| UTS) 
+(-1244 |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)}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((-2813 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -292) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -522) (QUOTE (-1188)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-918)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1033)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -315) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1049) 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 ((|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 
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 ((|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 
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 ((|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 
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 ((|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 
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 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{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 
-(-1249 R UP) 
+(-1251 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},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{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 
-(-1250 R UP) 
+(-1252 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 
-(-1251 R U) 
+(-1253 R U) 
 ((|constructor| (NIL "This package implements Karatsuba\\spad{'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\\spad{'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\\spad{'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\\spad{'s} trick at all."))) 
 NIL 
 NIL 
-(-1252 |x| R) 
+(-1254 |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}"))) 
-(((-4456 "*") |has| |#2| (-174)) (-4447 |has| |#2| (-564)) (-4450 |has| |#2| (-370)) (-4452 |has| |#2| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-564)))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-386)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-386))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -895) (QUOTE (-572)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-572))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-386)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -622) (LIST (QUOTE -901) (QUOTE (-572)))))) (-12 (|HasCategory| (-1093) (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#2| (LIST (QUOTE -622) (QUOTE (-544))))) (|HasCategory| |#2| (LIST (QUOTE -647) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (QUOTE (-572)))) (-2813 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasCategory| |#2| (LIST (QUOTE -1049) (LIST (QUOTE -415) (QUOTE (-572))))) (-2813 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-1163))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE -4452)) (|HasCategory| |#2| (QUOTE (-460))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (-2813 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-918)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-1253 R PR S PS) 
+(((-4458 "*") |has| |#2| (-174)) (-4449 |has| |#2| (-566)) (-4452 |has| |#2| (-372)) (-4454 |has| |#2| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-920))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1095) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (QUOTE (-574)))) (-2818 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (-2818 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1165))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE -4454)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (-2818 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-920)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-1255 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 
-(-1254 S R) 
+(-1256 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 \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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\\spad{'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| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-460))) (|HasCategory| |#2| (QUOTE (-564))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1163)))) 
-(-1255 R) 
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1165)))) 
+(-1257 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 \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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\\spad{'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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4450 |has| |#1| (-370)) (-4452 |has| |#1| (-6 -4452)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4452 |has| |#1| (-372)) (-4454 |has| |#1| (-6 -4454)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-1256 S |Coef| |Expon|) 
+(-1258 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{<=} \\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| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1123))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2940) (LIST (|devaluate| |#2|) (QUOTE (-1188)))))) 
-(-1257 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1125))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2943) (LIST (|devaluate| |#2|) (QUOTE (-1190)))))) 
+(-1259 |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{<=} \\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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1258 RC P) 
+(-1260 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1259 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1261 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1260 |Coef|) 
+(-1262 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1261 S |Coef| ULS) 
+(-1263 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 
-(-1262 |Coef| ULS) 
+(-1264 |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)}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1263 |Coef| ULS) 
+(-1265 |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)}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) 
-(-1264 |Coef| |var| |cen|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+(-1266 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4452 |has| |#1| (-370)) (-4446 |has| |#1| (-370)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#1| (QUOTE (-174))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572))) (|devaluate| |#1|)))) (|HasCategory| (-415 (-572)) (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-2813 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-564)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -415) (QUOTE (-572)))))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) 
-(-1265 R FE |var| |cen|) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4448 |has| |#1| (-372)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2818 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+(-1267 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
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-(-1266 A S) 
+(((-4458 "*") |has| (-1266 |#2| |#3| |#4|) (-174)) (-4449 |has| (-1266 |#2| |#3| |#4|) (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| (-1266 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-174))) (-2818 (|HasCategory| (-1266 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1266 |#2| |#3| |#4|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| (-1266 |#2| |#3| |#4|) (LIST (QUOTE -1051) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1266 |#2| |#3| |#4|) (LIST (QUOTE -1051) (QUOTE (-574)))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-372))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-462))) (|HasCategory| (-1266 |#2| |#3| |#4|) (QUOTE (-566)))) 
+(-1268 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\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{:=} \\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} \\spad{>=} 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} \\spad{>=} 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} \\spad{>=} 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4455))) 
-(-1267 S) 
+((|HasAttribute| |#1| (QUOTE -4457))) 
+(-1269 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\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{:=} \\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} \\spad{>=} 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} \\spad{>=} 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} \\spad{>=} 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1268 |Coef1| |Coef2| UTS1 UTS2) 
+(-1270 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1269 S |Coef|) 
+(-1271 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#2| (QUOTE (-968))) (|HasCategory| |#2| (QUOTE (-1214))) (|HasSignature| |#2| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3034) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1188))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#2| (QUOTE (-370)))) 
-(-1270 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-1216))) (|HasSignature| |#2| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2968) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1190))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) 
+(-1272 |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."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1271 |Coef| |var| |cen|) 
+(-1273 |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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{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}."))) 
-(((-4456 "*") |has| |#1| (-174)) (-4447 |has| |#1| (-564)) (-4448 . T) (-4449 . T) (-4451 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasCategory| |#1| (QUOTE (-564))) (-2813 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -909) (QUOTE (-1188)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-779)) (|devaluate| |#1|)))) (|HasCategory| (-779) (QUOTE (-1123))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasSignature| |#1| (LIST (QUOTE -2940) (LIST (|devaluate| |#1|) (QUOTE (-1188)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-779))))) (|HasCategory| |#1| (QUOTE (-370))) (-2813 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-572)))) (|HasCategory| |#1| (QUOTE (-968))) (|HasCategory| |#1| (QUOTE (-1214))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasSignature| |#1| (LIST (QUOTE -3034) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1188))))) (|HasSignature| |#1| (LIST (QUOTE -4353) (LIST (LIST (QUOTE -652) (QUOTE (-1188))) (|devaluate| |#1|))))))) 
-(-1272 |Coef| UTS) 
+(((-4458 "*") |has| |#1| (-174)) (-4449 |has| |#1| (-566)) (-4450 . T) (-4451 . T) (-4453 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2818 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-1190)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1125))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2943) (LIST (|devaluate| |#1|) (QUOTE (-1190)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2818 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1216))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2968) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1190))))) (|HasSignature| |#1| (LIST (QUOTE -4355) (LIST (LIST (QUOTE -654) (QUOTE (-1190))) (|devaluate| |#1|))))))) 
+(-1274 |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 
-(-1273 -1384 UP L UTS) 
+(-1275 -1386 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 (-564)))) 
-(-1274) 
+((|HasCategory| |#1| (QUOTE (-566)))) 
+(-1276) 
 ((|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 
-(-1275 |sym|) 
+(-1277 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1276 S R) 
+(-1278 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})\\spad{*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 (-1013))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (QUOTE (-734))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1277 R) 
+((|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1279 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})\\spad{*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4455 . T) (-4454 . T)) 
+((-4457 . T) (-4456 . T)) 
 NIL 
-(-1278 A B) 
+(-1280 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4455 . T) (-4454 . T)) 
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-(-1280) 
+((-4457 . T) (-4456 . T)) 
+((-2818 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2818 (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2818 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1062))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1062)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) 
+(-1282) 
 ((|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\\spad{'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 
-(-1281) 
+(-1283) 
 ((|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 
-(-1282) 
+(-1284) 
 ((|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 
-(-1283) 
+(-1285) 
 ((|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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 \\spad{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 
-(-1284) 
+(-1286) 
 ((|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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1285 A S) 
+(-1287 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1286 S) 
+(-1288 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}."))) 
-((-4449 . T) (-4448 . T)) 
+((-4451 . T) (-4450 . T)) 
 NIL 
-(-1287 R) 
+(-1289 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]\\spad{*v} + A[2]*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 
-(-1288 K R UP -1384) 
+(-1290 K R UP -1386) 
 ((|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 
-(-1289) 
+(-1291) 
 ((|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 
-(-1290) 
+(-1292) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1291 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1293 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: \\spad{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)"))) 
-((-4449 |has| |#1| (-174)) (-4448 |has| |#1| (-174)) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370)))) 
-(-1292 R E V P) 
+((-4451 |has| |#1| (-174)) (-4450 |has| |#1| (-174)) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) 
+(-1294 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}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{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 = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{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{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) 
-((-4455 . T) (-4454 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#4| (LIST (QUOTE -315) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -622) (QUOTE (-544)))) (|HasCategory| |#4| (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-564))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#4| (LIST (QUOTE -621) (QUOTE (-870))))) 
-(-1293 R) 
+((-4457 . T) (-4456 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) 
+(-1295 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.\\spad{fr})"))) 
-((-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1294 |vl| R) 
+(-1296 |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."))) 
-((-4451 . T) (-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4447))) 
-(-1295 R |VarSet| XPOLY) 
+((-4453 . T) (-4449 |has| |#2| (-6 -4449)) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4449))) 
+(-1297 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.\\spad{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 
-(-1296 |vl| R) 
+(-1298 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+((-4449 |has| |#2| (-6 -4449)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-1297 S -1384) 
+(-1299 S -1386) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-1298 -1384) 
+((|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) 
+(-1300 -1386) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4446 . T) (-4452 . T) (-4447 . T) ((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+((-4448 . T) (-4454 . T) (-4449 . T) ((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
-(-1299 |VarSet| R) 
+(-1301 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) 
-((-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -725) (LIST (QUOTE -415) (QUOTE (-572))))) (|HasAttribute| |#2| (QUOTE -4447))) 
-(-1300 |vl| R) 
+((-4449 |has| |#2| (-6 -4449)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -727) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasAttribute| |#2| (QUOTE -4449))) 
+(-1302 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) 
+((-4449 |has| |#2| (-6 -4449)) (-4451 . T) (-4450 . T) (-4453 . T)) 
 NIL 
-(-1301 R) 
+(-1303 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4447 |has| |#1| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4447))) 
-(-1302 R E) 
+((-4449 |has| |#1| (-6 -4449)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4449))) 
+(-1304 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-4451 . T) (-4452 |has| |#1| (-6 -4452)) (-4447 |has| |#1| (-6 -4447)) (-4449 . T) (-4448 . T)) 
-((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-370))) (|HasAttribute| |#1| (QUOTE -4451)) (|HasAttribute| |#1| (QUOTE -4452)) (|HasAttribute| |#1| (QUOTE -4447))) 
-(-1303 |VarSet| R) 
+((-4453 . T) (-4454 |has| |#1| (-6 -4454)) (-4449 |has| |#1| (-6 -4449)) (-4451 . T) (-4450 . T)) 
+((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4453)) (|HasAttribute| |#1| (QUOTE -4454)) (|HasAttribute| |#1| (QUOTE -4449))) 
+(-1305 |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."))) 
-((-4447 |has| |#2| (-6 -4447)) (-4449 . T) (-4448 . T) (-4451 . T)) 
-((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4447))) 
-(-1304) 
+((-4449 |has| |#2| (-6 -4449)) (-4451 . T) (-4450 . T) (-4453 . T)) 
+((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4449))) 
+(-1306) 
 ((|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 
-(-1305 A) 
+(-1307 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 
-(-1306 R |ls| |ls2|) 
+(-1308 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}(\\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{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}(\\spad{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 
-(-1307 R) 
+(-1309 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}\\spad{'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}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1308 |p|) 
+(-1310 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4456 "*") . T) (-4448 . T) (-4449 . T) (-4451 . T)) 
+(((-4458 "*") . T) (-4450 . T) (-4451 . T) (-4453 . T)) 
 NIL 
 NIL 
 NIL 
@@ -5180,4 +5188,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2267465 2267470 2267475 2267480) (-2 NIL 2267445 2267450 2267455 2267460) (-1 NIL 2267425 2267430 2267435 2267440) (0 NIL 2267405 2267410 2267415 2267420) (-1308 "ZMOD.spad" 2267214 2267227 2267343 2267400) (-1307 "ZLINDEP.spad" 2266280 2266291 2267204 2267209) (-1306 "ZDSOLVE.spad" 2256225 2256247 2266270 2266275) (-1305 "YSTREAM.spad" 2255720 2255731 2256215 2256220) (-1304 "YDIAGRAM.spad" 2255354 2255363 2255710 2255715) (-1303 "XRPOLY.spad" 2254574 2254594 2255210 2255279) (-1302 "XPR.spad" 2252369 2252382 2254292 2254391) (-1301 "XPOLY.spad" 2251924 2251935 2252225 2252294) (-1300 "XPOLYC.spad" 2251243 2251259 2251850 2251919) (-1299 "XPBWPOLY.spad" 2249680 2249700 2251023 2251092) (-1298 "XF.spad" 2248143 2248158 2249582 2249675) (-1297 "XF.spad" 2246586 2246603 2248027 2248032) (-1296 "XFALG.spad" 2243634 2243650 2246512 2246581) (-1295 "XEXPPKG.spad" 2242885 2242911 2243624 2243629) (-1294 "XDPOLY.spad" 2242499 2242515 2242741 2242810) (-1293 "XALG.spad" 2242159 2242170 2242455 2242494) (-1292 "WUTSET.spad" 2237998 2238015 2241805 2241832) (-1291 "WP.spad" 2237197 2237241 2237856 2237923) (-1290 "WHILEAST.spad" 2236995 2237004 2237187 2237192) (-1289 "WHEREAST.spad" 2236666 2236675 2236985 2236990) (-1288 "WFFINTBS.spad" 2234329 2234351 2236656 2236661) (-1287 "WEIER.spad" 2232551 2232562 2234319 2234324) (-1286 "VSPACE.spad" 2232224 2232235 2232519 2232546) (-1285 "VSPACE.spad" 2231917 2231930 2232214 2232219) (-1284 "VOID.spad" 2231594 2231603 2231907 2231912) (-1283 "VIEW.spad" 2229274 2229283 2231584 2231589) (-1282 "VIEWDEF.spad" 2224475 2224484 2229264 2229269) (-1281 "VIEW3D.spad" 2208436 2208445 2224465 2224470) (-1280 "VIEW2D.spad" 2196327 2196336 2208426 2208431) (-1279 "VECTOR.spad" 2195001 2195012 2195252 2195279) (-1278 "VECTOR2.spad" 2193640 2193653 2194991 2194996) (-1277 "VECTCAT.spad" 2191544 2191555 2193608 2193635) (-1276 "VECTCAT.spad" 2189255 2189268 2191321 2191326) (-1275 "VARIABLE.spad" 2189035 2189050 2189245 2189250) 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2146195 2148282 2148287) (-1255 "UPOLYC.spad" 2141209 2141220 2146011 2146164) (-1254 "UPOLYC.spad" 2136141 2136154 2140945 2140950) (-1253 "UPOLYC2.spad" 2135612 2135631 2136131 2136136) (-1252 "UP.spad" 2132811 2132826 2133198 2133351) (-1251 "UPMP.spad" 2131711 2131724 2132801 2132806) (-1250 "UPDIVP.spad" 2131276 2131290 2131701 2131706) (-1249 "UPDECOMP.spad" 2129521 2129535 2131266 2131271) (-1248 "UPCDEN.spad" 2128730 2128746 2129511 2129516) (-1247 "UP2.spad" 2128094 2128115 2128720 2128725) (-1246 "UNISEG.spad" 2127447 2127458 2128013 2128018) (-1245 "UNISEG2.spad" 2126944 2126957 2127403 2127408) (-1244 "UNIFACT.spad" 2126047 2126059 2126934 2126939) (-1243 "ULS.spad" 2116605 2116633 2117692 2118121) (-1242 "ULSCONS.spad" 2109001 2109021 2109371 2109520) (-1241 "ULSCCAT.spad" 2106738 2106758 2108847 2108996) (-1240 "ULSCCAT.spad" 2104583 2104605 2106694 2106699) (-1239 "ULSCAT.spad" 2102815 2102831 2104429 2104578) (-1238 "ULS2.spad" 2102329 2102382 2102805 2102810) (-1237 "UINT8.spad" 2102206 2102215 2102319 2102324) (-1236 "UINT64.spad" 2102082 2102091 2102196 2102201) (-1235 "UINT32.spad" 2101958 2101967 2102072 2102077) (-1234 "UINT16.spad" 2101834 2101843 2101948 2101953) (-1233 "UFD.spad" 2100899 2100908 2101760 2101829) (-1232 "UFD.spad" 2100026 2100037 2100889 2100894) (-1231 "UDVO.spad" 2098907 2098916 2100016 2100021) (-1230 "UDPO.spad" 2096400 2096411 2098863 2098868) (-1229 "TYPE.spad" 2096332 2096341 2096390 2096395) (-1228 "TYPEAST.spad" 2096251 2096260 2096322 2096327) (-1227 "TWOFACT.spad" 2094903 2094918 2096241 2096246) (-1226 "TUPLE.spad" 2094389 2094400 2094802 2094807) (-1225 "TUBETOOL.spad" 2091256 2091265 2094379 2094384) (-1224 "TUBE.spad" 2089903 2089920 2091246 2091251) (-1223 "TS.spad" 2088502 2088518 2089468 2089565) (-1222 "TSETCAT.spad" 2075629 2075646 2088470 2088497) (-1221 "TSETCAT.spad" 2062742 2062761 2075585 2075590) (-1220 "TRMANIP.spad" 2057108 2057125 2062448 2062453) (-1219 "TRIMAT.spad" 2056071 2056096 2057098 2057103) (-1218 "TRIGMNIP.spad" 2054598 2054615 2056061 2056066) (-1217 "TRIGCAT.spad" 2054110 2054119 2054588 2054593) (-1216 "TRIGCAT.spad" 2053620 2053631 2054100 2054105) (-1215 "TREE.spad" 2052195 2052206 2053227 2053254) (-1214 "TRANFUN.spad" 2052034 2052043 2052185 2052190) (-1213 "TRANFUN.spad" 2051871 2051882 2052024 2052029) (-1212 "TOPSP.spad" 2051545 2051554 2051861 2051866) (-1211 "TOOLSIGN.spad" 2051208 2051219 2051535 2051540) (-1210 "TEXTFILE.spad" 2049769 2049778 2051198 2051203) (-1209 "TEX.spad" 2046915 2046924 2049759 2049764) (-1208 "TEX1.spad" 2046471 2046482 2046905 2046910) (-1207 "TEMUTL.spad" 2046026 2046035 2046461 2046466) (-1206 "TBCMPPK.spad" 2044119 2044142 2046016 2046021) (-1205 "TBAGG.spad" 2043169 2043192 2044099 2044114) (-1204 "TBAGG.spad" 2042227 2042252 2043159 2043164) (-1203 "TANEXP.spad" 2041635 2041646 2042217 2042222) (-1202 "TALGOP.spad" 2041359 2041370 2041625 2041630) (-1201 "TABLE.spad" 2039770 2039793 2040040 2040067) (-1200 "TABLEAU.spad" 2039251 2039262 2039760 2039765) (-1199 "TABLBUMP.spad" 2036054 2036065 2039241 2039246) (-1198 "SYSTEM.spad" 2035282 2035291 2036044 2036049) (-1197 "SYSSOLP.spad" 2032765 2032776 2035272 2035277) (-1196 "SYSPTR.spad" 2032664 2032673 2032755 2032760) (-1195 "SYSNNI.spad" 2031846 2031857 2032654 2032659) (-1194 "SYSINT.spad" 2031250 2031261 2031836 2031841) (-1193 "SYNTAX.spad" 2027456 2027465 2031240 2031245) (-1192 "SYMTAB.spad" 2025524 2025533 2027446 2027451) (-1191 "SYMS.spad" 2021547 2021556 2025514 2025519) (-1190 "SYMPOLY.spad" 2020554 2020565 2020636 2020763) (-1189 "SYMFUNC.spad" 2020055 2020066 2020544 2020549) (-1188 "SYMBOL.spad" 2017558 2017567 2020045 2020050) (-1187 "SWITCH.spad" 2014329 2014338 2017548 2017553) (-1186 "SUTS.spad" 2011234 2011262 2012796 2012893) (-1185 "SUPXS.spad" 2008375 2008403 2009366 2009515) (-1184 "SUP.spad" 2005188 2005199 2005961 2006114) (-1183 "SUPFRACF.spad" 2004293 2004311 2005178 2005183) (-1182 "SUP2.spad" 2003685 2003698 2004283 2004288) (-1181 "SUMRF.spad" 2002659 2002670 2003675 2003680) (-1180 "SUMFS.spad" 2002296 2002313 2002649 2002654) (-1179 "SULS.spad" 1992841 1992869 1993941 1994370) (-1178 "SUCHTAST.spad" 1992610 1992619 1992831 1992836) (-1177 "SUCH.spad" 1992292 1992307 1992600 1992605) (-1176 "SUBSPACE.spad" 1984407 1984422 1992282 1992287) (-1175 "SUBRESP.spad" 1983577 1983591 1984363 1984368) (-1174 "STTF.spad" 1979676 1979692 1983567 1983572) (-1173 "STTFNC.spad" 1976144 1976160 1979666 1979671) (-1172 "STTAYLOR.spad" 1968779 1968790 1976025 1976030) (-1171 "STRTBL.spad" 1967284 1967301 1967433 1967460) (-1170 "STRING.spad" 1966693 1966702 1966707 1966734) (-1169 "STRICAT.spad" 1966481 1966490 1966661 1966688) (-1168 "STREAM.spad" 1963399 1963410 1966006 1966021) (-1167 "STREAM3.spad" 1962972 1962987 1963389 1963394) (-1166 "STREAM2.spad" 1962100 1962113 1962962 1962967) (-1165 "STREAM1.spad" 1961806 1961817 1962090 1962095) (-1164 "STINPROD.spad" 1960742 1960758 1961796 1961801) (-1163 "STEP.spad" 1959943 1959952 1960732 1960737) (-1162 "STEPAST.spad" 1959177 1959186 1959933 1959938) (-1161 "STBL.spad" 1957703 1957731 1957870 1957885) (-1160 "STAGG.spad" 1956778 1956789 1957693 1957698) (-1159 "STAGG.spad" 1955851 1955864 1956768 1956773) (-1158 "STACK.spad" 1955208 1955219 1955458 1955485) (-1157 "SREGSET.spad" 1952912 1952929 1954854 1954881) (-1156 "SRDCMPK.spad" 1951473 1951493 1952902 1952907) (-1155 "SRAGG.spad" 1946616 1946625 1951441 1951468) (-1154 "SRAGG.spad" 1941779 1941790 1946606 1946611) (-1153 "SQMATRIX.spad" 1939451 1939469 1940367 1940454) (-1152 "SPLTREE.spad" 1934003 1934016 1938887 1938914) (-1151 "SPLNODE.spad" 1930591 1930604 1933993 1933998) (-1150 "SPFCAT.spad" 1929400 1929409 1930581 1930586) (-1149 "SPECOUT.spad" 1927952 1927961 1929390 1929395) (-1148 "SPADXPT.spad" 1919547 1919556 1927942 1927947) (-1147 "spad-parser.spad" 1919012 1919021 1919537 1919542) (-1146 "SPADAST.spad" 1918713 1918722 1919002 1919007) (-1145 "SPACEC.spad" 1902912 1902923 1918703 1918708) (-1144 "SPACE3.spad" 1902688 1902699 1902902 1902907) (-1143 "SORTPAK.spad" 1902237 1902250 1902644 1902649) (-1142 "SOLVETRA.spad" 1900000 1900011 1902227 1902232) (-1141 "SOLVESER.spad" 1898528 1898539 1899990 1899995) (-1140 "SOLVERAD.spad" 1894554 1894565 1898518 1898523) (-1139 "SOLVEFOR.spad" 1893016 1893034 1894544 1894549) (-1138 "SNTSCAT.spad" 1892616 1892633 1892984 1893011) (-1137 "SMTS.spad" 1890888 1890914 1892181 1892278) (-1136 "SMP.spad" 1888363 1888383 1888753 1888880) (-1135 "SMITH.spad" 1887208 1887233 1888353 1888358) (-1134 "SMATCAT.spad" 1885318 1885348 1887152 1887203) (-1133 "SMATCAT.spad" 1883360 1883392 1885196 1885201) (-1132 "SKAGG.spad" 1882323 1882334 1883328 1883355) (-1131 "SINT.spad" 1881263 1881272 1882189 1882318) (-1130 "SIMPAN.spad" 1880991 1881000 1881253 1881258) (-1129 "SIG.spad" 1880321 1880330 1880981 1880986) (-1128 "SIGNRF.spad" 1879439 1879450 1880311 1880316) (-1127 "SIGNEF.spad" 1878718 1878735 1879429 1879434) (-1126 "SIGAST.spad" 1878103 1878112 1878708 1878713) (-1125 "SHP.spad" 1876031 1876046 1878059 1878064) (-1124 "SHDP.spad" 1865665 1865692 1866174 1866305) (-1123 "SGROUP.spad" 1865273 1865282 1865655 1865660) (-1122 "SGROUP.spad" 1864879 1864890 1865263 1865268) (-1121 "SGCF.spad" 1858018 1858027 1864869 1864874) (-1120 "SFRTCAT.spad" 1856948 1856965 1857986 1858013) (-1119 "SFRGCD.spad" 1856011 1856031 1856938 1856943) (-1118 "SFQCMPK.spad" 1850648 1850668 1856001 1856006) (-1117 "SFORT.spad" 1850087 1850101 1850638 1850643) (-1116 "SEXOF.spad" 1849930 1849970 1850077 1850082) (-1115 "SEX.spad" 1849822 1849831 1849920 1849925) (-1114 "SEXCAT.spad" 1847603 1847643 1849812 1849817) (-1113 "SET.spad" 1845927 1845938 1847024 1847063) (-1112 "SETMN.spad" 1844377 1844394 1845917 1845922) (-1111 "SETCAT.spad" 1843699 1843708 1844367 1844372) (-1110 "SETCAT.spad" 1843019 1843030 1843689 1843694) (-1109 "SETAGG.spad" 1839568 1839579 1842999 1843014) (-1108 "SETAGG.spad" 1836125 1836138 1839558 1839563) (-1107 "SEQAST.spad" 1835828 1835837 1836115 1836120) (-1106 "SEGXCAT.spad" 1834984 1834997 1835818 1835823) (-1105 "SEG.spad" 1834797 1834808 1834903 1834908) (-1104 "SEGCAT.spad" 1833722 1833733 1834787 1834792) (-1103 "SEGBIND.spad" 1833480 1833491 1833669 1833674) (-1102 "SEGBIND2.spad" 1833178 1833191 1833470 1833475) (-1101 "SEGAST.spad" 1832892 1832901 1833168 1833173) (-1100 "SEG2.spad" 1832327 1832340 1832848 1832853) (-1099 "SDVAR.spad" 1831603 1831614 1832317 1832322) (-1098 "SDPOL.spad" 1829029 1829040 1829320 1829447) (-1097 "SCPKG.spad" 1827118 1827129 1829019 1829024) (-1096 "SCOPE.spad" 1826271 1826280 1827108 1827113) (-1095 "SCACHE.spad" 1824967 1824978 1826261 1826266) (-1094 "SASTCAT.spad" 1824876 1824885 1824957 1824962) (-1093 "SAOS.spad" 1824748 1824757 1824866 1824871) (-1092 "SAERFFC.spad" 1824461 1824481 1824738 1824743) (-1091 "SAE.spad" 1822636 1822652 1823247 1823382) (-1090 "SAEFACT.spad" 1822337 1822357 1822626 1822631) (-1089 "RURPK.spad" 1819996 1820012 1822327 1822332) (-1088 "RULESET.spad" 1819449 1819473 1819986 1819991) (-1087 "RULE.spad" 1817689 1817713 1819439 1819444) (-1086 "RULECOLD.spad" 1817541 1817554 1817679 1817684) (-1085 "RTVALUE.spad" 1817276 1817285 1817531 1817536) (-1084 "RSTRCAST.spad" 1816993 1817002 1817266 1817271) (-1083 "RSETGCD.spad" 1813371 1813391 1816983 1816988) (-1082 "RSETCAT.spad" 1803307 1803324 1813339 1813366) (-1081 "RSETCAT.spad" 1793263 1793282 1803297 1803302) (-1080 "RSDCMPK.spad" 1791715 1791735 1793253 1793258) (-1079 "RRCC.spad" 1790099 1790129 1791705 1791710) (-1078 "RRCC.spad" 1788481 1788513 1790089 1790094) (-1077 "RPTAST.spad" 1788183 1788192 1788471 1788476) (-1076 "RPOLCAT.spad" 1767543 1767558 1788051 1788178) (-1075 "RPOLCAT.spad" 1746616 1746633 1767126 1767131) (-1074 "ROUTINE.spad" 1742499 1742508 1745263 1745290) (-1073 "ROMAN.spad" 1741827 1741836 1742365 1742494) (-1072 "ROIRC.spad" 1740907 1740939 1741817 1741822) (-1071 "RNS.spad" 1739810 1739819 1740809 1740902) (-1070 "RNS.spad" 1738799 1738810 1739800 1739805) (-1069 "RNG.spad" 1738534 1738543 1738789 1738794) (-1068 "RNGBIND.spad" 1737694 1737708 1738489 1738494) (-1067 "RMODULE.spad" 1737459 1737470 1737684 1737689) (-1066 "RMCAT2.spad" 1736879 1736936 1737449 1737454) (-1065 "RMATRIX.spad" 1735703 1735722 1736046 1736085) (-1064 "RMATCAT.spad" 1731282 1731313 1735659 1735698) (-1063 "RMATCAT.spad" 1726751 1726784 1731130 1731135) (-1062 "RLINSET.spad" 1726145 1726156 1726741 1726746) (-1061 "RINTERP.spad" 1726033 1726053 1726135 1726140) (-1060 "RING.spad" 1725503 1725512 1726013 1726028) (-1059 "RING.spad" 1724981 1724992 1725493 1725498) (-1058 "RIDIST.spad" 1724373 1724382 1724971 1724976) (-1057 "RGCHAIN.spad" 1722956 1722972 1723858 1723885) (-1056 "RGBCSPC.spad" 1722737 1722749 1722946 1722951) (-1055 "RGBCMDL.spad" 1722267 1722279 1722727 1722732) (-1054 "RF.spad" 1719909 1719920 1722257 1722262) (-1053 "RFFACTOR.spad" 1719371 1719382 1719899 1719904) (-1052 "RFFACT.spad" 1719106 1719118 1719361 1719366) (-1051 "RFDIST.spad" 1718102 1718111 1719096 1719101) (-1050 "RETSOL.spad" 1717521 1717534 1718092 1718097) (-1049 "RETRACT.spad" 1716949 1716960 1717511 1717516) (-1048 "RETRACT.spad" 1716375 1716388 1716939 1716944) (-1047 "RETAST.spad" 1716187 1716196 1716365 1716370) (-1046 "RESULT.spad" 1714247 1714256 1714834 1714861) (-1045 "RESRING.spad" 1713594 1713641 1714185 1714242) (-1044 "RESLATC.spad" 1712918 1712929 1713584 1713589) (-1043 "REPSQ.spad" 1712649 1712660 1712908 1712913) (-1042 "REP.spad" 1710203 1710212 1712639 1712644) (-1041 "REPDB.spad" 1709910 1709921 1710193 1710198) (-1040 "REP2.spad" 1699568 1699579 1709752 1709757) (-1039 "REP1.spad" 1693764 1693775 1699518 1699523) (-1038 "REGSET.spad" 1691561 1691578 1693410 1693437) (-1037 "REF.spad" 1690896 1690907 1691516 1691521) (-1036 "REDORDER.spad" 1690102 1690119 1690886 1690891) (-1035 "RECLOS.spad" 1688885 1688905 1689589 1689682) (-1034 "REALSOLV.spad" 1688025 1688034 1688875 1688880) (-1033 "REAL.spad" 1687897 1687906 1688015 1688020) (-1032 "REAL0Q.spad" 1685195 1685210 1687887 1687892) (-1031 "REAL0.spad" 1682039 1682054 1685185 1685190) (-1030 "RDUCEAST.spad" 1681760 1681769 1682029 1682034) (-1029 "RDIV.spad" 1681415 1681440 1681750 1681755) (-1028 "RDIST.spad" 1680982 1680993 1681405 1681410) (-1027 "RDETRS.spad" 1679846 1679864 1680972 1680977) (-1026 "RDETR.spad" 1677985 1678003 1679836 1679841) (-1025 "RDEEFS.spad" 1677084 1677101 1677975 1677980) (-1024 "RDEEF.spad" 1676094 1676111 1677074 1677079) (-1023 "RCFIELD.spad" 1673280 1673289 1675996 1676089) (-1022 "RCFIELD.spad" 1670552 1670563 1673270 1673275) (-1021 "RCAGG.spad" 1668480 1668491 1670542 1670547) (-1020 "RCAGG.spad" 1666335 1666348 1668399 1668404) (-1019 "RATRET.spad" 1665695 1665706 1666325 1666330) (-1018 "RATFACT.spad" 1665387 1665399 1665685 1665690) (-1017 "RANDSRC.spad" 1664706 1664715 1665377 1665382) (-1016 "RADUTIL.spad" 1664462 1664471 1664696 1664701) (-1015 "RADIX.spad" 1661383 1661397 1662929 1663022) (-1014 "RADFF.spad" 1659796 1659833 1659915 1660071) (-1013 "RADCAT.spad" 1659391 1659400 1659786 1659791) (-1012 "RADCAT.spad" 1658984 1658995 1659381 1659386) (-1011 "QUEUE.spad" 1658332 1658343 1658591 1658618) (-1010 "QUAT.spad" 1656790 1656801 1657133 1657198) (-1009 "QUATCT2.spad" 1656410 1656429 1656780 1656785) (-1008 "QUATCAT.spad" 1654580 1654591 1656340 1656405) (-1007 "QUATCAT.spad" 1652501 1652514 1654263 1654268) (-1006 "QUAGG.spad" 1651328 1651339 1652469 1652496) (-1005 "QQUTAST.spad" 1651096 1651105 1651318 1651323) (-1004 "QFORM.spad" 1650714 1650729 1651086 1651091) (-1003 "QFCAT.spad" 1649416 1649427 1650616 1650709) (-1002 "QFCAT.spad" 1647709 1647722 1648911 1648916) (-1001 "QFCAT2.spad" 1647401 1647418 1647699 1647704) (-1000 "QEQUAT.spad" 1646959 1646968 1647391 1647396) (-999 "QCMPACK.spad" 1641706 1641725 1646949 1646954) (-998 "QALGSET.spad" 1637785 1637817 1641620 1641625) (-997 "QALGSET2.spad" 1635781 1635799 1637775 1637780) (-996 "PWFFINTB.spad" 1633197 1633218 1635771 1635776) (-995 "PUSHVAR.spad" 1632536 1632555 1633187 1633192) (-994 "PTRANFN.spad" 1628664 1628674 1632526 1632531) (-993 "PTPACK.spad" 1625752 1625762 1628654 1628659) (-992 "PTFUNC2.spad" 1625575 1625589 1625742 1625747) (-991 "PTCAT.spad" 1624830 1624840 1625543 1625570) (-990 "PSQFR.spad" 1624137 1624161 1624820 1624825) (-989 "PSEUDLIN.spad" 1623023 1623033 1624127 1624132) (-988 "PSETPK.spad" 1608456 1608472 1622901 1622906) (-987 "PSETCAT.spad" 1602376 1602399 1608436 1608451) (-986 "PSETCAT.spad" 1596270 1596295 1602332 1602337) (-985 "PSCURVE.spad" 1595253 1595261 1596260 1596265) (-984 "PSCAT.spad" 1594036 1594065 1595151 1595248) (-983 "PSCAT.spad" 1592909 1592940 1594026 1594031) (-982 "PRTITION.spad" 1591607 1591615 1592899 1592904) (-981 "PRTDAST.spad" 1591326 1591334 1591597 1591602) (-980 "PRS.spad" 1580888 1580905 1591282 1591287) (-979 "PRQAGG.spad" 1580323 1580333 1580856 1580883) (-978 "PROPLOG.spad" 1579895 1579903 1580313 1580318) (-977 "PROPFUN2.spad" 1579518 1579531 1579885 1579890) (-976 "PROPFUN1.spad" 1578916 1578927 1579508 1579513) (-975 "PROPFRML.spad" 1577484 1577495 1578906 1578911) (-974 "PROPERTY.spad" 1576972 1576980 1577474 1577479) (-973 "PRODUCT.spad" 1574654 1574666 1574938 1574993) (-972 "PR.spad" 1573046 1573058 1573745 1573872) (-971 "PRINT.spad" 1572798 1572806 1573036 1573041) (-970 "PRIMES.spad" 1571051 1571061 1572788 1572793) (-969 "PRIMELT.spad" 1569132 1569146 1571041 1571046) (-968 "PRIMCAT.spad" 1568759 1568767 1569122 1569127) (-967 "PRIMARR.spad" 1567764 1567774 1567942 1567969) (-966 "PRIMARR2.spad" 1566531 1566543 1567754 1567759) (-965 "PREASSOC.spad" 1565913 1565925 1566521 1566526) (-964 "PPCURVE.spad" 1565050 1565058 1565903 1565908) (-963 "PORTNUM.spad" 1564825 1564833 1565040 1565045) (-962 "POLYROOT.spad" 1563674 1563696 1564781 1564786) (-961 "POLY.spad" 1561009 1561019 1561524 1561651) (-960 "POLYLIFT.spad" 1560274 1560297 1560999 1561004) (-959 "POLYCATQ.spad" 1558392 1558414 1560264 1560269) (-958 "POLYCAT.spad" 1551862 1551883 1558260 1558387) (-957 "POLYCAT.spad" 1544670 1544693 1551070 1551075) (-956 "POLY2UP.spad" 1544122 1544136 1544660 1544665) (-955 "POLY2.spad" 1543719 1543731 1544112 1544117) (-954 "POLUTIL.spad" 1542660 1542689 1543675 1543680) (-953 "POLTOPOL.spad" 1541408 1541423 1542650 1542655) (-952 "POINT.spad" 1540246 1540256 1540333 1540360) (-951 "PNTHEORY.spad" 1536948 1536956 1540236 1540241) (-950 "PMTOOLS.spad" 1535723 1535737 1536938 1536943) (-949 "PMSYM.spad" 1535272 1535282 1535713 1535718) (-948 "PMQFCAT.spad" 1534863 1534877 1535262 1535267) (-947 "PMPRED.spad" 1534342 1534356 1534853 1534858) (-946 "PMPREDFS.spad" 1533796 1533818 1534332 1534337) (-945 "PMPLCAT.spad" 1532876 1532894 1533728 1533733) (-944 "PMLSAGG.spad" 1532461 1532475 1532866 1532871) (-943 "PMKERNEL.spad" 1532040 1532052 1532451 1532456) (-942 "PMINS.spad" 1531620 1531630 1532030 1532035) (-941 "PMFS.spad" 1531197 1531215 1531610 1531615) (-940 "PMDOWN.spad" 1530487 1530501 1531187 1531192) (-939 "PMASS.spad" 1529497 1529505 1530477 1530482) (-938 "PMASSFS.spad" 1528464 1528480 1529487 1529492) (-937 "PLOTTOOL.spad" 1528244 1528252 1528454 1528459) (-936 "PLOT.spad" 1523167 1523175 1528234 1528239) (-935 "PLOT3D.spad" 1519631 1519639 1523157 1523162) (-934 "PLOT1.spad" 1518788 1518798 1519621 1519626) (-933 "PLEQN.spad" 1506078 1506105 1518778 1518783) (-932 "PINTERP.spad" 1505700 1505719 1506068 1506073) (-931 "PINTERPA.spad" 1505484 1505500 1505690 1505695) (-930 "PI.spad" 1505093 1505101 1505458 1505479) (-929 "PID.spad" 1504063 1504071 1505019 1505088) (-928 "PICOERCE.spad" 1503720 1503730 1504053 1504058) (-927 "PGROEB.spad" 1502321 1502335 1503710 1503715) (-926 "PGE.spad" 1493938 1493946 1502311 1502316) (-925 "PGCD.spad" 1492828 1492845 1493928 1493933) (-924 "PFRPAC.spad" 1491977 1491987 1492818 1492823) (-923 "PFR.spad" 1488640 1488650 1491879 1491972) (-922 "PFOTOOLS.spad" 1487898 1487914 1488630 1488635) (-921 "PFOQ.spad" 1487268 1487286 1487888 1487893) (-920 "PFO.spad" 1486687 1486714 1487258 1487263) (-919 "PF.spad" 1486261 1486273 1486492 1486585) (-918 "PFECAT.spad" 1483943 1483951 1486187 1486256) (-917 "PFECAT.spad" 1481653 1481663 1483899 1483904) (-916 "PFBRU.spad" 1479541 1479553 1481643 1481648) (-915 "PFBR.spad" 1477101 1477124 1479531 1479536) (-914 "PERM.spad" 1472908 1472918 1476931 1476946) (-913 "PERMGRP.spad" 1467678 1467688 1472898 1472903) (-912 "PERMCAT.spad" 1466339 1466349 1467658 1467673) (-911 "PERMAN.spad" 1464871 1464885 1466329 1466334) (-910 "PENDTREE.spad" 1464212 1464222 1464500 1464505) (-909 "PDRING.spad" 1462763 1462773 1464192 1464207) (-908 "PDRING.spad" 1461322 1461334 1462753 1462758) (-907 "PDEPROB.spad" 1460337 1460345 1461312 1461317) (-906 "PDEPACK.spad" 1454377 1454385 1460327 1460332) (-905 "PDECOMP.spad" 1453847 1453864 1454367 1454372) (-904 "PDECAT.spad" 1452203 1452211 1453837 1453842) (-903 "PCOMP.spad" 1452056 1452069 1452193 1452198) (-902 "PBWLB.spad" 1450644 1450661 1452046 1452051) (-901 "PATTERN.spad" 1445183 1445193 1450634 1450639) (-900 "PATTERN2.spad" 1444921 1444933 1445173 1445178) (-899 "PATTERN1.spad" 1443257 1443273 1444911 1444916) (-898 "PATRES.spad" 1440832 1440844 1443247 1443252) (-897 "PATRES2.spad" 1440504 1440518 1440822 1440827) (-896 "PATMATCH.spad" 1438701 1438732 1440212 1440217) (-895 "PATMAB.spad" 1438130 1438140 1438691 1438696) (-894 "PATLRES.spad" 1437216 1437230 1438120 1438125) (-893 "PATAB.spad" 1436980 1436990 1437206 1437211) (-892 "PARTPERM.spad" 1434988 1434996 1436970 1436975) (-891 "PARSURF.spad" 1434422 1434450 1434978 1434983) (-890 "PARSU2.spad" 1434219 1434235 1434412 1434417) (-889 "script-parser.spad" 1433739 1433747 1434209 1434214) (-888 "PARSCURV.spad" 1433173 1433201 1433729 1433734) (-887 "PARSC2.spad" 1432964 1432980 1433163 1433168) (-886 "PARPCURV.spad" 1432426 1432454 1432954 1432959) (-885 "PARPC2.spad" 1432217 1432233 1432416 1432421) (-884 "PARAMAST.spad" 1431345 1431353 1432207 1432212) (-883 "PAN2EXPR.spad" 1430757 1430765 1431335 1431340) (-882 "PALETTE.spad" 1429727 1429735 1430747 1430752) (-881 "PAIR.spad" 1428714 1428727 1429315 1429320) (-880 "PADICRC.spad" 1426048 1426066 1427219 1427312) (-879 "PADICRAT.spad" 1424063 1424075 1424284 1424377) (-878 "PADIC.spad" 1423758 1423770 1423989 1424058) (-877 "PADICCT.spad" 1422307 1422319 1423684 1423753) (-876 "PADEPAC.spad" 1420996 1421015 1422297 1422302) (-875 "PADE.spad" 1419748 1419764 1420986 1420991) (-874 "OWP.spad" 1418988 1419018 1419606 1419673) (-873 "OVERSET.spad" 1418561 1418569 1418978 1418983) (-872 "OVAR.spad" 1418342 1418365 1418551 1418556) (-871 "OUT.spad" 1417428 1417436 1418332 1418337) (-870 "OUTFORM.spad" 1406820 1406828 1417418 1417423) (-869 "OUTBFILE.spad" 1406238 1406246 1406810 1406815) (-868 "OUTBCON.spad" 1405244 1405252 1406228 1406233) (-867 "OUTBCON.spad" 1404248 1404258 1405234 1405239) (-866 "OSI.spad" 1403723 1403731 1404238 1404243) (-865 "OSGROUP.spad" 1403641 1403649 1403713 1403718) (-864 "ORTHPOL.spad" 1402126 1402136 1403558 1403563) (-863 "OREUP.spad" 1401579 1401607 1401806 1401845) (-862 "ORESUP.spad" 1400880 1400904 1401259 1401298) (-861 "OREPCTO.spad" 1398737 1398749 1400800 1400805) (-860 "OREPCAT.spad" 1392884 1392894 1398693 1398732) (-859 "OREPCAT.spad" 1386921 1386933 1392732 1392737) (-858 "ORDSET.spad" 1386093 1386101 1386911 1386916) (-857 "ORDSET.spad" 1385263 1385273 1386083 1386088) (-856 "ORDRING.spad" 1384653 1384661 1385243 1385258) (-855 "ORDRING.spad" 1384051 1384061 1384643 1384648) (-854 "ORDMON.spad" 1383906 1383914 1384041 1384046) (-853 "ORDFUNS.spad" 1383038 1383054 1383896 1383901) (-852 "ORDFIN.spad" 1382858 1382866 1383028 1383033) (-851 "ORDCOMP.spad" 1381323 1381333 1382405 1382434) (-850 "ORDCOMP2.spad" 1380616 1380628 1381313 1381318) (-849 "OPTPROB.spad" 1379254 1379262 1380606 1380611) (-848 "OPTPACK.spad" 1371663 1371671 1379244 1379249) (-847 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"HOAGG.spad" 821497 821507 824205 824210) (-496 "HOAGG.spad" 818554 818566 821264 821269) (-495 "HEXADEC.spad" 816656 816664 817021 817114) (-494 "HEUGCD.spad" 815691 815702 816646 816651) (-493 "HELLFDIV.spad" 815281 815305 815681 815686) (-492 "HEAP.spad" 814673 814683 814888 814915) (-491 "HEADAST.spad" 814206 814214 814663 814668) (-490 "HDP.spad" 803972 803988 804349 804480) (-489 "HDMP.spad" 801186 801201 801802 801929) (-488 "HB.spad" 799437 799445 801176 801181) (-487 "HASHTBL.spad" 797907 797938 798118 798145) (-486 "HASAST.spad" 797623 797631 797897 797902) (-485 "HACKPI.spad" 797114 797122 797525 797618) (-484 "GTSET.spad" 796053 796069 796760 796787) (-483 "GSTBL.spad" 794572 794607 794746 794761) (-482 "GSERIES.spad" 791743 791770 792704 792853) (-481 "GROUP.spad" 791016 791024 791723 791738) (-480 "GROUP.spad" 790297 790307 791006 791011) (-479 "GROEBSOL.spad" 788791 788812 790287 790292) (-478 "GRMOD.spad" 787362 787374 788781 788786) (-477 "GRMOD.spad" 785931 785945 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(-456 "GBF.spad" 742333 742371 746556 746561) (-455 "GBEUCLID.spad" 740215 740253 742323 742328) (-454 "GAUSSFAC.spad" 739528 739536 740205 740210) (-453 "GALUTIL.spad" 737854 737864 739484 739489) (-452 "GALPOLYU.spad" 736308 736321 737844 737849) (-451 "GALFACTU.spad" 734481 734500 736298 736303) (-450 "GALFACT.spad" 724670 724681 734471 734476) (-449 "FVFUN.spad" 721693 721701 724660 724665) (-448 "FVC.spad" 720745 720753 721683 721688) (-447 "FUNDESC.spad" 720423 720431 720735 720740) (-446 "FUNCTION.spad" 720272 720284 720413 720418) (-445 "FT.spad" 718569 718577 720262 720267) (-444 "FTEM.spad" 717734 717742 718559 718564) (-443 "FSUPFACT.spad" 716634 716653 717670 717675) (-442 "FST.spad" 714720 714728 716624 716629) (-441 "FSRED.spad" 714200 714216 714710 714715) (-440 "FSPRMELT.spad" 713082 713098 714157 714162) (-439 "FSPECF.spad" 711173 711189 713072 713077) (-438 "FS.spad" 705441 705451 710948 711168) (-437 "FS.spad" 699487 699499 704996 705001) (-436 "FSINT.spad" 699147 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270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-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 2268311 2268316 2268321 2268326) (-2 NIL 2268291 2268296 2268301 2268306) (-1 NIL 2268271 2268276 2268281 2268286) (0 NIL 2268251 2268256 2268261 2268266) (-1310 "ZMOD.spad" 2268060 2268073 2268189 2268246) (-1309 "ZLINDEP.spad" 2267126 2267137 2268050 2268055) (-1308 "ZDSOLVE.spad" 2257071 2257093 2267116 2267121) (-1307 "YSTREAM.spad" 2256566 2256577 2257061 2257066) (-1306 "YDIAGRAM.spad" 2256200 2256209 2256556 2256561) (-1305 "XRPOLY.spad" 2255420 2255440 2256056 2256125) (-1304 "XPR.spad" 2253215 2253228 2255138 2255237) (-1303 "XPOLY.spad" 2252770 2252781 2253071 2253140) (-1302 "XPOLYC.spad" 2252089 2252105 2252696 2252765) (-1301 "XPBWPOLY.spad" 2250526 2250546 2251869 2251938) (-1300 "XF.spad" 2248989 2249004 2250428 2250521) (-1299 "XF.spad" 2247432 2247449 2248873 2248878) (-1298 "XFALG.spad" 2244480 2244496 2247358 2247427) (-1297 "XEXPPKG.spad" 2243731 2243757 2244470 2244475) (-1296 "XDPOLY.spad" 2243345 2243361 2243587 2243656) (-1295 "XALG.spad" 2243005 2243016 2243301 2243340) (-1294 "WUTSET.spad" 2238844 2238861 2242651 2242678) (-1293 "WP.spad" 2238043 2238087 2238702 2238769) (-1292 "WHILEAST.spad" 2237841 2237850 2238033 2238038) (-1291 "WHEREAST.spad" 2237512 2237521 2237831 2237836) (-1290 "WFFINTBS.spad" 2235175 2235197 2237502 2237507) (-1289 "WEIER.spad" 2233397 2233408 2235165 2235170) (-1288 "VSPACE.spad" 2233070 2233081 2233365 2233392) (-1287 "VSPACE.spad" 2232763 2232776 2233060 2233065) (-1286 "VOID.spad" 2232440 2232449 2232753 2232758) (-1285 "VIEW.spad" 2230120 2230129 2232430 2232435) (-1284 "VIEWDEF.spad" 2225321 2225330 2230110 2230115) (-1283 "VIEW3D.spad" 2209282 2209291 2225311 2225316) (-1282 "VIEW2D.spad" 2197173 2197182 2209272 2209277) (-1281 "VECTOR.spad" 2195847 2195858 2196098 2196125) (-1280 "VECTOR2.spad" 2194486 2194499 2195837 2195842) (-1279 "VECTCAT.spad" 2192390 2192401 2194454 2194481) (-1278 "VECTCAT.spad" 2190101 2190114 2192167 2192172) (-1277 "VARIABLE.spad" 2189881 2189896 2190091 2190096) (-1276 "UTYPE.spad" 2189525 2189534 2189871 2189876) (-1275 "UTSODETL.spad" 2188820 2188844 2189481 2189486) (-1274 "UTSODE.spad" 2187036 2187056 2188810 2188815) (-1273 "UTS.spad" 2181840 2181868 2185503 2185600) (-1272 "UTSCAT.spad" 2179319 2179335 2181738 2181835) (-1271 "UTSCAT.spad" 2176442 2176460 2178863 2178868) (-1270 "UTS2.spad" 2176037 2176072 2176432 2176437) (-1269 "URAGG.spad" 2170710 2170721 2176027 2176032) (-1268 "URAGG.spad" 2165347 2165360 2170666 2170671) (-1267 "UPXSSING.spad" 2162992 2163018 2164428 2164561) (-1266 "UPXS.spad" 2160146 2160174 2161124 2161273) (-1265 "UPXSCONS.spad" 2157905 2157925 2158278 2158427) (-1264 "UPXSCCA.spad" 2156476 2156496 2157751 2157900) (-1263 "UPXSCCA.spad" 2155189 2155211 2156466 2156471) (-1262 "UPXSCAT.spad" 2153778 2153794 2155035 2155184) (-1261 "UPXS2.spad" 2153321 2153374 2153768 2153773) (-1260 "UPSQFREE.spad" 2151735 2151749 2153311 2153316) (-1259 "UPSCAT.spad" 2149522 2149546 2151633 2151730) (-1258 "UPSCAT.spad" 2147015 2147041 2149128 2149133) (-1257 "UPOLYC.spad" 2142055 2142066 2146857 2147010) (-1256 "UPOLYC.spad" 2136987 2137000 2141791 2141796) (-1255 "UPOLYC2.spad" 2136458 2136477 2136977 2136982) (-1254 "UP.spad" 2133657 2133672 2134044 2134197) (-1253 "UPMP.spad" 2132557 2132570 2133647 2133652) (-1252 "UPDIVP.spad" 2132122 2132136 2132547 2132552) (-1251 "UPDECOMP.spad" 2130367 2130381 2132112 2132117) (-1250 "UPCDEN.spad" 2129576 2129592 2130357 2130362) (-1249 "UP2.spad" 2128940 2128961 2129566 2129571) (-1248 "UNISEG.spad" 2128293 2128304 2128859 2128864) (-1247 "UNISEG2.spad" 2127790 2127803 2128249 2128254) (-1246 "UNIFACT.spad" 2126893 2126905 2127780 2127785) (-1245 "ULS.spad" 2117451 2117479 2118538 2118967) (-1244 "ULSCONS.spad" 2109847 2109867 2110217 2110366) (-1243 "ULSCCAT.spad" 2107584 2107604 2109693 2109842) (-1242 "ULSCCAT.spad" 2105429 2105451 2107540 2107545) (-1241 "ULSCAT.spad" 2103661 2103677 2105275 2105424) (-1240 "ULS2.spad" 2103175 2103228 2103651 2103656) (-1239 "UINT8.spad" 2103052 2103061 2103165 2103170) (-1238 "UINT64.spad" 2102928 2102937 2103042 2103047) (-1237 "UINT32.spad" 2102804 2102813 2102918 2102923) (-1236 "UINT16.spad" 2102680 2102689 2102794 2102799) (-1235 "UFD.spad" 2101745 2101754 2102606 2102675) (-1234 "UFD.spad" 2100872 2100883 2101735 2101740) (-1233 "UDVO.spad" 2099753 2099762 2100862 2100867) (-1232 "UDPO.spad" 2097246 2097257 2099709 2099714) (-1231 "TYPE.spad" 2097178 2097187 2097236 2097241) (-1230 "TYPEAST.spad" 2097097 2097106 2097168 2097173) (-1229 "TWOFACT.spad" 2095749 2095764 2097087 2097092) (-1228 "TUPLE.spad" 2095235 2095246 2095648 2095653) (-1227 "TUBETOOL.spad" 2092102 2092111 2095225 2095230) (-1226 "TUBE.spad" 2090749 2090766 2092092 2092097) (-1225 "TS.spad" 2089348 2089364 2090314 2090411) (-1224 "TSETCAT.spad" 2076475 2076492 2089316 2089343) (-1223 "TSETCAT.spad" 2063588 2063607 2076431 2076436) (-1222 "TRMANIP.spad" 2057954 2057971 2063294 2063299) (-1221 "TRIMAT.spad" 2056917 2056942 2057944 2057949) (-1220 "TRIGMNIP.spad" 2055444 2055461 2056907 2056912) (-1219 "TRIGCAT.spad" 2054956 2054965 2055434 2055439) (-1218 "TRIGCAT.spad" 2054466 2054477 2054946 2054951) (-1217 "TREE.spad" 2053041 2053052 2054073 2054100) (-1216 "TRANFUN.spad" 2052880 2052889 2053031 2053036) (-1215 "TRANFUN.spad" 2052717 2052728 2052870 2052875) (-1214 "TOPSP.spad" 2052391 2052400 2052707 2052712) (-1213 "TOOLSIGN.spad" 2052054 2052065 2052381 2052386) (-1212 "TEXTFILE.spad" 2050615 2050624 2052044 2052049) (-1211 "TEX.spad" 2047761 2047770 2050605 2050610) (-1210 "TEX1.spad" 2047317 2047328 2047751 2047756) (-1209 "TEMUTL.spad" 2046872 2046881 2047307 2047312) (-1208 "TBCMPPK.spad" 2044965 2044988 2046862 2046867) (-1207 "TBAGG.spad" 2044015 2044038 2044945 2044960) (-1206 "TBAGG.spad" 2043073 2043098 2044005 2044010) (-1205 "TANEXP.spad" 2042481 2042492 2043063 2043068) (-1204 "TALGOP.spad" 2042205 2042216 2042471 2042476) (-1203 "TABLE.spad" 2040616 2040639 2040886 2040913) (-1202 "TABLEAU.spad" 2040097 2040108 2040606 2040611) (-1201 "TABLBUMP.spad" 2036900 2036911 2040087 2040092) (-1200 "SYSTEM.spad" 2036128 2036137 2036890 2036895) (-1199 "SYSSOLP.spad" 2033611 2033622 2036118 2036123) (-1198 "SYSPTR.spad" 2033510 2033519 2033601 2033606) (-1197 "SYSNNI.spad" 2032692 2032703 2033500 2033505) (-1196 "SYSINT.spad" 2032096 2032107 2032682 2032687) (-1195 "SYNTAX.spad" 2028302 2028311 2032086 2032091) (-1194 "SYMTAB.spad" 2026370 2026379 2028292 2028297) (-1193 "SYMS.spad" 2022393 2022402 2026360 2026365) (-1192 "SYMPOLY.spad" 2021400 2021411 2021482 2021609) (-1191 "SYMFUNC.spad" 2020901 2020912 2021390 2021395) (-1190 "SYMBOL.spad" 2018404 2018413 2020891 2020896) (-1189 "SWITCH.spad" 2015175 2015184 2018394 2018399) (-1188 "SUTS.spad" 2012080 2012108 2013642 2013739) (-1187 "SUPXS.spad" 2009221 2009249 2010212 2010361) (-1186 "SUP.spad" 2006034 2006045 2006807 2006960) (-1185 "SUPFRACF.spad" 2005139 2005157 2006024 2006029) (-1184 "SUP2.spad" 2004531 2004544 2005129 2005134) (-1183 "SUMRF.spad" 2003505 2003516 2004521 2004526) (-1182 "SUMFS.spad" 2003142 2003159 2003495 2003500) (-1181 "SULS.spad" 1993687 1993715 1994787 1995216) (-1180 "SUCHTAST.spad" 1993456 1993465 1993677 1993682) (-1179 "SUCH.spad" 1993138 1993153 1993446 1993451) (-1178 "SUBSPACE.spad" 1985253 1985268 1993128 1993133) (-1177 "SUBRESP.spad" 1984423 1984437 1985209 1985214) (-1176 "STTF.spad" 1980522 1980538 1984413 1984418) (-1175 "STTFNC.spad" 1976990 1977006 1980512 1980517) (-1174 "STTAYLOR.spad" 1969625 1969636 1976871 1976876) (-1173 "STRTBL.spad" 1968130 1968147 1968279 1968306) (-1172 "STRING.spad" 1967539 1967548 1967553 1967580) (-1171 "STRICAT.spad" 1967327 1967336 1967507 1967534) (-1170 "STREAM.spad" 1964245 1964256 1966852 1966867) (-1169 "STREAM3.spad" 1963818 1963833 1964235 1964240) (-1168 "STREAM2.spad" 1962946 1962959 1963808 1963813) (-1167 "STREAM1.spad" 1962652 1962663 1962936 1962941) (-1166 "STINPROD.spad" 1961588 1961604 1962642 1962647) (-1165 "STEP.spad" 1960789 1960798 1961578 1961583) (-1164 "STEPAST.spad" 1960023 1960032 1960779 1960784) (-1163 "STBL.spad" 1958549 1958577 1958716 1958731) (-1162 "STAGG.spad" 1957624 1957635 1958539 1958544) (-1161 "STAGG.spad" 1956697 1956710 1957614 1957619) (-1160 "STACK.spad" 1956054 1956065 1956304 1956331) (-1159 "SREGSET.spad" 1953758 1953775 1955700 1955727) (-1158 "SRDCMPK.spad" 1952319 1952339 1953748 1953753) (-1157 "SRAGG.spad" 1947462 1947471 1952287 1952314) (-1156 "SRAGG.spad" 1942625 1942636 1947452 1947457) (-1155 "SQMATRIX.spad" 1940297 1940315 1941213 1941300) (-1154 "SPLTREE.spad" 1934849 1934862 1939733 1939760) (-1153 "SPLNODE.spad" 1931437 1931450 1934839 1934844) (-1152 "SPFCAT.spad" 1930246 1930255 1931427 1931432) (-1151 "SPECOUT.spad" 1928798 1928807 1930236 1930241) (-1150 "SPADXPT.spad" 1920393 1920402 1928788 1928793) (-1149 "spad-parser.spad" 1919858 1919867 1920383 1920388) (-1148 "SPADAST.spad" 1919559 1919568 1919848 1919853) (-1147 "SPACEC.spad" 1903758 1903769 1919549 1919554) (-1146 "SPACE3.spad" 1903534 1903545 1903748 1903753) (-1145 "SORTPAK.spad" 1903083 1903096 1903490 1903495) (-1144 "SOLVETRA.spad" 1900846 1900857 1903073 1903078) (-1143 "SOLVESER.spad" 1899374 1899385 1900836 1900841) (-1142 "SOLVERAD.spad" 1895400 1895411 1899364 1899369) (-1141 "SOLVEFOR.spad" 1893862 1893880 1895390 1895395) (-1140 "SNTSCAT.spad" 1893462 1893479 1893830 1893857) (-1139 "SMTS.spad" 1891734 1891760 1893027 1893124) (-1138 "SMP.spad" 1889209 1889229 1889599 1889726) (-1137 "SMITH.spad" 1888054 1888079 1889199 1889204) (-1136 "SMATCAT.spad" 1886164 1886194 1887998 1888049) (-1135 "SMATCAT.spad" 1884206 1884238 1886042 1886047) (-1134 "SKAGG.spad" 1883169 1883180 1884174 1884201) (-1133 "SINT.spad" 1882109 1882118 1883035 1883164) (-1132 "SIMPAN.spad" 1881837 1881846 1882099 1882104) (-1131 "SIG.spad" 1881167 1881176 1881827 1881832) (-1130 "SIGNRF.spad" 1880285 1880296 1881157 1881162) (-1129 "SIGNEF.spad" 1879564 1879581 1880275 1880280) (-1128 "SIGAST.spad" 1878949 1878958 1879554 1879559) (-1127 "SHP.spad" 1876877 1876892 1878905 1878910) (-1126 "SHDP.spad" 1866511 1866538 1867020 1867151) (-1125 "SGROUP.spad" 1866119 1866128 1866501 1866506) (-1124 "SGROUP.spad" 1865725 1865736 1866109 1866114) (-1123 "SGCF.spad" 1858864 1858873 1865715 1865720) (-1122 "SFRTCAT.spad" 1857794 1857811 1858832 1858859) (-1121 "SFRGCD.spad" 1856857 1856877 1857784 1857789) (-1120 "SFQCMPK.spad" 1851494 1851514 1856847 1856852) (-1119 "SFORT.spad" 1850933 1850947 1851484 1851489) (-1118 "SEXOF.spad" 1850776 1850816 1850923 1850928) (-1117 "SEX.spad" 1850668 1850677 1850766 1850771) (-1116 "SEXCAT.spad" 1848449 1848489 1850658 1850663) (-1115 "SET.spad" 1846773 1846784 1847870 1847909) (-1114 "SETMN.spad" 1845223 1845240 1846763 1846768) (-1113 "SETCAT.spad" 1844545 1844554 1845213 1845218) (-1112 "SETCAT.spad" 1843865 1843876 1844535 1844540) (-1111 "SETAGG.spad" 1840414 1840425 1843845 1843860) (-1110 "SETAGG.spad" 1836971 1836984 1840404 1840409) (-1109 "SEQAST.spad" 1836674 1836683 1836961 1836966) (-1108 "SEGXCAT.spad" 1835830 1835843 1836664 1836669) (-1107 "SEG.spad" 1835643 1835654 1835749 1835754) (-1106 "SEGCAT.spad" 1834568 1834579 1835633 1835638) (-1105 "SEGBIND.spad" 1834326 1834337 1834515 1834520) (-1104 "SEGBIND2.spad" 1834024 1834037 1834316 1834321) (-1103 "SEGAST.spad" 1833738 1833747 1834014 1834019) (-1102 "SEG2.spad" 1833173 1833186 1833694 1833699) (-1101 "SDVAR.spad" 1832449 1832460 1833163 1833168) (-1100 "SDPOL.spad" 1829875 1829886 1830166 1830293) (-1099 "SCPKG.spad" 1827964 1827975 1829865 1829870) (-1098 "SCOPE.spad" 1827117 1827126 1827954 1827959) (-1097 "SCACHE.spad" 1825813 1825824 1827107 1827112) (-1096 "SASTCAT.spad" 1825722 1825731 1825803 1825808) (-1095 "SAOS.spad" 1825594 1825603 1825712 1825717) (-1094 "SAERFFC.spad" 1825307 1825327 1825584 1825589) (-1093 "SAE.spad" 1823482 1823498 1824093 1824228) (-1092 "SAEFACT.spad" 1823183 1823203 1823472 1823477) (-1091 "RURPK.spad" 1820842 1820858 1823173 1823178) (-1090 "RULESET.spad" 1820295 1820319 1820832 1820837) (-1089 "RULE.spad" 1818535 1818559 1820285 1820290) (-1088 "RULECOLD.spad" 1818387 1818400 1818525 1818530) (-1087 "RTVALUE.spad" 1818122 1818131 1818377 1818382) (-1086 "RSTRCAST.spad" 1817839 1817848 1818112 1818117) (-1085 "RSETGCD.spad" 1814217 1814237 1817829 1817834) (-1084 "RSETCAT.spad" 1804153 1804170 1814185 1814212) (-1083 "RSETCAT.spad" 1794109 1794128 1804143 1804148) (-1082 "RSDCMPK.spad" 1792561 1792581 1794099 1794104) (-1081 "RRCC.spad" 1790945 1790975 1792551 1792556) (-1080 "RRCC.spad" 1789327 1789359 1790935 1790940) (-1079 "RPTAST.spad" 1789029 1789038 1789317 1789322) (-1078 "RPOLCAT.spad" 1768389 1768404 1788897 1789024) (-1077 "RPOLCAT.spad" 1747462 1747479 1767972 1767977) (-1076 "ROUTINE.spad" 1743345 1743354 1746109 1746136) (-1075 "ROMAN.spad" 1742673 1742682 1743211 1743340) (-1074 "ROIRC.spad" 1741753 1741785 1742663 1742668) (-1073 "RNS.spad" 1740656 1740665 1741655 1741748) (-1072 "RNS.spad" 1739645 1739656 1740646 1740651) (-1071 "RNG.spad" 1739380 1739389 1739635 1739640) (-1070 "RNGBIND.spad" 1738540 1738554 1739335 1739340) (-1069 "RMODULE.spad" 1738305 1738316 1738530 1738535) (-1068 "RMCAT2.spad" 1737725 1737782 1738295 1738300) (-1067 "RMATRIX.spad" 1736549 1736568 1736892 1736931) (-1066 "RMATCAT.spad" 1732128 1732159 1736505 1736544) (-1065 "RMATCAT.spad" 1727597 1727630 1731976 1731981) (-1064 "RLINSET.spad" 1726991 1727002 1727587 1727592) (-1063 "RINTERP.spad" 1726879 1726899 1726981 1726986) (-1062 "RING.spad" 1726349 1726358 1726859 1726874) (-1061 "RING.spad" 1725827 1725838 1726339 1726344) (-1060 "RIDIST.spad" 1725219 1725228 1725817 1725822) (-1059 "RGCHAIN.spad" 1723802 1723818 1724704 1724731) (-1058 "RGBCSPC.spad" 1723583 1723595 1723792 1723797) (-1057 "RGBCMDL.spad" 1723113 1723125 1723573 1723578) (-1056 "RF.spad" 1720755 1720766 1723103 1723108) (-1055 "RFFACTOR.spad" 1720217 1720228 1720745 1720750) (-1054 "RFFACT.spad" 1719952 1719964 1720207 1720212) (-1053 "RFDIST.spad" 1718948 1718957 1719942 1719947) (-1052 "RETSOL.spad" 1718367 1718380 1718938 1718943) (-1051 "RETRACT.spad" 1717795 1717806 1718357 1718362) (-1050 "RETRACT.spad" 1717221 1717234 1717785 1717790) (-1049 "RETAST.spad" 1717033 1717042 1717211 1717216) (-1048 "RESULT.spad" 1715093 1715102 1715680 1715707) (-1047 "RESRING.spad" 1714440 1714487 1715031 1715088) (-1046 "RESLATC.spad" 1713764 1713775 1714430 1714435) (-1045 "REPSQ.spad" 1713495 1713506 1713754 1713759) (-1044 "REP.spad" 1711049 1711058 1713485 1713490) (-1043 "REPDB.spad" 1710756 1710767 1711039 1711044) (-1042 "REP2.spad" 1700414 1700425 1710598 1710603) (-1041 "REP1.spad" 1694610 1694621 1700364 1700369) (-1040 "REGSET.spad" 1692407 1692424 1694256 1694283) (-1039 "REF.spad" 1691742 1691753 1692362 1692367) (-1038 "REDORDER.spad" 1690948 1690965 1691732 1691737) (-1037 "RECLOS.spad" 1689731 1689751 1690435 1690528) (-1036 "REALSOLV.spad" 1688871 1688880 1689721 1689726) (-1035 "REAL.spad" 1688743 1688752 1688861 1688866) (-1034 "REAL0Q.spad" 1686041 1686056 1688733 1688738) (-1033 "REAL0.spad" 1682885 1682900 1686031 1686036) (-1032 "RDUCEAST.spad" 1682606 1682615 1682875 1682880) (-1031 "RDIV.spad" 1682261 1682286 1682596 1682601) (-1030 "RDIST.spad" 1681828 1681839 1682251 1682256) (-1029 "RDETRS.spad" 1680692 1680710 1681818 1681823) (-1028 "RDETR.spad" 1678831 1678849 1680682 1680687) (-1027 "RDEEFS.spad" 1677930 1677947 1678821 1678826) (-1026 "RDEEF.spad" 1676940 1676957 1677920 1677925) (-1025 "RCFIELD.spad" 1674126 1674135 1676842 1676935) (-1024 "RCFIELD.spad" 1671398 1671409 1674116 1674121) (-1023 "RCAGG.spad" 1669326 1669337 1671388 1671393) (-1022 "RCAGG.spad" 1667181 1667194 1669245 1669250) (-1021 "RATRET.spad" 1666541 1666552 1667171 1667176) (-1020 "RATFACT.spad" 1666233 1666245 1666531 1666536) (-1019 "RANDSRC.spad" 1665552 1665561 1666223 1666228) (-1018 "RADUTIL.spad" 1665308 1665317 1665542 1665547) (-1017 "RADIX.spad" 1662229 1662243 1663775 1663868) (-1016 "RADFF.spad" 1660642 1660679 1660761 1660917) (-1015 "RADCAT.spad" 1660237 1660246 1660632 1660637) (-1014 "RADCAT.spad" 1659830 1659841 1660227 1660232) (-1013 "QUEUE.spad" 1659178 1659189 1659437 1659464) (-1012 "QUAT.spad" 1657636 1657647 1657979 1658044) (-1011 "QUATCT2.spad" 1657256 1657275 1657626 1657631) (-1010 "QUATCAT.spad" 1655426 1655437 1657186 1657251) (-1009 "QUATCAT.spad" 1653347 1653360 1655109 1655114) (-1008 "QUAGG.spad" 1652174 1652185 1653315 1653342) (-1007 "QQUTAST.spad" 1651942 1651951 1652164 1652169) (-1006 "QFORM.spad" 1651560 1651575 1651932 1651937) (-1005 "QFCAT.spad" 1650262 1650273 1651462 1651555) (-1004 "QFCAT.spad" 1648555 1648568 1649757 1649762) (-1003 "QFCAT2.spad" 1648247 1648264 1648545 1648550) (-1002 "QEQUAT.spad" 1647805 1647814 1648237 1648242) (-1001 "QCMPACK.spad" 1642551 1642571 1647795 1647800) (-1000 "QALGSET.spad" 1638629 1638662 1642465 1642470) (-999 "QALGSET2.spad" 1636625 1636643 1638619 1638624) (-998 "PWFFINTB.spad" 1634041 1634062 1636615 1636620) (-997 "PUSHVAR.spad" 1633380 1633399 1634031 1634036) (-996 "PTRANFN.spad" 1629508 1629518 1633370 1633375) (-995 "PTPACK.spad" 1626596 1626606 1629498 1629503) (-994 "PTFUNC2.spad" 1626419 1626433 1626586 1626591) (-993 "PTCAT.spad" 1625674 1625684 1626387 1626414) (-992 "PSQFR.spad" 1624981 1625005 1625664 1625669) (-991 "PSEUDLIN.spad" 1623867 1623877 1624971 1624976) (-990 "PSETPK.spad" 1609300 1609316 1623745 1623750) (-989 "PSETCAT.spad" 1603220 1603243 1609280 1609295) (-988 "PSETCAT.spad" 1597114 1597139 1603176 1603181) (-987 "PSCURVE.spad" 1596097 1596105 1597104 1597109) (-986 "PSCAT.spad" 1594880 1594909 1595995 1596092) (-985 "PSCAT.spad" 1593753 1593784 1594870 1594875) (-984 "PRTITION.spad" 1592451 1592459 1593743 1593748) (-983 "PRTDAST.spad" 1592170 1592178 1592441 1592446) (-982 "PRS.spad" 1581732 1581749 1592126 1592131) (-981 "PRQAGG.spad" 1581167 1581177 1581700 1581727) (-980 "PROPLOG.spad" 1580739 1580747 1581157 1581162) (-979 "PROPFUN2.spad" 1580362 1580375 1580729 1580734) (-978 "PROPFUN1.spad" 1579760 1579771 1580352 1580357) (-977 "PROPFRML.spad" 1578328 1578339 1579750 1579755) (-976 "PROPERTY.spad" 1577816 1577824 1578318 1578323) (-975 "PRODUCT.spad" 1575498 1575510 1575782 1575837) (-974 "PR.spad" 1573890 1573902 1574589 1574716) (-973 "PRINT.spad" 1573642 1573650 1573880 1573885) (-972 "PRIMES.spad" 1571895 1571905 1573632 1573637) (-971 "PRIMELT.spad" 1569976 1569990 1571885 1571890) (-970 "PRIMCAT.spad" 1569603 1569611 1569966 1569971) (-969 "PRIMARR.spad" 1568608 1568618 1568786 1568813) (-968 "PRIMARR2.spad" 1567375 1567387 1568598 1568603) (-967 "PREASSOC.spad" 1566757 1566769 1567365 1567370) (-966 "PPCURVE.spad" 1565894 1565902 1566747 1566752) (-965 "PORTNUM.spad" 1565669 1565677 1565884 1565889) (-964 "POLYROOT.spad" 1564518 1564540 1565625 1565630) (-963 "POLY.spad" 1561853 1561863 1562368 1562495) (-962 "POLYLIFT.spad" 1561118 1561141 1561843 1561848) (-961 "POLYCATQ.spad" 1559236 1559258 1561108 1561113) (-960 "POLYCAT.spad" 1552706 1552727 1559104 1559231) (-959 "POLYCAT.spad" 1545514 1545537 1551914 1551919) (-958 "POLY2UP.spad" 1544966 1544980 1545504 1545509) (-957 "POLY2.spad" 1544563 1544575 1544956 1544961) (-956 "POLUTIL.spad" 1543504 1543533 1544519 1544524) (-955 "POLTOPOL.spad" 1542252 1542267 1543494 1543499) (-954 "POINT.spad" 1541090 1541100 1541177 1541204) (-953 "PNTHEORY.spad" 1537792 1537800 1541080 1541085) (-952 "PMTOOLS.spad" 1536567 1536581 1537782 1537787) (-951 "PMSYM.spad" 1536116 1536126 1536557 1536562) (-950 "PMQFCAT.spad" 1535707 1535721 1536106 1536111) (-949 "PMPRED.spad" 1535186 1535200 1535697 1535702) (-948 "PMPREDFS.spad" 1534640 1534662 1535176 1535181) (-947 "PMPLCAT.spad" 1533720 1533738 1534572 1534577) (-946 "PMLSAGG.spad" 1533305 1533319 1533710 1533715) (-945 "PMKERNEL.spad" 1532884 1532896 1533295 1533300) (-944 "PMINS.spad" 1532464 1532474 1532874 1532879) (-943 "PMFS.spad" 1532041 1532059 1532454 1532459) (-942 "PMDOWN.spad" 1531331 1531345 1532031 1532036) (-941 "PMASS.spad" 1530341 1530349 1531321 1531326) (-940 "PMASSFS.spad" 1529308 1529324 1530331 1530336) (-939 "PLOTTOOL.spad" 1529088 1529096 1529298 1529303) (-938 "PLOT.spad" 1524011 1524019 1529078 1529083) (-937 "PLOT3D.spad" 1520475 1520483 1524001 1524006) (-936 "PLOT1.spad" 1519632 1519642 1520465 1520470) (-935 "PLEQN.spad" 1506922 1506949 1519622 1519627) (-934 "PINTERP.spad" 1506544 1506563 1506912 1506917) (-933 "PINTERPA.spad" 1506328 1506344 1506534 1506539) (-932 "PI.spad" 1505937 1505945 1506302 1506323) (-931 "PID.spad" 1504907 1504915 1505863 1505932) (-930 "PICOERCE.spad" 1504564 1504574 1504897 1504902) (-929 "PGROEB.spad" 1503165 1503179 1504554 1504559) (-928 "PGE.spad" 1494782 1494790 1503155 1503160) (-927 "PGCD.spad" 1493672 1493689 1494772 1494777) (-926 "PFRPAC.spad" 1492821 1492831 1493662 1493667) (-925 "PFR.spad" 1489484 1489494 1492723 1492816) (-924 "PFOTOOLS.spad" 1488742 1488758 1489474 1489479) (-923 "PFOQ.spad" 1488112 1488130 1488732 1488737) (-922 "PFO.spad" 1487531 1487558 1488102 1488107) (-921 "PF.spad" 1487105 1487117 1487336 1487429) (-920 "PFECAT.spad" 1484787 1484795 1487031 1487100) (-919 "PFECAT.spad" 1482497 1482507 1484743 1484748) (-918 "PFBRU.spad" 1480385 1480397 1482487 1482492) (-917 "PFBR.spad" 1477945 1477968 1480375 1480380) (-916 "PERM.spad" 1473752 1473762 1477775 1477790) (-915 "PERMGRP.spad" 1468522 1468532 1473742 1473747) (-914 "PERMCAT.spad" 1467183 1467193 1468502 1468517) (-913 "PERMAN.spad" 1465715 1465729 1467173 1467178) (-912 "PENDTREE.spad" 1465056 1465066 1465344 1465349) (-911 "PDRING.spad" 1463607 1463617 1465036 1465051) (-910 "PDRING.spad" 1462166 1462178 1463597 1463602) (-909 "PDEPROB.spad" 1461181 1461189 1462156 1462161) (-908 "PDEPACK.spad" 1455221 1455229 1461171 1461176) (-907 "PDECOMP.spad" 1454691 1454708 1455211 1455216) (-906 "PDECAT.spad" 1453047 1453055 1454681 1454686) (-905 "PCOMP.spad" 1452900 1452913 1453037 1453042) (-904 "PBWLB.spad" 1451488 1451505 1452890 1452895) (-903 "PATTERN.spad" 1446027 1446037 1451478 1451483) (-902 "PATTERN2.spad" 1445765 1445777 1446017 1446022) (-901 "PATTERN1.spad" 1444101 1444117 1445755 1445760) (-900 "PATRES.spad" 1441676 1441688 1444091 1444096) (-899 "PATRES2.spad" 1441348 1441362 1441666 1441671) (-898 "PATMATCH.spad" 1439545 1439576 1441056 1441061) (-897 "PATMAB.spad" 1438974 1438984 1439535 1439540) (-896 "PATLRES.spad" 1438060 1438074 1438964 1438969) (-895 "PATAB.spad" 1437824 1437834 1438050 1438055) (-894 "PARTPERM.spad" 1435832 1435840 1437814 1437819) (-893 "PARSURF.spad" 1435266 1435294 1435822 1435827) (-892 "PARSU2.spad" 1435063 1435079 1435256 1435261) (-891 "script-parser.spad" 1434583 1434591 1435053 1435058) (-890 "PARSCURV.spad" 1434017 1434045 1434573 1434578) (-889 "PARSC2.spad" 1433808 1433824 1434007 1434012) (-888 "PARPCURV.spad" 1433270 1433298 1433798 1433803) (-887 "PARPC2.spad" 1433061 1433077 1433260 1433265) (-886 "PARAMAST.spad" 1432189 1432197 1433051 1433056) (-885 "PAN2EXPR.spad" 1431601 1431609 1432179 1432184) (-884 "PALETTE.spad" 1430571 1430579 1431591 1431596) (-883 "PAIR.spad" 1429558 1429571 1430159 1430164) (-882 "PADICRC.spad" 1426892 1426910 1428063 1428156) (-881 "PADICRAT.spad" 1424907 1424919 1425128 1425221) (-880 "PADIC.spad" 1424602 1424614 1424833 1424902) (-879 "PADICCT.spad" 1423151 1423163 1424528 1424597) (-878 "PADEPAC.spad" 1421840 1421859 1423141 1423146) (-877 "PADE.spad" 1420592 1420608 1421830 1421835) (-876 "OWP.spad" 1419832 1419862 1420450 1420517) (-875 "OVERSET.spad" 1419405 1419413 1419822 1419827) (-874 "OVAR.spad" 1419186 1419209 1419395 1419400) (-873 "OUT.spad" 1418272 1418280 1419176 1419181) (-872 "OUTFORM.spad" 1407664 1407672 1418262 1418267) (-871 "OUTBFILE.spad" 1407082 1407090 1407654 1407659) (-870 "OUTBCON.spad" 1406088 1406096 1407072 1407077) (-869 "OUTBCON.spad" 1405092 1405102 1406078 1406083) (-868 "OSI.spad" 1404567 1404575 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222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 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170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 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"ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 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2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 2b56a4db..094dd195 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,1125 +1,1125 @@
 
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183049) ((-558 . -107) 182999) ((-1015 . -384) 182981) ((-1015 . -345) 182963) ((-97 . -1111) T) ((-973 . -23) 182774) ((-485 . -21) T) ((-485 . -25) T) ((-823 . -23) 182644) ((-1188 . -621) 182626) ((-59 . -19) 182610) ((-1188 . -622) 182532) ((-1184 . -734) T) ((-1136 . -734) T) ((-524 . -19) 182516) ((-504 . -19) 182500) ((-59 . -612) 182477) ((-1098 . -1111) T) ((-910 . -102) 182455) ((-862 . -734) T) ((-790 . -1111) T) ((-524 . -612) 182432) ((-504 . -612) 182409) ((-788 . -1111) T) ((-788 . -1076) 182376) ((-469 . -1111) T) ((-462 . -1111) T) ((-594 . -725) 182351) ((-657 . -1111) T) ((-1271 . -47) 182328) ((-1265 . -102) T) ((-1264 . -47) 182298) ((-1243 . -47) 182275) ((-1223 . -174) 182226) ((-1185 . -313) 182205) ((-1179 . -313) 182184) ((-1107 . -624) 182165) ((-1101 . -624) 182146) ((-1091 . -564) 182097) ((-1015 . -909) NIL) ((-1091 . -1233) 182048) ((-678 . -132) T) ((-635 . -1123) T) ((-1084 . -624) 182029) ((-1077 . -624) 182010) ((-1047 . -624) 181991) ((-1030 . -624) 181972) ((-707 . -654) 181922) ((-280 . -1111) T) ((-85 . -449) T) ((-85 . -403) T) ((-722 . -1067) 181892) ((-719 . -174) T) ((-50 . -1111) T) ((-603 . -47) 181869) ((-227 . -656) 181834) ((-589 . -1111) T) ((-526 . -1111) T) ((-495 . -828) T) ((-495 . -929) T) ((-366 . -1233) T) ((-360 . -1233) T) ((-352 . -1233) T) ((-325 . -1123) T) ((-322 . -1062) 181744) ((-319 . -1062) 181673) ((-108 . -1233) T) ((-634 . -624) 181654) ((-366 . -564) T) ((-219 . -929) T) ((-219 . -828) T) ((-322 . -648) 181564) ((-319 . -648) 181493) ((-360 . -564) T) ((-352 . -564) T) ((-491 . -624) 181474) ((-108 . -564) T) ((-666 . -725) 181444) ((-1179 . -1033) NIL) ((-220 . -624) 181425) ((-325 . -23) T) ((-67 . -1229) T) ((-1011 . -621) 181357) ((-702 . -233) 181339) ((-722 . -111) 181304) ((-652 . -34) T) ((-249 . -497) 181288) ((-1308 . -1163) T) ((-1303 . -21) T) ((-1303 . -25) T) ((-1113 . -1109) 181272) ((-173 . -1111) T) ((-1301 . -132) T) ((-1299 . -132) T) ((-1292 . -102) T) ((-1275 . -621) 181238) ((-1271 . -1229) T) ((-961 . -918) 181217) ((-1264 . -1229) T) ((-1264 . -1049) 181152) ((-1243 . -1229) T) ((-523 . -624) 181136) ((-1243 . -895) NIL) ((-1243 . -893) 181088) ((-1243 . -1049) 181054) ((-489 . -918) 181033) ((-1223 . -522) 181000) ((-1201 . -622) NIL) ((-1098 . -725) 180849) ((-1073 . -656) 180821) ((-961 . -656) 180710) ((-605 . -498) 180691) ((-593 . -498) 180672) ((-790 . -725) 180501) ((-605 . -621) 180467) ((-593 . -621) 180433) ((-544 . -621) 180415) ((-544 . -622) 180396) ((-788 . -725) 180245) ((-1088 . -102) T) ((-388 . -25) T) ((-631 . -654) 180217) ((-388 . -21) T) ((-489 . -656) 180106) ((-469 . -725) 180077) ((-462 . -725) 179926) ((-998 . -102) T) ((-1201 . -621) 179908) ((-1153 . -1134) 179853) ((-1057 . -1222) 179782) ((-745 . -102) T) ((-118 . -654) 179712) ((-613 . -624) 179694) ((-910 . -315) 179632) ((-884 . -93) T) ((-539 . -25) T) ((-722 . -624) 179586) ((-689 . -93) T) ((-684 . -93) T) ((-653 . -498) 179567) ((-142 . -102) T) ((-44 . -132) T) ((-672 . -621) 179549) ((-603 . -1229) T) ((-350 . -1069) T) ((-295 . -1123) T) ((-653 . -621) 179502) ((-486 . -93) T) ((-362 . -621) 179484) ((-359 . -621) 179466) ((-351 . -621) 179448) ((-269 . -622) 179196) ((-269 . -621) 179178) ((-251 . -621) 179160) ((-251 . -622) 179021) ((-134 . -93) T) ((-139 . -93) T) ((-138 . -93) T) ((-1152 . -621) 179003) ((-1131 . -648) 178990) ((-1131 . -1062) 178977) ((-827 . -734) T) ((-827 . -865) T) ((-610 . -294) 178954) ((-589 . -725) 178919) ((-487 . -622) NIL) ((-487 . -621) 178901) ((-526 . -725) 178846) ((-322 . -102) T) ((-319 . -102) T) ((-295 . -23) T) ((-153 . -132) T) ((-919 . -621) 178828) ((-919 . -622) 178810) ((-394 . -734) T) ((-880 . -1067) 178762) ((-880 . -111) 178700) ((-722 . -1060) T) ((-720 . -1255) 178684) ((-702 . -356) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-527 . -621) 178616) ((-386 . -803) T) ((-225 . -1111) T) ((-169 . -1229) T) ((-386 . -800) T) ((-227 . -802) T) ((-227 . -799) T) ((-59 . -622) 178577) ((-59 . -621) 178489) ((-227 . -734) T) ((-524 . -622) 178450) ((-524 . -621) 178362) ((-505 . -621) 178294) ((-504 . -622) 178255) ((-504 . -621) 178167) ((-1091 . -370) 178118) ((-40 . -419) 178095) ((-77 . -1229) T) ((-879 . -918) NIL) ((-366 . -335) 178079) ((-366 . -370) T) ((-360 . -335) 178063) ((-360 . -370) T) ((-352 . -335) 178047) ((-352 . -370) T) ((-322 . -290) 178026) ((-108 . -370) T) ((-70 . -1229) T) ((-1243 . -345) 177978) ((-879 . -656) 177923) ((-1243 . -384) 177875) ((-973 . -132) 177730) ((-823 . -132) 177600) ((-967 . -659) 177584) ((-1098 . -174) 177495) ((-967 . -380) 177479) ((-1073 . -802) T) ((-1073 . -799) T) ((-880 . -624) 177377) ((-790 . -174) 177268) ((-788 . -174) 177179) ((-824 . -47) 177141) ((-1073 . -734) T) ((-333 . -497) 177125) ((-961 . -734) T) ((-1292 . -315) 177063) ((-462 . -174) 176974) ((-249 . -292) 176926) ((-1271 . -909) 176839) ((-1264 . -909) 176745) ((-1263 . -1067) 176580) ((-489 . -734) T) ((-1243 . -909) 176413) ((-1242 . -1067) 176221) ((-1223 . -296) 176200) ((-1198 . -1229) T) ((-1195 . -375) T) ((-1194 . -375) T) ((-1157 . -152) 176184) ((-1131 . -102) T) ((-1129 . -1111) T) ((-1091 . -23) T) ((-1091 . -1123) T) ((-1086 . -102) T) ((-1068 . -621) 176151) ((-936 . -964) T) ((-745 . -315) 176089) ((-75 . -1229) T) ((-672 . -389) 176061) ((-171 . -918) 176014) ((-30 . -964) T) ((-112 . -852) T) ((-1 . -621) 175996) ((-1014 . -417) 175968) ((-129 . -659) 175950) ((-50 . -628) 175934) ((-702 . -654) 175869) ((-603 . -909) 175782) ((-446 . -102) T) ((-129 . -380) 175764) ((-142 . -315) NIL) ((-880 . -1060) T) ((-841 . -858) 175743) ((-81 . -1229) T) ((-719 . -296) T) ((-40 . -1069) T) ((-589 . -174) T) ((-526 . -174) T) ((-519 . -621) 175725) ((-171 . -656) 175599) ((-515 . -621) 175581) ((-358 . -148) 175563) ((-358 . -146) T) ((-366 . -1123) T) ((-360 . -1123) T) ((-352 . -1123) T) ((-1015 . -313) T) ((-923 . -313) T) ((-880 . -247) T) ((-108 . -1123) T) ((-880 . -237) 175542) ((-1263 . -111) 175363) 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-1111) T) ((-319 . -1163) NIL) ((-295 . -132) T) ((-402 . -1111) T) ((-878 . -1069) T) ((-702 . -377) 173467) ((-361 . -654) 173397) ((-225 . -628) 173374) ((-333 . -292) 173326) ((-482 . -111) 173147) ((-1263 . -1060) T) ((-1242 . -1060) T) ((-824 . -384) 173131) ((-171 . -734) T) ((-662 . -102) T) ((-1263 . -247) 173110) ((-1263 . -237) 173062) ((-1242 . -237) 172967) ((-1242 . -247) 172946) ((-1014 . -410) NIL) ((-678 . -647) 172894) ((-322 . -38) 172804) ((-319 . -38) 172733) ((-69 . -621) 172715) ((-325 . -501) 172681) ((-48 . -654) 172631) ((-1201 . -294) 172610) ((-1237 . -858) T) ((-1124 . -1123) 172520) ((-83 . -1229) T) ((-61 . -621) 172502) ((-487 . -294) 172481) ((-1294 . -1049) 172458) ((-1176 . -1111) T) ((-1124 . -23) 172328) ((-824 . -909) 172264) ((-1252 . -734) T) ((-1113 . -1229) T) ((-482 . -624) 172090) ((-1098 . -296) 172021) ((-975 . -1111) T) ((-902 . -102) T) ((-790 . -296) 171932) ((-333 . -19) 171916) ((-59 . -294) 171893) ((-788 . -296) 171824) ((-863 . -734) T) ((-118 . -856) NIL) ((-524 . -294) 171801) ((-333 . -612) 171778) ((-504 . -294) 171755) ((-462 . -296) 171686) ((-1046 . -315) 171537) ((-884 . -498) 171518) ((-884 . -621) 171484) ((-689 . -498) 171465) ((-579 . -734) T) ((-684 . -498) 171446) ((-689 . -621) 171396) ((-684 . -621) 171362) ((-670 . -621) 171344) ((-486 . -498) 171325) ((-486 . -621) 171291) ((-249 . -622) 171252) ((-249 . -498) 171229) ((-139 . -498) 171210) ((-138 . -498) 171191) ((-134 . -498) 171172) ((-249 . -621) 171064) ((-215 . -102) T) ((-139 . -621) 171030) ((-138 . -621) 170996) ((-134 . -621) 170962) ((-1158 . -34) T) ((-952 . -1229) T) ((-350 . -725) 170907) ((-678 . -25) T) ((-678 . -21) T) ((-1188 . -624) 170888) ((-482 . -1060) T) ((-643 . -425) 170853) ((-615 . -425) 170818) ((-1131 . -1163) T) ((-720 . -1062) 170641) ((-589 . -296) T) ((-526 . -296) T) ((-1264 . -313) 170620) ((-482 . -237) 170572) ((-482 . -247) 170551) ((-1243 . -313) 170530) ((-720 . -648) 170359) ((-1243 . -1033) NIL) 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-21) T) ((-44 . -25) T) ((-823 . -647) 169046) ((-825 . -564) 169025) ((-256 . -1049) 168852) ((-255 . -1049) 168679) ((-127 . -120) 168663) ((-919 . -1067) 168628) ((-720 . -102) T) ((-707 . -1069) T) ((-605 . -624) 168609) ((-593 . -624) 168590) ((-544 . -626) 168493) ((-350 . -174) T) ((-88 . -621) 168475) ((-153 . -21) T) ((-153 . -25) T) ((-919 . -111) 168431) ((-40 . -725) 168376) ((-878 . -1111) T) ((-672 . -624) 168353) ((-653 . -624) 168334) ((-362 . -624) 168271) ((-359 . -624) 168208) ((-555 . -1111) T) ((-351 . -624) 168145) ((-333 . -622) 168106) ((-333 . -621) 168018) ((-269 . -624) 167771) ((-251 . -624) 167556) ((-1242 . -800) 167509) ((-1242 . -803) 167462) ((-256 . -384) 167431) ((-255 . -384) 167400) ((-662 . -38) 167370) ((-616 . -34) T) ((-490 . -1123) 167280) ((-483 . -34) T) ((-1124 . -132) 167150) ((-973 . -25) 166961) ((-919 . -624) 166911) ((-882 . -621) 166893) ((-973 . -21) 166848) ((-823 . -21) 166758) ((-823 . -25) 166609) ((-1235 . -375) T) ((-631 . -1069) T) ((-1190 . -564) 166588) ((-1184 . -47) 166565) ((-362 . -1060) T) ((-359 . -1060) T) ((-490 . -23) 166435) ((-351 . -1060) T) ((-269 . -1060) T) ((-251 . -1060) T) ((-1136 . -47) 166407) ((-118 . -1069) T) ((-1045 . -656) 166381) ((-967 . -34) T) ((-362 . -237) 166360) ((-362 . -247) T) ((-359 . -237) 166339) ((-359 . -247) T) ((-351 . -237) 166318) ((-351 . -247) T) ((-269 . -332) 166290) ((-251 . -332) 166247) ((-269 . -237) 166226) ((-1168 . -152) 166210) ((-256 . -909) 166142) ((-255 . -909) 166074) ((-1093 . -858) T) ((-422 . -1123) T) ((-1065 . -23) T) ((-919 . -1060) T) ((-328 . -656) 166056) ((-1035 . -856) T) ((-678 . -235) 166029) ((-1223 . -1013) 165995) ((-1185 . -929) 165974) ((-1179 . -929) 165953) ((-1179 . -828) NIL) ((-1010 . -1062) 165849) ((-976 . -1229) T) ((-919 . -247) T) ((-825 . -370) 165828) ((-392 . -23) T) ((-128 . -1111) 165806) ((-122 . -1111) 165784) ((-919 . -237) T) ((-129 . -34) T) ((-386 . -656) 165749) ((-1010 . -648) 165697) ((-878 . -725) 165684) ((-1308 . -654) 165656) ((-1057 . -152) 165621) ((-1004 . -1229) T) ((-40 . -174) T) ((-702 . -419) 165603) ((-720 . -315) 165590) ((-844 . -656) 165550) ((-835 . -656) 165524) ((-325 . -25) T) ((-325 . -21) T) ((-666 . -292) 165503) ((-588 . -1111) T) ((-572 . -1111) T) ((-503 . -1111) T) ((-249 . -294) 165480) ((-1184 . -1229) T) ((-319 . -233) 165441) ((-1184 . -895) NIL) ((-55 . -1111) T) ((-1136 . -895) 165300) ((-130 . -858) T) ((-1184 . -1049) 165180) ((-1136 . -1049) 165063) ((-185 . -621) 165045) ((-862 . -1049) 164941) ((-790 . -292) 164868) ((-825 . -1123) T) ((-1045 . -734) T) ((-610 . -659) 164852) ((-1057 . -987) 164781) ((-1010 . -102) T) ((-825 . -23) T) ((-720 . -1163) 164759) ((-702 . -1069) T) ((-610 . -380) 164743) ((-358 . -460) T) ((-350 . -296) T) ((-1280 . -1111) T) ((-252 . -1111) T) ((-407 . -102) T) ((-295 . -21) T) ((-295 . -25) T) ((-368 . -734) T) ((-718 . -1111) T) ((-707 . -1111) T) ((-368 . -481) T) ((-1223 . -621) 164725) ((-1184 . -384) 164709) ((-1136 . -384) 164693) ((-1035 . -419) 164655) ((-142 . -231) 164637) ((-386 . -802) T) ((-386 . -799) T) ((-878 . -174) T) ((-386 . -734) T) ((-719 . -621) 164619) ((-720 . -38) 164448) ((-1279 . -1277) 164432) ((-358 . -410) T) ((-1279 . -1111) 164382) ((-1202 . -1111) T) ((-588 . -725) 164369) ((-572 . -725) 164356) ((-503 . -725) 164321) ((-1265 . -654) 164211) ((-322 . -637) 164190) ((-844 . -734) T) ((-835 . -734) T) ((-652 . -1229) T) ((-1091 . -647) 164138) ((-1184 . -909) 164081) ((-1136 . -909) 164065) ((-823 . -235) 164011) ((-670 . -1067) 163995) ((-108 . -647) 163977) ((-490 . -132) 163847) ((-1190 . -1123) T) ((-961 . -47) 163816) ((-631 . -1111) T) ((-670 . -111) 163795) ((-499 . -621) 163761) ((-333 . -294) 163738) ((-489 . -47) 163695) ((-1190 . -23) T) ((-118 . -1111) T) ((-103 . -102) 163673) ((-1291 . -1123) T) ((-556 . -858) T) ((-227 . -1229) T) ((-1065 . -132) T) ((-1035 . -1069) T) ((-827 . -1049) 163657) ((-1291 . -23) T) ((-1014 . -732) 163629) 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. -23) T) ((-415 . -102) T) ((-268 . -102) T) ((-110 . -113) T) ((-702 . -296) T) ((-874 . -38) 153518) ((-589 . -111) 153474) ((-526 . -111) 153403) ((-1098 . -624) 153139) ((-426 . -1123) T) ((-322 . -1069) 153029) ((-319 . -1069) T) ((-129 . -1229) T) ((-790 . -624) 152777) ((-788 . -624) 152543) ((-666 . -1060) T) ((-1308 . -1111) T) ((-462 . -624) 152328) ((-171 . -313) 152259) ((-426 . -23) T) ((-40 . -621) 152241) ((-40 . -622) 152225) ((-108 . -1003) 152207) ((-117 . -877) 152191) ((-657 . -624) 152175) ((-48 . -522) 152141) ((-1215 . -1021) 152125) ((-1193 . -621) 152092) ((-1201 . -34) T) ((-963 . -621) 152058) ((-930 . -621) 152040) ((-1124 . -858) 151991) ((-779 . -621) 151973) ((-680 . -621) 151955) ((-1168 . -315) 151893) ((-487 . -34) T) ((-1103 . -1229) T) ((-485 . -460) T) ((-1152 . -34) T) ((-1098 . -1060) T) ((-50 . -624) 151862) ((-790 . -1060) T) ((-788 . -1060) T) ((-655 . -239) 151846) ((-640 . -239) 151792) ((-589 . -624) 151742) ((-526 . -624) 151672) ((-490 . 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T) ((-1073 . -828) T) ((-589 . -375) T) ((-526 . -375) T) ((-1292 . -522) 146422) ((-1271 . -564) 146401) ((-1264 . -1233) 146380) ((-358 . -1163) T) ((-333 . -34) T) ((-44 . -425) 146364) ((-1193 . -624) 146300) ((-881 . -1229) T) ((-398 . -752) 146284) ((-1264 . -564) 146235) ((-1263 . -1229) T) ((-1153 . -654) 146194) ((-739 . -132) T) ((-680 . -624) 146178) ((-1243 . -1233) 146157) ((-1243 . -564) 146108) ((-1242 . -1229) T) ((-1242 . -895) 145981) ((-1242 . -893) 145951) ((-1186 . -132) T) ((-317 . -1094) T) ((-1185 . -132) T) ((-745 . -522) 145884) ((-1179 . -132) T) ((-1137 . -132) T) ((-902 . -1111) T) ((-145 . -852) T) ((-1035 . -1013) T) ((-699 . -621) 145866) ((-1015 . -23) T) ((-531 . -315) 145804) ((-1015 . -1123) T) ((-142 . -522) NIL) ((-874 . -654) 145749) ((-1014 . -356) NIL) ((-982 . -23) T) ((-923 . -1123) T) ((-358 . -38) 145714) ((-923 . -23) T) ((-880 . -909) 145673) ((-82 . -621) 145655) ((-40 . -1060) T) ((-878 . -1067) 145642) ((-878 . -111) 145627) ((-709 . -102) T) ((-702 . -621) 145609) ((-610 . -1229) T) ((-604 . -564) 145588) ((-435 . -1123) T) ((-346 . -1062) 145572) ((-215 . -1111) T) ((-176 . -1062) 145504) ((-482 . -47) 145474) ((-135 . -102) T) ((-40 . -237) 145446) ((-40 . -247) T) ((-117 . -102) T) ((-603 . -564) 145425) ((-346 . -648) 145409) ((-702 . -622) 145317) ((-322 . -522) 145283) ((-176 . -648) 145215) ((-319 . -522) 145107) ((-495 . -235) 145094) ((-1263 . -1049) 145078) ((-1242 . -1049) 144864) ((-1010 . -419) 144848) ((-219 . -235) 144835) ((-435 . -23) T) ((-1131 . -174) T) ((-1265 . -296) T) ((-662 . -725) 144805) ((-145 . -1111) T) ((-48 . -1013) T) ((-415 . -233) 144789) ((-301 . -239) 144739) ((-879 . -929) T) ((-879 . -828) NIL) ((-878 . -624) 144711) ((-872 . -858) T) ((-1242 . -345) 144681) ((-1242 . -384) 144651) ((-224 . -1132) 144635) ((-1279 . -294) 144612) ((-482 . -1229) T) ((-1223 . -656) 144537) ((-1014 . -654) 144467) ((-972 . -21) T) ((-972 . -25) T) ((-743 . -21) T) ((-743 . -25) T) ((-723 . -21) 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. -132) T) ((-666 . -656) 142125) ((-249 . -1021) 142109) ((-880 . -313) T) ((-1303 . -1293) 142093) ((-779 . -800) T) ((-779 . -803) T) ((-709 . -38) 142080) ((-572 . -237) T) ((-503 . -247) T) ((-503 . -237) T) ((-1161 . -239) 142030) ((-1098 . -918) 142009) ((-117 . -38) 141996) ((-211 . -808) T) ((-210 . -808) T) ((-209 . -808) T) ((-208 . -808) T) ((-880 . -1033) 141974) ((-1292 . -497) 141958) ((-790 . -918) 141937) ((-788 . -918) 141916) ((-362 . -1229) 141895) ((-359 . -1229) 141874) ((-351 . -1229) 141853) ((-1201 . -1229) T) ((-269 . -1229) 141832) ((-462 . -918) 141811) ((-745 . -497) 141795) ((-1098 . -656) 141684) ((-707 . -624) 141619) ((-790 . -656) 141508) ((-631 . -1067) 141495) ((-487 . -1229) T) ((-350 . -375) T) ((-142 . -497) 141477) ((-788 . -656) 141366) ((-1152 . -1229) T) ((-557 . -858) T) ((-469 . -656) 141337) ((-269 . -895) 141196) ((-251 . -895) NIL) ((-118 . -1067) 141141) ((-462 . -656) 141030) ((-672 . -1049) 141007) ((-631 . -111) 140992) ((-398 . 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. -622) 135444) ((-745 . -621) 135426) ((-1179 . -235) 135307) ((-807 . -858) 135286) ((-1171 . -152) 135233) ((-1010 . -522) 135145) ((-361 . -237) T) ((-361 . -247) T) ((-396 . -624) 135126) ((-1015 . -25) T) ((-142 . -621) 135108) ((-142 . -622) 135067) ((-919 . -313) T) ((-1015 . -21) T) ((-982 . -25) T) ((-923 . -21) T) ((-923 . -25) T) ((-435 . -21) T) ((-435 . -25) T) ((-851 . -419) 135051) ((-48 . -1060) T) ((-1301 . -1293) 135035) ((-1299 . -1293) 135019) ((-1046 . -612) 134994) ((-322 . -622) 134855) ((-322 . -621) 134837) ((-319 . -622) NIL) ((-319 . -621) 134819) ((-48 . -247) T) ((-48 . -237) T) ((-662 . -292) 134780) ((-558 . -239) 134730) ((-140 . -621) 134697) ((-137 . -621) 134679) ((-115 . -621) 134661) ((-485 . -38) 134626) ((-1303 . -1300) 134605) ((-1294 . -132) T) ((-1302 . -1069) T) ((-1093 . -102) T) ((-88 . -1229) T) ((-508 . -315) NIL) ((-1011 . -107) 134589) ((-898 . -1111) T) ((-894 . -1111) T) ((-1279 . -659) 134573) ((-1279 . -380) 134557) ((-333 . -1229) T) ((-601 . -858) T) ((-1153 . -1111) T) ((-1153 . -1064) 134497) ((-103 . -522) 134430) ((-936 . -621) 134412) ((-350 . -734) T) ((-30 . -621) 134394) ((-874 . -1111) T) ((-851 . -1069) 134373) ((-40 . -656) 134280) ((-227 . -1233) T) ((-415 . -1069) T) ((-1170 . -152) 134262) ((-1010 . -296) 134213) ((-625 . -1111) T) ((-227 . -564) T) ((-325 . -1260) 134197) ((-325 . -1257) 134167) ((-709 . -654) 134139) ((-1201 . -1205) 134118) ((-1086 . -621) 134100) ((-1201 . -107) 134050) ((-655 . -152) 134034) ((-640 . -152) 133980) ((-117 . -654) 133952) ((-487 . -1205) 133931) ((-495 . -148) T) ((-495 . -146) NIL) ((-1131 . -622) 133846) ((-446 . -621) 133828) ((-219 . -148) T) ((-219 . -146) NIL) ((-1131 . -621) 133810) ((-130 . -102) T) ((-52 . -102) T) ((-1243 . -647) 133762) ((-487 . -107) 133712) ((-1004 . -23) T) ((-1303 . -38) 133682) ((-1184 . -1123) T) ((-1136 . -1123) T) ((-1073 . -1233) T) ((-244 . -235) 133628) ((-317 . -102) T) ((-862 . -1123) T) ((-961 . -1233) 133607) ((-489 . 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132797) ((-930 . -802) T) ((-930 . -734) T) ((-779 . -801) T) ((-779 . -802) T) ((-514 . -1111) T) ((-510 . -1111) T) ((-779 . -734) T) ((-227 . -370) T) ((-1301 . -1062) 132781) ((-1299 . -1062) 132765) ((-1301 . -648) 132735) ((-1168 . -1111) 132713) ((-879 . -1233) T) ((-1299 . -648) 132683) ((-662 . -621) 132665) ((-879 . -564) T) ((-702 . -375) NIL) ((-44 . -1062) 132649) ((-1308 . -624) 132631) ((-1302 . -1111) T) ((-678 . -102) T) ((-366 . -1286) 132615) ((-360 . -1286) 132599) ((-44 . -648) 132583) ((-352 . -1286) 132567) ((-556 . -102) T) ((-528 . -858) 132546) ((-1057 . -1111) T) ((-825 . -460) 132525) ((-153 . -1062) 132509) ((-1057 . -1082) 132438) ((-1038 . -987) 132407) ((-827 . -1123) T) ((-1014 . -725) 132352) ((-153 . -648) 132336) ((-394 . -1123) T) ((-484 . -987) 132305) ((-471 . -987) 132274) ((-110 . -152) 132256) ((-73 . -621) 132238) ((-902 . -621) 132220) ((-1091 . -732) 132199) ((-1308 . -1060) T) ((-824 . -647) 132147) ((-300 . -1069) 132089) ((-171 . -1233) 131994) ((-227 . -1123) T) ((-330 . -23) T) ((-1179 . -1003) 131946) ((-851 . -1111) T) ((-1265 . -1067) 131851) ((-1137 . -748) 131830) ((-1263 . -929) 131809) ((-1242 . -929) 131788) ((-878 . -734) T) ((-171 . -564) 131699) ((-588 . -656) 131686) ((-572 . -656) 131658) ((-415 . -1111) T) ((-268 . -1111) T) ((-215 . -621) 131640) ((-503 . -656) 131590) ((-227 . -23) T) ((-1242 . -828) 131543) ((-1301 . -102) T) ((-361 . -1298) 131520) ((-1299 . -102) T) ((-1265 . -111) 131412) ((-823 . -1062) 131309) ((-823 . -648) 131251) ((-145 . -621) 131233) ((-1004 . -132) T) ((-44 . -102) T) ((-244 . -858) 131184) ((-1252 . -1233) 131163) ((-103 . -497) 131147) ((-1302 . -725) 131117) ((-1098 . -47) 131078) ((-1073 . -1123) T) ((-961 . -1123) T) ((-128 . -34) T) ((-122 . -34) T) ((-790 . -47) 131055) ((-788 . -47) 131027) ((-1252 . -564) 130938) ((-361 . -375) T) ((-489 . -1123) T) ((-1184 . -132) T) ((-1136 . -132) T) ((-462 . -47) 130917) ((-879 . -370) T) ((-862 . -132) T) ((-153 . -102) T) 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-1049) 128953) ((-1098 . -1229) 128932) ((-1046 . -294) 128907) ((-588 . -734) T) ((-572 . -802) T) ((-171 . -370) 128858) ((-572 . -799) T) ((-572 . -734) T) ((-503 . -734) T) ((-790 . -1229) T) ((-1157 . -497) 128842) ((-1098 . -895) NIL) ((-879 . -1123) T) ((-118 . -918) NIL) ((-1301 . -1300) 128818) ((-1299 . -1300) 128797) ((-790 . -895) NIL) ((-788 . -895) 128656) ((-1294 . -25) T) ((-1294 . -21) T) ((-1226 . -102) 128634) ((-1117 . -403) T) ((-631 . -656) 128621) ((-462 . -895) NIL) ((-683 . -102) 128599) ((-1098 . -1049) 128426) ((-879 . -23) T) ((-790 . -1049) 128285) ((-788 . -1049) 128142) ((-118 . -656) 128087) ((-462 . -1049) 127963) ((-322 . -624) 127527) ((-319 . -624) 127410) ((-398 . -654) 127379) ((-657 . -1049) 127363) ((-589 . -1229) T) ((-635 . -102) T) ((-526 . -1229) T) ((-224 . -497) 127347) ((-1279 . -34) T) ((-629 . -654) 127306) ((-295 . -1062) 127293) ((-137 . -624) 127277) ((-295 . -648) 127264) ((-643 . -725) 127248) ((-615 . -725) 127232) ((-678 . -38) 127192) ((-325 . -102) T) ((-85 . -621) 127174) ((-50 . -1049) 127158) ((-1131 . -1067) 127145) ((-1098 . -384) 127129) ((-790 . -384) 127113) ((-707 . -734) T) ((-707 . -802) T) ((-707 . -799) T) ((-589 . -1049) 127100) ((-526 . -1049) 127077) ((-60 . -57) 127039) ((-330 . -132) T) ((-322 . -1060) 126929) ((-319 . -1060) T) ((-171 . -1123) T) ((-788 . -384) 126913) ((-45 . -152) 126863) ((-1015 . -1003) 126845) ((-462 . -384) 126829) ((-415 . -174) T) ((-322 . -247) 126808) ((-319 . -247) T) ((-319 . -237) NIL) ((-300 . -1111) 126590) ((-227 . -132) T) ((-1131 . -111) 126575) ((-171 . -23) T) ((-807 . -148) 126554) ((-807 . -146) 126533) ((-256 . -647) 126439) ((-255 . -647) 126345) ((-325 . -290) 126311) ((-1168 . -522) 126244) ((-485 . -654) 126194) ((-1144 . -1111) T) ((-227 . -1071) T) ((-823 . -315) 126132) ((-1098 . -909) 126067) ((-790 . -909) 126010) ((-788 . -909) 125994) ((-1301 . -38) 125964) ((-1299 . -38) 125934) ((-1252 . -1123) T) ((-863 . -1123) T) ((-462 . -909) 125911) ((-866 . -1111) T) ((-1252 . -23) T) ((-1131 . -624) 125883) ((-1073 . -132) T) ((-579 . -1123) T) ((-863 . -23) T) ((-631 . -734) T) ((-362 . -929) T) ((-359 . -929) T) ((-295 . -102) T) ((-351 . -929) T) ((-981 . -1094) T) ((-961 . -132) T) ((-824 . -235) 125856) ((-118 . -802) NIL) ((-118 . -799) NIL) ((-118 . -734) T) ((-702 . -918) NIL) ((-1057 . -522) 125757) ((-489 . -132) T) ((-579 . -23) T) ((-683 . -315) 125695) ((-643 . -769) T) ((-615 . -769) T) ((-1243 . -858) NIL) ((-1091 . -1062) 125605) ((-1014 . -296) T) ((-702 . -656) 125555) ((-256 . -21) T) ((-358 . -1111) T) ((-256 . -25) T) ((-255 . -21) T) ((-255 . -25) T) ((-153 . -38) 125539) ((-2 . -102) T) ((-919 . -929) T) ((-1091 . -648) 125407) ((-490 . -1286) 125377) ((-1131 . -1060) T) ((-719 . -313) T) ((-366 . -1062) 125329) ((-360 . -1062) 125281) ((-352 . -1062) 125233) ((-366 . -648) 125185) ((-225 . -1049) 125162) ((-360 . -648) 125114) ((-108 . -1062) 125064) ((-352 . -648) 125016) ((-300 . -725) 124958) 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-132) T) ((-629 . -856) 122778) ((-1157 . -621) 122740) ((-1157 . -622) 122701) ((-1035 . -799) T) ((-1035 . -802) T) ((-1035 . -734) T) ((-720 . -1067) 122524) ((-492 . -315) 122462) ((-461 . -425) 122432) ((-358 . -174) T) ((-256 . -235) 122378) ((-255 . -235) 122324) ((-295 . -38) 122311) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-276 . -102) T) ((-275 . -102) T) ((-274 . -102) T) ((-350 . -1049) 122288) ((-273 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-361 . -734) T) ((-720 . -111) 122097) ((-678 . -233) 122081) ((-589 . -313) T) ((-526 . -313) T) ((-300 . -522) 122030) ((-108 . -315) NIL) ((-72 . -403) T) ((-1124 . -102) 121820) ((-841 . -419) 121804) ((-1131 . -803) T) ((-1131 . -800) T) ((-709 . -1111) T) ((-586 . -621) 121786) ((-386 . -370) T) ((-171 . -501) 121764) ((-224 . -621) 121696) ((-135 . -1111) T) ((-117 . -1111) T) ((-975 . -1229) T) ((-48 . -734) T) ((-1057 . -497) 121661) ((-142 . -433) 121643) ((-142 . -375) T) ((-1038 . -102) T) ((-520 . -517) 121622) ((-720 . -624) 121378) ((-484 . -102) T) ((-471 . -102) T) ((-1045 . -1123) T) ((-1236 . -621) 121360) ((-1193 . -1049) 121296) ((-1186 . -35) 121262) ((-1186 . -95) 121228) ((-1186 . -1217) 121194) ((-1186 . -1214) 121160) ((-1185 . -1214) 121126) ((-1185 . -1217) 121092) ((-1170 . -315) NIL) ((-89 . -404) T) ((-89 . -403) T) ((-1091 . -1163) 121071) ((-40 . -1229) 121043) ((-1185 . -95) 121009) ((-1045 . -23) T) ((-1185 . -35) 120975) ((-579 . -501) T) ((-1179 . -1214) 120941) ((-1179 . -1217) 120907) ((-1179 . -95) 120873) ((-1179 . -35) 120839) ((-368 . -1123) T) ((-366 . -1163) 120818) ((-360 . -1163) 120797) ((-352 . -1163) 120776) ((-1115 . -292) 120732) ((-1137 . -35) 120698) ((-1137 . -95) 120664) 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. -102) T) ((-110 . -102) T) ((-490 . -648) 119420) ((-40 . -384) 119397) ((-96 . -102) T) ((-661 . -860) 119381) ((-1184 . -235) 119368) ((-1146 . -1094) T) ((-1073 . -21) T) ((-1073 . -25) T) ((-1065 . -1062) 119352) ((-823 . -233) 119321) ((-961 . -25) T) ((-961 . -21) T) ((-1065 . -648) 119263) ((-629 . -1069) T) ((-1131 . -375) T) ((-1038 . -315) 119201) ((-678 . -654) 119160) ((-489 . -25) T) ((-489 . -21) T) ((-392 . -1062) 119144) ((-898 . -621) 119126) ((-894 . -621) 119108) ((-531 . -522) 119041) ((-256 . -858) 118992) ((-255 . -858) 118943) ((-392 . -648) 118913) ((-879 . -647) 118890) ((-484 . -315) 118828) ((-471 . -315) 118766) ((-358 . -296) T) ((-1168 . -1267) 118750) ((-1153 . -621) 118712) ((-1153 . -622) 118673) ((-1151 . -102) T) ((-1010 . -1067) 118569) ((-40 . -909) 118521) ((-1168 . -612) 118498) ((-1308 . -656) 118485) ((-874 . -498) 118462) ((-1074 . -152) 118408) ((-880 . -1233) T) ((-1010 . -111) 118290) ((-346 . -725) 118274) ((-874 . -621) 118236) ((-176 . -725) 118168) ((-415 . -292) 118126) ((-880 . -564) T) ((-108 . -408) 118108) ((-84 . -391) T) ((-84 . -403) T) ((-709 . -174) T) ((-625 . -621) 118090) ((-99 . -734) T) ((-490 . -102) 117880) ((-99 . -481) T) ((-117 . -174) T) ((-1301 . -654) 117839) ((-1299 . -654) 117798) ((-1124 . -38) 117768) ((-171 . -647) 117716) ((-1065 . -102) T) ((-1010 . -624) 117606) ((-879 . -25) T) ((-823 . -242) 117585) ((-879 . -21) T) ((-826 . -102) T) ((-44 . -654) 117528) ((-422 . -102) T) ((-392 . -102) T) ((-110 . -315) NIL) ((-229 . -102) 117506) ((-128 . -1229) T) ((-122 . -1229) T) ((-825 . -1062) 117457) ((-825 . -648) 117399) ((-1045 . -132) T) ((-678 . -374) 117383) ((-153 . -654) 117342) ((-643 . -292) 117300) ((-615 . -292) 117258) ((-1308 . -734) T) ((-1010 . -1060) T) ((-1252 . -647) 117206) ((-1115 . -621) 117188) ((-1014 . -621) 117170) ((-572 . -1229) T) ((-503 . -1229) T) ((-523 . -23) T) ((-518 . -23) T) ((-350 . -313) T) ((-516 . -23) T) ((-328 . -132) T) ((-3 . -1111) T) ((-1014 . -622) 117154) ((-1010 . -247) 117133) ((-1010 . -237) 117112) ((-1271 . -146) 117091) ((-1271 . -148) 117070) ((-841 . -1111) T) ((-1264 . -148) 117049) ((-1264 . -146) 117028) ((-1263 . -1233) 117007) ((-1243 . -146) 116914) ((-1243 . -148) 116821) ((-1242 . -1233) 116800) ((-386 . -132) T) ((-227 . -235) 116787) ((-572 . -895) 116769) ((0 . -1111) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1111) T) ((-1265 . -656) 116674) ((-1263 . -564) 116625) ((-722 . -1123) T) ((-1242 . -564) 116576) ((-572 . -1049) 116558) ((-603 . -148) 116537) ((-603 . -146) 116516) ((-503 . -1049) 116459) ((-1146 . -1148) T) ((-87 . -391) T) ((-87 . -403) T) ((-880 . -370) T) ((-844 . -132) T) ((-835 . -132) T) ((-973 . -654) 116403) ((-722 . -23) T) ((-514 . -621) 116369) ((-510 . -621) 116351) ((-823 . -654) 116101) ((-1303 . -1069) T) ((-386 . -1071) T) ((-1037 . -1111) 116079) ((-55 . -1049) 116061) ((-910 . -34) T) ((-490 . -315) 115999) ((-600 . -102) T) ((-1168 . -622) 115960) 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113521) ((-394 . -858) 113500) ((-1271 . -1217) 113466) ((-1271 . -1214) 113432) ((-1264 . -1214) 113398) ((-523 . -132) T) ((-1264 . -1217) 113364) ((-1243 . -1214) 113330) ((-1243 . -1217) 113296) ((-1271 . -35) 113262) ((-1271 . -95) 113228) ((-1264 . -95) 113194) ((-643 . -621) 113163) ((-615 . -621) 113132) ((-227 . -858) T) ((-1264 . -35) 113098) ((-1263 . -1123) T) ((-1243 . -95) 113064) ((-1131 . -656) 113036) ((-1243 . -35) 113002) ((-1242 . -1123) T) ((-601 . -152) 112984) ((-1091 . -356) 112963) ((-176 . -296) T) ((-118 . -384) 112940) ((-118 . -345) 112917) ((-171 . -235) 112862) ((-878 . -313) T) ((-319 . -802) NIL) ((-319 . -799) NIL) ((-322 . -734) 112711) ((-319 . -734) T) ((-482 . -370) 112690) ((-366 . -356) 112669) ((-360 . -356) 112648) ((-352 . -356) 112627) ((-322 . -481) 112606) ((-1263 . -23) T) ((-1242 . -23) T) ((-726 . -1123) T) ((-722 . -132) T) ((-661 . -102) T) ((-485 . -725) 112571) ((-45 . -288) 112521) ((-105 . -1111) T) ((-68 . -621) 112503) ((-981 . 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-958) 110256) ((-361 . -1229) T) ((-1153 . -237) 110235) ((-1093 . -1111) T) ((-1045 . -25) T) ((-1045 . -21) T) ((-1014 . -1067) 110180) ((-914 . -102) T) ((-874 . -1060) T) ((-702 . -909) NIL) ((-362 . -335) 110164) ((-362 . -370) T) ((-359 . -335) 110148) ((-359 . -370) T) ((-351 . -335) 110132) ((-351 . -370) T) ((-495 . -102) T) ((-1291 . -38) 110102) ((-554 . -858) T) ((-531 . -695) 110052) ((-219 . -102) T) ((-1035 . -1049) 109932) ((-1014 . -111) 109861) ((-1186 . -984) 109830) ((-1185 . -984) 109792) ((-528 . -152) 109776) ((-1091 . -377) 109755) ((-358 . -621) 109737) ((-328 . -21) T) ((-361 . -1049) 109714) ((-328 . -25) T) ((-1179 . -984) 109683) ((-48 . -1229) T) ((-76 . -621) 109665) ((-1137 . -984) 109632) ((-707 . -313) T) ((-130 . -852) T) ((-919 . -370) T) ((-386 . -25) T) ((-386 . -21) T) ((-919 . -335) 109619) ((-86 . -621) 109601) ((-707 . -1033) T) ((-685 . -858) T) ((-1263 . -132) T) ((-1242 . -132) T) ((-910 . -1021) 109585) ((-844 . -21) T) ((-48 . -1049) 109528) ((-844 . -25) T) ((-835 . -25) T) ((-835 . -21) T) ((-1124 . -654) 109278) ((-1301 . -1069) T) ((-557 . -102) T) ((-1299 . -1069) T) ((-662 . -734) T) ((-1115 . -626) 109181) ((-1014 . -624) 109111) ((-1302 . -1067) 109095) ((-823 . -419) 109064) ((-103 . -120) 109048) ((-130 . -1111) T) ((-52 . -1111) T) ((-935 . -621) 109030) ((-879 . -1003) 109007) ((-831 . -102) T) ((-1302 . -111) 108986) ((-661 . -38) 108956) ((-579 . -858) T) ((-362 . -1123) T) ((-359 . -1123) T) ((-351 . -1123) T) ((-269 . -1123) T) ((-251 . -1123) T) ((-631 . -313) 108935) ((-1161 . -315) 108739) ((-672 . -23) T) ((-532 . -1094) T) ((-317 . -1111) T) ((-490 . -233) 108708) ((-153 . -1069) T) ((-362 . -23) T) ((-359 . -23) T) ((-351 . -23) T) ((-118 . -313) T) ((-269 . -23) T) ((-251 . -23) T) ((-1014 . -1060) T) ((-720 . -918) 108687) ((-1168 . -624) 108664) ((-1014 . -237) 108636) ((-1014 . -247) T) ((-118 . -1033) NIL) ((-919 . -1123) T) ((-1264 . -460) 108615) ((-1243 . -460) 108594) ((-531 . -621) 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-984) 104138) ((-325 . -1111) T) ((-415 . -803) 104117) ((-415 . -800) 104096) ((-508 . -497) 104078) ((-1265 . -1049) 104044) ((-1263 . -21) T) ((-1263 . -25) T) ((-1242 . -21) T) ((-1242 . -25) T) ((-823 . -725) 103986) ((-358 . -624) 103916) ((-707 . -412) T) ((-1292 . -1229) T) ((-1124 . -419) 103885) ((-614 . -102) T) ((-1088 . -1229) T) ((-1014 . -375) NIL) ((-679 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1190 . -654) 103795) ((-745 . -1229) T) ((-739 . -1062) 103638) ((-44 . -769) T) ((-739 . -648) 103487) ((-601 . -102) T) ((-661 . -664) 103471) ((-77 . -404) T) ((-77 . -403) T) ((-142 . -1229) T) ((-879 . -148) T) ((-879 . -146) NIL) ((-1228 . -93) T) ((-358 . -1060) T) ((-70 . -390) T) ((-70 . -403) T) ((-1177 . -102) T) ((-678 . -522) 103404) ((-1291 . -654) 103349) ((-697 . -315) 103287) ((-972 . -38) 103184) ((-1192 . -621) 103166) ((-743 . -38) 103136) ((-558 . -315) 102940) ((-1186 . -1062) 102823) ((-322 . 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-1217) 96617) ((-171 . -1214) 96595) ((-211 . -1111) T) ((-210 . -1111) T) ((-117 . -1060) T) ((-209 . -1111) T) ((-208 . -1111) T) ((-205 . -1111) T) ((-204 . -1111) T) ((-203 . -1111) T) ((-202 . -1111) T) ((-201 . -1111) T) ((-200 . -1111) T) ((-199 . -1111) T) ((-198 . -1111) T) ((-197 . -1111) T) ((-196 . -1111) T) ((-195 . -1111) T) ((-244 . -102) 96385) ((-171 . -35) 96363) ((-171 . -95) 96341) ((-662 . -1049) 96237) ((-490 . -1069) 96167) ((-1124 . -1111) 95957) ((-1153 . -34) T) ((-678 . -497) 95941) ((-73 . -1229) T) ((-105 . -621) 95923) ((-1303 . -621) 95905) ((-388 . -621) 95887) ((-346 . -624) 95839) ((-176 . -624) 95756) ((-1228 . -498) 95737) ((-739 . -38) 95586) ((-579 . -1217) T) ((-579 . -1214) T) ((-539 . -621) 95568) ((-528 . -315) 95506) ((-508 . -621) 95488) ((-508 . -622) 95470) ((-1228 . -621) 95436) ((-1179 . -1163) NIL) ((-1038 . -1082) 95405) ((-1038 . -1111) T) ((-1015 . -102) T) ((-982 . -102) T) ((-923 . -102) T) ((-902 . -1049) 95382) ((-1153 . -734) T) 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-375) T) ((-532 . -102) T) ((-503 . -27) T) ((-244 . -315) 94111) ((-1098 . -1123) T) ((-1302 . -656) 94085) ((-790 . -1123) T) ((-788 . -1123) T) ((-1190 . -419) 94069) ((-462 . -1123) T) ((-1073 . -460) T) ((-1162 . -1111) T) ((-961 . -460) 94020) ((-1126 . -1094) T) ((-110 . -1111) T) ((-1098 . -23) T) ((-1171 . -522) 93803) ((-825 . -1069) T) ((-790 . -23) T) ((-788 . -23) T) ((-489 . -460) 93754) ((-469 . -23) T) ((-388 . -389) 93733) ((-362 . -235) 93706) ((-359 . -235) 93679) ((-351 . -235) 93652) ((-462 . -23) T) ((-269 . -235) 93625) ((-96 . -1111) T) ((-720 . -1229) T) ((-678 . -292) 93602) ((-492 . -522) 93535) ((-1271 . -1062) 93418) ((-1271 . -648) 93315) ((-1264 . -648) 93156) ((-1264 . -1062) 92991) ((-1243 . -648) 92787) ((-295 . -296) T) ((-1243 . -1062) 92577) ((-1093 . -621) 92559) ((-1093 . -622) 92540) ((-415 . -918) 92519) ((-1223 . -132) T) ((-50 . -1123) T) ((-1179 . -408) 92471) ((-1035 . -929) T) ((-1014 . -734) T) ((-851 . -656) 92444) ((-720 . -895) NIL) 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T) ((-1291 . -1069) T) ((-1271 . -102) T) ((-1131 . -553) T) ((-587 . -102) T) ((-130 . -498) 91234) ((-1264 . -102) T) ((-398 . -1067) 91218) ((-1184 . -958) 91187) ((-44 . -292) 91164) ((-130 . -621) 91131) ((-52 . -621) 91113) ((-1136 . -958) 91080) ((-661 . -419) 91064) ((-1243 . -102) T) ((-1170 . -522) NIL) ((-670 . -25) T) ((-629 . -1067) 91048) ((-670 . -21) T) ((-972 . -654) 90958) ((-743 . -654) 90903) ((-723 . -654) 90875) ((-398 . -111) 90854) ((-224 . -259) 90838) ((-1065 . -1064) 90778) ((-1065 . -1111) T) ((-1015 . -1163) T) ((-826 . -1111) T) ((-461 . -654) 90693) ((-350 . -1233) T) ((-643 . -656) 90677) ((-629 . -111) 90656) ((-615 . -656) 90640) ((-604 . -102) T) ((-317 . -498) 90621) ((-594 . -132) T) ((-603 . -102) T) ((-422 . -1111) T) ((-392 . -1111) T) ((-317 . -621) 90587) ((-229 . -1111) 90565) ((-655 . -522) 90498) ((-640 . -522) 90342) ((-841 . -1060) 90321) ((-652 . -152) 90305) ((-350 . -564) T) ((-720 . -909) 90248) ((-558 . -231) 90198) ((-1271 . -290) 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87547) ((-1294 . -648) 87517) ((-485 . -247) T) ((-824 . -102) T) ((-722 . -148) 87496) ((-722 . -146) 87475) ((-492 . -497) 87459) ((-493 . -342) 87428) ((-1303 . -111) 87407) ((-520 . -1111) T) ((-490 . -174) 87386) ((-1010 . -384) 87370) ((-421 . -102) T) ((-388 . -111) 87349) ((-1010 . -345) 87333) ((-284 . -994) 87317) ((-283 . -994) 87301) ((-1301 . -621) 87283) ((-1299 . -621) 87265) ((-110 . -522) NIL) ((-1184 . -1255) 87249) ((-862 . -860) 87233) ((-1190 . -1111) T) ((-103 . -1229) T) ((-961 . -958) 87194) ((-825 . -725) 87136) ((-1243 . -1163) NIL) ((-489 . -958) 87081) ((-1073 . -144) T) ((-60 . -102) 87059) ((-44 . -621) 87041) ((-78 . -621) 87023) ((-358 . -656) 86968) ((-1291 . -1111) T) ((-519 . -858) T) ((-295 . -292) 86947) ((-350 . -1123) T) ((-301 . -1111) T) ((-1010 . -909) 86906) ((-301 . -618) 86885) ((-1303 . -624) 86834) ((-1271 . -38) 86731) ((-1264 . -38) 86572) ((-1243 . -38) 86368) ((-495 . -1069) T) ((-388 . -624) 86352) ((-219 . -1069) T) ((-350 . -23) T) 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. -146) 83472) ((-1242 . -148) 83397) ((-1294 . -1300) 83376) ((-484 . -497) 83360) ((-471 . -497) 83344) ((-531 . -34) T) ((-661 . -725) 83314) ((-112 . -978) T) ((-670 . -858) 83293) ((-1190 . -174) 83244) ((-372 . -102) T) ((-244 . -242) 83223) ((-256 . -102) T) ((-255 . -102) T) ((-1252 . -958) 83192) ((-249 . -858) 83171) ((-824 . -38) 83020) ((-45 . -522) 82812) ((-1170 . -292) 82762) ((-216 . -1111) T) ((-1161 . -1111) T) ((-1161 . -618) 82741) ((-594 . -25) T) ((-594 . -21) T) ((-1113 . -315) 82679) ((-972 . -419) 82663) ((-707 . -1233) T) ((-640 . -292) 82616) ((-1098 . -647) 82564) ((-790 . -647) 82512) ((-788 . -647) 82460) ((-350 . -132) T) ((-295 . -621) 82442) ((-914 . -1111) T) ((-707 . -564) T) ((-130 . -624) 82424) ((-878 . -1123) T) ((-462 . -647) 82372) ((-914 . -912) 82356) ((-386 . -460) T) ((-495 . -1111) T) ((-952 . -315) 82294) ((-709 . -656) 82266) ((-557 . -852) T) ((-219 . -1111) T) ((-322 . -929) 82245) ((-319 . -929) T) ((-319 . -828) NIL) ((-398 . -728) T) 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. -564) T) ((-469 . -21) T) ((-462 . -25) T) ((-462 . -21) T) ((-1263 . -95) 80896) ((-1162 . -93) T) ((-1153 . -1049) 80792) ((-825 . -296) 80771) ((-1246 . -102) 80749) ((-831 . -1111) T) ((-975 . -978) T) ((-678 . -111) 80728) ((-625 . -1229) T) ((-301 . -522) 80520) ((-1243 . -233) 80472) ((-1242 . -1214) 80438) ((-1242 . -1217) 80404) ((-256 . -315) 80342) ((-255 . -315) 80280) ((-1237 . -375) T) ((-1171 . -622) NIL) ((-1171 . -621) 80262) ((-1234 . -852) T) ((-1153 . -384) 80246) ((-1131 . -828) T) ((-96 . -93) T) ((-1131 . -929) T) ((-1124 . -612) 80223) ((-1091 . -622) 80207) ((-1015 . -654) 80157) ((-923 . -654) 80094) ((-823 . -294) 80071) ((-492 . -621) 80003) ((-616 . -152) 79950) ((-495 . -725) 79900) ((-426 . -1069) T) ((-490 . -497) 79884) ((-435 . -654) 79843) ((-333 . -858) 79822) ((-346 . -656) 79796) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -725) 79746) ((-171 . -732) 79717) ((-176 . -656) 79649) ((-589 . -21) T) ((-589 . -25) T) ((-526 . -25) T) ((-526 . -21) T) 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-292) 78826) ((-1014 . -1229) 78798) ((-129 . -152) 78780) ((-1153 . -909) 78739) ((-44 . -111) 78718) ((-1234 . -1111) T) ((-1193 . -1274) T) ((-1178 . -498) 78699) ((-1178 . -621) 78665) ((-678 . -1060) T) ((-1170 . -622) NIL) ((-1170 . -621) 78647) ((-1074 . -618) 78622) ((-1074 . -1111) T) ((-1005 . -498) 78603) ((-74 . -449) T) ((-74 . -403) T) ((-1005 . -621) 78569) ((-153 . -1067) 78553) ((-678 . -237) 78532) ((-579 . -562) 78516) ((-362 . -148) 78495) ((-362 . -146) 78446) ((-359 . -148) 78425) ((-359 . -146) 78376) ((-351 . -148) 78355) ((-351 . -146) 78306) ((-269 . -146) 78285) ((-269 . -148) 78264) ((-256 . -38) 78234) ((-251 . -148) 78213) ((-118 . -370) T) ((-251 . -146) 78192) ((-255 . -38) 78162) ((-153 . -111) 78141) ((-1014 . -1049) 78029) ((-1179 . -856) NIL) ((-702 . -1233) T) ((-807 . -1069) T) ((-707 . -1123) T) ((-1299 . -1060) T) ((-1168 . -1229) T) ((-1014 . -384) 78006) ((-919 . -146) T) ((-919 . -148) 77988) ((-878 . -132) T) ((-823 . -1067) 77885) ((-707 . -23) T) ((-702 . -564) T) ((-227 . -1062) 77850) ((-655 . -621) 77782) ((-655 . -622) 77743) ((-640 . -622) NIL) ((-640 . -621) 77725) ((-495 . -174) T) ((-227 . -648) 77690) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-482 . -1217) 77656) ((-482 . -1214) 77622) ((-279 . -621) 77604) ((-278 . -621) 77586) ((-277 . -621) 77568) ((-276 . -621) 77550) ((-275 . -621) 77532) ((-508 . -659) 77514) ((-274 . -621) 77496) ((-346 . -734) T) ((-273 . -621) 77478) ((-110 . -19) 77460) ((-176 . -734) T) ((-508 . -380) 77442) ((-214 . -621) 77424) ((-528 . -1160) 77408) ((-508 . -124) T) ((-110 . -612) 77383) ((-213 . -621) 77365) ((-482 . -35) 77331) ((-482 . -95) 77297) ((-211 . -621) 77279) ((-210 . -621) 77261) ((-209 . -621) 77243) ((-208 . -621) 77225) ((-205 . -621) 77207) ((-204 . -621) 77189) ((-203 . -621) 77171) ((-202 . -621) 77153) ((-201 . -621) 77135) ((-200 . -621) 77117) ((-199 . -621) 77099) ((-544 . -1114) 77051) ((-198 . -621) 77033) ((-197 . -621) 77015) ((-45 . -497) 76952) ((-196 . -621) 76934) ((-195 . -621) 76916) ((-153 . -624) 76885) ((-1126 . -102) T) ((-823 . -111) 76775) ((-652 . -102) 76725) ((-490 . -292) 76702) ((-1302 . -1049) 76686) ((-1124 . -621) 76417) ((-1112 . -1111) T) ((-1057 . -1229) T) ((-1184 . -315) 76404) ((-1073 . -1062) 76391) ((-1146 . -1111) T) ((-961 . -1062) 76234) ((-1136 . -315) 76221) ((-1107 . -1094) T) ((-631 . -1123) T) ((-1073 . -648) 76208) ((-1101 . -1094) T) ((-961 . -648) 76057) ((-1098 . -235) 76030) ((-489 . -1062) 75873) ((-1084 . -1094) T) ((-1077 . -1094) T) ((-1047 . -1094) T) ((-1030 . -1094) T) ((-118 . -1123) T) ((-489 . -648) 75722) ((-790 . -235) 75709) ((-827 . -102) T) ((-634 . -1094) T) ((-631 . -23) T) ((-1161 . -522) 75501) ((-491 . -1094) T) ((-394 . -102) T) ((-330 . -102) T) ((-220 . -1094) T) ((-972 . -1111) T) ((-153 . -1060) T) ((-739 . -419) 75485) ((-118 . -23) T) ((-1014 . -909) 75437) ((-743 . -1111) T) ((-723 . -1111) T) ((-461 . -1111) T) ((-415 . -1229) T) ((-322 . -438) 75421) 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\ No newline at end of file
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-500) 189852) ((-612 . -294) 189804) ((-615 . -623) 189771) ((-398 . -102) T) ((-1133 . -144) T) ((-127 . -623) 189703) ((-884 . -1113) T) ((-668 . -421) 189687) ((-724 . -623) 189669) ((-255 . -623) 189636) ((-189 . -623) 189618) ((-163 . -623) 189600) ((-158 . -623) 189582) ((-1296 . -736) T) ((-1115 . -34) T) ((-881 . -805) NIL) ((-881 . -802) NIL) ((-868 . -860) T) ((-741 . -897) NIL) ((-1305 . -132) T) ((-390 . -132) T) ((-903 . -626) 189550) ((-915 . -102) T) ((-741 . -1051) 189426) ((-1188 . -1231) T) ((-541 . -132) T) ((-1187 . -1231) T) ((-1100 . -421) 189410) ((-1013 . -499) 189394) ((-118 . -410) 189371) ((-1181 . -1231) T) ((-792 . -421) 189355) ((-790 . -421) 189339) ((-954 . -34) T) ((-704 . -1165) NIL) ((-258 . -658) 189111) ((-257 . -658) 188870) ((-827 . -931) 188849) ((-464 . -421) 188833) ((-612 . -19) 188817) ((-1159 . -1224) 188786) ((-1181 . -897) NIL) ((-1181 . -895) 188738) ((-612 . -614) 188715) ((-1217 . -623) 188647) ((-1189 . -623) 188629) ((-62 . -405) T) 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187304) ((-1187 . -911) 187210) ((-1181 . -911) 187043) ((-1139 . -911) 187027) ((-680 . -1125) T) ((-363 . -1165) T) ((-655 . -93) T) ((-330 . -1069) 187009) ((-258 . -801) 186988) ((-258 . -804) 186939) ((-31 . -500) 186920) ((-258 . -803) 186899) ((-257 . -801) 186878) ((-257 . -804) 186829) ((-257 . -803) 186808) ((-31 . -623) 186774) ((-50 . -1071) T) ((-258 . -736) 186684) ((-257 . -736) 186594) ((-1225 . -1113) T) ((-680 . -23) T) ((-591 . -1071) T) ((-528 . -1071) T) ((-388 . -1069) 186559) ((-330 . -111) 186534) ((-73 . -392) T) ((-73 . -405) T) ((-1037 . -38) 186471) ((-704 . -410) 186453) ((-99 . -102) T) ((-721 . -1113) T) ((-1310 . -1064) 186440) ((-1016 . -146) 186412) ((-1016 . -148) 186384) ((-880 . -656) 186356) ((-388 . -111) 186312) ((-327 . -1235) 186291) ((-484 . -1015) 186257) ((-363 . -38) 186222) ((-40 . -379) 186194) ((-883 . -623) 186066) ((-128 . -126) 186050) ((-122 . -126) 186034) ((-846 . -1069) 186004) ((-843 . -21) 185956) ((-837 . -1069) 185940) ((-843 . -25) 185892) ((-327 . -566) 185843) ((-527 . -626) 185824) ((-574 . -838) T) ((-246 . -1231) T) ((-1047 . -626) 185793) ((-846 . -111) 185758) ((-837 . -111) 185737) ((-1265 . -623) 185719) ((-1244 . -623) 185701) ((-1244 . -624) 185372) ((-1186 . -920) 185351) ((-1138 . -920) 185330) ((-48 . -38) 185295) ((-1303 . -1125) T) ((-546 . -294) 185251) ((-612 . -623) 185163) ((-612 . -624) 185124) ((-1301 . -1125) T) ((-370 . -626) 185108) ((-330 . -626) 185092) ((-246 . -1051) 184919) ((-1186 . -658) 184808) ((-1138 . -658) 184697) ((-864 . -658) 184671) ((-728 . -623) 184653) ((-556 . -377) T) ((-1303 . -23) T) ((-1301 . -23) T) ((-501 . -1113) T) ((-388 . -626) 184603) ((-388 . -628) 184585) ((-1047 . -1062) T) ((-875 . -102) T) ((-1203 . -294) 184564) ((-171 . -377) 184515) ((-1017 . -1231) T) ((-846 . -626) 184469) ((-837 . -626) 184424) ((-44 . -23) T) ((-489 . -294) 184403) ((-596 . -1113) T) ((-1159 . -1122) 184372) ((-1117 . -1116) 184324) ((-400 . -21) T) ((-400 . -25) T) ((-153 . -1125) T) ((-1310 . -102) T) ((-1017 . -895) 184306) ((-1017 . -897) 184288) ((-1225 . -727) 184185) ((-633 . -233) 184169) ((-631 . -21) T) ((-297 . -566) T) ((-631 . -25) T) ((-1211 . -1113) T) ((-721 . -727) 184134) ((-246 . -386) 184103) ((-1017 . -1051) 184063) ((-388 . -1062) T) ((-225 . -1071) T) ((-118 . -233) 184040) ((-59 . -294) 183992) ((-153 . -23) T) ((-526 . -294) 183944) ((-335 . -524) 183877) ((-506 . -294) 183829) ((-388 . -249) T) ((-388 . -239) T) ((-846 . -1062) T) ((-837 . -1062) T) ((-722 . -960) 183798) ((-711 . -860) T) ((-484 . -623) 183780) ((-1267 . -1064) 183685) ((-590 . -656) 183657) ((-574 . -656) 183629) ((-505 . -656) 183579) ((-837 . -239) 183558) ((-135 . -860) T) ((-1267 . -650) 183450) ((-668 . -1113) T) ((-1203 . -614) 183429) ((-560 . -1207) 183408) ((-345 . -1113) T) ((-327 . -372) 183387) ((-417 . -148) 183366) ((-417 . -146) 183345) ((-975 . -1125) 183244) ((-246 . -911) 183176) ((-825 . -1125) 183086) ((-664 . -862) 183070) ((-489 . -614) 183049) ((-560 . -107) 182999) ((-1017 . -386) 182981) ((-1017 . -347) 182963) ((-97 . -1113) T) ((-975 . -23) 182774) ((-487 . -21) T) ((-487 . -25) T) ((-825 . -23) 182644) ((-1190 . -623) 182626) ((-59 . -19) 182610) ((-1190 . -624) 182532) ((-1186 . -736) T) ((-1138 . -736) T) ((-526 . -19) 182516) ((-506 . -19) 182500) ((-59 . -614) 182477) ((-1100 . -1113) T) ((-912 . -102) 182455) ((-864 . -736) T) ((-792 . -1113) T) ((-526 . -614) 182432) ((-506 . -614) 182409) ((-790 . -1113) T) ((-790 . -1078) 182376) ((-471 . -1113) T) ((-464 . -1113) T) ((-596 . -727) 182351) ((-659 . -1113) T) ((-1273 . -47) 182328) ((-1267 . -102) T) ((-1266 . -47) 182298) ((-1245 . -47) 182275) ((-1225 . -174) 182226) ((-1187 . -315) 182205) ((-1181 . -315) 182184) ((-1109 . -626) 182165) ((-1103 . -626) 182146) ((-1093 . -566) 182097) ((-1017 . -911) NIL) ((-1093 . -1235) 182048) ((-680 . -132) T) ((-637 . -1125) T) ((-1086 . -626) 182029) ((-1079 . -626) 182010) ((-1049 . -626) 181991) ((-1032 . -626) 181972) ((-709 . -656) 181922) ((-282 . -1113) T) ((-85 . -451) T) ((-85 . -405) T) ((-724 . -1069) 181892) ((-721 . -174) T) ((-50 . -1113) T) ((-605 . -47) 181869) ((-227 . -658) 181834) ((-591 . -1113) T) ((-528 . -1113) T) ((-497 . -830) T) ((-497 . -931) T) ((-368 . -1235) T) ((-362 . -1235) T) ((-354 . -1235) T) ((-327 . -1125) T) ((-324 . -1064) 181744) ((-321 . -1064) 181673) ((-108 . -1235) T) ((-636 . -626) 181654) ((-368 . -566) T) ((-219 . -931) T) ((-219 . -830) T) ((-324 . -650) 181564) ((-321 . -650) 181493) ((-362 . -566) T) ((-354 . -566) T) ((-493 . -626) 181474) ((-108 . -566) T) ((-668 . -727) 181444) ((-1181 . -1035) NIL) ((-220 . -626) 181425) ((-327 . -23) T) ((-67 . -1231) T) ((-1013 . -623) 181357) ((-704 . -233) 181339) ((-724 . -111) 181304) ((-654 . -34) T) ((-251 . -499) 181288) ((-1310 . -1165) T) ((-1305 . -21) T) ((-1305 . -25) T) ((-1115 . -1111) 181272) ((-173 . -1113) T) ((-1303 . -132) T) ((-1301 . -132) T) ((-1294 . -102) T) ((-1277 . -623) 181238) 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178577) ((-59 . -623) 178489) ((-227 . -736) T) ((-526 . -624) 178450) ((-526 . -623) 178362) ((-507 . -623) 178294) ((-506 . -624) 178255) ((-506 . -623) 178167) ((-1093 . -372) 178118) ((-40 . -421) 178095) ((-77 . -1231) T) ((-881 . -920) NIL) ((-368 . -337) 178079) ((-368 . -372) T) ((-362 . -337) 178063) ((-362 . -372) T) ((-354 . -337) 178047) ((-354 . -372) T) ((-324 . -292) 178026) ((-108 . -372) T) ((-70 . -1231) T) ((-1245 . -347) 177978) ((-881 . -658) 177923) ((-1245 . -386) 177875) ((-975 . -132) 177730) ((-825 . -132) 177600) ((-969 . -661) 177584) ((-1100 . -174) 177495) ((-969 . -382) 177479) ((-1075 . -804) T) ((-1075 . -801) T) ((-882 . -626) 177377) ((-792 . -174) 177268) ((-790 . -174) 177179) ((-826 . -47) 177141) ((-1075 . -736) T) ((-335 . -499) 177125) ((-963 . -736) T) ((-1294 . -317) 177063) ((-464 . -174) 176974) ((-251 . -294) 176926) ((-1273 . -911) 176839) ((-1266 . -911) 176745) ((-1265 . -1069) 176580) ((-491 . -736) T) ((-1245 . -911) 176413) ((-1244 . -1069) 176221) ((-1225 . -298) 176200) ((-1200 . -1231) T) ((-1197 . -377) T) ((-1196 . -377) T) ((-1159 . -152) 176184) ((-1133 . -102) T) ((-1131 . -1113) T) ((-1093 . -23) T) ((-1093 . -1125) T) ((-1088 . -102) T) ((-1070 . -623) 176151) ((-938 . -966) T) ((-747 . -317) 176089) ((-75 . -1231) T) ((-674 . -391) 176061) ((-171 . -920) 176014) ((-30 . -966) T) ((-112 . -854) T) ((-1 . -623) 175996) ((-1016 . -419) 175968) ((-129 . -661) 175950) ((-50 . -630) 175934) ((-704 . -656) 175869) ((-605 . -911) 175782) ((-448 . -102) T) ((-129 . -382) 175764) ((-142 . -317) NIL) ((-882 . -1062) T) ((-843 . -860) 175743) ((-81 . -1231) T) ((-721 . -298) T) ((-40 . -1071) T) ((-591 . -174) T) ((-528 . -174) T) ((-521 . -623) 175725) ((-171 . -658) 175599) ((-517 . -623) 175581) ((-360 . -148) 175563) ((-360 . -146) T) ((-368 . -1125) T) ((-362 . -1125) T) ((-354 . -1125) T) ((-1017 . -315) T) ((-925 . -315) T) ((-882 . -249) T) ((-108 . -1125) T) ((-882 . -239) 175542) ((-1265 . -111) 175363) 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-1113) T) ((-321 . -1165) NIL) ((-297 . -132) T) ((-404 . -1113) T) ((-880 . -1071) T) ((-704 . -379) 173467) ((-363 . -656) 173397) ((-225 . -630) 173374) ((-335 . -294) 173326) ((-484 . -111) 173147) ((-1265 . -1062) T) ((-1244 . -1062) T) ((-826 . -386) 173131) ((-171 . -736) T) ((-664 . -102) T) ((-1265 . -249) 173110) ((-1265 . -239) 173062) ((-1244 . -239) 172967) ((-1244 . -249) 172946) ((-1016 . -412) NIL) ((-680 . -649) 172894) ((-324 . -38) 172804) ((-321 . -38) 172733) ((-69 . -623) 172715) ((-327 . -503) 172681) ((-48 . -656) 172631) ((-1203 . -296) 172610) ((-1239 . -860) T) ((-1126 . -1125) 172520) ((-83 . -1231) T) ((-61 . -623) 172502) ((-489 . -296) 172481) ((-1296 . -1051) 172458) ((-1178 . -1113) T) ((-1126 . -23) 172328) ((-826 . -911) 172264) ((-1254 . -736) T) ((-1115 . -1231) T) ((-484 . -626) 172090) ((-1100 . -298) 172021) ((-977 . -1113) T) ((-904 . -102) T) ((-792 . -298) 171932) ((-335 . -19) 171916) ((-59 . -296) 171893) ((-790 . -298) 171824) ((-865 . -736) T) ((-118 . -858) NIL) ((-526 . -296) 171801) ((-335 . -614) 171778) ((-506 . -296) 171755) ((-464 . -298) 171686) ((-1048 . -317) 171537) ((-886 . -500) 171518) ((-886 . -623) 171484) ((-691 . -500) 171465) ((-581 . -736) T) ((-686 . -500) 171446) ((-691 . -623) 171396) ((-686 . -623) 171362) ((-672 . -623) 171344) ((-488 . -500) 171325) ((-488 . -623) 171291) ((-251 . -624) 171252) ((-251 . -500) 171229) ((-139 . -500) 171210) ((-138 . -500) 171191) ((-134 . -500) 171172) ((-251 . -623) 171064) ((-215 . -102) T) ((-139 . -623) 171030) ((-138 . -623) 170996) ((-134 . -623) 170962) ((-1160 . -34) T) ((-954 . -1231) T) ((-352 . -727) 170907) ((-680 . -25) T) ((-680 . -21) T) ((-1190 . -626) 170888) ((-484 . -1062) T) ((-645 . -427) 170853) ((-617 . -427) 170818) ((-1133 . -1165) T) ((-722 . -1064) 170641) ((-591 . -298) T) ((-528 . -298) T) ((-1266 . -315) 170620) ((-484 . -239) 170572) ((-484 . -249) 170551) ((-1245 . -315) 170530) ((-722 . -650) 170359) ((-1245 . -1035) NIL) ((-1093 . -132) T) ((-882 . -805) 170338) ((-145 . -102) T) ((-40 . -1113) T) ((-882 . -802) 170317) ((-654 . -1023) 170301) ((-590 . -1071) T) ((-574 . -1071) T) ((-505 . -1071) T) ((-417 . -462) T) ((-368 . -132) T) ((-324 . -410) 170285) ((-321 . -410) 170246) ((-362 . -132) T) ((-354 . -132) T) ((-1195 . -1113) T) ((-1133 . -38) 170233) ((-1107 . -623) 170200) ((-108 . -132) T) ((-965 . -1113) T) ((-932 . -1113) T) ((-781 . -1113) T) ((-682 . -1113) T) ((-711 . -148) T) ((-117 . -148) T) ((-1303 . -21) T) ((-1303 . -25) T) ((-1301 . -21) T) ((-1301 . -25) T) ((-674 . -1069) 170184) ((-541 . -860) T) ((-510 . -860) T) ((-364 . -1069) 170136) ((-361 . -1069) 170088) ((-353 . -1069) 170040) ((-258 . -1231) T) ((-257 . -1231) T) ((-271 . -1069) 169883) ((-253 . -1069) 169726) ((-674 . -111) 169705) ((-557 . -854) T) ((-364 . -111) 169643) ((-361 . -111) 169581) ((-353 . -111) 169519) ((-271 . -111) 169348) ((-253 . -111) 169177) ((-827 . -1235) 169156) ((-633 . -421) 169140) ((-44 . -21) T) ((-44 . -25) T) ((-825 . -649) 169046) ((-827 . -566) 169025) ((-258 . -1051) 168852) ((-257 . -1051) 168679) ((-127 . -120) 168663) ((-921 . -1069) 168628) ((-722 . -102) T) ((-709 . -1071) T) ((-607 . -626) 168609) ((-595 . -626) 168590) ((-546 . -628) 168493) ((-352 . -174) T) ((-88 . -623) 168475) ((-153 . -21) T) ((-153 . -25) T) ((-921 . -111) 168431) ((-40 . -727) 168376) ((-880 . -1113) T) ((-674 . -626) 168353) ((-655 . -626) 168334) ((-364 . -626) 168271) ((-361 . -626) 168208) ((-557 . -1113) T) ((-353 . -626) 168145) ((-335 . -624) 168106) ((-335 . -623) 168018) ((-271 . -626) 167771) ((-253 . -626) 167556) ((-1244 . -802) 167509) ((-1244 . -805) 167462) ((-258 . -386) 167431) ((-257 . -386) 167400) ((-664 . -38) 167370) ((-618 . -34) T) ((-492 . -1125) 167280) ((-485 . -34) T) ((-1126 . -132) 167150) ((-975 . -25) 166961) ((-921 . -626) 166911) ((-884 . -623) 166893) ((-975 . -21) 166848) ((-825 . -21) 166758) ((-825 . -25) 166609) ((-1237 . -377) T) ((-633 . -1071) T) ((-1192 . -566) 166588) ((-1186 . -47) 166565) ((-364 . -1062) T) ((-361 . -1062) T) ((-492 . -23) 166435) ((-353 . -1062) T) ((-271 . -1062) T) ((-253 . -1062) T) ((-1138 . -47) 166407) ((-118 . -1071) T) ((-1047 . -658) 166381) ((-969 . -34) T) ((-364 . -239) 166360) ((-364 . -249) T) ((-361 . -239) 166339) ((-361 . -249) T) ((-353 . -239) 166318) ((-353 . -249) T) ((-271 . -334) 166290) ((-253 . -334) 166247) ((-271 . -239) 166226) ((-1170 . -152) 166210) ((-258 . -911) 166142) ((-257 . -911) 166074) ((-1095 . -860) T) ((-424 . -1125) T) ((-1067 . -23) T) ((-921 . -1062) T) ((-330 . -658) 166056) ((-1037 . -858) T) ((-680 . -235) 166029) ((-1225 . -1015) 165995) ((-1187 . -931) 165974) ((-1181 . -931) 165953) ((-1181 . -830) NIL) ((-1012 . -1064) 165849) ((-978 . -1231) T) ((-921 . -249) T) ((-827 . -372) 165828) ((-394 . -23) T) ((-128 . -1113) 165806) ((-122 . -1113) 165784) ((-921 . -239) T) ((-129 . -34) T) ((-388 . -658) 165749) ((-1012 . -650) 165697) ((-880 . -727) 165684) ((-1310 . -656) 165656) ((-1059 . -152) 165621) ((-1006 . -1231) T) ((-40 . -174) T) ((-704 . -421) 165603) ((-722 . -317) 165590) ((-846 . -658) 165550) ((-837 . -658) 165524) ((-327 . -25) T) ((-327 . -21) T) ((-668 . -294) 165503) ((-590 . -1113) T) ((-574 . -1113) T) ((-505 . -1113) T) ((-251 . -296) 165480) ((-1186 . -1231) T) ((-321 . -233) 165441) ((-1186 . -897) NIL) ((-55 . -1113) T) ((-1138 . -897) 165300) ((-130 . -860) T) ((-1186 . -1051) 165180) ((-1138 . -1051) 165063) ((-185 . -623) 165045) ((-864 . -1051) 164941) ((-792 . -294) 164868) ((-827 . -1125) T) ((-1047 . -736) T) ((-612 . -661) 164852) ((-1059 . -989) 164781) ((-1012 . -102) T) ((-827 . -23) T) ((-722 . -1165) 164759) ((-704 . -1071) T) ((-612 . -382) 164743) ((-360 . -462) T) ((-352 . -298) T) ((-1282 . -1113) T) ((-254 . -1113) T) ((-409 . -102) T) ((-297 . -21) T) ((-297 . -25) T) ((-370 . -736) T) ((-720 . -1113) T) ((-709 . -1113) T) ((-370 . -483) T) ((-1225 . -623) 164725) ((-1186 . -386) 164709) ((-1138 . -386) 164693) ((-1037 . -421) 164655) ((-142 . -231) 164637) ((-388 . -804) T) ((-388 . -801) T) ((-880 . -174) T) ((-388 . -736) T) ((-721 . -623) 164619) ((-722 . -38) 164448) ((-1281 . -1279) 164432) ((-360 . -412) T) ((-1281 . -1113) 164382) ((-1204 . -1113) T) ((-590 . -727) 164369) ((-574 . -727) 164356) ((-505 . -727) 164321) ((-1267 . -656) 164211) ((-324 . -639) 164190) ((-846 . -736) T) ((-837 . -736) T) ((-654 . -1231) T) ((-1093 . -649) 164138) ((-1186 . -911) 164081) ((-1138 . -911) 164065) ((-825 . -235) 164011) ((-672 . -1069) 163995) ((-108 . -649) 163977) ((-492 . -132) 163847) ((-1192 . -1125) T) ((-963 . -47) 163816) ((-633 . -1113) T) ((-672 . -111) 163795) ((-501 . -623) 163761) ((-335 . -296) 163738) ((-491 . -47) 163695) ((-1192 . -23) T) ((-118 . -1113) T) ((-103 . -102) 163673) ((-1293 . -1125) T) ((-558 . -860) T) ((-227 . -1231) T) ((-1067 . -132) T) ((-1037 . -1071) T) ((-829 . -1051) 163657) ((-1293 . -23) T) ((-1016 . -734) 163629) 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-746) 162718) ((-345 . -623) 162700) ((-68 . -392) T) ((-68 . -405) T) ((-1115 . -107) 162684) ((-1075 . -897) 162666) ((-963 . -897) 162591) ((-663 . -1125) T) ((-633 . -727) 162578) ((-491 . -897) NIL) ((-1159 . -102) T) ((-1107 . -628) 162562) ((-1075 . -1051) 162544) ((-97 . -623) 162526) ((-487 . -148) T) ((-963 . -1051) 162406) ((-118 . -727) 162351) ((-663 . -23) T) ((-491 . -1051) 162227) ((-1100 . -624) NIL) ((-1100 . -623) 162209) ((-792 . -624) NIL) ((-792 . -623) 162170) ((-790 . -624) 161804) ((-790 . -623) 161718) ((-1126 . -649) 161624) ((-471 . -623) 161606) ((-464 . -623) 161588) ((-464 . -624) 161449) ((-1048 . -231) 161395) ((-882 . -920) 161374) ((-127 . -34) T) ((-827 . -132) T) ((-659 . -623) 161356) ((-588 . -102) T) ((-364 . -1300) 161340) ((-361 . -1300) 161324) ((-353 . -1300) 161308) ((-128 . -524) 161241) ((-122 . -524) 161174) ((-521 . -802) T) ((-521 . -805) T) ((-520 . -804) T) ((-103 . -317) 161112) ((-224 . -102) 161090) ((-709 . -174) T) ((-704 . -1113) T) ((-882 . -658) 161006) ((-65 . -393) T) ((-282 . -623) 160988) ((-65 . -405) T) ((-963 . -386) 160972) ((-880 . -298) T) ((-50 . -623) 160954) ((-1012 . -38) 160902) ((-1133 . -656) 160874) ((-591 . -623) 160856) ((-491 . -386) 160840) ((-591 . -624) 160822) ((-528 . -623) 160804) ((-921 . -1300) 160791) ((-881 . -1231) T) ((-711 . -462) T) ((-505 . -524) 160757) ((-497 . -372) T) ((-364 . -377) 160736) ((-361 . -377) 160715) ((-353 . -377) 160694) ((-724 . -736) T) ((-219 . -372) T) ((-117 . -462) T) ((-1304 . -1295) 160678) ((-881 . -895) 160655) ((-881 . -897) NIL) ((-975 . -860) 160554) ((-825 . -860) 160505) ((-1238 . -102) T) ((-664 . -666) 160489) ((-1217 . -34) T) ((-173 . -623) 160471) ((-1126 . -21) 160381) ((-1126 . -25) 160232) ((-881 . -1051) 160209) ((-963 . -911) 160190) ((-1254 . -47) 160167) ((-921 . -377) T) ((-59 . -661) 160151) ((-526 . -661) 160135) ((-491 . -911) 160112) ((-71 . -451) T) ((-71 . -405) T) ((-506 . -661) 160096) ((-59 . -382) 160080) 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((-176 . -462) T) ((-224 . -317) 158747) ((-86 . -451) T) ((-86 . -405) T) ((-108 . -235) 158734) ((-219 . -23) T) ((-1305 . -1298) 158713) ((-687 . -1051) 158697) ((-590 . -298) T) ((-574 . -298) T) ((-505 . -298) T) ((-137 . -480) 158652) ((-1254 . -1231) T) ((-664 . -656) 158611) ((-48 . -1113) T) ((-722 . -233) 158595) ((-881 . -911) NIL) ((-1254 . -897) NIL) ((-900 . -102) T) ((-896 . -102) T) ((-398 . -1113) T) ((-171 . -386) 158579) ((-171 . -347) 158563) ((-1254 . -1051) 158443) ((-865 . -1051) 158339) ((-1155 . -102) T) ((-672 . -802) 158318) ((-663 . -132) T) ((-672 . -805) 158297) ((-118 . -524) 158205) ((-581 . -1051) 158187) ((-302 . -1288) 158157) ((-876 . -102) T) ((-974 . -566) 158136) ((-1225 . -1069) 158019) ((-1016 . -1064) 157964) ((-492 . -649) 157870) ((-915 . -1113) T) ((-1037 . -727) 157807) ((-721 . -1069) 157772) ((-1016 . -650) 157717) ((-627 . -102) T) ((-612 . -34) T) ((-1160 . -1231) T) ((-1225 . -111) 157586) ((-484 . -658) 157483) ((-363 . -727) 157428) 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T) ((-1067 . -21) T) ((-721 . -1062) T) ((-394 . -21) T) ((-394 . -25) T) ((-704 . -524) NIL) ((-1037 . -174) T) ((-721 . -249) T) ((-1075 . -555) T) ((-722 . -656) 156242) ((-516 . -102) T) ((-512 . -102) T) ((-363 . -174) T) ((-352 . -623) 156224) ((-417 . -1064) 156176) ((-404 . -623) 156158) ((-1133 . -858) T) ((-484 . -736) T) ((-903 . -1051) 156126) ((-417 . -650) 156078) ((-108 . -860) T) ((-668 . -1069) 156062) ((-497 . -132) T) ((-1267 . -1071) T) ((-219 . -132) T) ((-1170 . -102) 156040) ((-99 . -1113) T) ((-251 . -676) 156024) ((-251 . -661) 156008) ((-668 . -111) 155987) ((-596 . -626) 155971) ((-324 . -421) 155955) ((-251 . -382) 155939) ((-1173 . -241) 155886) ((-1012 . -233) 155870) ((-74 . -1231) T) ((-48 . -174) T) ((-711 . -397) T) ((-711 . -144) T) ((-1304 . -102) T) ((-1211 . -626) 155852) ((-1100 . -1069) 155695) ((-1089 . -1231) T) ((-271 . -920) 155674) ((-253 . -920) 155653) ((-792 . -1069) 155476) ((-790 . -1069) 155319) ((-618 . -1231) T) ((-1178 . -623) 155301) ((-1100 . -111) 155130) ((-1059 . -102) T) ((-485 . -1231) T) ((-471 . -1069) 155101) ((-464 . -1069) 154944) ((-674 . -658) 154928) ((-881 . -315) T) ((-792 . -111) 154737) ((-790 . -111) 154566) ((-364 . -658) 154518) ((-361 . -658) 154470) ((-353 . -658) 154422) ((-271 . -658) 154311) ((-253 . -658) 154200) ((-1172 . -860) T) ((-1101 . -1051) 154184) ((-471 . -111) 154145) ((-464 . -111) 153974) ((-1089 . -1051) 153951) ((-1013 . -34) T) ((-977 . -623) 153933) ((-969 . -1231) T) ((-127 . -1023) 153917) ((-974 . -1125) T) ((-881 . -1035) NIL) ((-745 . -1125) T) ((-725 . -1125) T) ((-668 . -626) 153835) ((-1281 . -499) 153819) ((-1155 . -38) 153779) ((-974 . -23) T) ((-921 . -658) 153744) ((-875 . -1113) T) ((-853 . -102) T) ((-827 . -21) T) ((-645 . -1064) 153728) ((-617 . -1064) 153712) ((-827 . -25) T) ((-745 . -23) T) ((-725 . -23) T) ((-645 . -650) 153696) ((-110 . -671) T) ((-617 . -650) 153680) ((-591 . -1069) 153645) ((-528 . -1069) 153590) ((-229 . -57) 153548) ((-463 . -23) T) ((-417 . -102) T) ((-270 . -102) T) ((-110 . -113) T) ((-704 . -298) T) ((-876 . -38) 153518) ((-591 . -111) 153474) ((-528 . -111) 153403) ((-1100 . -626) 153139) ((-428 . -1125) T) ((-324 . -1071) 153029) ((-321 . -1071) T) ((-129 . -1231) T) ((-792 . -626) 152777) ((-790 . -626) 152543) ((-668 . -1062) T) ((-1310 . -1113) T) ((-464 . -626) 152328) ((-171 . -315) 152259) ((-428 . -23) T) ((-40 . -623) 152241) ((-40 . -624) 152225) ((-108 . -1005) 152207) ((-117 . -879) 152191) ((-659 . -626) 152175) ((-48 . -524) 152141) ((-1217 . -1023) 152125) ((-1195 . -623) 152092) ((-1203 . -34) T) ((-965 . -623) 152058) ((-932 . -623) 152040) ((-1126 . -860) 151991) ((-781 . -623) 151973) ((-682 . -623) 151955) ((-1170 . -317) 151893) ((-489 . -34) T) ((-1105 . -1231) T) ((-487 . -462) T) ((-1154 . -34) T) ((-1100 . -1062) T) ((-50 . -626) 151862) ((-792 . -1062) T) ((-790 . -1062) T) ((-657 . -241) 151846) ((-642 . -241) 151792) ((-591 . -626) 151742) ((-528 . -626) 151672) ((-492 . -235) 151618) ((-1254 . -315) 151597) ((-1100 . -334) 151558) ((-464 . -1062) T) ((-1192 . -21) T) ((-1100 . -239) 151537) ((-792 . -334) 151514) ((-792 . -239) T) ((-790 . -334) 151486) ((-741 . -1235) 151465) ((-335 . -661) 151449) ((-1192 . -25) T) ((-59 . -34) T) ((-529 . -34) T) ((-526 . -34) T) ((-464 . -334) 151428) ((-335 . -382) 151412) ((-507 . -34) T) ((-506 . -34) T) ((-1016 . -1165) NIL) ((-741 . -566) 151343) ((-645 . -102) T) ((-617 . -102) T) ((-364 . -736) T) ((-361 . -736) T) ((-353 . -736) T) ((-271 . -736) T) ((-253 . -736) T) ((-388 . -1231) T) ((-1059 . -317) 151251) ((-1293 . -21) T) ((-912 . -1113) 151229) ((-50 . -1062) T) ((-1293 . -25) T) ((-1188 . -566) 151208) ((-1187 . -1235) 151187) ((-1187 . -566) 151138) ((-1181 . -1235) 151117) ((-1181 . -566) 151068) ((-591 . -1062) T) ((-528 . -1062) T) ((-1037 . -298) T) ((-370 . -1051) 151052) ((-330 . -1051) 151036) ((-1016 . -38) 150981) ((-388 . -897) 150963) ((-1012 . -656) 150886) ((-846 . -1231) T) ((-837 . -1231) 150865) ((-809 . -1125) T) ((-921 . -736) T) ((-591 . -249) T) ((-591 . -239) T) ((-528 . -239) T) ((-528 . -249) T) ((-1139 . -566) 150844) ((-363 . -298) T) ((-657 . -705) 150828) ((-388 . -1051) 150788) ((-302 . -1064) 150709) ((-1133 . -1071) T) ((-103 . -126) 150693) ((-302 . -650) 150635) ((-809 . -23) T) ((-1303 . -1298) 150611) ((-1281 . -294) 150563) ((-417 . -317) 150528) ((-1301 . -1298) 150507) ((-1267 . -1113) T) ((-880 . -623) 150489) ((-846 . -1051) 150458) ((-205 . -797) T) ((-204 . -797) T) ((-203 . -797) T) ((-202 . -797) T) ((-201 . -797) T) ((-200 . -797) T) ((-199 . -797) T) ((-198 . -797) T) ((-197 . -797) T) ((-196 . -797) T) ((-557 . -623) 150440) ((-505 . -1015) T) ((-281 . -849) T) ((-280 . -849) T) ((-279 . -849) T) ((-278 . -849) T) ((-48 . -298) T) ((-277 . -849) T) ((-276 . -849) T) ((-275 . -849) T) ((-195 . -797) T) ((-622 . -860) T) ((-664 . -421) 150424) ((-225 . -626) 150386) ((-110 . -860) T) ((-663 . -21) T) ((-663 . -25) T) ((-1304 . -38) 150356) ((-118 . -294) 150307) ((-1281 . -19) 150291) ((-1281 . -614) 150268) ((-1294 . -1113) T) ((-360 . -1064) 150213) ((-1090 . -1113) T) ((-1000 . -1113) T) ((-974 . -132) T) ((-827 . -235) 150200) ((-747 . -1113) T) ((-360 . -650) 150145) ((-745 . -132) T) ((-725 . -132) T) ((-521 . -803) T) ((-521 . -804) T) ((-463 . -132) T) ((-417 . -1165) 150123) ((-225 . -1062) T) ((-302 . -102) 149905) ((-142 . -1113) T) ((-709 . -1015) T) ((-1118 . -294) 149861) ((-91 . -1231) T) ((-128 . -623) 149793) ((-122 . -623) 149725) ((-1310 . -174) T) ((-1187 . -372) 149704) ((-1181 . -372) 149683) ((-324 . -1113) T) ((-428 . -132) T) ((-321 . -1113) T) ((-417 . -38) 149635) ((-1146 . -102) T) ((-1267 . -727) 149527) ((-664 . -1071) T) ((-1148 . -1276) T) ((-327 . -146) 149506) ((-327 . -148) 149485) ((-140 . -1113) T) ((-137 . -1113) T) ((-115 . -1113) T) ((-868 . -102) T) ((-590 . -623) 149467) ((-574 . -624) 149366) ((-574 . -623) 149348) ((-505 . -623) 149330) ((-505 . -624) 149275) ((-495 . 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. -132) T) ((-668 . -658) 142125) ((-251 . -1023) 142109) ((-882 . -315) T) ((-1305 . -1295) 142093) ((-781 . -802) T) ((-781 . -805) T) ((-711 . -38) 142080) ((-574 . -239) T) ((-505 . -249) T) ((-505 . -239) T) ((-1163 . -241) 142030) ((-1100 . -920) 142009) ((-117 . -38) 141996) ((-211 . -810) T) ((-210 . -810) T) ((-209 . -810) T) ((-208 . -810) T) ((-882 . -1035) 141974) ((-1294 . -499) 141958) ((-792 . -920) 141937) ((-790 . -920) 141916) ((-364 . -1231) 141895) ((-361 . -1231) 141874) ((-353 . -1231) 141853) ((-1203 . -1231) T) ((-271 . -1231) 141832) ((-464 . -920) 141811) ((-747 . -499) 141795) ((-1100 . -658) 141684) ((-709 . -626) 141619) ((-792 . -658) 141508) ((-633 . -1069) 141495) ((-489 . -1231) T) ((-352 . -377) T) ((-142 . -499) 141477) ((-790 . -658) 141366) ((-1154 . -1231) T) ((-559 . -860) T) ((-471 . -658) 141337) ((-271 . -897) 141196) ((-253 . -897) NIL) ((-118 . -1069) 141141) ((-464 . -658) 141030) ((-674 . -1051) 141007) ((-633 . -111) 140992) ((-400 . 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-1231) T) ((-603 . -860) T) ((-1155 . -1113) T) ((-1155 . -1066) 134497) ((-103 . -524) 134430) ((-938 . -623) 134412) ((-352 . -736) T) ((-30 . -623) 134394) ((-876 . -1113) T) ((-853 . -1071) 134373) ((-40 . -658) 134280) ((-227 . -1235) T) ((-417 . -1071) T) ((-1172 . -152) 134262) ((-1012 . -298) 134213) ((-627 . -1113) T) ((-227 . -566) T) ((-327 . -1262) 134197) ((-327 . -1259) 134167) ((-711 . -656) 134139) ((-1203 . -1207) 134118) ((-1088 . -623) 134100) ((-1203 . -107) 134050) ((-657 . -152) 134034) ((-642 . -152) 133980) ((-117 . -656) 133952) ((-489 . -1207) 133931) ((-497 . -148) T) ((-497 . -146) NIL) ((-1133 . -624) 133846) ((-448 . -623) 133828) ((-219 . -148) T) ((-219 . -146) NIL) ((-1133 . -623) 133810) ((-130 . -102) T) ((-52 . -102) T) ((-1245 . -649) 133762) ((-489 . -107) 133712) ((-1006 . -23) T) ((-1305 . -38) 133682) ((-1186 . -1125) T) ((-1138 . -1125) T) ((-1075 . -1235) T) ((-246 . -235) 133628) ((-319 . -102) T) ((-864 . -1125) T) ((-963 . -1235) 133607) 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-152) 132797) ((-932 . -804) T) ((-932 . -736) T) ((-781 . -803) T) ((-781 . -804) T) ((-516 . -1113) T) ((-512 . -1113) T) ((-781 . -736) T) ((-227 . -372) T) ((-1303 . -1064) 132781) ((-1301 . -1064) 132765) ((-1303 . -650) 132735) ((-1170 . -1113) 132713) ((-881 . -1235) T) ((-1301 . -650) 132683) ((-664 . -623) 132665) ((-881 . -566) T) ((-704 . -377) NIL) ((-44 . -1064) 132649) ((-1310 . -626) 132631) ((-1304 . -1113) T) ((-680 . -102) T) ((-368 . -1288) 132615) ((-362 . -1288) 132599) ((-44 . -650) 132583) ((-354 . -1288) 132567) ((-558 . -102) T) ((-530 . -860) 132546) ((-1059 . -1113) T) ((-827 . -462) 132525) ((-153 . -1064) 132509) ((-1059 . -1084) 132438) ((-1040 . -989) 132407) ((-829 . -1125) T) ((-1016 . -727) 132352) ((-153 . -650) 132336) ((-396 . -1125) T) ((-486 . -989) 132305) ((-473 . -989) 132274) ((-110 . -152) 132256) ((-73 . -623) 132238) ((-904 . -623) 132220) ((-1093 . -734) 132199) ((-1310 . -1062) T) ((-826 . -649) 132147) ((-302 . -1071) 132089) ((-171 . -1235) 131994) ((-227 . -1125) T) ((-332 . -23) T) ((-1181 . -1005) 131946) ((-853 . -1113) T) ((-1267 . -1069) 131851) ((-1139 . -750) 131830) ((-1265 . -931) 131809) ((-1244 . -931) 131788) ((-880 . -736) T) ((-171 . -566) 131699) ((-590 . -658) 131686) ((-574 . -658) 131658) ((-417 . -1113) T) ((-270 . -1113) T) ((-215 . -623) 131640) ((-505 . -658) 131590) ((-227 . -23) T) ((-1244 . -830) 131543) ((-1303 . -102) T) ((-363 . -1300) 131520) ((-1301 . -102) T) ((-1267 . -111) 131412) ((-825 . -1064) 131309) ((-825 . -650) 131251) ((-145 . -623) 131233) ((-1006 . -132) T) ((-44 . -102) T) ((-246 . -860) 131184) ((-1254 . -1235) 131163) ((-103 . -499) 131147) ((-1304 . -727) 131117) ((-1100 . -47) 131078) ((-1075 . -1125) T) ((-963 . -1125) T) ((-128 . -34) T) ((-122 . -34) T) ((-792 . -47) 131055) ((-790 . -47) 131027) ((-1254 . -566) 130938) ((-363 . -377) T) ((-491 . -1125) T) ((-1186 . -132) T) ((-1138 . -132) T) ((-464 . -47) 130917) ((-881 . -372) T) ((-864 . -132) T) ((-153 . -102) T) ((-1075 . -23) T) ((-963 . -23) T) ((-581 . -566) T) ((-826 . -25) T) ((-826 . -21) T) ((-1155 . -524) 130850) ((-602 . -1096) T) ((-596 . -1051) 130834) ((-1267 . -626) 130708) ((-491 . -23) T) ((-360 . -1071) T) ((-1225 . -911) 130689) ((-680 . -317) 130627) ((-1126 . -1288) 130597) ((-709 . -658) 130562) ((-1017 . -860) T) ((-1016 . -174) T) ((-974 . -146) 130541) ((-645 . -1113) T) ((-617 . -1113) T) ((-974 . -148) 130520) ((-745 . -148) 130499) ((-745 . -146) 130478) ((-668 . -1231) T) ((-984 . -860) T) ((-1273 . -235) 130431) ((-1266 . -235) 130377) ((-1245 . -235) 130258) ((-843 . -656) 130175) ((-484 . -931) 130154) ((-327 . -1064) 129989) ((-324 . -1069) 129899) ((-321 . -1069) 129828) ((-1012 . -294) 129786) ((-417 . -727) 129738) ((-327 . -650) 129579) ((-605 . -235) 129532) ((-711 . -858) T) ((-1267 . -1062) T) ((-324 . -111) 129428) ((-321 . -111) 129341) ((-975 . -102) T) ((-825 . -102) 129131) ((-722 . -624) NIL) ((-722 . -623) 129113) ((-1267 . -334) 129057) 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. -38) 127192) ((-327 . -102) T) ((-85 . -623) 127174) ((-50 . -1051) 127158) ((-1133 . -1069) 127145) ((-1100 . -386) 127129) ((-792 . -386) 127113) ((-709 . -736) T) ((-709 . -804) T) ((-709 . -801) T) ((-591 . -1051) 127100) ((-528 . -1051) 127077) ((-60 . -57) 127039) ((-332 . -132) T) ((-324 . -1062) 126929) ((-321 . -1062) T) ((-171 . -1125) T) ((-790 . -386) 126913) ((-45 . -152) 126863) ((-1017 . -1005) 126845) ((-464 . -386) 126829) ((-417 . -174) T) ((-324 . -249) 126808) ((-321 . -249) T) ((-321 . -239) NIL) ((-302 . -1113) 126590) ((-227 . -132) T) ((-1133 . -111) 126575) ((-171 . -23) T) ((-809 . -148) 126554) ((-809 . -146) 126533) ((-258 . -649) 126439) ((-257 . -649) 126345) ((-327 . -292) 126311) ((-1170 . -524) 126244) ((-487 . -656) 126194) ((-1146 . -1113) T) ((-227 . -1073) T) ((-825 . -317) 126132) ((-1100 . -911) 126067) ((-792 . -911) 126010) ((-790 . -911) 125994) ((-1303 . -38) 125964) ((-1301 . -38) 125934) ((-1254 . -1125) T) ((-865 . -1125) T) ((-464 . -911) 125911) ((-868 . -1113) T) ((-1254 . -23) T) ((-1133 . -626) 125883) ((-1075 . -132) T) ((-581 . -1125) T) ((-865 . -23) T) ((-633 . -736) T) ((-364 . -931) T) ((-361 . -931) T) ((-297 . -102) T) ((-353 . -931) T) ((-983 . -1096) T) ((-963 . -132) T) ((-826 . -235) 125856) ((-118 . -804) NIL) ((-118 . -801) NIL) ((-118 . -736) T) ((-704 . -920) NIL) ((-1059 . -524) 125757) ((-491 . -132) T) ((-581 . -23) T) ((-685 . -317) 125695) ((-645 . -771) T) ((-617 . -771) T) ((-1245 . -860) NIL) ((-1093 . -1064) 125605) ((-1016 . -298) T) ((-704 . -658) 125555) ((-258 . -21) T) ((-360 . -1113) T) ((-258 . -25) T) ((-257 . -21) T) ((-257 . -25) T) ((-153 . -38) 125539) ((-2 . -102) T) ((-921 . -931) T) ((-1093 . -650) 125407) ((-492 . -1288) 125377) ((-1133 . -1062) T) ((-721 . -315) T) ((-368 . -1064) 125329) ((-362 . -1064) 125281) ((-354 . -1064) 125233) ((-368 . -650) 125185) ((-225 . -1051) 125162) ((-362 . -650) 125114) ((-108 . -1064) 125064) ((-354 . -650) 125016) ((-302 . -727) 124958) ((-711 . -1071) T) ((-497 . -462) T) ((-417 . -524) 124870) ((-108 . -650) 124820) ((-219 . -462) T) ((-1133 . -239) T) ((-303 . -152) 124770) ((-1012 . -624) 124731) ((-1012 . -623) 124713) ((-1002 . -623) 124695) ((-117 . -1071) T) ((-664 . -1069) 124679) ((-227 . -503) T) ((-409 . -623) 124661) ((-409 . -624) 124638) ((-1067 . -1288) 124608) ((-664 . -111) 124587) ((-1155 . -499) 124571) ((-1305 . -656) 124530) ((-390 . -656) 124499) ((-825 . -38) 124469) ((-63 . -451) T) ((-63 . -405) T) ((-1173 . -102) T) ((-881 . -132) T) ((-494 . -102) 124447) ((-1310 . -377) T) ((-1093 . -102) T) ((-1074 . -102) T) ((-360 . -727) 124392) ((-741 . -148) 124371) ((-741 . -146) 124350) ((-664 . -626) 124268) ((-1037 . -658) 124205) ((-533 . -1113) 124183) ((-368 . -102) T) ((-362 . -102) T) ((-354 . -102) T) ((-108 . -102) T) ((-514 . -1113) T) ((-363 . -658) 124128) ((-1186 . -649) 124076) ((-1138 . -649) 124024) ((-394 . -519) 124003) ((-843 . -858) 123982) ((-388 . -1235) T) ((-704 . -736) T) ((-1245 . -1005) 123934) ((-348 . -1071) T) ((-112 . -1231) T) ((-176 . -1071) T) ((-103 . -623) 123866) ((-1188 . -146) 123845) ((-1188 . -148) 123824) ((-388 . -566) T) ((-1187 . -148) 123803) ((-1187 . -146) 123782) ((-1181 . -146) 123689) ((-417 . -298) T) ((-1181 . -148) 123596) ((-1139 . -148) 123575) ((-1139 . -146) 123554) ((-327 . -38) 123395) ((-171 . -132) T) ((-321 . -805) NIL) ((-321 . -802) NIL) ((-664 . -1062) T) ((-48 . -658) 123345) ((-1126 . -1064) 123242) ((-904 . -626) 123219) ((-1126 . -650) 123161) ((-1180 . -102) T) ((-1007 . -102) T) ((-1006 . -21) T) ((-128 . -1023) 123145) ((-122 . -1023) 123129) ((-1006 . -25) T) ((-912 . -120) 123113) ((-1172 . -102) T) ((-1254 . -132) T) ((-1186 . -25) T) ((-352 . -1231) T) ((-1186 . -21) T) ((-865 . -132) T) ((-1138 . -25) T) ((-1138 . -21) T) ((-864 . -25) T) ((-864 . -21) T) ((-792 . -315) 123092) ((-1173 . -317) 122887) ((-1170 . -499) 122871) ((-657 . -102) 122849) ((-642 . -102) T) ((-1163 . -152) 122799) 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T) ((-711 . -1113) T) ((-588 . -623) 121786) ((-388 . -372) T) ((-171 . -503) 121764) ((-224 . -623) 121696) ((-135 . -1113) T) ((-117 . -1113) T) ((-977 . -1231) T) ((-48 . -736) T) ((-1059 . -499) 121661) ((-142 . -435) 121643) ((-142 . -377) T) ((-1040 . -102) T) ((-522 . -519) 121622) ((-722 . -626) 121378) ((-486 . -102) T) ((-473 . -102) T) ((-1047 . -1125) T) ((-1238 . -623) 121360) ((-1195 . -1051) 121296) ((-1188 . -35) 121262) ((-1188 . -95) 121228) ((-1188 . -1219) 121194) ((-1188 . -1216) 121160) ((-1187 . -1216) 121126) ((-1187 . -1219) 121092) ((-1172 . -317) NIL) ((-89 . -406) T) ((-89 . -405) T) ((-1093 . -1165) 121071) ((-40 . -1231) 121043) ((-1187 . -95) 121009) ((-1047 . -23) T) ((-1187 . -35) 120975) ((-581 . -503) T) ((-1181 . -1216) 120941) ((-1181 . -1219) 120907) ((-1181 . -95) 120873) ((-1181 . -35) 120839) ((-370 . -1125) T) ((-368 . -1165) 120818) ((-362 . -1165) 120797) ((-354 . -1165) 120776) ((-1117 . -294) 120732) ((-1139 . -35) 120698) ((-1139 . -95) 120664) ((-108 . -1165) T) ((-1139 . -1219) 120630) ((-843 . -1071) 120609) ((-657 . -317) 120547) ((-642 . -317) 120398) ((-1139 . -1216) 120364) ((-722 . -1062) T) ((-1075 . -649) 120346) ((-1093 . -38) 120214) ((-963 . -649) 120162) ((-1017 . -148) T) ((-1017 . -146) NIL) ((-388 . -1125) T) ((-332 . -25) T) ((-330 . -23) T) ((-954 . -860) 120141) ((-722 . -334) 120118) ((-491 . -649) 120066) ((-40 . -1051) 119954) ((-722 . -239) T) ((-711 . -727) 119941) ((-348 . -1113) T) ((-176 . -1113) T) ((-339 . -860) T) ((-428 . -462) 119891) ((-388 . -23) T) ((-368 . -38) 119856) ((-362 . -38) 119821) ((-354 . -38) 119786) ((-80 . -451) T) ((-80 . -405) T) ((-227 . -25) T) ((-227 . -21) T) ((-846 . -1125) T) ((-108 . -38) 119736) ((-837 . -1125) T) ((-784 . -1113) T) ((-117 . -727) 119723) ((-682 . -1051) 119707) ((-622 . -102) T) ((-846 . -23) T) ((-837 . -23) T) ((-1170 . -294) 119659) ((-1126 . -317) 119597) ((-492 . -1064) 119494) ((-1115 . -241) 119478) ((-64 . -406) T) ((-64 . -405) T) 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115960) ((-1170 . -623) 115892) ((-1192 . -1064) 115775) ((-45 . -102) T) ((-827 . -102) T) ((-1192 . -650) 115672) ((-1254 . -25) T) ((-1254 . -21) T) ((-1075 . -235) 115659) ((-865 . -25) T) ((-44 . -376) 115643) ((-865 . -21) T) ((-741 . -462) 115594) ((-1304 . -623) 115576) ((-1293 . -1064) 115546) ((-1067 . -317) 115484) ((-681 . -1096) T) ((-616 . -1096) T) ((-400 . -1113) T) ((-581 . -25) T) ((-581 . -21) T) ((-182 . -1096) T) ((-162 . -1096) T) ((-157 . -1096) T) ((-155 . -1096) T) ((-1293 . -650) 115454) ((-631 . -1113) T) ((-709 . -897) 115436) ((-1281 . -1231) T) ((-229 . -317) 115374) ((-145 . -377) T) ((-1059 . -624) 115316) ((-1059 . -623) 115259) ((-321 . -920) NIL) ((-1239 . -854) T) ((-709 . -1051) 115204) ((-721 . -931) T) ((-484 . -1235) 115183) ((-1187 . -462) 115162) ((-1181 . -462) 115141) ((-338 . -102) T) ((-882 . -1125) T) ((-327 . -656) 115023) ((-324 . -658) 114752) ((-321 . -658) 114681) ((-484 . -566) 114632) ((-348 . -524) 114598) ((-560 . -152) 114548) 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-231) 113521) ((-396 . -860) 113500) ((-1273 . -1219) 113466) ((-1273 . -1216) 113432) ((-1266 . -1216) 113398) ((-525 . -132) T) ((-1266 . -1219) 113364) ((-1245 . -1216) 113330) ((-1245 . -1219) 113296) ((-1273 . -35) 113262) ((-1273 . -95) 113228) ((-1266 . -95) 113194) ((-645 . -623) 113163) ((-617 . -623) 113132) ((-227 . -860) T) ((-1266 . -35) 113098) ((-1265 . -1125) T) ((-1245 . -95) 113064) ((-1133 . -658) 113036) ((-1245 . -35) 113002) ((-1244 . -1125) T) ((-603 . -152) 112984) ((-1093 . -358) 112963) ((-176 . -298) T) ((-118 . -386) 112940) ((-118 . -347) 112917) ((-171 . -235) 112862) ((-880 . -315) T) ((-321 . -804) NIL) ((-321 . -801) NIL) ((-324 . -736) 112711) ((-321 . -736) T) ((-484 . -372) 112690) ((-368 . -358) 112669) ((-362 . -358) 112648) ((-354 . -358) 112627) ((-324 . -483) 112606) ((-1265 . -23) T) ((-1244 . -23) T) ((-728 . -1125) T) ((-724 . -132) T) ((-663 . -102) T) ((-487 . -727) 112571) ((-45 . -290) 112521) ((-105 . -1113) T) ((-68 . -623) 112503) 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-1051) 109528) ((-846 . -25) T) ((-837 . -25) T) ((-837 . -21) T) ((-1126 . -656) 109278) ((-1303 . -1071) T) ((-559 . -102) T) ((-1301 . -1071) T) ((-664 . -736) T) ((-1117 . -628) 109181) ((-1016 . -626) 109111) ((-1304 . -1069) 109095) ((-825 . -421) 109064) ((-103 . -120) 109048) ((-130 . -1113) T) ((-52 . -1113) T) ((-937 . -623) 109030) ((-881 . -1005) 109007) ((-833 . -102) T) ((-1304 . -111) 108986) ((-663 . -38) 108956) ((-581 . -860) T) ((-364 . -1125) T) ((-361 . -1125) T) ((-353 . -1125) T) ((-271 . -1125) T) ((-253 . -1125) T) ((-633 . -315) 108935) ((-1163 . -317) 108739) ((-674 . -23) T) ((-534 . -1096) T) ((-319 . -1113) T) ((-492 . -233) 108708) ((-153 . -1071) T) ((-364 . -23) T) ((-361 . -23) T) ((-353 . -23) T) ((-118 . -315) T) ((-271 . -23) T) ((-253 . -23) T) ((-1016 . -1062) T) ((-722 . -920) 108687) ((-1170 . -626) 108664) ((-1016 . -239) 108636) ((-1016 . -249) T) ((-118 . -1035) NIL) ((-921 . -1125) T) ((-1266 . -462) 108615) ((-1245 . -462) 108594) ((-533 . -623) 108526) ((-722 . -658) 108415) ((-417 . -1069) 108367) ((-514 . -623) 108349) ((-921 . -23) T) ((-497 . -317) NIL) ((-1304 . -626) 108305) ((-484 . -132) T) ((-219 . -317) NIL) ((-417 . -111) 108243) ((-825 . -1071) 108173) ((-747 . -1111) 108157) ((-1265 . -503) 108123) ((-1244 . -503) 108089) ((-558 . -854) T) ((-142 . -1111) 108071) ((-487 . -298) T) ((-1304 . -1062) T) ((-1236 . -102) T) ((-1076 . -102) T) ((-853 . -626) 107939) ((-510 . -524) NIL) ((-492 . -244) 107918) ((-417 . -626) 107816) ((-974 . -1064) 107699) ((-745 . -1064) 107669) ((-974 . -650) 107566) ((-1186 . -146) 107545) ((-745 . -650) 107515) ((-463 . -1064) 107485) ((-1186 . -148) 107464) ((-1138 . -148) 107443) ((-1138 . -146) 107422) ((-645 . -1069) 107406) ((-617 . -1069) 107390) ((-463 . -650) 107360) ((-1188 . -1272) 107344) ((-1188 . -1259) 107321) ((-1187 . -1264) 107282) ((-680 . -1113) T) ((-680 . -1066) 107222) ((-1187 . -1259) 107192) ((-558 . -1113) T) ((-497 . -1165) T) ((-1187 . -1262) 107176) 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-986) 104138) ((-327 . -1113) T) ((-417 . -805) 104117) ((-417 . -802) 104096) ((-510 . -499) 104078) ((-1267 . -1051) 104044) ((-1265 . -21) T) ((-1265 . -25) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-825 . -727) 103986) ((-360 . -626) 103916) ((-709 . -414) T) ((-1294 . -1231) T) ((-1126 . -421) 103885) ((-616 . -102) T) ((-1090 . -1231) T) ((-1016 . -377) NIL) ((-681 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1192 . -656) 103795) ((-747 . -1231) T) ((-741 . -1064) 103638) ((-44 . -771) T) ((-741 . -650) 103487) ((-603 . -102) T) ((-663 . -666) 103471) ((-77 . -406) T) ((-77 . -405) T) ((-142 . -1231) T) ((-881 . -148) T) ((-881 . -146) NIL) ((-1230 . -93) T) ((-360 . -1062) T) ((-70 . -392) T) ((-70 . -405) T) ((-1179 . -102) T) ((-680 . -524) 103404) ((-1293 . -656) 103349) ((-699 . -317) 103287) ((-974 . -38) 103184) ((-1194 . -623) 103166) ((-745 . -38) 103136) ((-560 . -317) 102940) ((-1188 . -1064) 102823) ((-324 . 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-1219) 96617) ((-171 . -1216) 96595) ((-211 . -1113) T) ((-210 . -1113) T) ((-117 . -1062) T) ((-209 . -1113) T) ((-208 . -1113) T) ((-205 . -1113) T) ((-204 . -1113) T) ((-203 . -1113) T) ((-202 . -1113) T) ((-201 . -1113) T) ((-200 . -1113) T) ((-199 . -1113) T) ((-198 . -1113) T) ((-197 . -1113) T) ((-196 . -1113) T) ((-195 . -1113) T) ((-246 . -102) 96385) ((-171 . -35) 96363) ((-171 . -95) 96341) ((-664 . -1051) 96237) ((-492 . -1071) 96167) ((-1126 . -1113) 95957) ((-1155 . -34) T) ((-680 . -499) 95941) ((-73 . -1231) T) ((-105 . -623) 95923) ((-1305 . -623) 95905) ((-390 . -623) 95887) ((-348 . -626) 95839) ((-176 . -626) 95756) ((-1230 . -500) 95737) ((-741 . -38) 95586) ((-581 . -1219) T) ((-581 . -1216) T) ((-541 . -623) 95568) ((-530 . -317) 95506) ((-510 . -623) 95488) ((-510 . -624) 95470) ((-1230 . -623) 95436) ((-1181 . -1165) NIL) ((-1040 . -1084) 95405) ((-1040 . -1113) T) ((-1017 . -102) T) ((-984 . -102) T) ((-925 . -102) T) ((-904 . -1051) 95382) ((-1155 . -736) T) ((-1016 . -658) 95289) ((-486 . -1113) T) ((-473 . -1113) T) ((-596 . -23) T) ((-581 . -35) T) ((-581 . -95) T) ((-437 . -102) T) ((-1076 . -231) 95235) ((-1188 . -38) 95132) ((-876 . -736) T) ((-704 . -931) T) ((-521 . -25) T) ((-517 . -21) T) ((-517 . -25) T) ((-1187 . -38) 94973) ((-348 . -1062) T) ((-1181 . -38) 94769) ((-1093 . -174) T) ((-176 . -1062) T) ((-1139 . -38) 94666) ((-722 . -47) 94643) ((-368 . -174) T) ((-362 . -174) T) ((-529 . -57) 94617) ((-507 . -57) 94567) ((-360 . -1300) 94544) ((-227 . -462) T) ((-327 . -298) 94495) ((-354 . -174) T) ((-176 . -249) T) ((-1244 . -860) 94394) ((-108 . -174) T) ((-882 . -1005) 94378) ((-668 . -1125) T) ((-591 . -372) T) ((-591 . -337) 94365) ((-528 . -337) 94342) ((-528 . -372) T) ((-324 . -315) 94321) ((-321 . -315) T) ((-612 . -860) 94300) ((-1126 . -727) 94242) ((-530 . -290) 94226) ((-668 . -23) T) ((-428 . -233) 94210) ((-321 . -1035) NIL) ((-345 . -23) T) ((-103 . -1023) 94194) ((-45 . -36) 94173) ((-622 . -1113) T) ((-360 . -377) T) ((-534 . -102) T) ((-505 . -27) T) ((-246 . -317) 94111) ((-1100 . -1125) T) ((-1304 . -658) 94085) ((-792 . -1125) T) ((-790 . -1125) T) ((-1192 . -421) 94069) ((-464 . -1125) T) ((-1075 . -462) T) ((-1164 . -1113) T) ((-963 . -462) 94020) ((-1128 . -1096) T) ((-110 . -1113) T) ((-1100 . -23) T) ((-1173 . -524) 93803) ((-827 . -1071) T) ((-792 . -23) T) ((-790 . -23) T) ((-491 . -462) 93754) ((-471 . -23) T) ((-390 . -391) 93733) ((-364 . -235) 93706) ((-361 . -235) 93679) ((-353 . -235) 93652) ((-464 . -23) T) ((-271 . -235) 93625) ((-96 . -1113) T) ((-722 . -1231) T) ((-680 . -294) 93602) ((-494 . -524) 93535) ((-1273 . -1064) 93418) ((-1273 . -650) 93315) ((-1266 . -650) 93156) ((-1266 . -1064) 92991) ((-1245 . -650) 92787) ((-297 . -298) T) ((-1245 . -1064) 92577) ((-1095 . -623) 92559) ((-1095 . -624) 92540) ((-417 . -920) 92519) ((-1225 . -132) T) ((-50 . -1125) T) ((-1181 . -410) 92471) ((-1037 . -931) T) ((-1016 . -736) T) ((-853 . -658) 92444) ((-722 . -897) NIL) ((-606 . -1064) 92404) ((-591 . -1125) T) ((-528 . -1125) T) ((-605 . -1064) 92287) ((-1170 . -34) T) ((-1017 . -317) NIL) ((-825 . -499) 92271) ((-606 . -650) 92244) ((-363 . -931) T) ((-605 . -650) 92141) ((-921 . -235) 92128) ((-417 . -658) 92044) ((-50 . -23) T) ((-721 . -132) T) ((-722 . -1051) 91924) ((-591 . -23) T) ((-108 . -524) NIL) ((-528 . -23) T) ((-171 . -419) 91895) ((-1153 . -1113) T) ((-1296 . -1295) 91879) ((-711 . -805) T) ((-711 . -802) T) ((-1133 . -315) T) ((-388 . -148) T) ((-288 . -623) 91861) ((-287 . -623) 91843) ((-1244 . -1005) 91813) ((-48 . -931) T) ((-685 . -499) 91797) ((-258 . -1288) 91767) ((-257 . -1288) 91737) ((-1190 . -860) T) ((-1126 . -174) 91716) ((-1133 . -1035) T) ((-1059 . -34) T) ((-846 . -148) 91695) ((-846 . -146) 91674) ((-747 . -107) 91658) ((-622 . -133) T) ((-492 . -1113) 91448) ((-1192 . -1071) T) ((-881 . -462) T) ((-85 . -1231) T) ((-246 . -38) 91418) ((-142 . -107) 91400) ((-722 . -386) 91384) ((-843 . -626) 91252) ((-1304 . -736) T) ((-1293 . -1071) T) ((-1273 . -102) T) ((-1133 . -555) T) ((-589 . -102) T) ((-130 . -500) 91234) ((-1266 . -102) T) ((-400 . -1069) 91218) ((-1186 . -960) 91187) ((-44 . -294) 91164) ((-130 . -623) 91131) ((-52 . -623) 91113) ((-1138 . -960) 91080) ((-663 . -421) 91064) ((-1245 . -102) T) ((-1172 . -524) NIL) ((-672 . -25) T) ((-631 . -1069) 91048) ((-672 . -21) T) ((-974 . -656) 90958) ((-745 . -656) 90903) ((-725 . -656) 90875) ((-400 . -111) 90854) ((-224 . -261) 90838) ((-1067 . -1066) 90778) ((-1067 . -1113) T) ((-1017 . -1165) T) ((-828 . -1113) T) ((-463 . -656) 90693) ((-352 . -1235) T) ((-645 . -658) 90677) ((-631 . -111) 90656) ((-617 . -658) 90640) ((-606 . -102) T) ((-319 . -500) 90621) ((-596 . -132) T) ((-605 . -102) T) ((-424 . -1113) T) ((-394 . -1113) T) ((-319 . -623) 90587) ((-229 . -1113) 90565) ((-657 . -524) 90498) ((-642 . -524) 90342) ((-843 . -1062) 90321) ((-654 . -152) 90305) ((-352 . -566) T) ((-722 . -911) 90248) ((-560 . -231) 90198) ((-1273 . -292) 90164) ((-1266 . -292) 90130) ((-1093 . -298) 90081) ((-497 . -858) T) ((-225 . -1125) T) ((-1245 . -292) 90047) ((-1225 . -503) 90013) ((-1017 . -38) 89963) ((-219 . -858) T) ((-428 . -656) 89922) ((-925 . -38) 89874) ((-853 . -804) 89853) ((-853 . -801) 89832) ((-853 . -736) 89811) ((-368 . -298) T) ((-362 . -298) T) ((-354 . -298) T) ((-171 . -462) 89742) ((-437 . -38) 89726) ((-108 . -298) T) ((-225 . -23) T) ((-417 . -804) 89705) ((-417 . -801) 89684) ((-417 . -736) T) ((-510 . -296) 89659) ((-487 . -1069) 89624) ((-668 . -132) T) ((-631 . -626) 89593) ((-1126 . -524) 89526) ((-345 . -132) T) ((-171 . -412) 89505) ((-492 . -727) 89447) ((-825 . -294) 89424) ((-487 . -111) 89380) ((-663 . -1071) T) ((-826 . -1064) 89223) ((-1292 . -1096) T) ((-1254 . -462) 89154) ((-826 . -650) 89003) ((-1291 . -1096) T) ((-1100 . -132) T) ((-1067 . -727) 88945) ((-792 . -132) T) ((-790 . -132) T) ((-581 . -462) T) ((-1040 . -524) 88878) ((-631 . -1062) T) ((-602 . -1113) T) ((-543 . -175) T) ((-471 . -132) T) ((-464 . -132) T) ((-1012 . -1231) 88819) ((-45 . -1113) T) ((-394 . -727) 88789) ((-827 . -1113) T) ((-486 . -524) 88722) ((-473 . -524) 88655) ((-1306 . -626) 88637) ((-463 . -376) 88607) ((-45 . -620) 88586) ((-324 . -310) T) ((-487 . -626) 88536) ((-1245 . -317) 88421) ((-680 . -623) 88383) ((-59 . -860) 88362) ((-1017 . -410) 88344) ((-558 . -623) 88326) ((-809 . -656) 88285) ((-825 . -614) 88262) ((-526 . -860) 88241) ((-506 . -860) 88220) ((-40 . -1235) T) ((-1012 . -1051) 88116) ((-50 . -132) T) ((-591 . -132) T) ((-528 . -132) T) ((-302 . -658) 87976) ((-352 . -337) 87953) ((-352 . -372) T) ((-330 . -331) 87930) ((-327 . -294) 87888) ((-40 . -566) T) ((-388 . -1216) T) ((-388 . -1219) T) ((-1048 . -1207) 87863) ((-1203 . -241) 87813) ((-1181 . -233) 87765) ((-338 . -1113) T) ((-388 . -95) T) ((-388 . -35) T) ((-1048 . -107) 87711) ((-487 . -1062) T) ((-1305 . -1069) 87695) ((-489 . -241) 87645) ((-1173 . -499) 87579) ((-1296 . -1064) 87563) ((-390 . -1069) 87547) ((-1296 . -650) 87517) ((-487 . -249) T) ((-826 . -102) T) ((-724 . -148) 87496) ((-724 . -146) 87475) ((-494 . -499) 87459) ((-495 . -344) 87428) ((-1305 . -111) 87407) ((-522 . -1113) T) ((-492 . -174) 87386) ((-1012 . -386) 87370) ((-423 . -102) T) ((-390 . -111) 87349) ((-1012 . -347) 87333) ((-286 . -996) 87317) ((-285 . -996) 87301) ((-1303 . -623) 87283) ((-1301 . -623) 87265) ((-110 . -524) NIL) ((-1186 . -1257) 87249) ((-864 . -862) 87233) ((-1192 . -1113) T) ((-103 . -1231) T) ((-963 . -960) 87194) ((-827 . -727) 87136) ((-1245 . -1165) NIL) ((-491 . -960) 87081) ((-1075 . -144) T) ((-60 . -102) 87059) ((-44 . -623) 87041) ((-78 . -623) 87023) ((-360 . -658) 86968) ((-1293 . -1113) T) ((-521 . -860) T) ((-297 . -294) 86947) ((-352 . -1125) T) ((-303 . -1113) T) ((-1012 . -911) 86906) ((-303 . -620) 86885) ((-1305 . -626) 86834) ((-1273 . -38) 86731) ((-1266 . -38) 86572) ((-1245 . -38) 86368) ((-497 . -1071) T) ((-390 . -626) 86352) ((-219 . -1071) T) ((-352 . -23) T) 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. -146) 83472) ((-1244 . -148) 83397) ((-1296 . -1302) 83376) ((-486 . -499) 83360) ((-473 . -499) 83344) ((-533 . -34) T) ((-663 . -727) 83314) ((-112 . -980) T) ((-672 . -860) 83293) ((-1192 . -174) 83244) ((-374 . -102) T) ((-246 . -244) 83223) ((-258 . -102) T) ((-257 . -102) T) ((-1254 . -960) 83192) ((-251 . -860) 83171) ((-826 . -38) 83020) ((-45 . -524) 82812) ((-1172 . -294) 82762) ((-216 . -1113) T) ((-1163 . -1113) T) ((-1163 . -620) 82741) ((-596 . -25) T) ((-596 . -21) T) ((-1115 . -317) 82679) ((-974 . -421) 82663) ((-709 . -1235) T) ((-642 . -294) 82616) ((-1100 . -649) 82564) ((-792 . -649) 82512) ((-790 . -649) 82460) ((-352 . -132) T) ((-297 . -623) 82442) ((-916 . -1113) T) ((-709 . -566) T) ((-130 . -626) 82424) ((-880 . -1125) T) ((-464 . -649) 82372) ((-916 . -914) 82356) ((-388 . -462) T) ((-497 . -1113) T) ((-954 . -317) 82294) ((-711 . -658) 82266) ((-559 . -854) T) ((-219 . -1113) T) ((-324 . -931) 82245) ((-321 . -931) T) ((-321 . -830) NIL) ((-400 . -730) T) 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. -566) T) ((-471 . -21) T) ((-464 . -25) T) ((-464 . -21) T) ((-1265 . -95) 80896) ((-1164 . -93) T) ((-1155 . -1051) 80792) ((-827 . -298) 80771) ((-1248 . -102) 80749) ((-833 . -1113) T) ((-977 . -980) T) ((-680 . -111) 80728) ((-627 . -1231) T) ((-303 . -524) 80520) ((-1245 . -233) 80472) ((-1244 . -1216) 80438) ((-1244 . -1219) 80404) ((-258 . -317) 80342) ((-257 . -317) 80280) ((-1239 . -377) T) ((-1173 . -624) NIL) ((-1173 . -623) 80262) ((-1236 . -854) T) ((-1155 . -386) 80246) ((-1133 . -830) T) ((-96 . -93) T) ((-1133 . -931) T) ((-1126 . -614) 80223) ((-1093 . -624) 80207) ((-1017 . -656) 80157) ((-925 . -656) 80094) ((-825 . -296) 80071) ((-494 . -623) 80003) ((-618 . -152) 79950) ((-497 . -727) 79900) ((-428 . -1071) T) ((-492 . -499) 79884) ((-437 . -656) 79843) ((-335 . -860) 79822) ((-348 . -658) 79796) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -727) 79746) ((-171 . -734) 79717) ((-176 . -658) 79649) ((-591 . -21) T) ((-591 . -25) T) ((-528 . -25) T) ((-528 . -21) T) ((-485 . -152) 79599) ((-1093 . -623) 79581) ((-1074 . -623) 79563) ((-1006 . -102) T) ((-872 . -102) T) ((-809 . -421) 79526) ((-40 . -132) T) ((-709 . -372) T) ((-711 . -736) T) ((-711 . -804) T) ((-711 . -801) T) ((-214 . -906) T) ((-590 . -1125) T) ((-574 . -1125) T) ((-505 . -1125) T) ((-368 . -623) 79508) ((-362 . -623) 79490) ((-354 . -623) 79472) ((-66 . -406) T) ((-66 . -405) T) ((-108 . -624) 79402) ((-108 . -623) 79344) ((-213 . -906) T) ((-969 . -152) 79328) ((-781 . -132) T) ((-680 . -626) 79246) ((-135 . -736) T) ((-117 . -736) T) ((-1265 . -35) 79212) ((-1067 . -499) 79196) ((-590 . -23) T) ((-574 . -23) T) ((-505 . -23) T) ((-1244 . -95) 79162) ((-1244 . -35) 79128) ((-1186 . -102) T) ((-1138 . -102) T) ((-864 . -102) T) ((-229 . -499) 79112) ((-1303 . -111) 79091) ((-1301 . -111) 79070) ((-44 . -1069) 79054) ((-1303 . -626) 79000) ((-1303 . -1062) T) ((-1301 . -626) 78929) ((-1254 . -1257) 78913) ((-865 . -862) 78897) ((-1192 . -298) 78876) ((-1117 . -1231) T) ((-110 . -294) 78826) ((-1016 . -1231) 78798) ((-129 . -152) 78780) ((-1155 . -911) 78739) ((-44 . -111) 78718) ((-1236 . -1113) T) ((-1195 . -1276) T) ((-1180 . -500) 78699) ((-1180 . -623) 78665) ((-680 . -1062) T) ((-1172 . -624) NIL) ((-1172 . -623) 78647) ((-1076 . -620) 78622) ((-1076 . -1113) T) ((-1007 . -500) 78603) ((-74 . -451) T) ((-74 . -405) T) ((-1007 . -623) 78569) ((-153 . -1069) 78553) ((-680 . -239) 78532) ((-581 . -564) 78516) ((-364 . -148) 78495) ((-364 . -146) 78446) ((-361 . -148) 78425) ((-361 . -146) 78376) ((-353 . -148) 78355) ((-353 . -146) 78306) ((-271 . -146) 78285) ((-271 . -148) 78264) ((-258 . -38) 78234) ((-253 . -148) 78213) ((-118 . -372) T) ((-253 . -146) 78192) ((-257 . -38) 78162) ((-153 . -111) 78141) ((-1016 . -1051) 78029) ((-1181 . -858) NIL) ((-704 . -1235) T) ((-809 . -1071) T) ((-709 . -1125) T) ((-1301 . -1062) T) ((-1170 . -1231) T) ((-1016 . -386) 78006) ((-921 . -146) T) ((-921 . -148) 77988) ((-880 . -132) T) ((-825 . -1069) 77885) ((-709 . -23) T) ((-704 . -566) T) ((-227 . -1064) 77850) ((-657 . -623) 77782) ((-657 . -624) 77743) ((-642 . -624) NIL) ((-642 . -623) 77725) ((-497 . -174) T) ((-227 . -650) 77690) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-484 . -1219) 77656) ((-484 . -1216) 77622) ((-281 . -623) 77604) ((-280 . -623) 77586) ((-279 . -623) 77568) ((-278 . -623) 77550) ((-277 . -623) 77532) ((-510 . -661) 77514) ((-276 . -623) 77496) ((-348 . -736) T) ((-275 . -623) 77478) ((-110 . -19) 77460) ((-176 . -736) T) ((-510 . -382) 77442) ((-214 . -623) 77424) ((-530 . -1162) 77408) ((-510 . -124) T) ((-110 . -614) 77383) ((-213 . -623) 77365) ((-484 . -35) 77331) ((-484 . -95) 77297) ((-211 . -623) 77279) ((-210 . -623) 77261) ((-209 . -623) 77243) ((-208 . -623) 77225) ((-205 . -623) 77207) ((-204 . -623) 77189) ((-203 . -623) 77171) ((-202 . -623) 77153) ((-201 . -623) 77135) ((-200 . -623) 77117) ((-199 . -623) 77099) ((-546 . -1116) 77051) ((-198 . -623) 77033) ((-197 . -623) 77015) ((-45 . -499) 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. -626) 67931) ((-362 . -626) 67868) ((-354 . -626) 67805) ((-76 . -1231) T) ((-108 . -626) 67755) ((-112 . -113) T) ((-1075 . -38) 67742) ((-674 . -383) 67721) ((-963 . -38) 67570) ((-741 . -1113) T) ((-491 . -38) 67419) ((-86 . -1231) T) ((-602 . -500) 67400) ((-1245 . -858) NIL) ((-581 . -292) T) ((-1188 . -1113) T) ((-602 . -623) 67366) ((-1187 . -1113) T) ((-1181 . -1113) T) ((-1093 . -1062) T) ((-360 . -1051) 67343) ((-827 . -500) 67327) ((-1017 . -1071) T) ((-45 . -623) 67309) ((-45 . -624) NIL) ((-925 . -1071) T) ((-827 . -623) 67278) ((-1160 . -102) 67256) ((-1093 . -249) 67207) ((-437 . -1071) T) ((-368 . -1062) T) ((-362 . -1062) T) ((-374 . -373) 67184) ((-354 . -1062) T) ((-352 . -235) 67171) ((-258 . -244) 67150) ((-257 . -244) 67129) ((-1093 . -239) 67054) ((-1139 . -1113) T) ((-302 . -911) 67013) ((-108 . -1062) T) ((-704 . -132) T) ((-428 . -524) 66855) ((-368 . -239) 66834) ((-368 . -249) T) ((-44 . -730) T) ((-362 . -239) 66813) ((-362 . -249) T) ((-354 . -239) 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28174) ((-1017 . -249) T) ((-1017 . -239) T) ((-437 . -1062) T) ((-969 . -1113) 28124) ((-925 . -249) T) ((-876 . -132) T) ((-709 . -462) T) ((-853 . -1125) 28103) ((-108 . -911) NIL) ((-1225 . -292) 28069) ((-1126 . -1231) T) ((-882 . -858) 28048) ((-1012 . -25) T) ((-916 . -736) T) ((-171 . -524) 27960) ((-1012 . -21) T) ((-916 . -483) T) ((-417 . -1125) T) ((-497 . -804) T) ((-497 . -801) T) ((-921 . -358) T) ((-497 . -736) T) ((-219 . -804) T) ((-219 . -801) T) ((-722 . -235) 27947) ((-219 . -736) T) ((-853 . -23) 27899) ((-1198 . -1113) T) ((-668 . -1064) 27883) ((-1197 . -1113) T) ((-534 . -626) 27864) ((-1196 . -1113) T) ((-327 . -315) 27843) ((-1048 . -241) 27789) ((-668 . -650) 27759) ((-417 . -23) T) ((-954 . -624) 27720) ((-954 . -623) 27632) ((-654 . -499) 27616) ((-45 . -1023) 27566) ((-1126 . -1051) 27393) ((-627 . -980) T) ((-501 . -102) T) ((-339 . -623) 27375) ((-1006 . -294) 27342) ((-603 . -661) 27324) ((-131 . -1113) T) ((-129 . -1113) T) ((-603 . -382) 27306) 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. -1231) T) ((-1016 . -235) 10812) ((-969 . -294) 10764) ((-297 . -931) T) ((-827 . -315) 10743) ((-880 . -102) T) ((-792 . -233) 10727) ((-925 . -658) 10679) ((-721 . -656) 10629) ((-704 . -734) 10596) ((-645 . -21) T) ((-645 . -25) T) ((-617 . -21) T) ((-557 . -102) T) ((-352 . -38) 10561) ((-497 . -895) 10543) ((-497 . -897) 10525) ((-484 . -727) 10366) ((-219 . -895) 10348) ((-64 . -1231) T) ((-219 . -897) 10330) ((-617 . -25) T) ((-437 . -658) 10304) ((-1186 . -626) 10073) ((-497 . -1051) 10033) ((-882 . -524) 9945) ((-1138 . -626) 9737) ((-864 . -626) 9655) ((-219 . -1051) 9615) ((-246 . -34) T) ((-1013 . -1113) 9593) ((-590 . -1064) 9580) ((-574 . -1064) 9567) ((-505 . -1064) 9532) ((-1265 . -174) 9463) ((-1244 . -174) 9394) ((-590 . -650) 9381) ((-574 . -650) 9368) ((-505 . -650) 9333) ((-722 . -146) 9312) ((-722 . -148) 9291) ((-711 . -132) T) ((-137 . -475) 9268) ((-1160 . -623) 9200) ((-668 . -666) 9184) ((-129 . -294) 9134) ((-117 . -132) T) ((-487 . -1235) T) ((-618 . -614) 9110) ((-485 . -614) 9089) ((-345 . -344) 9058) ((-607 . -1113) T) ((-595 . -1113) T) ((-546 . -1113) T) ((-487 . -566) T) ((-1186 . -1062) T) ((-1138 . -1062) T) ((-864 . -1062) T) ((-246 . -801) 9037) ((-246 . -804) 8988) ((-246 . -803) 8967) ((-1186 . -334) 8944) ((-246 . -736) 8854) ((-969 . -19) 8838) ((-497 . -386) 8820) ((-497 . -347) 8802) ((-1138 . -334) 8774) ((-363 . -1288) 8751) ((-219 . -386) 8733) ((-219 . -347) 8715) ((-969 . -614) 8692) ((-1186 . -239) T) ((-1277 . -1113) T) ((-674 . -1113) T) ((-655 . -1113) T) ((-1203 . -1113) T) ((-1100 . -260) 8629) ((-596 . -656) 8589) ((-364 . -1113) T) ((-361 . -1113) T) ((-353 . -1113) T) ((-271 . -1113) T) ((-253 . -1113) T) ((-84 . -1231) T) ((-128 . -102) 8567) ((-122 . -102) 8545) ((-1244 . -524) 8405) ((-1203 . -620) 8384) ((-1154 . -1113) T) ((-1128 . -626) 8365) ((-1093 . -931) 8316) ((-489 . -1113) T) ((-1017 . -804) T) ((-1017 . -801) T) ((-489 . -620) 8295) ((-258 . -805) 8246) ((-258 . -802) 8197) ((-257 . -805) 8148) ((-40 . -1165) NIL) ((-257 . -802) 8099) ((-1017 . -736) T) ((-129 . -19) 8081) ((-984 . -804) T) ((-709 . -1064) 8046) ((-925 . -736) T) ((-921 . -1113) T) ((-903 . -623) 8028) ((-129 . -614) 8003) ((-709 . -650) 7968) ((-91 . -499) 7952) ((-497 . -911) NIL) ((-882 . -298) T) ((-227 . -1069) 7917) ((-846 . -294) 7896) ((-219 . -911) NIL) ((-843 . -1125) 7875) ((-59 . -1113) 7825) ((-529 . -1113) 7803) ((-526 . -1113) 7753) ((-507 . -1113) 7731) ((-506 . -1113) 7681) ((-590 . -102) T) ((-574 . -102) T) ((-505 . -102) T) ((-484 . -174) 7612) ((-368 . -931) T) ((-362 . -931) T) ((-354 . -931) T) ((-227 . -111) 7568) ((-843 . -23) 7520) ((-437 . -736) T) ((-108 . -931) T) ((-40 . -38) 7465) ((-108 . -830) T) ((-591 . -358) T) ((-528 . -358) T) ((-668 . -656) 7424) ((-324 . -462) 7403) ((-321 . -462) T) ((-612 . -524) 7336) ((-417 . -235) 7309) ((-348 . -132) T) ((-176 . -132) T) ((-302 . -25) 7173) ((-302 . -21) 7056) ((-45 . -1207) 7035) ((-66 . -623) 7017) ((-55 . -102) T) ((-345 . -656) 6999) ((-1282 . -102) T) ((-45 . -107) 6949) ((-829 . -626) 6933) ((-1281 . -102) 6883) ((-1273 . -658) 6808) ((-1266 . -658) 6705) ((-1245 . -658) 6557) ((-1245 . -920) NIL) ((-1115 . -435) 6541) ((-1115 . -377) 6520) ((-396 . -626) 6504) ((-332 . -626) 6488) ((-1212 . -623) 6470) ((-1204 . -102) T) ((-1076 . -1231) T) ((-1100 . -656) 6380) ((-1075 . -1069) 6367) ((-1075 . -111) 6352) ((-963 . -1069) 6195) ((-963 . -111) 6024) ((-792 . -656) 5934) ((-790 . -656) 5844) ((-633 . -1064) 5831) ((-674 . -727) 5815) ((-633 . -650) 5802) ((-491 . -1069) 5645) ((-487 . -372) T) ((-471 . -656) 5601) ((-464 . -656) 5511) ((-227 . -626) 5461) ((-364 . -727) 5413) ((-361 . -727) 5365) ((-118 . -1064) 5310) ((-353 . -727) 5262) ((-271 . -727) 5111) ((-253 . -727) 4960) ((-1109 . -93) T) ((-1103 . -93) T) ((-118 . -650) 4905) ((-1086 . -93) T) ((-954 . -661) 4889) ((-1079 . -93) T) ((-491 . -111) 4718) ((-1070 . -1113) 4696) ((-1049 . -93) T) ((-954 . -382) 4680) ((-254 . -102) T) ((-1032 . -93) T) ((-74 . -623) 4662) ((-974 . -47) 4641) ((-720 . -102) T) ((-709 . -102) T) ((-1 . -1113) T) ((-631 . -1125) T) ((-1101 . -623) 4623) ((-636 . -93) T) ((-1089 . -623) 4605) ((-921 . -727) 4570) ((-127 . -499) 4554) ((-493 . -93) T) ((-631 . -23) T) ((-400 . -23) T) ((-87 . -1231) T) ((-220 . -93) T) ((-618 . -623) 4536) ((-618 . -624) NIL) ((-485 . -624) NIL) ((-485 . -623) 4518) ((-360 . -25) T) ((-360 . -21) T) ((-50 . -656) 4477) ((-521 . -1113) T) ((-517 . -1113) T) ((-128 . -317) 4415) ((-122 . -317) 4353) ((-606 . -658) 4327) ((-605 . -658) 4252) ((-591 . -656) 4202) ((-227 . -1062) T) ((-528 . -656) 4132) ((-388 . -1015) T) ((-227 . -249) T) ((-227 . -239) T) ((-1075 . -626) 4104) ((-1075 . -628) 4085) ((-969 . -624) 4046) ((-969 . -623) 3958) ((-963 . -626) 3747) ((-880 . -38) 3734) ((-723 . -626) 3684) ((-1265 . -298) 3635) ((-1244 . -298) 3586) ((-491 . -626) 3371) ((-1133 . -462) T) ((-512 . -860) T) ((-324 . -1152) 3350) ((-1012 . -148) 3329) ((-1012 . -146) 3308) ((-505 . -317) 3295) ((-303 . -1207) 3274) ((-1198 . -623) 3256) ((-1197 . -623) 3238) ((-1196 . -623) 3220) ((-881 . -1069) 3165) ((-487 . -1125) T) ((-140 . -845) 3147) ((-115 . -845) 3128) ((-633 . -102) T) ((-1217 . -499) 3112) ((-258 . -377) 3091) ((-257 . -377) 3070) ((-1075 . -1062) T) ((-303 . -107) 3020) ((-131 . -623) 3002) ((-129 . -624) NIL) ((-129 . -623) 2946) ((-118 . -102) T) ((-963 . -1062) T) ((-881 . -111) 2875) ((-487 . -23) T) ((-463 . -1231) T) ((-491 . -1062) T) ((-1075 . -239) T) ((-963 . -334) 2844) ((-491 . -334) 2801) ((-364 . -174) T) ((-361 . -174) T) ((-353 . -174) T) ((-271 . -174) 2712) ((-253 . -174) 2623) ((-974 . -1051) 2519) ((-527 . -500) 2500) ((-745 . -1051) 2471) ((-527 . -623) 2437) ((-428 . -1231) 2354) ((-1118 . -102) T) ((-1105 . -623) 2313) ((-1047 . -623) 2295) ((-704 . -1064) 2245) ((-1294 . -152) 2229) ((-1292 . -626) 2210) ((-1291 . -626) 2191) ((-1286 . -623) 2173) ((-1273 . -736) T) ((-704 . -650) 2123) ((-1266 . -736) T) ((-1245 . -801) NIL) ((-1245 . -804) NIL) ((-171 . -1069) 2033) ((-921 . -174) T) ((-881 . -626) 1963) ((-1245 . -736) T) ((-1016 . -351) 1937) ((-225 . -656) 1889) ((-1013 . -524) 1822) ((-853 . -860) 1801) ((-574 . -1165) T) ((-484 . -298) 1752) ((-606 . -736) T) ((-370 . -623) 1734) ((-330 . -623) 1716) ((-428 . -1051) 1612) ((-605 . -736) T) ((-417 . -860) 1563) ((-171 . -111) 1459) ((-843 . -132) 1411) ((-747 . -152) 1395) ((-1281 . -317) 1333) ((-497 . -315) T) ((-388 . -623) 1300) ((-530 . -1023) 1284) ((-388 . -624) 1198) ((-219 . -315) T) ((-142 . -152) 1180) ((-724 . -294) 1159) ((-497 . -1035) T) ((-590 . -38) 1146) ((-574 . -38) 1133) ((-505 . -38) 1098) ((-219 . -1035) T) ((-881 . -1062) T) ((-846 . -623) 1080) ((-837 . -623) 1062) ((-835 . -623) 1044) ((-826 . -920) 1023) ((-1305 . -1125) T) ((-1254 . -1069) 846) ((-865 . -1069) 830) ((-881 . -249) T) ((-881 . -239) NIL) ((-699 . -1231) T) ((-1305 . -23) T) ((-826 . -658) 719) ((-560 . -1231) T) ((-428 . -347) 703) ((-581 . -1069) 690) ((-1254 . -111) 499) ((-711 . -649) 481) ((-865 . -111) 460) ((-390 . -23) T) ((-171 . -626) 238) ((-1203 . -524) 30) ((-886 . -1113) T) ((-691 . -1113) T) ((-686 . -1113) T) ((-672 . -1113) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index c8e8d1c5..dc5fb70c 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3485510914)            
-(4457 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3485633347)            
+(4459 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -68,8 +68,9 @@
  |Dequeue| |DeRhamComplex| |DefiniteIntegrationTools| |DoubleFloat|
  |DoubleFloatSpecialFunctions| |DenavitHartenbergMatrix| |Dictionary&|
  |Dictionary| |DifferentialExtension&| |DifferentialExtension|
- |DifferentialDomain&| |DifferentialDomain| |DifferentialRing&|
- |DifferentialRing| |DictionaryOperations&| |DictionaryOperations|
+ |DifferentialDomain&| |DifferentialDomain| |DifferentialSpace&|
+ |DifferentialSpace| |DifferentialRing&| |DifferentialRing|
+ |DictionaryOperations&| |DictionaryOperations|
  |DiophantineSolutionPackage| |DirectProductCategory&|
  |DirectProductCategory| |DirectProductFunctions2| |DirectProduct|
  |DisplayPackage| |DivisionRing&| |DivisionRing|
@@ -484,664 +485,664 @@
  |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram|
  |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
  |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |direction| |resetAttributeButtons| |parents|
- |interval| |factorsOfCyclicGroupSize| |conditionP| |updatD| |curve|
- |systemCommand| |inv| |ravel| |match?| |partialNumerators| |iicos|
- |mainSquareFreePart| |startStats!| |startPolynomial| |autoCoerce|
- |updateStatus!| |linear?| |fintegrate| |normalDenom| |sechIfCan|
- |ground?| |reshape| |nthRootIfCan| |zeroDim?| |setScreenResolution3D|
- |myDegree| |OMreadFile| |UP2ifCan| |members| |assign| |intersect|
- |ground| |d01gaf| |indicialEquationAtInfinity|
- |semiSubResultantGcdEuclidean2| |setProperty| |algSplitSimple|
- |leftRecip| |showScalarValues| |cyclotomicDecomposition| |UnVectorise|
- |leadingMonomial| |normal| |s21baf| |sup| |toseLastSubResultant|
- |particularSolution| |f01rdf| |permutationGroup| |rCoord|
- |OMputEndAttr| |multisect| |leadingCoefficient| |cTanh| |index?|
- |colorDef| |rspace| |OMclose| |setRealSteps| |supDimElseRittWu?|
- |leftDivide| |totalGroebner| |primitiveMonomials| |close| |e02def|
- |primintfldpoly| |cAsech| |makeSin| F |setrest!| |e04fdf| |f01rcf|
- |chvar| |areEquivalent?| |reductum| |update| |compactFraction|
- |scalarTypeOf| |resize| |intensity| |s13aaf| |satisfy?|
- |bivariatePolynomials| |sizeMultiplication| |infinite?| |display|
- |conditionsForIdempotents| |modularGcdPrimitive| |laurentIfCan|
- |supersub| |paraboloidal| |isobaric?| |OMreadStr| |e01sef|
- |extractIfCan| |bipolarCylindrical| |exprToXXP| |revert| |extension|
- |stopTableInvSet!| |leadingExponent| |mapdiv| |ramifiedAtInfinity?|
- |tRange| |expressIdealMember| |s20acf| |reindex| |OMsend|
- |palglimint0| |pmintegrate| |radicalSimplify| |quasiRegular|
- |swapRows!| |acosIfCan| |eyeDistance| |degreePartition| |coerceImages|
- |headRemainder| |readUInt16!| |pushup| |orthonormalBasis| |pomopo!|
- |groebgen| |position| |shiftRoots| |leftScalarTimes!| |OMmakeConn|
- |expr| |totalDifferential| |deepCopy| |graphs| |viewThetaDefault|
- |createPrimitiveNormalPoly| |solveLinearPolynomialEquationByRecursion|
- |input| ** |discriminantEuclidean| |sub| |argscript| |colorFunction|
- |operation| |directSum| |critMTonD1| |nil?| |polygamma| |weierstrass|
- |library| |node?| |numerators| |algebraicOf| |closeComponent| |hMonic|
- |explicitlyEmpty?| |LyndonWordsList1| |geometric| |uniform01|
- |diagonals| |nthExpon| |testModulus| |symbol?| |SturmHabicht|
- |rootSplit| |closed?| |environment| |sqfrFactor| |localUnquote|
- |algebraic?| |ignore?| |problemPoints| |semiSubResultantGcdEuclidean1|
- |size| |variable| |sincos| |ratDenom| |rightRemainder| |pop!|
- |shiftRight| |gcdcofactprim| |factorPolynomial| |balancedBinaryTree|
- |npcoef| |over| |iterators| |fglmIfCan| |basisOfRightNucleus|
- |extractBottom!| |prindINFO| |clearTheSymbolTable| |reorder|
- |constantRight| |set| |nthFractionalTerm| |basisOfCommutingElements|
- |genericLeftTrace| |Ci| |exprHasAlgebraicWeight| |jokerMode| |d02gbf|
- |e02baf| |maxPoints3D| |conjugate| |arbitrary| |s13adf| |legendre|
- |denominator| |previous| |jordanAlgebra?| |tubePointsDefault| |updatF|
- |ddFact| |ksec| |tab1| |fullDisplay| |radicalOfLeftTraceForm| |round|
- |complexNormalize| |lowerCase?| |figureUnits| |divisorCascade|
- |f01qcf| |basicSet| |queue| |besselK| |oblateSpheroidal| |iiasec|
- |nthExponent| |stiffnessAndStabilityFactor| |integralBasisAtInfinity|
- |trivialIdeal?| |setCondition!| |iiatan| |alternative?| |resetNew|
- |basisOfRightNucloid| |cSech| |startTableInvSet!| |dequeue| |coord|
- |purelyAlgebraic?| |iFTable| |rightDivide| |say| |leftMult| |rk4a|
- |gcdPrimitive| |true| |iipow| |arguments| |createPrimitivePoly|
- |lexico| |rewriteIdealWithRemainder| |sts2stst| |internal?|
- |definingEquations| |e01daf| |inverseColeman| |unaryFunction|
- |category| |cAsec| |bandedJacobian| |expint| |bivariateSLPEBR|
- |quartic| |reset| |divideExponents| |bfEntry| |node| |evaluate|
- |acscIfCan| |loopPoints| |domain| |unary?| |mkcomm| |commutative?|
- |cCot| |frst| |internalDecompose| |insert| |patternMatch| |hdmpToP|
- |phiCoord| |package| |signAround| |linearDependence| |deriv| |write|
- |regime| |uniform| |inc| |exactQuotient| |singRicDE| |ParCondList|
- |exp| |rightTraceMatrix| |leftOne| |save| |every?| |empty| |coerceL|
- |s17agf| |roughBase?| |show| |radix| |deepestTail|
- |createNormalPrimitivePoly| |iroot| |s17ajf| |negative?|
- |OMgetEndBVar| |createThreeSpace| |d01apf| |drawComplex| |writable?|
- |btwFact| |normInvertible?| |size?| |d01akf| |bsolve| |rombergo|
- |trace| |ef2edf| |intcompBasis| |halfExtendedSubResultantGcd1|
- |palgint| |diagonalMatrix| |hermite| |exptMod| |airyBi| |badNum|
- |universe| |harmonic| |branchIfCan| |outputArgs| |innerSolve1|
- |mathieu12| |inspect| |viewSizeDefault| |varList| |radicalSolve|
- |primes| |invmod| |infieldint| |setStatus| |irreducibleRepresentation|
- |e02agf| |ldf2lst| |associative?| |normalElement| |clipParametric|
- |rootSimp| |f01brf| |buildSyntax| |f07fef| |divide| |collect|
- |recoverAfterFail| |basisOfRightAnnihilator| |elliptic| |open|
- |sequence| |clipBoolean| |adaptive| |Si| |exponent|
- |nextsousResultant2| |ran| |tanintegrate| |mainVariable?| |df2mf|
- |monicModulo| |nlde| |numberOfHues| |e02dff| |evaluateInverse|
- |mathieu24| |space| |se2rfi| |check| |obj| |retractIfCan| |delete!|
- |isOr| |nilFactor| |double| |concat!| |notelem| |localIntegralBasis|
- |spherical| |cache| |constant| |setErrorBound| |ode| |xn| |cAtan|
- |pmComplexintegrate| |content| |e02gaf| |isOp| |operations| |rightGcd|
- |gethi| |inHallBasis?| |complexIntegrate| |makingStats?| |trueEqual|
- |tan2cot| |bitLength| |showTheRoutinesTable| |solve|
- |inverseIntegralMatrix| |f02ajf| |moduleSum| |hasSolution?| |OMread|
- |singularAtInfinity?| |lepol| |log10| |rational?| |patternMatchTimes|
- |subspace| |lowerPolynomial| |extractClosed| |topFortranOutputStack|
- |iiatanh| |zeroSetSplit| |indicialEquation| |bitand|
- |zeroDimensional?| |infinity| |critM| |diagonal| |putColorInfo|
- |printTypes| |d01alf| |fortranInteger| |getExplanations| |column|
- |bitior| |doubleRank| |c06gbf| |weighted| |edf2ef|
- |reduceByQuasiMonic| |var1StepsDefault| |headAst| |keys| |mix|
- |bumptab| |ip4Address| |coerceS| |semiResultantEuclideannaif| |merge|
- UTS2UP |clipPointsDefault| |double?| |tracePowMod|
- |selectFiniteRoutines| |kmax| |kernel| |mkAnswer| |map|
- |leastMonomial| |outlineRender| |ScanArabic| |isQuotient|
- |leastAffineMultiple| |nthFlag| |seed| |isNot| |symbolTableOf|
- |OMconnOutDevice| |list| |cCos| |getRef| |halfExtendedResultant1|
- |print| |hasPredicate?| |llprop| |lhs| |subQuasiComponent?|
- |compBound| |iiacos| |pascalTriangle| |draw| |euclideanNormalForm|
- |innerint| |resolve| |cAcoth| |makeViewport3D| |startTable!| |bat1|
- |rhs| |iterationVar| |pseudoQuotient|
- |dimensionOfIrreducibleRepresentation| |lowerCase| |adjoint|
- |cylindrical| |tableForDiscreteLogarithm| |ref| |RittWuCompare|
- |mapSolve| |imagK| |trailingCoefficient| |df2fi| |rootOf| |iicsc|
- |currentEnv| |yCoordinates| |headReduce| |eigenvector| |s17adf|
- |makeTerm| |tanSum| |univariate?| |binding| |commaSeparate|
- |trigs2explogs| |derivative| |convert| |gbasis| |lexGroebner|
- |OMreceive| |height| |f02aff| |empty?| |open?| |monomials| |cos2sec|
- |makeObject| |lllip| |numberOfNormalPoly| |splitDenominator|
- |monicRightDivide| |quotientByP| |lieAlgebra?| |deepExpand|
- |parseString| |binary| |leadingCoefficientRicDE| |normalise| |coef|
- |leftPower| |pr2dmp| |setPredicates| |more?| |inconsistent?| |parts|
- |member?| |rightExtendedGcd| |chiSquare1| |lazyPremWithDefault| |dom|
- |fortranLogical| |radicalRoots| |iibinom| |mapUnivariate|
- |genericRightDiscriminant| |factorByRecursion| |finite?|
- |primitivePart| |integralDerivationMatrix| |idealiserMatrix|
- |primitiveElement| Y |complexEigenvalues| |acotIfCan| |compound?|
- |numberOfOperations| |bothWays| |one?| |maxrank| |wreath|
- |degreeSubResultant| |subset?| |coleman| |invertible?| |iidsum|
- |halfExtendedResultant2| |rootDirectory| |Hausdorff| |label|
- |makeSeries| |terms| |internalSubPolSet?| |graphCurves| |dominantTerm|
- |showRegion| |eulerPhi| |listYoungTableaus| |genericRightTrace|
- |entry| |jacobian| |e02bbf| |range| |OMputEndApp| |edf2df|
- |represents| |intPatternMatch| |setMaxPoints3D| |power!| |triangulate|
- |dark| |createMultiplicationTable| |isExpt| |sumOfSquares| |vspace|
- |eigenvectors| |modularFactor| |f04mcf| |symmetricRemainder|
- |clearTheIFTable| |subscriptedVariables| |modulus| |maxint| |d02ejf|
- |hconcat| |ListOfTerms| RF2UTS |setleaves!| |s18acf|
- |rewriteSetByReducingWithParticularGenerators| |setDifference|
- |purelyTranscendental?| |iicot| |errorKind| |hcrf| |basisOfNucleus|
- |gcdprim| |low| |matrixGcd| |constantOperator|
- |transcendentalDecompose| |rootNormalize| |c06fuf| |numFunEvals3D|
- |repSq| |incr| |cAtanh| |resultantEuclidean|
- |setLegalFortranSourceExtensions| |pdf2df| |solid| |multiEuclidean|
- |aQuadratic| |infiniteProduct| |alphanumeric| |constructor| |hi|
- |univariatePolynomialsGcds| |escape| |c05pbf| |messagePrint| |tail|
- |compdegd| |nativeModuleExtension| |meatAxe| |digamma| |saturate|
- |epilogue| |readInt16!| |f02wef| |df2ef| |option| |youngGroup|
- |selectMultiDimensionalRoutines| |inverse| |cot2trig| |showSummary|
- |less?| |indices| |ratPoly| |insertMatch| |setTex!|
- |basisOfLeftNucleus| |constantOpIfCan| |edf2fi| |leftFactor|
- |OMencodingSGML| |rules| |units| |s18adf| |resultantnaif|
- |radicalEigenvalues| |testDim| |top| |shanksDiscLogAlgorithm| |even?|
- |polyPart| |pToHdmp| |showAttributes| |sumOfDivisors| |var1Steps|
- |inrootof| |getVariableOrder| |stosePrepareSubResAlgo| |continue|
- |listBranches| |changeMeasure| |algint| |structuralConstants|
- |reopen!| |LagrangeInterpolation| |selectAndPolynomials| |removeZero|
- |normDeriv2| |bag| |f04arf| |f01maf| |wordInStrongGenerators|
- |simplifyExp| |setMinPoints3D| |norm| |mainCoefficients| |name|
- |bipolar| |unknown| |integralMatrix| |RemainderList| |monicLeftDivide|
- |insert!| |principalIdeal| |leftRank| |comment| |normalForm|
- |convergents| |body| |largest| |internalIntegrate0|
- |extendedSubResultantGcd| |iisec| |extractIndex| |code| |simplify|
- |PDESolve| |leastPower| |ptFunc| |argument| |frobenius| |sequences|
- |f2st| |pol| |binaryFunction| |support| |eulerE| |setStatus!| |recip|
- |null| |badValues| |children| |lfunc| UP2UTS |increment|
- |rationalPower| |subResultantsChain| |OMencodingBinary| |unitNormal|
- |delta| |not| EQ |exponential| |lex| |normal?| |minrank| |OMputAtp|
- |logGamma| |alphanumeric?| |torsionIfCan| |s17acf| |and|
- |removeDuplicates| |leaf?| |mathieu22| |nodes| |cCsch| |iisqrt3|
- |generate| |computeCycleEntry| |maximumExponent|
- |SturmHabichtSequence| |or| |complexSolve| |replaceKthElement|
- |binomThmExpt| |retractable?| |subSet| |chebyshevT| |tubePoints|
- |pointLists| |lambert| |outputSpacing| |xor| |assert| |surface|
- |subResultantChain| |stoseLastSubResultant| |f04asf| |incrementBy|
- |ratpart| |rightFactorIfCan| |port| |polygon?| |leftRemainder|
- |pattern| |case| |uncouplingMatrices| |pushdterm| |gensym|
- |approxSqrt| |argumentListOf| |infinityNorm| |expand| |factorial|
- |checkRur| |complexRoots| |Zero| |contract| |palgRDE0| |setUnion|
- |expandTrigProducts| |LyndonCoordinates| |complexZeros| |filterWhile|
- |cschIfCan| |reflect| |t| |quadraticNorm| |One|
- |derivationCoordinates| |countRealRoots| |setsubMatrix!| |readIfCan!|
- |supRittWu?| |perfectNthRoot| |filterUntil| |reducedContinuedFraction|
- |currentCategoryFrame| |overset?| |lambda| |groebSolve| |lflimitedint|
- |distance| |redmat| |changeWeightLevel| |search| |s15adf| |select|
- |sylvesterSequence| |physicalLength| |integers|
- |variationOfParameters| |message| |nor| |dmp2rfi| |modifyPoint|
- |df2st| |pack!| |palgRDE| |removeRoughlyRedundantFactorsInContents|
- |cRationalPower| |pointSizeDefault| |setButtonValue|
- |antisymmetricTensors| |upperCase!| |fTable| |s17dcf| |sinhIfCan|
- |pointColor| |linkToFortran| |backOldPos| |identity| |nrows| |module|
- |digits| |isAbsolutelyIrreducible?| |removeSinhSq| |splitLinear|
- |removeIrreducibleRedundantFactors| |absolutelyIrreducible?| |ncols|
- |elt| |processTemplate| |normalizedDivide| |rotatey| |separate|
- |list?| |freeOf?| |cCosh| |retract| |repeating?|
- |cyclotomicFactorization| |cAcosh| |read!| |e04mbf| |newLine| |dilog|
- |zero| |pquo| |newTypeLists| |integerIfCan| |nonLinearPart| |ocf2ocdf|
- |OMsupportsCD?| |replace| |cons| |OMlistCDs| |sin| |makeRecord|
- |returns| |lprop| |showClipRegion| |block| |restorePrecision|
- |nothing| |And| |cos| |csch2sinh| |rational| |initials| |cartesian|
- |fortranDouble| |hex| |rootBound| |abelianGroup| |Or|
- |indiceSubResultant| |tan| |bottom!| |nextSublist| |tensorProduct|
- |e02dcf| |product| |taylorQuoByVar| |showAllElements| |factorList|
- |Not| |cot| |putProperty| |nodeOf?| |nsqfree| |OMputSymbol|
- |symmetricTensors| |basisOfLeftNucloid| |mainValue| |condition|
- |mainContent| |sec| |c06ekf| |dot| |e02akf| |associator|
- |leftMinimalPolynomial| |rename| |iflist2Result| |csc| |ReduceOrder|
- |maxdeg| |scan| |sin?| |knownInfBasis| |pointData| |optAttributes|
- |qPot| |dAndcExp| |interpret| |source| |asin| |swap| |makeop|
- |cycleTail| |prime| |squareFree| |getMultiplicationMatrix|
- |fortranCarriageReturn| |dec| |isAtom| |acos| |PollardSmallFactor|
- |meshPar2Var| |taylorRep| |limitedIntegrate| |makeSUP|
- |createLowComplexityTable| |readInt32!| |atan| |plusInfinity| |reseed|
- |primeFrobenius| |complementaryBasis| |numFunEvals| |vconcat| |atoms|
- |minGbasis| |constantLeft| |acot| |minusInfinity| |startTableGcd!|
- |nullSpace| |char| |relerror| |relationsIdeal| |extractTop!|
- |prinshINFO| |inputOutputBinaryFile| |asec| |nthFactor| |xCoord|
- |infRittWu?| |innerEigenvectors| |deepestInitial| |zeroDimPrimary?|
- |horizConcat| |isList| |acsc| |target| |laguerreL| |quatern|
- |scaleRoots| |back| |mkIntegral| |reducedForm| |unitNormalize| |sinh|
- |setIntersection| |fractionPart| |wholeRagits|
- |standardBasisOfCyclicSubmodule| |primlimitedint| |preprocess|
- |zerosOf| |normalize| |normal01| |cosh| |signatureAst| |subNodeOf?|
- |generalInfiniteProduct| |typeList| |rst| |polyred| |leadingBasisTerm|
- |doubleDisc| |type| |tanh| |viewpoint| |OMgetEndApp| |resultant|
- |hclf| |subNode?| |outputList| |collectUnder| |mvar| |s14aaf| |curve?|
- |tryFunctionalDecomposition?| |coth| |binaryTree|
- |SturmHabichtCoefficients| |option?| |makeMulti| |iiperm| |tablePow|
- |computePowers| |setOfMinN| |float| |qelt| |LyndonBasis|
- |integralMatrixAtInfinity| |cSec| |sech| |primlimintfrac|
- |interpretString| |primPartElseUnitCanonical!| |second| |qsetelt|
- |roughUnitIdeal?| |cycleSplit!| |OMgetEndError| |yCoord|
- |pointColorPalette| |partialDenominators| |componentUpperBound| |csch|
- |pointPlot| |hue| |d03eef| |third| |graeffe| |interactiveEnv|
- |viewDefaults| |generators| |xRange| |s20adf| |ParCond| |asinh|
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- |positiveSolve| |nary?| |acosh| |accuracyIF| |makeViewport2D|
- |numberOfFractionalTerms| |max| |linearMatrix| |complement|
- |rightScalarTimes!| |screenResolution| |zRange|
- |exprHasWeightCosWXorSinWX| |sn| |conjunction| |atanh| |leadingIndex|
- |monomial?| |identityMatrix| |point?| |sncndn| |map!|
- |internalLastSubResultant| |expPot| |univariateSolve| |pade| |f02akf|
- |acoth| |OMputString| |integralLastSubResultant| |e02ddf| |ridHack1|
- |qsetelt!| |palginfieldint| |findBinding| |rightMult|
- |pseudoRemainder| |ODESolve| |safeCeiling| |asech| |lfinfieldint|
- |prem| |f04jgf| |diagonal?| |float?| |printHeader| |OMputInteger|
- |solveLinearlyOverQ| |hdmpToDmp| |createRandomElement|
- |repeatUntilLoop| |packageCall| |orbits| |viewport3D| |qinterval|
- |fill!| |factorSFBRlcUnit| |KrullNumber| GE |d02cjf|
- |zeroSquareMatrix| |multiple| |predicates| |tab| |numberOfDivisors|
- |mindegTerm| |imports| |just| |nextPartition| GT |usingTable?|
- |s14abf| |rightCharacteristicPolynomial| |applyQuote| |rightLcm|
- |components| |mapExponents| |listexp| |exp1| |iExquo| |qroot| |head|
- LE |shallowExpand| |numberOfImproperPartitions| |setvalue!|
- |karatsubaDivide| |normalizeAtInfinity| |leftTraceMatrix| |predicate|
- |noLinearFactor?| |elRow2!| |determinant| |shallowCopy| LT |acsch|
- |nextNormalPoly| |expenseOfEvaluation| |OMputEndBind|
- |groebnerFactorize| |LowTriBddDenomInv| |powerAssociative?| |prinb|
- |minPol| |upperCase| |has?| |mathieu11| |setOrder| |critBonD|
- |ruleset| |sPol| |outputForm| |deleteRoutine!| |root?| |hyperelliptic|
- |cyclicSubmodule| |clearTheFTable| |readLineIfCan!| |subst|
- |OMputEndBVar| |associatedSystem| |possiblyNewVariety?| |mapCoef|
- |integralRepresents| |heap| |mulmod| |lintgcd| |getMatch|
- |unknownEndian| |modTree| |basisOfCentroid| |coerceP| |prinpolINFO|
- |rightTrace| |BumInSepFFE| |nextItem| |rdregime| |moebius| |s17dhf|
- |nextPrimitiveNormalPoly| |complexElementary| |iiasin| |directory|
- |makeVariable| |polyRDE| |suchThat| |presub| |currentScope|
- |monomRDEsys| |tree| |index| |computeCycleLength|
- |removeRoughlyRedundantFactorsInPols| |iiacosh| |socf2socdf|
- |completeHensel| |besselJ| |hspace| |pole?| |adaptive?| |setValue!|
- |in?| |nextPrime| |isConnected?| |OMopenFile| |initial| |const|
- |mapBivariate| |doubleFloatFormat| |complete| |normalDeriv|
- |fullPartialFraction| |multiple?| |sinh2csch| |functionIsOscillatory|
- |returnType!| |odd?| |primextintfrac| |curryLeft| |f02awf|
- |unitVector| |simpson| |squareFreePolynomial| |pair| |mapMatrixIfCan|
- |s21bdf| |bezoutResultant| |linGenPos| |vedf2vef| |objects| |biRank|
- |rightTrim| |select!| |monicDecomposeIfCan| |bright| |quasiMonic?|
- |selectPolynomials| |monomRDE| |parameters| |primitivePart!|
- |stronglyReduced?| |lagrange| |getGraph| |readUInt32!| |base|
- |leftTrim| |airyAi| |lazyEvaluate| |s18aef| |innerSolve| |sech2cosh|
- |arg1| |green| |parent| |lowerBound| |ode1| |lllp| |mergeFactors|
- |triangular?| |unrankImproperPartitions1| |eval| |linears| |plotPolar|
- |arg2| |squareTop| |isEquiv| |leftRegularRepresentation|
- |virtualDegree| |minimumDegree| |color| |irreducible?| |separant|
- |crushedSet| |endSubProgram| |functionIsContinuousAtEndPoints|
- |stoseInvertible?sqfreg| |sturmSequence| |removeSinSq| |disjunction|
- |externalList| |permutation| |varselect| |schema| |thetaCoord|
- |conditions| |identification| |squareFreeLexTriangular| |component|
- |symmetricPower| |hessian| |error| |makeFR| |rightPower| |d02bhf|
- |setProperties| |monicDivide| |addPoint2| |match| |curry| |plot|
- |setClipValue| |semiDiscriminantEuclidean| |parametersOf| |nullary?|
- |moebiusMu| |cap| |equation| |readInt8!| |wholePart| |useNagFunctions|
- |decreasePrecision| |cyclePartition| |iiacsch| |companionBlocks| |is?|
- |elColumn2!| |zero?| |SturmHabichtMultiple| |choosemon| |abs|
- |createMultiplicationMatrix| |f01ref| |smith| |removeDuplicates!|
- |function| |currentSubProgram| |optimize|
- |leftCharacteristicPolynomial| |ramified?| |numerator| |e01bhf|
- |hostPlatform| |genericLeftTraceForm| |invertIfCan| |style|
- |extractPoint| |csubst| |alternatingGroup| |completeHermite|
- |numberOfComponents| |genericRightNorm| |contours| |cPower|
- |padicallyExpand| |denomLODE| |expt| |c06frf| BY |besselI|
- |arrayStack| |alphabetic| |d01amf| |setClosed| |cycles| |prevPrime|
- |exportedOperators| |OMbindTCP| |iteratedInitials| |expintegrate|
- |totalfract| |monicCompleteDecompose| |nextNormalPrimitivePoly|
- |OMgetEndAttr| |OMgetFloat| |semiResultantEuclidean2|
- |sylvesterMatrix| |acothIfCan| |collectUpper| |minimumExponent| |cCsc|
- |s18dcf| |OMcloseConn| |prepareSubResAlgo| |c05nbf| |initiallyReduce|
- |separateDegrees| |cCoth| |trace2PowMod| |gderiv| |rightExactQuotient|
- |selectfirst| |dflist| |s14baf| |algintegrate| |s19abf| |sort|
- |tubePlot| |clearTable!| |lieAdmissible?| |irDef| |lSpaceBasis|
- |extend| |times!| |symmetricDifference| |categoryFrame| |deref|
- |idealSimplify| |enterInCache| |noValueMode| |rem| |imagk| |multiset|
- |roughSubIdeal?| |dn| |rectangularMatrix| |properties| |goto|
- |vertConcat| |stoseSquareFreePart| |showTheSymbolTable|
- |polarCoordinates| |quo| |ricDsolve| |critT| |maxRowIndex| |c06fpf|
- |padicFraction| |id| |eigenvalues| NOT |mesh?| |argumentList!|
- |translate| |child?| |tanQ| |setnext!| |fortranReal| |readLine!|
- |f01bsf| |sh| |lo| |mkPrim| OR |firstUncouplingMatrix| |random|
- |jacobiIdentity?| |getDatabase| |squareMatrix|
- |genericRightMinimalPolynomial| |div| |d01anf| |algDsolve|
- |palgextint| |quoByVar| |lcm| |ScanFloatIgnoreSpaces| AND |asimpson|
- |logIfCan| |diophantineSystem| |algebraicSort| |diag|
- |associatedEquations| |exquo| |delete| |getOperator|
- |fortranCompilerName| |OMgetVariable| |s17aef| |sign| |upDateBranches|
- |stoseInvertible?| |mapmult| |rewriteIdealWithHeadRemainder|
- |associates?| ~= |complexNumericIfCan| |hitherPlane| |var2Steps|
- |ldf2vmf| |lift| |sorted?| |leftRankPolynomial| |append| |middle|
- |sec2cos| |maxColIndex| |OMgetAtp| |ellipticCylindrical| |#| |setPoly|
- |linearlyDependentOverZ?| |arity| |monicRightFactorIfCan| |reduce|
- |pow| |OMgetSymbol| |legendreP| |midpoints| |gcd| |setlast!|
- |rightRankPolynomial| |toScale| ~ |linearPart| |fixedPoints| |quoted?|
- |car| |representationType| |solveid| |quasiAlgebraicSet| |false|
- |partitions| |rationalApproximation| |integralCoordinates| |Lazard|
- |overlabel| |reduced?| |OMputEndObject| |cfirst| |outputMeasure|
- |rightUnits| |opeval| |trunc| |cAcot| |insertTop!| |printingInfo?|
- |apply| |imagj| |subresultantSequence| |rootsOf| |dmpToP|
- |alphabetic?| |distribute| |c06gsf| |setMinPoints| |clip|
- |highCommonTerms| |/\\| |cyclicCopy| |matrix| |first| |setleft!|
- |nthCoef| |d03edf| |setPrologue!| |useEisensteinCriterion?| |shape|
- |listLoops| |mainDefiningPolynomial| |randomLC| |\\/| |rest|
- |finiteBasis| |strongGenerators| |debug3D| |lp| |sinhcosh|
- |generalizedContinuumHypothesisAssumed| |chainSubResultants|
- |writeByte!| |nthRoot| |rotatez| |makeResult| |front| |insertBottom!|
- |simpleBounds?| |raisePolynomial| |bat| |coerce| * |rangeIsFinite|
- |s17ahf| |prepareDecompose| |e02zaf| |inGroundField?|
- |generalPosition| |d01fcf| |brillhartIrreducible?| |leftUnit|
- |bezoutMatrix| |certainlySubVariety?| |construct| |delay|
- |showArrayValues| |order| |removeSquaresIfCan| |subMatrix|
- |computeBasis| |e01sff| |e04jaf| |postfix| |numer| |logical?|
- |secIfCan| |s15aef| |generator| |setAdaptive| |minPoly|
- |bezoutDiscriminant| |build| |writeUInt8!| |wordInGenerators| |denom|
- |critpOrder| |getStream| |swapColumns!| = |getOrder| |morphism|
- |clipWithRanges| |zeroVector| |leviCivitaSymbol| |lazyPrem| |submod|
- |asinhIfCan| |cAcsc| |voidMode| |rowEch| |polyRicDE|
- |changeThreshhold| |showIntensityFunctions| |reducedSystem|
- |intChoose| |OMReadError?| |Lazard2| |pi| |triangSolve| |byte|
- |complexEigenvectors| |octon| |tanhIfCan| < |drawCurves|
- |initiallyReduced?| |child| |augment| |weakBiRank| |unitCanonical|
- F2FG |width| |writeBytes!| |asecIfCan| > |mainVariables| |e02daf|
- |oddInfiniteProduct| |fixedPoint| |readByte!| |showAll?|
- |getButtonValue| |fortranCharacter| |f02bbf| |redpps|
- |evenInfiniteProduct| <= |diff| |f02bjf| |power| |cosSinInfo|
- |setAdaptive3D| |makeprod| |paren| |integrate| |push| |printCode|
- |numericIfCan| |pseudoDivide| >= |extensionDegree| |coefChoose|
- |OMputError| |rightAlternative?| |stiffnessAndStabilityOfODEIF|
- |univariatePolynomials| |setFormula!| |f04adf| |rootPower|
- |integralAtInfinity?| |makeYoungTableau| |factorset| |lowerCase!|
- |minimalPolynomial| |transpose| |multMonom| |s17dgf| |log2|
- |addMatchRestricted| |infieldIntegrate| |pureLex| |cubic|
- |OMUnknownSymbol?| |clikeUniv| |explicitlyFinite?| |polygon|
- |chiSquare| |iiexp| |stoseInternalLastSubResultant|
- |generalizedEigenvector| |fmecg| |lfextendedint| |lyndon?| |elRow1!|
- |positive?| + |rowEchelon| |doubleResultant| |printInfo!|
- |basisOfLeftAnnihilator| |value| |external?| |clearCache|
- |ScanFloatIgnoreSpacesIfCan| |findCycle| |singleFactorBound| |numeric|
- |explimitedint| |int| - |viewZoomDefault| |gramschmidt|
- |LazardQuotient2| |iicosh| |OMconnectTCP| |iicsch|
- |selectOrPolynomials| |radical| |getPickedPoints| |antiCommutator|
- |semiIndiceSubResultantEuclidean| |applyRules| |optional|
- |linearAssociatedExp| |reduction| |createNormalElement| /
- |simplifyPower| |leftFactorIfCan| |mdeg| |principalAncestors| |cTan|
- |logpart| |rk4f| |s13acf| |symmetricGroup| |log| |inverseLaplace|
- |simpsono| |createIrreduciblePoly| |rightMinimalPolynomial| |zag|
- |f2df| |sumOfKthPowerDivisors| |presuper| |cyclicParents|
- |gcdPolynomial| |connect| |resultantReduitEuclidean|
- |selectPDERoutines| |critB| |youngDiagram| |create| |reverse!|
- |rewriteIdealWithQuasiMonicGenerators| |bombieriNorm| |laguerre|
- |signature| |getMultiplicationTable| |limit| |setelt| |setPosition|
- |relativeApprox| |bernoulliB| |orbit| |callForm?| |attributeData|
- |continuedFraction| |binomial| |besselY| |incrementKthElement|
- |setEmpty!| |specialTrigs| |toseInvertible?| |brillhartTrials|
- |safeFloor| |declare!| |high| |commutativeEquality| |cscIfCan|
- |att2Result| |unit| |parabolicCylindrical| |setMaxPoints| |copy|
- |edf2efi| |mergeDifference| |stoseInvertibleSetsqfreg| |minPoints3D|
- |unmakeSUP| |whatInfinity| |qqq| |separateFactors| |e02bcf|
- |limitedint| |minIndex| |swap!| |divideIfCan| |fprindINFO|
- |OMputEndError| |baseRDEsys| |printStatement| |genericPosition|
- |coshIfCan| |cyclicEntries| |datalist| |nextPrimitivePoly|
- |normalizeIfCan| |iifact| |rightOne| |B1solve| |quadraticForm|
- |SFunction| |trapezoidalo| |mainMonomials| |perfectSqrt|
- |rationalIfCan| |outputGeneral| |An| |endOfFile?| |rischNormalize|
- |c06fqf| |modifyPointData| |wholeRadix| |henselFact|
- |tryFunctionalDecomposition| |compiledFunction| |rightZero| |iiabs|
- |options| |imagI| |curveColorPalette| |jacobi| |schwerpunkt| |trim|
- |GospersMethod| |FormatArabic| |powers| |routines| |composites|
- |unprotectedRemoveRedundantFactors| |tanh2coth| |binaryTournament|
- |integral| |basisOfCenter| |redPol| |fibonacci| |normalizedAssociate|
- |controlPanel| |approximants| |iprint| |degreeSubResultantEuclidean|
- |returnTypeOf| |gradient| |minset| |exponents| |slash| |lazy?|
- |htrigs| |segment| |flagFactor| |linearDependenceOverZ| |c02agf|
- |implies| |OMgetAttr| |output| |string| |expextendedint| |sinIfCan|
- |leftUnits| |irVar| |bitTruth| |e04dgf| |symmetricSquare| |roman|
- |graphState| |moreAlgebraic?| |bubbleSort!| |weights| |exactQuotient!|
- |drawToScale| |numberOfComputedEntries| |omError| |dequeue!|
- |bringDown| |insertRoot!| |removeSuperfluousQuasiComponents|
- |integral?| |rischDEsys| |genericLeftDiscriminant| |realEigenvalues|
- |getMeasure| |leftGcd| |newSubProgram| |f04qaf| |sqfree| |polar|
- |wronskianMatrix| |jordanAdmissible?| |nextLatticePermutation| |cond|
- |sample| |rationalFunction| |minordet| |beauzamyBound|
- |resultantReduit| |e02ajf| |stFuncN| |mainMonomial| |lazyResidueClass|
- |getOperands| |f07aef| |perspective| |linearAssociatedLog| |errorInfo|
- |pointColorDefault| |dimensionsOf| |evenlambert| |weight|
- |perfectSquare?| |pastel| |LazardQuotient| |stopTable!| |iomode|
- |imagJ| |whitePoint| |monic?| |ord| |semiLastSubResultantEuclidean|
- |c06gqf| |part?| |iitanh| |noKaratsuba| |antiAssociative?| |sort!|
- |cyclic?| |littleEndian| |f04axf| |leadingTerm| |wrregime|
- |showFortranOutputStack| |f04atf| |rationalPoints|
- |reducedDiscriminant| |cSin| |selectsecond| |invertibleSet| |lifting1|
- |s17akf| |setAttributeButtonStep| |subtractIfCan| |credPol| |remove|
- |genericRightTraceForm| |fractRadix| |splitConstant| |crest|
- |solveRetract| |skewSFunction| |acschIfCan| |factorFraction|
- |triangularSystems| |homogeneous?| |elseBranch| |listRepresentation|
- |leftNorm| |s21bbf| |integer?| |taylorIfCan| |mainForm|
- |elaborateFile| |partition| |elem?| |getCurve| |discreteLog|
- |scalarMatrix| |center| |last| |hypergeometric0F1| |s19aaf| |f04maf|
- |f02abf| |measure2Result| |symbolIfCan| |rk4qc| |initTable!| |assoc|
- |laplace| |rk4| |mainKernel| |genericLeftNorm| |top!| |OMgetEndObject|
- |iCompose| |maxIndex| |leadingIdeal| |constantIfCan| |formula|
- |extract!| |dfRange| |randnum| |allRootsOf|
- |semiResultantReduitEuclidean| |infLex?| |OMlistSymbols|
- |selectIntegrationRoutines| |hexDigit?| |screenResolution3D| |yellow|
- |changeNameToObjf| |HermiteIntegrate| |bernoulli| |coordinate| |zoom|
- |findConstructor| |rightRank| |ScanRoman| |rangePascalTriangle|
- |pushucoef| |cyclic| |numberOfFactors| |matrixConcat3D| |call| |untab|
- |imagi| |lazyGintegrate| |getGoodPrime| |removeRedundantFactors|
- |partialQuotients| |OMgetObject| |digit| |zCoord| |f04mbf|
- |nextColeman| |withPredicates| |hasHi| |kroneckerDelta| |cycleLength|
- |rischDE| |expandPower| |refine| |lquo| |changeName|
- |nextsubResultant2| |f02aef| |countable?| |realRoots| |contains?|
- |expenseOfEvaluationIF| |viewWriteDefault| |getIdentifier|
- |halfExtendedSubResultantGcd2| |lazyPseudoQuotient| |quasiComponent|
- |Aleph| |outputFloating| |leftTrace| |constantCoefficientRicDE|
- |dictionary| |hasTopPredicate?| |groebner| |s17def| |primitive?|
- |imagE| |unrankImproperPartitions0| |twoFactor| |bivariate?|
- |autoReduced?| |iicoth| |variable?| |mapDown!| |e04gcf|
- |leftDiscriminant| |subResultantGcd| |changeVar| |genus|
- |branchPointAtInfinity?| |charpol| |twist| |rur| |getProperty|
- |leftExactQuotient| |floor| |stoseInvertible?reg| |s19adf| |anfactor|
- |outputAsScript| |generalSqFr| |numberOfComposites| |viewport2D|
- |fortranLiteralLine| |numberOfChildren| |iiacoth| |fixPredicate|
- |putProperties| |acoshIfCan| |modularGcd| |squareFreePrim| |makeEq|
- |cycleEntry| |powerSum| |primeFactor| |OMputObject| |kovacic|
- |decomposeFunc| |regularRepresentation| |f01mcf| |lastSubResultant|
- |addiag| |finiteBound| |f02xef| |noncommutativeJordanAlgebra?|
- |calcRanges| |clipSurface| |seriesToOutputForm| |e04naf|
- |dualSignature| |irreducibleFactors| |psolve| |magnitude| |hexDigit|
- |setref| |identitySquareMatrix| |iiGamma| |stFunc1| |leaves|
- |contractSolve| |unvectorise| |Nul| |sturmVariationsOf| |solid?|
- |reify| |lexTriangular| |closedCurve| |rootProduct| |shufflein|
- |nextSubsetGray| |squareFreePart| |nil| |setLabelValue| |isAnd|
- |c06gcf| |asinIfCan| |macroExpand| |leftLcm| |numberOfVariables|
- |f07fdf| |coercePreimagesImages| |semicolonSeparate|
- |rightDiscriminant| |lazyVariations| |stoseInvertibleSetreg|
- |constantToUnaryFunction| |minColIndex| |flexible?|
- |selectOptimizationRoutines| |headReduced?| |discriminant| |blue|
- |numberOfCycles| |generic| |lyndon| |traverse| |mainExpression| |mat|
- |e01bgf| |listOfMonoms| |OMwrite| |approximate| |listConjugateBases|
- FG2F |irreducibleFactor| |scanOneDimSubspaces| |stopMusserTrials|
- |remove!| |axes| |fractRagits| |sum| |stronglyReduce| |complex|
- |removeZeroes| |drawStyle| |s17aff| |repeating| |OMopenString|
- |nextIrreduciblePoly| |subResultantGcdEuclidean| |isOpen?|
- |OMputFloat| |minus!| |OMsupportsSymbol?| |lazyPseudoRemainder|
- |selectNonFiniteRoutines| |atanhIfCan| |tubeRadius|
- |resetVariableOrder| |generalTwoFactor| |minPoints| |rootRadius|
- |bumprow| |corrPoly| |rank| |quickSort| |plus!| |comparison|
- |transform| |elements| |f02axf| |point| |vark| |tValues| |cn|
- |mightHaveRoots| |f02aaf| |viewPhiDefault| |showTheIFTable| |debug|
- |failed| |enqueue!| |optpair| |trigs| |exists?| |appendPoint|
- |constantKernel| |rotatex| |number?| |numericalIntegration| |radPoly|
- D |balancedFactorisation| |parabolic| |cAcos| |generalizedInverse|
- |inputBinaryFile| |ceiling| |s21bcf| |mappingAst| |idealiser|
- |Vectorise| |univcase| |series| |someBasis| |permutations| |complex?|
- |e01sbf| |completeSmith| |axesColorDefault| |firstSubsetGray|
- |inverseIntegralMatrixAtInfinity| |defineProperty| |OMgetError|
- |failed?| |extendIfCan| |froot| |fortranTypeOf| |perfectNthPower?|
- |lighting| |moduloP| |shuffle| |makeGraphImage|
- |resultantEuclideannaif| |gcdcofact| |LiePoly|
- |solveLinearPolynomialEquation| |cyclicEqual?| |patternVariable|
- |f04faf| |getBadValues| |super| |removeConstantTerm| |lists| |conical|
- |checkForZero| |d01asf| |min| |OMgetEndBind| |padecf| |chebyshevU|
- |newReduc| |connectTo| |bracket| |inf| |symFunc| |goodnessOfFit|
- |c06eaf| |isPlus| |printInfo| |transcendenceDegree| |permanent|
- |remainder| |safetyMargin| |elaboration| |singular?| |rootKerSimp|
- |iisech| |dihedral| |torsion?| |branchPoint?| |coHeight|
- |functionIsFracPolynomial?| |getProperties| |aQuartic| |close!|
- |checkPrecision| |enumerate| |d02gaf| |upperBound| |Ei| |substring?|
- |s19acf| |key| |aLinear| |powern| |enterPointData| |droot|
- |chineseRemainder| |palglimint| |d03faf| |quasiMonicPolynomials|
- |roughBasicSet| |coerceListOfPairs| |graphStates| |constant?| |leader|
- |setLength!| |unravel| |conjugates| |karatsubaOnce| |suffix?|
- |initializeGroupForWordProblem| |filename| |fixedPointExquo|
- |removeCosSq| |rewriteSetWithReduction|
- |removeRedundantFactorsInContents| |lookup| |linearlyDependent?|
- |ode2| |localAbs| |meshFun2Var| |symbolTable| |loadNativeModule|
- |dimensions| |squareFreeFactors| |zeroSetSplitIntoTriangularSystems|
- |factorGroebnerBasis| |critMonD1| |lyndonIfCan| |expintfldpoly|
- |generalLambert| |prefix?| |parametric?| |element?| |parse| |capacity|
- |setchildren!| |traceMatrix| |pleskenSplit| |fortran| |iisqrt2|
- |aspFilename| |distFact| |bandedHessian| |plus| |probablyZeroDim?|
- |pushFortranOutputStack| |bindings| |rightNorm| |red|
- |matrixDimensions| |createLowComplexityNormalBasis| |c06ecf|
- |changeBase| |intermediateResultsIF| |splitNodeOf!|
- |popFortranOutputStack| |setVariableOrder| |e02aef| |slex| |elaborate|
- |rightUnit| |internalAugment| |truncate| |createGenericMatrix|
- |definingPolynomial| |outputAsFortran| |linSolve| |toroidal| |powmod|
- |completeEval| |find| |closed| |e01bef| |s18def| |definingInequation|
- |table| |eq?| |light| |scale| |factorsOfDegree| |exponentialOrder|
- |anticoord| |precision| |s18aff| |stripCommentsAndBlanks| |times|
- |midpoint| |new| |atanIfCan| |semiResultantEuclidean1| |Frobenius|
- |linearPolynomials| |nand| |totalLex| |charClass| |rename!|
- |typeLists| |infix?| |ptree| |shrinkable| |iisinh| |principal?|
- |viewPosDefault| |domainTemplate| |flatten| |move| |rationalPoint?|
- |mathieu23| |mask| |pushuconst| |exponential1| |sortConstraints|
- |subscript| |e02bdf| |divideIfCan!| |init| |lfextlimint| |subCase?|
- |fi2df| |rightRegularRepresentation| |medialSet| |entry?|
- |minRowIndex| |scopes| |equality| |OMgetBVar| |systemSizeIF|
- |lineColorDefault| |rowEchelonLocal| |monom| |csc2sin| |recur|
- |factorSquareFree| |setright!| |iiacot| |subHeight| |bytes|
- |OMputVariable| |generateIrredPoly| |rule| |OMgetType| |optional?|
- |string?| |tanNa| |extendedResultant| |decrease| |neglist|
- |euclideanSize| |realZeros| |charthRoot| |status| |compose|
- |internalInfRittWu?| |decimal| |hasoln| |inR?| |stoseInvertibleSet|
- |common| |tanAn| |mappingMode| |iidprod| |split| |collectQuasiMonic|
- |script| |setRow!| |recolor| |groebner?| |clearFortranOutputStack|
- |monomialIntegrate| |rotate!| |validExponential|
- |generalizedEigenvectors| |mapUp!| |encodingDirectory| |title|
- |combineFeatureCompatibility| |polynomialZeros| |f01qef| |po| |prime?|
- |lastSubResultantEuclidean| |aCubic| |exprToUPS| |symmetricProduct|
- |isImplies| |toseInvertibleSet| |basisOfMiddleNucleus| |integerBound|
- |left| |vector| |c02aff| |qfactor| |merge!| |null?| |tex|
- |explogs2trigs| |outerProduct| |primintegrate| |mainCharacterization|
- |substitute| |prefixRagits| |right| |differentiate| |userOrdered?|
- |euclideanGroebner| |primPartElseUnitCanonical| |consnewpol| |e|
- |palgLODE| |monomialIntPoly| |nullary| |closedCurve?| |addMatch|
- |var2StepsDefault| |quote| |graphImage|
- |semiDegreeSubResultantEuclidean| |stopTableGcd!| |realEigenvectors|
- |Beta| |cLog| |internalSubQuasiComponent?| |functorData|
- |genericLeftMinimalPolynomial| |rquo| |lazyIrreducibleFactors|
- |multiplyCoefficients| |polCase| |mainVariable| |fortranDoubleComplex|
- |OMParseError?| |seriesSolve| |makeFloatFunction| |flexibleArray|
- |multinomial| |cSinh| |completeEchelonBasis| |roughEqualIdeals?|
- |useEisensteinCriterion| |pile| |makeSketch| |setTopPredicate|
- |addBadValue| |laplacian| |f07adf| |prolateSpheroidal| |interpolate|
- |ffactor| |unitsColorDefault| |useSingleFactorBound?|
- |selectODEIVPRoutines| |palgextint0| |box| |doublyTransitive?|
- |c06ebf| |copy!| |zeroDimPrime?| |shift| |exprHasLogarithmicWeights|
- |categoryMode| |generalizedContinuumHypothesisAssumed?|
- |rightFactorCandidate| |any| |OMputApp| |hash| |OMputEndAtp| |bounds|
- |atom?| |trapezoidal| |denomRicDE| |writeLine!| |fillPascalTriangle|
- |measure| |count| |nthr| |leftZero| |rarrow| |next| |maxPoints|
- |coefficient| |makeCos| |d02raf| |exQuo| |quotedOperators| |mapGen|
- |reciprocalPolynomial| |fractionFreeGauss!| |associatorDependence|
- |numberOfIrreduciblePoly| |e02adf| |countRealRootsMultiple|
- |cyclicGroup| |internalZeroSetSplit| |OMserve| |fixedDivisor|
- |transcendent?| |iitan| |ipow| |extendedEuclidean| |aromberg|
- |tubeRadiusDefault| |e01bff| |bumptab1| |symbol| |push!| |elementary|
- |cardinality| |cosIfCan| |divisors| |sin2csc| |rowEchLocal| |isTimes|
- |musserTrials| |cothIfCan| |expression| |solve1| |iiasech| |d01gbf|
- |eof?| |karatsuba| |difference| |tanh2trigh| |minimize| |bit?|
- |integer| |cross| |reduceBasisAtInfinity| |makeCrit| |Is|
- |rightQuotient| |reduceLODE| |tanIfCan| |linear|
- |createPrimitiveElement| |write!| |qualifier| |setFieldInfo|
- |constDsolve| |shellSort| |composite| |toseSquareFreePart|
- |algebraicVariables| |printStats!| |limitPlus| |fortranLinkerArgs|
- |reducedQPowers| |birth| |f02adf| |differentialVariables| |expIfCan|
- |superscript| |polynomial| |makeUnit| |dmpToHdmp| |complexForm|
- |possiblyInfinite?| |hostByteOrder| |FormatRoman| |equiv| |computeInt|
- |leadingSupport| |OMgetApp| |prologue| |cosh2sech| |overlap| |points|
- |subTriSet?| |digit?| |setprevious!| |erf| |primaryDecomp| |result|
- |factorAndSplit| |rroot| |atrapezoidal| |explicitEntries?|
- |multiplyExponents| |alternating| |li| |superHeight| |sumSquares|
- |mapExpon| |rootPoly| |curveColor| |oddintegers| |operators|
- |extendedint| |d01aqf| |stack| |denominators| |tower| |position!|
- |normFactors| |radicalEigenvectors| |factorOfDegree| |copyInto!|
- |OMgetInteger| |OMgetString| |putGraph| |getConstant| |HenselLift|
- |plenaryPower| |nonQsign| |writeInt8!| |thenBranch| |divergence|
- |oneDimensionalArray| |diagonalProduct| |cycle|
- |stoseIntegralLastSubResultant| |entries|
- |indiceSubResultantEuclidean| |useSingleFactorBound| |irCtor| |d02bbf|
- |solveLinear| |approxNthRoot| |setImagSteps| |antiCommutative?|
- |indicialEquations| |mapUnivariateIfCan| |eq| |complexExpand|
- |create3Space| |ideal| |cExp| |iter| |dim| |pToDmp| |realSolve|
- |lazyPseudoDivide| |purelyAlgebraicLeadingMonomial?| |e02bef| |length|
- |primextendedint| |asechIfCan| |symmetric?| |reverseLex| |dioSolve|
- |quadratic?| |solveInField| |divisor| |complexNumeric| |f02fjf| |step|
- |scripts| |groebnerIdeal| |rightRecip| |characteristicSerie|
- |distdfact| |summation| |rootOfIrreduciblePoly| |readBytes!| |isPower|
- |lookupFunction| |concat| |removeSuperfluousCases| |shiftLeft| |mesh|
- |numericalOptimization| |test| |kernels| |heapSort| |showTheFTable|
- |zeroOf| GF2FG |vectorise| |expandLog| |readUInt8!| |upperCase?|
- |increasePrecision| |operator| |row| |extractSplittingLeaf| |increase|
- |outputBinaryFile| |cyclotomic| |iisin| |setfirst!| |e01baf|
- |leftExtendedGcd| |real?| |LiePolyIfCan| |rdHack1| |overbar|
- |firstNumer| |subPolSet?| |host| |bigEndian| |decompose|
- |createZechTable| |univariate| |shade| |scripted?| |central?|
- |bitCoef| |splitSquarefree| |firstDenom| |key?|
- |getSyntaxFormsFromFile| |coth2tanh| |OMencodingUnknown|
- |resetBadValues| |d02kef| |getlo| |coth2trigh| LODO2FUN |sdf2lst|
- |subresultantVector| |palgint0| |square?| |mirror| |addmod| |prefix|
- |OMencodingXML| |quotient| |pdct| |sizeLess?| |factor| |integralBasis|
- |positiveRemainder| |bits| |redPo| |OMsetEncoding| |dimension|
- |factors| |laurentRep| |sqrt| |OMputBind|
- |solveLinearPolynomialEquationByFractions|
- |selectSumOfSquaresRoutines| |outputAsTex| |elliptic?| |readable?|
- |algebraicDecompose| |isMult| |rubiksGroup| |real| |infix|
- |extendedIntegrate| |f01qdf| |commonDenominator| |goodPoint| |exprex|
- |mainPrimitivePart| |cycleElt| |fortranLiteral| |imag| |byteBuffer|
- |characteristic| |declare| |characteristicPolynomial| |stop|
- |character?| |ranges| |setColumn!| |stirling1| |setelt!| |ratDsolve|
- |directProduct| |pushNewContour| |duplicates| |leftQuotient| |cAcsch|
- |mr| |iilog| |fortranComplex| |janko2| |coefficients| |topPredicate|
- |sizePascalTriangle| |randomR| |singularitiesOf| |createNormalPoly|
- |OMUnknownCD?| SEGMENT |Gamma| |localReal?| |cdr| |brace| |kind|
- |tube| |sparsityIF| |OMgetBind| |drawComplexVectorField| |categories|
- |complexLimit| |dihedralGroup| |interReduce| |lifting| |s17dlf|
- |destruct| |realElementary| |getZechTable| |op| |cotIfCan|
- |inRadical?| |iiacsc| |mantissa| |pushdown|
- |factorSquareFreePolynomial| |depth| |multiEuclideanTree| |lazyPquo|
- |addPointLast| |exprToGenUPS| |baseRDE| |factor1| |cup| |typeForm|
- |e04ycf| |factorSquareFreeByRecursion| |c05adf|
- |permutationRepresentation| |physicalLength!| |extractProperty|
- |oddlambert| |palgintegrate| |curryRight| |level| |romberg| |cot2tan|
- |whileLoop| |d01bbf| |numberOfPrimitivePoly| |meshPar1Var|
- |commutator| |mpsode| |cycleRagits| |coordinates| |invmultisect|
- |eisensteinIrreducible?| |duplicates?| |monomial| |unit?|
- |outputFixed| |addPoint| |dual| |normalized?| |insertionSort!|
- |viewDeltaXDefault| |doubleComplex?| |adaptive3D?| |multivariate|
- |blankSeparate| |deleteProperty!| |removeRoughlyRedundantFactorsInPol|
- |latex| |stirling2| |forLoop| |fracPart| |irForm| |boundOfCauchy|
- |variables| |f02agf| |rotate| |OMunhandledSymbol| |union|
- |partialFraction| |cAsin| |palgLODE0| |maxrow| |basis| |BasicMethod|
- |e04ucf| |setEpilogue!| |univariatePolynomial| |bfKeys|
- |numberOfMonomials| |copies| |linearAssociatedOrder| |prod| |euler|
- |quasiRegular?| |removeRedundantFactorsInPols| |stFunc2| |OMgetEndAtp|
- |algebraicCoefficients?| |sayLength| |before?| |any?| |tableau|
- |split!| |e01saf| |antisymmetric?| |tan2trig| |clearDenominator|
- |exteriorDifferential| |simplifyLog| |LyndonWordsList| |degree|
- |viewWriteAvailable| |nonSingularModel| |listOfLists| |root| |conjug|
- |OMputBVar| |removeCoshSq| |lfintegrate| |invertibleElseSplit?|
- |taylor| |leftAlternative?| |mindeg| |unparse| |comp| |property|
- |belong?| |binarySearchTree| |imaginary| |zeroMatrix| |poisson|
- |laurent| |pair?| |factorials| |internalIntegrate| |characteristicSet|
- |UpTriBddDenomInv| |eigenMatrix| |viewDeltaYDefault| |iiasinh|
- |wordsForStrongGenerators| |reverse| |puiseux| |getCode| |cAsinh|
- |generic?| |quadratic| |d01ajf| |pdf2ef| |OMputAttr| |nullity|
- |lastSubResultantElseSplit| |OMconnInDevice| |setScreenResolution|
- |unexpand| |nil| |infinite| |arbitraryExponent| |approximate|
+ |Record| |Union| |lookupFunction| |decrease| |setRealSteps| |npcoef|
+ |checkRur| |linearDependenceOverZ| |parents| |roughSubIdeal?|
+ |systemCommand| |inv| |ravel| |match?| |cylindrical|
+ |rightDiscriminant| |orbits| |removeSuperfluousCases| |autoCoerce|
+ |over| |supDimElseRittWu?| |complexRoots| |c02agf| |dn| |neglist|
+ |ground?| |reshape| |tableForDiscreteLogarithm| |lazyVariations|
+ |viewport3D| |shiftLeft| |fglmIfCan| |contract| |implies|
+ |euclideanSize| |rectangularMatrix| |ground| |ref| |qinterval|
+ |stoseInvertibleSetreg| |mesh| |basisOfRightNucleus| |palgRDE0|
+ |OMgetAttr| |goto| |realZeros| |leadingMonomial| |normal|
+ |RittWuCompare| |constantToUnaryFunction| |fill!|
+ |numericalOptimization| |extractBottom!| |expextendedint| |setUnion|
+ |vertConcat| |charthRoot| |leadingCoefficient| |mapSolve|
+ |factorSFBRlcUnit| |minColIndex| |heapSort| |prindINFO| |sinIfCan|
+ |expandTrigProducts| |stoseSquareFreePart| |status|
+ |primitiveMonomials| |close| |imagK| |flexible?| |KrullNumber|
+ |showTheFTable| F |clearTheSymbolTable| |leftUnits|
+ |LyndonCoordinates| |compose| |showTheSymbolTable| |reductum| |update|
+ |trailingCoefficient| |d02cjf| |selectOptimizationRoutines| |zeroOf|
+ |reorder| |complexZeros| |irVar| |polarCoordinates|
+ |internalInfRittWu?| |display| |df2fi| |zeroSquareMatrix|
+ |headReduced?| GF2FG |constantRight| |bitTruth| |cschIfCan| |decimal|
+ |ricDsolve| |rootOf| |predicates| |discriminant| |vectorise|
+ |nthFractionalTerm| |reflect| |e04dgf| |critT| |hasoln| |OMreadStr|
+ |iicsc| |blue| |tab| |expandLog| |basisOfCommutingElements|
+ |quadraticNorm| |symmetricSquare| |inR?| |maxRowIndex| |yCoordinates|
+ |numberOfDivisors| |numberOfCycles| |readUInt8!| |genericLeftTrace|
+ |derivationCoordinates| |roman| |c06fpf| |stoseInvertibleSet|
+ |position| |generic| |headReduce| |expr| |mindegTerm| |upperCase?|
+ |Ci| |countRealRoots| |graphState| |padicFraction| |tanAn| |input| **
+ |eigenvector| |imports| |lyndon| |increasePrecision|
+ |exprHasAlgebraicWeight| |operation| |setsubMatrix!| |moreAlgebraic?|
+ |eigenvalues| |mappingMode| |library| |s17adf| |just| |traverse| |row|
+ |iidprod| |jokerMode| |bubbleSort!| |readIfCan!| |direction| |mesh?|
+ |makeTerm| |nextPartition| |mainExpression| |extractSplittingLeaf|
+ |resetAttributeButtons| |d02gbf| |weights| |supRittWu?| |split|
+ |argumentList!| |mat| |tanSum| |size| |usingTable?| |variable|
+ |increase| |interval| |e02baf| |perfectNthRoot| |exactQuotient!|
+ |child?| |collectQuasiMonic| |e01bgf| |univariate?| |s14abf|
+ |iterators| |outputBinaryFile| |setRow!| |maxPoints3D|
+ |reducedContinuedFraction| |drawToScale| |tanQ|
+ |factorsOfCyclicGroupSize| |set| |binding|
+ |rightCharacteristicPolynomial| |listOfMonoms| |cyclotomic| |setnext!|
+ |conjugate| |numberOfComputedEntries| |currentCategoryFrame| |recolor|
+ |conditionP| |commaSeparate| |OMwrite| |rightLcm| |iisin| |arbitrary|
+ |previous| |fortranReal| |omError| |overset?| |updatD| |groebner?|
+ |trigs2explogs| |listConjugateBases| |components| |setfirst!|
+ |clearFortranOutputStack| |s13adf| |groebSolve| |dequeue!| |curve|
+ |readLine!| |derivative| |mapExponents| FG2F |e01baf|
+ |partialNumerators| |legendre| |bringDown| |lflimitedint|
+ |monomialIntegrate| |f01bsf| |gbasis| |irreducibleFactor| |listexp|
+ |leftExtendedGcd| |insertRoot!| |iicos| |distance| |rotate!| |sh|
+ |say| |exp1| |lexGroebner| |true| |scanOneDimSubspaces| |real?|
+ |arguments| |validExponential| |redmat|
+ |removeSuperfluousQuasiComponents| |mkPrim| |mainSquareFreePart|
+ |OMreceive| |stopMusserTrials| |iExquo| |LiePolyIfCan| |category|
+ |generalizedEigenvectors| |integral?| |changeWeightLevel|
+ |startStats!| |reset| |intensity| |firstUncouplingMatrix| |node|
+ |f02aff| |qroot| |remove!| |rdHack1| |domain| |mapUp!|
+ |startPolynomial| |s15adf| |rischDEsys| |jacobiIdentity?| |s13aaf|
+ |insert| |head| |axes| |overbar| |package| |encodingDirectory|
+ |genericLeftDiscriminant| |sylvesterSequence| |updateStatus!| |write|
+ |getDatabase| |inc| |content| |shallowExpand| |fractRagits| |exp|
+ |firstNumer| |combineFeatureCompatibility| |save| |physicalLength|
+ |realEigenvalues| |linear?| |squareMatrix| |e02gaf| |show|
+ |numberOfImproperPartitions| |stronglyReduce| |subPolSet?|
+ |polynomialZeros| |getMeasure| |integers|
+ |genericRightMinimalPolynomial| |fintegrate| |isOp| |rspace|
+ |setvalue!| |removeZeroes| |host| |normalDenom| |d01anf| |f01qef|
+ |rightGcd| |trace| |OMclose| |karatsubaDivide| |drawStyle| |bigEndian|
+ |setMinPoints3D| |toseInvertible?| |algDsolve| |po| |sechIfCan|
+ |gethi| |normalizeAtInfinity| |s17aff| |decompose| |brillhartTrials|
+ |norm| |palgextint| |prime?| |varList| |nthRootIfCan| |inHallBasis?|
+ |leftTraceMatrix| |repeating| |createZechTable| |safeFloor|
+ |mainCoefficients| |zeroDim?| |lastSubResultantEuclidean| |quoByVar|
+ |complexIntegrate| |shade| |bipolar| |high| |ScanFloatIgnoreSpaces|
+ |aCubic| |setScreenResolution3D| |makingStats?| |option?| |bivariate?|
+ |open| |scripted?| |integralMatrix| |commutativeEquality| |exprToUPS|
+ |myDegree| |asimpson| |trueEqual| |makeMulti| |autoReduced?|
+ |central?| |cscIfCan| |RemainderList| |symmetricProduct| |logIfCan|
+ |OMreadFile| |tan2cot| |iiperm| |iicoth| |bitCoef| |obj|
+ |retractIfCan| |att2Result| |monicLeftDivide| |UP2ifCan| |double|
+ |bitLength| |variable?| |tablePow| |splitSquarefree| |cache|
+ |constant| |unit| |insert!| |e02aef| |f01ref| |members|
+ |showTheRoutinesTable| |mapDown!| |computePowers| |operations|
+ |firstDenom| |parabolicCylindrical| |principalIdeal| |smith| |slex|
+ |assign| |solve| |e04gcf| |setOfMinN| |key?| |leftRank| |setMaxPoints|
+ |elaborate| |removeDuplicates!| |intersect| |inverseIntegralMatrix|
+ |log10| |leftDiscriminant| |LyndonBasis| |edf2efi| |normalForm|
+ |rightUnit| |currentSubProgram| |d01gaf| |integralMatrixAtInfinity|
+ |f02ajf| |bitand| |subResultantGcd| |factorAndSplit| |infinity|
+ |convergents| |mergeDifference| |leftCharacteristicPolynomial|
+ |internalAugment| |indicialEquationAtInfinity| |moduleSum| |cSec|
+ |changeVar| |bitior| |rroot| |stoseInvertibleSetsqfreg| |largest|
+ |ramified?| |truncate| |semiSubResultantGcdEuclidean2| |genus|
+ |hasSolution?| |primlimintfrac| |keys| |atrapezoidal|
+ |internalIntegrate0| |minPoints3D| |numerator| |createGenericMatrix|
+ |setProperty| |OMread| |branchPointAtInfinity?| |interpretString|
+ |kernel| |explicitEntries?| |e01bhf| |map| |extendedSubResultantGcd|
+ |unmakeSUP| |isQuotient| |definingPolynomial| |algSplitSimple|
+ |degree| |singularAtInfinity?| |charpol| |primPartElseUnitCanonical!|
+ |list| |multiplyExponents| |iisec| |linSolve| |leftRecip|
+ |whatInfinity| |print| |hostPlatform| |lhs| |viewWriteAvailable|
+ |lepol| |twist| |roughUnitIdeal?| |alternating| |draw| |toroidal|
+ |nonSingularModel| |extractIndex| |qqq| |genericLeftTraceForm|
+ |resolve| |rhs| |showScalarValues| |rational?| |rur| |cycleSplit!|
+ |superHeight| |separateFactors| |simplify| |powmod| |invertIfCan|
+ |cyclotomicDecomposition| |listOfLists| |patternMatchTimes|
+ |getProperty| |OMgetEndError| |sumSquares| |style| |e02bcf| |PDESolve|
+ |currentEnv| |completeEval| |UnVectorise| |root| |subspace|
+ |leftExactQuotient| |yCoord| |mapExpon| |find| |convert| |leastPower|
+ |limitedint| |height| |extractPoint| |s21baf| |conjug|
+ |lowerPolynomial| |pointColorPalette| |floor| |rootPoly| |makeObject|
+ |minIndex| |ptFunc| |closed| |csubst| |OMputBVar| |sup|
+ |extractClosed| |partialDenominators| |stoseInvertible?reg|
+ |curveColor| |coef| |swap!| |argument| |e01bef| |alternatingGroup|
+ |parts| |removeCoshSq| |topFortranOutputStack| |s19adf|
+ |componentUpperBound| |oddintegers| |dom| |frobenius| |divideIfCan|
+ |s18def| |completeHermite| |lfintegrate| |iiatanh| |anfactor|
+ |pointPlot| |operators| |fprindINFO| |sequences| Y
+ |definingInequation| |numberOfComponents| |invertibleElseSplit?|
+ |zeroSetSplit| |hue| |outputAsScript| |extendedint| |f2st|
+ |OMputEndError| |eq?| |genericRightNorm| |leftAlternative?|
+ |indicialEquation| |d03eef| |generalSqFr| |d01aqf| |label| |pol|
+ |baseRDEsys| |light| |contours| |mindeg| |zeroDimensional?| |graeffe|
+ |numberOfComposites| |denominators| |entry| |printStatement|
+ |binaryFunction| |cPower| |scale| |unparse| |critM| |interactiveEnv|
+ |viewport2D| |position!| |genericPosition| |support| |factorsOfDegree|
+ |padicallyExpand| |property| |diagonal| |fortranLiteralLine|
+ |viewDefaults| |normFactors| |eulerE| |coshIfCan| |exponentialOrder|
+ |denomLODE| |belong?| |toseLastSubResultant| |putColorInfo|
+ |generators| |numberOfChildren| |radicalEigenvectors| |setStatus!|
+ |cyclicEntries| |anticoord| |expt| |binarySearchTree|
+ |particularSolution| |printTypes| |iiacoth| |s20adf| |factorOfDegree|
+ |e02def| |nextPrimitivePoly| |recip| |c06frf| |s18aff| |imaginary|
+ |d01alf| |incr| |ParCond| |fixPredicate| |copyInto!| |primintfldpoly|
+ |normalizeIfCan| |badValues| |besselI| |stripCommentsAndBlanks|
+ |zeroMatrix| |constructor| |fortranInteger| |hi| |putProperties|
+ |totolex| |OMgetInteger| |tail| |iifact| |children| |arrayStack|
+ |midpoint| |poisson| |getExplanations| |acoshIfCan| |lazyIntegrate|
+ |OMgetString| |option| |rightOne| |lfunc| |alphabetic| |atanIfCan|
+ |showSummary| |pair?| |column| |modularGcd| |e02ahf| |putGraph|
+ |factorials| |B1solve| UP2UTS |d01amf| |semiResultantEuclidean1|
+ |rules| |units| |doubleRank| |squareFreePrim| |hermiteH| |getConstant|
+ |top| |increment| |quadraticForm| |setClosed| |Frobenius|
+ |showAttributes| |internalIntegrate| |c06gbf| |makeEq| |s01eaf|
+ |HenselLift| |continue| |SFunction| |rationalPower| |cycles|
+ |linearPolynomials| |characteristicSet| |weighted|
+ |radicalEigenvector| |cycleEntry| |plenaryPower| |subResultantsChain|
+ |trapezoidalo| |nand| |prevPrime| |UpTriBddDenomInv| |powerSum|
+ |edf2ef| |box| |name| |region| |unknown| |nonQsign| |OMencodingBinary|
+ |mainMonomials| |exportedOperators| |totalLex| |eigenMatrix| |comment|
+ |primeFactor| |reduceByQuasiMonic| |totalDegree| |body| |writeInt8!|
+ |unitNormal| |perfectSqrt| |charClass| |OMbindTCP| |code|
+ |viewDeltaYDefault| |var1StepsDefault| |OMputObject| |positiveSolve|
+ |thenBranch| |rationalIfCan| |exponential| |rename!|
+ |iteratedInitials| |iiasinh| |headAst| |nary?| |kovacic| |divergence|
+ |null| |outputGeneral| |lex| |expintegrate| |typeLists|
+ |wordsForStrongGenerators| |mix| |accuracyIF| |decomposeFunc|
+ |oneDimensionalArray| |delta| |not| EQ |normal?| |An| |shrinkable|
+ |totalfract| |getCode| |bumptab| |regularRepresentation|
+ |makeViewport2D| |diagonalProduct| |and| |minrank| |endOfFile?|
+ |iisinh| |monicCompleteDecompose| |cAsinh| |ip4Address| |generate|
+ |f01mcf| |numberOfFractionalTerms| |cycle| |or| |rischNormalize|
+ |OMputAtp| |principal?| |nextNormalPrimitivePoly| |generic?| |coerceS|
+ |max| |lastSubResultant| |stoseIntegralLastSubResultant| |logGamma|
+ |xor| |c06fqf| |OMgetEndAttr| |assert| |viewPosDefault| |quadratic|
+ |linearMatrix| |incrementBy| |semiResultantEuclideannaif| |port|
+ |addiag| |entries| |pattern| |case| |alphanumeric?| |modifyPointData|
+ |domainTemplate| |OMgetFloat| |d01ajf| |expand| |merge| |finiteBound|
+ |complement| |indiceSubResultantEuclidean| |Zero| |torsionIfCan|
+ |wholeRadix| |semiResultantEuclidean2| |move| |pdf2ef|
+ |rightScalarTimes!| |filterWhile| UTS2UP |f02xef| |t|
+ |useSingleFactorBound| |One| |s17acf| |henselFact| |sylvesterMatrix|
+ |rationalPoint?| |OMputAttr| |clipPointsDefault| |filterUntil|
+ |noncommutativeJordanAlgebra?| |screenResolution| |irCtor| |lambda|
+ |removeDuplicates| |tryFunctionalDecomposition| |f01rdf| |mathieu23|
+ |acothIfCan| |search| |nullity| |double?| |select|
+ |exprHasWeightCosWXorSinWX| |calcRanges| |d02bbf| |message|
+ |compiledFunction| |permutationGroup| |leaf?| |pushuconst|
+ |collectUpper| |lastSubResultantElseSplit| |tracePowMod| |conjunction|
+ |clipSurface| |solveLinear| |rightZero| |mathieu22| |minimumExponent|
+ |exponential1| |OMconnInDevice| |selectFiniteRoutines| |leadingIndex|
+ |seriesToOutputForm| |approxNthRoot| |nrows| |iiabs| |nodes|
+ |sortConstraints| |cCsc| |setScreenResolution| |e04naf| |monomial?|
+ |setImagSteps| |ncols| |elt| |cCsch| |imagI| |s18dcf| |subscript|
+ |unexpand| |outputArgs| |dualSignature| |identityMatrix| |retract|
+ |antiCommutative?| |curveColorPalette| |iisqrt3| |e02bdf|
+ |OMcloseConn| |innerSolve1| |dilog| |zero| |irreducibleFactors|
+ |point?| |indicialEquations| |computeCycleEntry| |jacobi|
+ |divideIfCan!| |prepareSubResAlgo| |cons| |mathieu12| |sin|
+ |makeRecord| |sncndn| |psolve| |mapUnivariateIfCan| |lfextlimint|
+ |c05nbf| |inspect| |nothing| |And| |cos| |internalLastSubResultant|
+ |magnitude| |complexExpand| |gramschmidt| |infiniteProduct| |subCase?|
+ |initiallyReduce| |Or| |tan| |viewSizeDefault| |hexDigit| |expPot|
+ |create3Space| |alphanumeric| |LazardQuotient2| |separateDegrees|
+ |fi2df| |Not| |radicalSolve| |cot| |setref| |univariateSolve| |ideal|
+ |iicosh| |univariatePolynomialsGcds| |rightRegularRepresentation|
+ |cCoth| |condition| |primes| |sec| |cExp| |f01rcf| |escape|
+ |OMconnectTCP| |trace2PowMod| |medialSet| |invmod| |csc|
+ |HermiteIntegrate| |numFunEvals| |pToDmp| |chvar| |iicsch| |c05pbf|
+ |entry?| |gderiv| |interpret| |infieldint| |source| |asin| |vconcat|
+ |bernoulli| |realSolve| |messagePrint| |selectOrPolynomials|
+ |rightExactQuotient| |minRowIndex| |dec| |setStatus| |acos|
+ |coordinate| |atoms| |lazyPseudoDivide| |compdegd| |getPickedPoints|
+ |minGbasis| |irreducibleRepresentation| |atan| |plusInfinity| |zoom|
+ |purelyAlgebraicLeadingMonomial?| |antiCommutator|
+ |nativeModuleExtension| |s19acf| |unrankImproperPartitions1|
+ |findConstructor| |e02agf| |acot| |constantLeft| |minusInfinity|
+ |e02bef| |char| |semiIndiceSubResultantEuclidean| |meatAxe| |linears|
+ |aLinear| |ldf2lst| |asec| |rightRank| |startTableGcd!|
+ |primextendedint| |applyRules| |digamma| |plotPolar| |powern|
+ |associative?| |acsc| |target| |ScanRoman| |nullSpace|
+ |linearAssociatedExp| |saturate| |squareTop| |enterPointData|
+ |normalElement| |sinh| |relerror| |rangePascalTriangle| |rowEchLocal|
+ |postfix| |reduction| |epilogue| |droot| |isEquiv| |clipParametric|
+ |cosh| |relationsIdeal| |pushucoef| |logical?| |isTimes|
+ |createNormalElement| |readInt16!| |leftRegularRepresentation|
+ |chineseRemainder| |rootSimp| |cyclic| |tanh| |extractTop!| |type|
+ |musserTrials| |secIfCan| |outputList| |simplifyPower| |f02wef|
+ |virtualDegree| |palglimint| |f01brf| |coth| |numberOfFactors|
+ |prinshINFO| |s15aef| |cothIfCan| |df2ef| |d03faf| |minimumDegree|
+ |leftFactorIfCan| |float| |qelt| |invmultisect| |solve1| |sech|
+ |buildSyntax| |inputOutputBinaryFile| |matrixConcat3D| |setAdaptive|
+ |second| |qsetelt| |youngGroup| |mdeg| |quasiMonicPolynomials| |color|
+ |eisensteinIrreducible?| |iiasech| |f07fef| |csch| |call| |nthFactor|
+ |minPoly| |third| |principalAncestors| |irreducible?|
+ |selectMultiDimensionalRoutines| |roughBasicSet| |xRange|
+ |duplicates?| |divide| |asinh| |xCoord| |untab| |bezoutDiscriminant|
+ |d01gbf| |separant| |compile| |cTan| |inverse| |coerceListOfPairs|
+ |yRange| |unit?| |void| |collect| |acosh| |imagi| |infRittWu?| |build|
+ |eof?| |logpart| |crushedSet| |cot2trig| |graphStates| |zRange|
+ |outputFixed| |sn| |recoverAfterFail| |atanh| |innerEigenvectors|
+ |lazyGintegrate| |writeUInt8!| |karatsuba| |map!| |rk4f| |less?|
+ |endSubProgram| |constant?| |addPoint| |basisOfRightAnnihilator|
+ |acoth| |getGoodPrime| |deepestInitial| |wordInGenerators|
+ |difference| |setLength!| |indices| |s13acf|
+ |functionIsContinuousAtEndPoints| |qsetelt!| |dual| |elliptic| |asech|
+ |zeroDimPrimary?| |removeRedundantFactors| |critpOrder| |tanh2trigh|
+ |ratPoly| |symmetricGroup| |unravel| |stoseInvertible?sqfreg|
+ |normalized?| |sequence| |partialQuotients| |horizConcat| |minimize|
+ |getStream| |inverseLaplace| |conjugates| |insertMatch|
+ |sturmSequence| GE |insertionSort!| |clipBoolean| |multiple|
+ |OMgetObject| |isList| |bit?| |swapColumns!| GT |simpsono| |setTex!|
+ |removeSinSq| |karatsubaOnce| |viewDeltaXDefault| |applyQuote|
+ |adaptive| |digit| |laguerreL| |getOrder| |cross| |basisOfLeftNucleus|
+ |createIrreduciblePoly| |initializeGroupForWordProblem| |disjunction|
+ LE |doubleComplex?| |Si| |zCoord| |quatern| |morphism|
+ |reduceBasisAtInfinity| |predicate| |constantOpIfCan|
+ |rightMinimalPolynomial| LT |externalList| |fixedPointExquo| |acsch|
+ |adaptive3D?| |clipWithRanges| |exponent| |scaleRoots| |f04mbf|
+ |makeCrit| |conditionsForIdempotents| |edf2fi| |zag| |permutation|
+ |removeCosSq| |blankSeparate| |nextsousResultant2| |ruleset| |back|
+ |nextColeman| |zeroVector| |Is| |f2df| |leftFactor| |varselect|
+ |rewriteSetWithReduction| |deleteProperty!| |subst| |leviCivitaSymbol|
+ |ran| |mkIntegral| |withPredicates| |modularGcdPrimitive|
+ |rightQuotient| |sumOfKthPowerDivisors| |OMencodingSGML| |schema|
+ |removeRedundantFactorsInContents|
+ |removeRoughlyRedundantFactorsInPol| |reducedForm| |tanintegrate|
+ |reduceLODE| |hasHi| |lazyPrem| |laurentIfCan| |s18adf| |presuper|
+ |lookup| |thetaCoord| |directory| |latex| |kroneckerDelta|
+ |mainVariable?| |suchThat| |unitNormalize| |submod| |tanIfCan| |tree|
+ |index| |resultantnaif| |cyclicParents| |identification|
+ |linearlyDependent?| |stirling2| |df2mf| |setIntersection|
+ |cycleLength| |createPrimitiveElement| |asinhIfCan| |gcdPolynomial|
+ |radicalEigenvalues| |squareFreeLexTriangular| |ode2| |initial|
+ |forLoop| |monicModulo| |rischDE| |fractionPart| |write!| |cAcsc|
+ |testDim| |connect| |localAbs| |component| |fracPart| |voidMode|
+ |nlde| |wholeRagits| |expandPower| |index?| |qualifier| |pair|
+ |shanksDiscLogAlgorithm| |resultantReduitEuclidean| |symmetricPower|
+ |meshFun2Var| |irForm| |objects| |numberOfHues| |rightTrim|
+ |setFieldInfo| |bright| |standardBasisOfCyclicSubmodule| |refine|
+ |rowEch| |colorDef| |parameters| |even?| |selectPDERoutines| |hessian|
+ |dimensions| |base| |boundOfCauchy| |leftTrim| |e02dff|
+ |primlimitedint| |lquo| |constDsolve| |polyRicDE| |arg1| |polyPart|
+ |critB| |makeFR| |squareFreeFactors| |f02agf| |changeName|
+ |evaluateInverse| |preprocess| |eval| |shellSort| |changeThreshhold|
+ |arg2| |pToHdmp| |youngDiagram| |rightPower|
+ |zeroSetSplitIntoTriangularSystems| |rotate| |mathieu24| |zerosOf|
+ |nextsubResultant2| |showIntensityFunctions| |composite|
+ |sumOfDivisors| |create| |factorGroebnerBasis| |d02bhf|
+ |OMunhandledSymbol| |space| |f02aef| |normalize| |reducedSystem|
+ |toseSquareFreePart| |conditions| |var1Steps| |reverse!|
+ |setProperties| |critMonD1| |partialFraction| |countable?| |se2rfi|
+ |error| |normal01| |intChoose| |algebraicVariables| |supersub| |match|
+ |inrootof| |rewriteIdealWithQuasiMonicGenerators| |lyndonIfCan|
+ |monicDivide| |cAsin| |realRoots| |check| |signatureAst| |equation|
+ |OMReadError?| |printStats!| |paraboloidal| |bombieriNorm|
+ |getVariableOrder| |expintfldpoly| |addPoint2| |palgLODE0| |delete!|
+ |contains?| |subNodeOf?| |Lazard2| |limitPlus| |curry|
+ |stosePrepareSubResAlgo| |laguerre| |function| |generalLambert|
+ |maxrow| |optimize| |isOr| |expenseOfEvaluationIF|
+ |generalInfiniteProduct| |fortranLinkerArgs| |triangSolve|
+ |getMultiplicationTable| |listBranches| |parametric?| |plot| |basis|
+ |nilFactor| |typeList| |viewWriteDefault| |reducedQPowers|
+ |complexEigenvectors| |limit| |changeMeasure| |setClipValue|
+ |element?| |BasicMethod| BY |concat!| |getIdentifier| |rst| |octon|
+ |birth| |setPosition| |algint| |capacity| |semiDiscriminantEuclidean|
+ |e04ucf| |notelem| |polyred| |halfExtendedSubResultantGcd2| |f02adf|
+ |tanhIfCan| |relativeApprox| |structuralConstants| |setchildren!|
+ |parametersOf| |setEpilogue!| |localIntegralBasis| |leadingBasisTerm|
+ |lazyPseudoQuotient| |differentialVariables| |drawCurves| |reopen!|
+ |bernoulliB| |nullary?| |traceMatrix| |univariatePolynomial|
+ |spherical| |doubleDisc| |quasiComponent| |expIfCan|
+ |initiallyReduced?| |orbit| |LagrangeInterpolation| |sort|
+ |pleskenSplit| |moebiusMu| |bfKeys| |setErrorBound| |Aleph|
+ |viewpoint| |child| |superscript| |callForm?| |selectAndPolynomials|
+ |cap| |iisqrt2| |numberOfMonomials| |rem| |ode| |outputFloating|
+ |OMgetEndApp| |makeUnit| |augment| |properties| |attributeData|
+ |removeZero| |readInt8!| |aspFilename| |copies| |xn| |quo| |leftTrace|
+ |resultant| |weakBiRank| |dmpToHdmp| |id| |distFact| NOT |normDeriv2|
+ |continuedFraction| |translate| |wholePart| |linearAssociatedOrder|
+ |cAtan| |hclf| |constantCoefficientRicDE| |unitCanonical|
+ |complexForm| |lo| |bag| OR |binomial| |random| |useNagFunctions|
+ |bandedHessian| |prod| |pmComplexintegrate| |div| |dictionary|
+ |subNode?| F2FG |possiblyInfinite?| |decreasePrecision| AND |f04arf|
+ |besselY| |lcm| |probablyZeroDim?| |euler| |delete| |exquo|
+ |hasTopPredicate?| |collectUnder| |writeBytes!| |hostByteOrder|
+ |f01maf| |incrementKthElement| |bindings| |cyclePartition|
+ |quasiRegular?| |evaluate| ~= |groebner| |mvar| |FormatRoman|
+ |asecIfCan| |lift| |iiacsch| |rightNorm| |wordInStrongGenerators|
+ |setEmpty!| |append| |revert| |removeRedundantFactorsInPols|
+ |acscIfCan| |#| |s14aaf| |s17def| |equiv| |mainVariables| |reduce|
+ |specialTrigs| |extension| |simplifyExp| |companionBlocks| |red| |gcd|
+ |stFunc2| |loopPoints| ~ |primitive?| |curve?| |computeInt| |e02daf|
+ |matrixDimensions| |stopTableInvSet!| |is?| |false| |OMgetEndAtp|
+ |unary?| |tryFunctionalDecomposition?| |imagE| |leadingSupport|
+ |oddInfiniteProduct| |f02bjf| |showRegion|
+ |createLowComplexityNormalBasis| |leadingExponent| |elColumn2!|
+ |algebraicCoefficients?| |mkcomm| |binaryTree|
+ |unrankImproperPartitions0| |apply| |fixedPoint| |OMgetApp| |eulerPhi|
+ |power| |c06ecf| |mapdiv| |zero?| |sayLength| |commutative?| |/\\|
+ |SturmHabichtCoefficients| |twoFactor| |matrix| |first| |readByte!|
+ |prologue| |listYoungTableaus| |cosSinInfo| |ramifiedAtInfinity?|
+ |changeBase| |SturmHabichtMultiple| |before?| |cCot| |\\/| |rest|
+ |showAll?| |cosh2sech| |genericRightTrace| |setAdaptive3D| |lp|
+ |intermediateResultsIF| |choosemon| |tRange| |any?| |frst|
+ |setAttributeButtonStep| |cartesian| |getButtonValue| |overlap|
+ |jacobian| |makeprod| |coerce| * |expressIdealMember| |abs|
+ |splitNodeOf!| |tableau| |internalDecompose| |subtractIfCan|
+ |fortranDouble| |fortranCharacter| |points| |e02bbf| |paren|
+ |construct| |createMultiplicationMatrix| |s20acf| |setVariableOrder|
+ |split!| |patternMatch| |credPol| |hex| |f02bbf| |numer| |subTriSet?|
+ |range| |integrate| |reindex| |generator| |e01saf| |hdmpToP|
+ |rootBound| |genericRightTraceForm| |digit?| |redpps| |denom| |push|
+ |socf2socdf| |OMputEndApp| |firstSubsetGray| = |OMsend|
+ |antisymmetric?| |phiCoord| |abelianGroup| |fractRadix| |setprevious!|
+ |evenInfiniteProduct| |edf2df| |printCode|
+ |inverseIntegralMatrixAtInfinity| |completeHensel| |palglimint0|
+ |tan2trig| |signAround| |splitConstant| |indiceSubResultant|
+ |primaryDecomp| |diff| |pi| |byte| |represents| |numericIfCan| <
+ |besselJ| |defineProperty| |pmintegrate| |clearDenominator|
+ |linearDependence| |bottom!| |crest| |intPatternMatch| |width|
+ |pseudoDivide| > |OMgetError| |hspace| |radicalSimplify|
+ |exteriorDifferential| |deriv| |nextSublist| |solveRetract|
+ |insertTop!| |ffactor| |setMaxPoints3D| |extensionDegree| <= |failed?|
+ |pole?| |quasiRegular| |simplifyLog| |regime| |skewSFunction|
+ |tensorProduct| |printingInfo?| |unitsColorDefault| |power!|
+ |coefChoose| |e01sef| >= |adaptive?| |extendIfCan| |swapRows!|
+ |LyndonWordsList| |uniform| |e02dcf| |acschIfCan|
+ |useSingleFactorBound?| |imagj| |triangulate| |OMputError|
+ |extractIfCan| |froot| |setValue!| |acosIfCan| |exactQuotient|
+ |factorFraction| |product| |selectODEIVPRoutines|
+ |subresultantSequence| |bipolarCylindrical| |rightAlternative?| |dark|
+ |in?| |fortranTypeOf| |cAcsch| |eyeDistance| |singRicDE|
+ |taylorQuoByVar| |triangularSystems| |rootsOf| |palgextint0|
+ |stiffnessAndStabilityOfODEIF| |createMultiplicationTable| |exprToXXP|
+ |perfectNthPower?| + |nextPrime| |iilog| |degreePartition|
+ |doublyTransitive?| |value| |ParCondList| |clearCache| |homogeneous?|
+ |showAllElements| |numeric| |dmpToP| |isConnected?| |int| |isExpt|
+ |univariatePolynomials| - |lighting| |fortranComplex| |coerceImages|
+ |alphabetic?| |rightTraceMatrix| |factorList| |elseBranch| |radical|
+ |c06ebf| |sumOfSquares| |optional| |setFormula!| / |OMopenFile|
+ |moduloP| |janko2| |headRemainder| |leftOne| |putProperty|
+ |listRepresentation| |distribute| |copy!| |f04adf| |vspace| |log|
+ |const| |shuffle| |readUInt16!| |coefficients| |every?| |leftNorm|
+ |nodeOf?| |zeroDimPrime?| |c06gsf| |rootPower| |eigenvectors|
+ |makeGraphImage| |mapBivariate| |topPredicate| |pushup| |empty|
+ |nsqfree| |s21bbf| |exprHasLogarithmicWeights| |setMinPoints|
+ |signature| |integralAtInfinity?| |modularFactor| |setelt|
+ |doubleFloatFormat| |resultantEuclideannaif| |sizePascalTriangle|
+ |orthonormalBasis| |coerceL| |OMputSymbol| |integer?| |clip|
+ |categoryMode| |f04mcf| |makeYoungTableau| |gcdcofact| |complete|
+ |pomopo!| |randomR| |declare!| |s17agf| |symmetricTensors|
+ |taylorIfCan| |generalizedContinuumHypothesisAssumed?|
+ |highCommonTerms| |symmetricRemainder| |factorset| |copy|
+ |normalDeriv| |LiePoly| |singularitiesOf| |groebgen| |roughBase?|
+ |basisOfLeftNucloid| |mainForm| |rightFactorCandidate| |cyclicCopy|
+ |clearTheIFTable| |lowerCase!| |fullPartialFraction|
+ |solveLinearPolynomialEquation| |createNormalPoly| |shiftRoots|
+ |radix| |elaborateFile| |mainValue| |setleft!| |OMputApp| |datalist|
+ |subscriptedVariables| |minimalPolynomial| |multiple?| |cyclicEqual?|
+ |leftScalarTimes!| |OMUnknownCD?| |deepestTail| |partition|
+ |mainContent| |nthCoef| |OMputEndAtp| |areEquivalent?| |modulus|
+ |transpose| |patternVariable| |sinh2csch| |Gamma| |OMmakeConn|
+ |createNormalPrimitivePoly| |elem?| |c06ekf| |d03edf| |bounds|
+ |options| |compactFraction| |multMonom| |maxint|
+ |functionIsOscillatory| |f04faf| |totalDifferential| |localReal?|
+ |iroot| |getCurve| |dot| |atom?| |setPrologue!| |d02ejf| |s17dgf|
+ |getBadValues| |returnType!| |cdr| |deepCopy| |s17ajf| |discreteLog|
+ |e02akf| |useEisensteinCriterion?| |trapezoidal| |log2| |hconcat|
+ |removeConstantTerm| |odd?| |tube| |graphs| |segment| |associator|
+ |negative?| |scalarMatrix| |denomRicDE| |shape| |output| |string|
+ |addMatchRestricted| |ListOfTerms| |conical| |primextintfrac|
+ |sparsityIF| |viewThetaDefault| |OMgetEndBVar| |hypergeometric0F1|
+ |leftMinimalPolynomial| |writeLine!| |listLoops| |infieldIntegrate|
+ RF2UTS |checkForZero| |curryLeft| |createPrimitiveNormalPoly|
+ |OMgetBind| |createThreeSpace| |s19aaf| |rename| |fillPascalTriangle|
+ |mainDefiningPolynomial| |scalarTypeOf| |setleaves!| |pureLex|
+ |d01asf| |f02awf| |drawComplexVectorField|
+ |solveLinearPolynomialEquationByRecursion| |iflist2Result| |d01apf|
+ |cond| |f04maf| |randomLC| |measure| |multisect| |resize| |s18acf|
+ |cubic| |OMgetEndBind| |unitVector| |complexLimit|
+ |discriminantEuclidean| |drawComplex| |f02abf| |ReduceOrder|
+ |finiteBasis| |nthr| |cTanh| |OMUnknownSymbol?|
+ |rewriteSetByReducingWithParticularGenerators| |simpson| |padecf|
+ |dihedralGroup| |sub| |writable?| |measure2Result| |maxdeg| |leftZero|
+ |strongGenerators| |setDifference| |clikeUniv| |squareFreePolynomial|
+ |chebyshevU| |interReduce| |argscript| |btwFact| |symbolIfCan| |scan|
+ |rarrow| |debug3D| |purelyTranscendental?| |explicitlyFinite?|
+ |newReduc| |mapMatrixIfCan| |colorFunction| |lifting|
+ |normInvertible?| |sin?| |rk4qc| |maxPoints| |sinhcosh| |iicot|
+ |leftDivide| |polygon| |remove| |s21bdf| |connectTo| |directSum|
+ |s17dlf| |size?| |knownInfBasis| |initTable!|
+ |generalizedContinuumHypothesisAssumed| |coefficient| |totalGroebner|
+ |errorKind| |chiSquare| |bezoutResultant| |bracket| |realElementary|
+ |critMTonD1| |d01akf| |laplace| |pointData| |makeCos|
+ |chainSubResultants| |iiexp| |hcrf| |center| |last| |inf| |linGenPos|
+ |getZechTable| |bsolve| |optAttributes| |rk4| |d02raf| |writeByte!|
+ |assoc| |basisOfNucleus| |stoseInternalLastSubResultant| |vedf2vef|
+ |symFunc| |cotIfCan| |rombergo| |mainKernel| |qPot| |exQuo| |nthRoot|
+ |formula| |generalizedEigenvector| |gcdprim| |biRank| |goodnessOfFit|
+ |inRadical?| |ef2edf| |genericLeftNorm| |dAndcExp| |rotatez|
+ |quotedOperators| |select!| |low| |fmecg| |c06eaf| |satisfy?| |iiacsc|
+ |intcompBasis| |top!| |swap| |mapGen| |makeResult| |matrixGcd|
+ |lfextendedint| |bivariatePolynomials| |isPlus| |monicDecomposeIfCan|
+ |pushdown| |halfExtendedSubResultantGcd1| |OMgetEndObject| |makeop|
+ |reciprocalPolynomial| |front| |constantOperator| |lyndon?|
+ |quasiMonic?| |transcendenceDegree| |factorSquareFreePolynomial|
+ |palgint| |iCompose| |cycleTail| |insertBottom!| |fractionFreeGauss!|
+ |elRow1!| |transcendentalDecompose| |permanent| |selectPolynomials|
+ |multiEuclideanTree| |diagonalMatrix| |maxIndex| |prime|
+ |simpleBounds?| |associatorDependence| |rootNormalize| |positive?|
+ |remainder| |monomRDE| |lazyPquo| |hermite| |leadingIdeal|
+ |squareFree| |raisePolynomial| |numberOfIrreduciblePoly| |c06fuf|
+ |rowEchelon| |safetyMargin| |primitivePart!| |addPointLast| |exptMod|
+ |getMultiplicationMatrix| |constantIfCan| |e02adf| |bat|
+ |doubleResultant| |numFunEvals3D| |elaboration| |stronglyReduced?|
+ |exprToGenUPS| |airyBi| |extract!| |fortranCarriageReturn|
+ |rangeIsFinite| |countRealRootsMultiple| |repSq| |printInfo!|
+ |singular?| |lagrange| |baseRDE| |badNum| |dfRange| |isAtom| |s17ahf|
+ |cyclicGroup| |basisOfLeftAnnihilator| |cAtanh| |rootKerSimp|
+ |getGraph| |factor1| |universe| |PollardSmallFactor| |randnum|
+ |prepareDecompose| |internalZeroSetSplit| |iisech| |external?|
+ |resultantEuclidean| |sizeMultiplication| |readUInt32!| |cup|
+ |harmonic| |meshPar2Var| |allRootsOf| |e02zaf| |OMserve| |dihedral|
+ |setLegalFortranSourceExtensions| |ScanFloatIgnoreSpacesIfCan|
+ |airyAi| |infinite?| |e04ycf| |branchIfCan|
+ |semiResultantReduitEuclidean| |taylorRep| |fixedDivisor|
+ |inGroundField?| |pdf2df| |lazyEvaluate| |findCycle| |torsion?|
+ |leaves| |factorSquareFreeByRecursion| |limitedIntegrate| |infLex?|
+ |generalPosition| |transcendent?| |solid| |singleFactorBound|
+ |branchPoint?| |s18aef| |c05adf| |denominator| |nil| |OMlistSymbols|
+ |makeSUP| |iitan| |d01fcf| |macroExpand| |multiEuclidean|
+ |explimitedint| |innerSolve| |coHeight| |permutationRepresentation|
+ |jordanAlgebra?| |createLowComplexityTable|
+ |selectIntegrationRoutines| |brillhartIrreducible?| |ipow|
+ |aQuadratic| |viewZoomDefault| |functionIsFracPolynomial?| |sech2cosh|
+ |physicalLength!| |tubePointsDefault| |hexDigit?| |readInt32!|
+ |extendedEuclidean| |leftUnit| |getProperties| |green|
+ |extractProperty| |updatF| |approximate| |screenResolution3D| |reseed|
+ |bezoutMatrix| |aromberg| |empty?| |aQuartic| |parent| |oddlambert|
+ |ddFact| |sum| |complex| |yellow| |primeFrobenius|
+ |certainlySubVariety?| |tubeRadiusDefault| |open?| |close!|
+ |lowerBound| |palgintegrate| |ksec| |changeNameToObjf|
+ |complementaryBasis| |e01bff| |delay| |monomials| |enumerate| |ode1|
+ |curryRight| |tab1| |showArrayValues| |bumptab1| |cos2sec| |rank|
+ |d02gaf| |lllp| |romberg| |fullDisplay| |variationOfParameters|
+ |leftGcd| |point| |push!| |order| |cn| |lllip| |mergeFactors|
+ |upperBound| |debug| |cot2tan| |radicalOfLeftTraceForm| |failed| |nor|
+ |newSubProgram| |elementary| |cAsech| |removeSquaresIfCan|
+ |numberOfNormalPoly| |Ei| |triangular?| |whileLoop| D |round| |f04qaf|
+ |dmp2rfi| |cardinality| |makeSin| |subMatrix| |splitDenominator|
+ |d01bbf| |sqfree| |complexNormalize| |modifyPoint| |series|
+ |computeBasis| |cosIfCan| |monicRightDivide| |noLinearFactor?|
+ |OMopenString| |numberOfPrimitivePoly| |lowerCase?| |polar| |df2st|
+ |divisors| |e01sff| |quotientByP| |nextIrreduciblePoly| |elRow2!|
+ |meshPar1Var| |figureUnits| |pack!| |wronskianMatrix| |e04jaf|
+ |sin2csc| |lieAlgebra?| |subResultantGcdEuclidean| |determinant|
+ |commutator| |divisorCascade| |jordanAdmissible?| |palgRDE| |super|
+ |deepExpand| |lists| |isOpen?| |shallowCopy| |mpsode| |f01qcf| |min|
+ |removeRoughlyRedundantFactorsInContents| |nextLatticePermutation|
+ |isImplies| |diophantineSystem| |parseString| |nextNormalPoly|
+ |OMputFloat| |cycleRagits| |cRationalPower| |basicSet| |printInfo|
+ |sample| |toseInvertibleSet| |algebraicSort| |binary|
+ |expenseOfEvaluation| |minus!| |coordinates| |queue|
+ |rationalFunction| |pointSizeDefault| |basisOfMiddleNucleus| |diag|
+ |leadingCoefficientRicDE| |OMputEndBind| |OMsupportsSymbol?|
+ |associatedEquations| |checkPrecision| |besselK| |setButtonValue|
+ |minordet| |integerBound| |substring?| |normalise| |key|
+ |groebnerFactorize| |lazyPseudoRemainder| |getSyntaxFormsFromFile|
+ |oblateSpheroidal| |beauzamyBound| |antisymmetricTensors| |c02aff|
+ |getOperator| |leftPower| |selectNonFiniteRoutines|
+ |LowTriBddDenomInv| |coth2tanh| |leader| |iiasec| |qfactor|
+ |resultantReduit| |upperCase!| |fortranCompilerName| |suffix?|
+ |filename| |pr2dmp| |powerAssociative?| |atanhIfCan|
+ |OMencodingUnknown| |nthExponent| |fTable| |e02ajf| |OMgetVariable|
+ |merge!| |symbolTable| |loadNativeModule| |setPredicates| |tubeRadius|
+ |prinb| |resetBadValues| |stiffnessAndStabilityFactor| |s17aef|
+ |s17dcf| |stFuncN| |prefix?| |null?| |more?| |parse| |minPol|
+ |resetVariableOrder| |d02kef| |isobaric?| |fortran|
+ |integralBasisAtInfinity| |explogs2trigs| |sinhIfCan| |mainMonomial|
+ |plus| |sign| |pushFortranOutputStack| |inconsistent?| |upperCase|
+ |generalTwoFactor| |getlo| |trivialIdeal?| |pointColor|
+ |lazyResidueClass| |primintegrate| |upDateBranches|
+ |popFortranOutputStack| |member?| |has?| |minPoints| |coth2trigh|
+ |setCondition!| |linkToFortran| |getOperands| |mainCharacterization|
+ |stoseInvertible?| |outputAsFortran| |rightExtendedGcd| |rootRadius|
+ |mathieu11| LODO2FUN |iiatan| |backOldPos| |f07aef| |substitute|
+ |mapmult| |table| |chiSquare1| |bumprow| |setOrder| |sdf2lst|
+ |identity| |alternative?| |precision| |perspective| |times|
+ |rewriteIdealWithHeadRemainder| |prefixRagits| |new|
+ |lazyPremWithDefault| |critBonD| |corrPoly| |subresultantVector|
+ |linearAssociatedLog| |resetNew| |module| |associates?| |userOrdered?|
+ |infix?| |ptree| |fortranLogical| |quickSort| |sPol| |palgint0|
+ |basisOfRightNucloid| |euclideanGroebner| |flatten| |errorInfo|
+ |digits| |mask| |complexNumericIfCan| |radicalRoots| |plus!|
+ |outputForm| |square?| |cSech| |init| |isAbsolutelyIrreducible?|
+ |pointColorDefault| |primPartElseUnitCanonical| |hitherPlane|
+ |iibinom| |comparison| |deleteRoutine!| |mirror| |var2Steps|
+ |startTableInvSet!| |dimensionsOf| |removeSinhSq| |consnewpol| |monom|
+ |mapUnivariate| |transform| |root?| |addmod| |dequeue| |splitLinear|
+ |ldf2vmf| |evenlambert| |palgLODE| |rule| |genericRightDiscriminant|
+ |hyperelliptic| |elements| |OMencodingXML| |coord| |weight|
+ |removeIrreducibleRedundantFactors| |sorted?| |monomialIntPoly|
+ |factorByRecursion| |f02axf| |cyclicSubmodule| |quotient| |common|
+ |purelyAlgebraic?| |absolutelyIrreducible?| |perfectSquare?|
+ |leftRankPolynomial| |nullary| |finite?| |clearTheFTable| |vark|
+ |pdct| |script| |iFTable| |processTemplate| |pastel| |middle|
+ |closedCurve?| |primitivePart| |tValues| |readLineIfCan!| |sizeLess?|
+ |rightDivide| |title| |normalizedDivide| |LazardQuotient| |addMatch|
+ |sec2cos| |integralDerivationMatrix| |OMputEndBVar| |mightHaveRoots|
+ |integralBasis| |leftMult| |rotatey| |stopTable!| |maxColIndex|
+ |var2StepsDefault| |left| |vector| |idealiserMatrix|
+ |associatedSystem| |f02aaf| |positiveRemainder| |tex| |rk4a|
+ |outerProduct| |iomode| |separate| |OMgetAtp| |quote| |right|
+ |differentiate| |primitiveElement| |possiblyNewVariety?|
+ |viewPhiDefault| |bits| |e| |gcdPrimitive| |rCoord| |imagJ| |list?|
+ |ellipticCylindrical| |graphImage| |complexEigenvalues| |mapCoef|
+ |showTheIFTable| |redPo| |iipow| |OMputEndAttr| |freeOf?| |whitePoint|
+ |setPoly| |semiDegreeSubResultantEuclidean| |acotIfCan|
+ |integralRepresents| |enqueue!| |OMsetEncoding| |createPrimitivePoly|
+ |cCosh| |monic?| |stopTableGcd!| |linearlyDependentOverZ?| |compound?|
+ |heap| |optpair| |dimension| |lexico| |ord| |repeating?|
+ |realEigenvectors| |arity| |numberOfOperations| |mulmod| |trigs|
+ |factors| |rewriteIdealWithRemainder| |cyclotomicFactorization|
+ |semiLastSubResultantEuclidean| |Beta| |monicRightFactorIfCan|
+ |bothWays| |exists?| |lintgcd| |laurentRep| |shift| |sts2stst|
+ |cAcosh| |c06gqf| |cLog| |pow| |any| |one?| |hash| |appendPoint|
+ |getMatch| |OMputBind| |internal?| |read!| |part?| |OMgetSymbol|
+ |internalSubQuasiComponent?| |count| |maxrank| |unknownEndian|
+ |constantKernel| |next| |solveLinearPolynomialEquationByFractions|
+ |definingEquations| |iitanh| |e04mbf| |functorData| |legendreP|
+ |wreath| |modTree| |rotatex| |selectSumOfSquaresRoutines| |e01daf|
+ |newLine| |noKaratsuba| |genericLeftMinimalPolynomial| |midpoints|
+ |degreeSubResultant| |basisOfCentroid| |number?| |outputAsTex|
+ |antiAssociative?| |inverseColeman| |pquo| |setrest!| |setlast!|
+ |rquo| |symbol| |subset?| |coerceP| |numericalIntegration| |elliptic?|
+ |sort!| |unaryFunction| |e04fdf| |newTypeLists| |rightRankPolynomial|
+ |lazyIrreducibleFactors| |expression| |coleman| |radPoly|
+ |prinpolINFO| |readable?| |cAsec| |integerIfCan| |cyclic?| |toScale|
+ |multiplyCoefficients| |integer| |invertible?| |balancedFactorisation|
+ |rightTrace| |algebraicDecompose| |littleEndian| |bandedJacobian|
+ |nonLinearPart| |linear| |linearPart| |polCase| |iidsum| |parabolic|
+ |BumInSepFFE| |isMult| |expint| |ocf2ocdf| |f04axf| |fixedPoints|
+ |mainVariable| |halfExtendedResultant2| |cAcos| |nextItem|
+ |rubiksGroup| |leadingTerm| |bivariateSLPEBR| |OMsupportsCD?|
+ |polynomial| |fortranDoubleComplex| |quoted?| |rootDirectory|
+ |generalizedInverse| |rdregime| |infix| |quartic| |wrregime| |replace|
+ |OMParseError?| |car| |Hausdorff| |inputBinaryFile| |moebius|
+ |extendedIntegrate| |showFortranOutputStack| |erf| |divideExponents|
+ |result| |OMlistCDs| |seriesSolve| |representationType| |makeSeries|
+ |s17dhf| |ceiling| |li| |f01qdf| |bfEntry| |returns| |f04atf|
+ |solveid| |makeFloatFunction| |terms| |nextPrimitiveNormalPoly|
+ |s21bcf| |stack| |commonDenominator| |tower| |rationalPoints| |lprop|
+ |flexibleArray| |quasiAlgebraicSet| |internalSubPolSet?| |mappingAst|
+ |complexElementary| |goodPoint| |nil?| |reducedDiscriminant|
+ |showClipRegion| |multinomial| |partitions| |graphCurves| |iiasin|
+ |idealiser| |exprex| |polygamma| |block| |cSin|
+ |rationalApproximation| |cSinh| |dominantTerm| |makeVariable|
+ |Vectorise| |mainPrimitivePart| |weierstrass| |integralCoordinates|
+ |restorePrecision| |selectsecond| |eq| |completeEchelonBasis|
+ |univcase| |polyRDE| |cycleElt| |node?| |iter| |dim| |invertibleSet|
+ |csch2sinh| |Lazard| |roughEqualIdeals?| |kmax| |length| |someBasis|
+ |presub| |fortranLiteral| |numerators| |useEisensteinCriterion|
+ |lifting1| |rational| |complexNumeric| |overlabel| |mkAnswer| |step|
+ |scripts| |permutations| |currentScope| |byteBuffer| |algebraicOf|
+ |s17akf| |initials| |pile| |reduced?| |leastMonomial| |concat|
+ |complex?| |monomRDEsys| |characteristic| |closeComponent|
+ |makeSketch| |test| |kernels| |OMputEndObject| |outlineRender|
+ |computeCycleLength| |e01sbf| |characteristicPolynomial| |hMonic|
+ |schwerpunkt| |maximumExponent| |operator| |setTopPredicate| |cfirst|
+ |ScanArabic| |removeRoughlyRedundantFactorsInPols| |completeSmith|
+ |character?| |explicitlyEmpty?| |SturmHabichtSequence| |trim|
+ |outputMeasure| |addBadValue| |leastAffineMultiple| |iiacosh|
+ |axesColorDefault| |ranges| |LyndonWordsList1| |complexSolve|
+ |GospersMethod| |rightUnits| |laplacian| |univariate| |nthFlag|
+ |setColumn!| |geometric| |FormatArabic| |replaceKthElement| |f07adf|
+ |opeval| |seed| |identitySquareMatrix| |pade| |stirling1| |uniform01|
+ |binomThmExpt| |powers| |prolateSpheroidal| |trunc| |isNot| |iiGamma|
+ |f02akf| |setelt!| |prefix| |diagonals| |retractable?| |routines|
+ |cAcot| |factor| |interpolate| |symbolTableOf| |OMputString| |stFunc1|
+ |ratDsolve| |nthExpon| |subSet| |composites| |sqrt| |OMconnOutDevice|
+ |integralLastSubResultant| |contractSolve| |pushNewContour|
+ |testModulus| |chebyshevT| |unprotectedRemoveRedundantFactors|
+ |scopes| |selectfirst| |real| |cCos| |e02ddf| |unvectorise|
+ |duplicates| |symbol?| |tubePoints| |tanh2coth| |equality| |dflist|
+ |imag| |Nul| |getRef| |declare| |ridHack1| |stop| |leftQuotient|
+ |SturmHabicht| |binaryTournament| |pointLists| |s14baf| |OMgetBVar|
+ |directProduct| |halfExtendedResultant1| |palginfieldint|
+ |sturmVariationsOf| |rootSplit| |mr| |integral| |lambert|
+ |systemSizeIF| |algintegrate| |hasPredicate?| |solid?| |findBinding|
+ |asechIfCan| |basisOfCenter| |closed?| |outputSpacing| SEGMENT
+ |s19abf| |lineColorDefault| |brace| |kind| |llprop| |reify|
+ |rightMult| |symmetric?| |environment| |tubePlot| |redPol| |surface|
+ |categories| |rowEchelonLocal| |destruct| |lexTriangular|
+ |subQuasiComponent?| |op| |pseudoRemainder| |reverseLex| |sqfrFactor|
+ |fibonacci| |mantissa| |subResultantChain| |depth| |clearTable!|
+ |csc2sin| |compBound| |ODESolve| |closedCurve| |dioSolve|
+ |localUnquote| |typeForm| |normalizedAssociate|
+ |stoseLastSubResultant| |lieAdmissible?| |recur| |iiacos|
+ |rootProduct| |safeCeiling| |quadratic?| |level| |algebraic?| |f04asf|
+ |controlPanel| |irDef| |factorSquareFree| |pascalTriangle|
+ |lfinfieldint| |shufflein| |solveInField| |ignore?| |approximants|
+ |ratpart| |setright!| |lSpaceBasis| |monomial| |euclideanNormalForm|
+ |nextSubsetGray| |prem| |divisor| |problemPoints| |iprint|
+ |rightFactorIfCan| |iiacot| |extend| |multivariate| |innerint|
+ |f04jgf| |squareFreePart| |f02fjf| |semiSubResultantGcdEuclidean1|
+ |degreeSubResultantEuclidean| |polygon?| |times!| |subHeight|
+ |variables| |setLabelValue| |cAcoth| |diagonal?| |union|
+ |groebnerIdeal| |sincos| |leftRemainder| |returnTypeOf| |bytes|
+ |symmetricDifference| |makeViewport3D| |isAnd| |float?| |rightRecip|
+ |ratDenom| |uncouplingMatrices| |gradient| |categoryFrame|
+ |OMputVariable| |startTable!| |c06gcf| |printHeader|
+ |characteristicSerie| |rightRemainder| |pushdterm| |minset|
+ |generateIrredPoly| |deref| |bat1| |OMputInteger| |asinIfCan|
+ |distdfact| |pop!| |exponents| |gensym| |OMgetType| |idealSimplify|
+ |iterationVar| |leftLcm| |solveLinearlyOverQ| |summation| |shiftRight|
+ |approxSqrt| |slash| |optional?| |enterInCache| |taylor| |comp|
+ |pseudoQuotient| |hdmpToDmp| |numberOfVariables|
+ |rootOfIrreduciblePoly| |gcdcofactprim| |lazy?| |argumentListOf|
+ |noValueMode| |string?| |laurent|
+ |dimensionOfIrreducibleRepresentation| |f07fdf| |createRandomElement|
+ |readBytes!| |factorPolynomial| |infinityNorm| |htrigs| |imagk|
+ |tanNa| |reverse| |puiseux| |lowerCase| |repeatUntilLoop|
+ |coercePreimagesImages| |isPower| |balancedBinaryTree| |factorial|
+ |flagFactor| |multiset| |extendedResultant| |adjoint| |packageCall|
+ |semicolonSeparate| |nil| |infinite| |arbitraryExponent| |approximate|
  |complex| |shallowMutable| |canonical| |noetherian| |central|
  |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed|
  |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 1a469919..bada1c95 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5400 +1,5409 @@
 
-(3237344 . 3485510938)       
-((-2852 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3314 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3140 ((|#2| $ (-572) |#2|) NIL) ((|#2| $ (-1246 (-572)) |#2|) 44)) (-3133 (($ $) 80)) (-2865 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-1439 (((-572) (-1 (-112) |#2|) $) 27) (((-572) |#2| $) NIL) (((-572) |#2| $ (-572)) 96)) (-1863 (((-652 |#2|) $) 13)) (-1767 (($ (-1 (-112) |#2| |#2|) $ $) 64) (($ $ $) NIL)) (-2442 (($ (-1 |#2| |#2|) $) 37)) (-1776 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 60)) (-1593 (($ |#2| $ (-572)) NIL) (($ $ $ (-572)) 67)) (-3770 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 29)) (-1612 (((-112) (-1 (-112) |#2|) $) 23)) (-2196 ((|#2| $ (-572) |#2|) NIL) ((|#2| $ (-572)) NIL) (($ $ (-1246 (-572))) 66)) (-2835 (($ $ (-572)) 76) (($ $ (-1246 (-572))) 75)) (-3973 (((-779) (-1 (-112) |#2|) $) 34) (((-779) |#2| $) NIL)) (-4095 (($ $ $ (-572)) 69)) (-3164 (($ $) 68)) (-2953 (($ (-652 |#2|)) 73)) (-4155 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 87) (($ (-652 $)) 85)) (-2940 (((-870) $) 92)) (-4380 (((-112) (-1 (-112) |#2|) $) 22)) (-2978 (((-112) $ $) 95)) (-3003 (((-112) $ $) 99))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -2978 ((-112) |#1| |#1|)) (-15 -2940 ((-870) |#1|)) (-15 -3003 ((-112) |#1| |#1|)) (-15 -3314 (|#1| |#1|)) (-15 -3314 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -3133 (|#1| |#1|)) (-15 -4095 (|#1| |#1| |#1| (-572))) (-15 -2852 ((-112) |#1|)) (-15 -1767 (|#1| |#1| |#1|)) (-15 -1439 ((-572) |#2| |#1| (-572))) (-15 -1439 ((-572) |#2| |#1|)) (-15 -1439 ((-572) (-1 (-112) |#2|) |#1|)) (-15 -2852 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -1767 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -3140 (|#2| |#1| (-1246 (-572)) |#2|)) (-15 -1593 (|#1| |#1| |#1| (-572))) (-15 -1593 (|#1| |#2| |#1| (-572))) (-15 -2835 (|#1| |#1| (-1246 (-572)))) (-15 -2835 (|#1| |#1| (-572))) (-15 -1776 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -4155 (|#1| (-652 |#1|))) (-15 -4155 (|#1| |#1| |#1|)) (-15 -4155 (|#1| |#2| |#1|)) (-15 -4155 (|#1| |#1| |#2|)) (-15 -2196 (|#1| |#1| (-1246 (-572)))) (-15 -2953 (|#1| (-652 |#2|))) (-15 -3770 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2865 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2865 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2865 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2196 (|#2| |#1| (-572))) (-15 -2196 (|#2| |#1| (-572) |#2|)) (-15 -3140 (|#2| |#1| (-572) |#2|)) (-15 -3973 ((-779) |#2| |#1|)) (-15 -1863 ((-652 |#2|) |#1|)) (-15 -3973 ((-779) (-1 (-112) |#2|) |#1|)) (-15 -1612 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -4380 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -2442 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1776 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3164 (|#1| |#1|))) (-19 |#2|) (-1229)) (T -18)) 
+(3238065 . 3485633371)       
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 NIL 
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-(((-19 |#1|) (-141) (-1229)) (T -19)) 
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+(((-19 |#1|) (-141) (-1231)) (T -19)) 
 NIL 
-(-13 (-380 |t#1|) (-10 -7 (-6 -4455))) 
-(((-34) . T) ((-102) -2813 (|has| |#1| (-1111)) (|has| |#1| (-858))) ((-621 (-870)) -2813 (|has| |#1| (-1111)) (|has| |#1| (-858)) (|has| |#1| (-621 (-870)))) ((-152 |#1|) . T) ((-622 (-544)) |has| |#1| (-622 (-544))) ((-292 #0=(-572) |#1|) . T) ((-292 (-1246 (-572)) $) . T) ((-294 #0# |#1|) . T) ((-315 |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-380 |#1|) . T) ((-497 |#1|) . T) ((-612 #0# |#1|) . T) ((-522 |#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-659 |#1|) . T) ((-858) |has| |#1| (-858)) ((-1111) -2813 (|has| |#1| (-1111)) (|has| |#1| (-858))) ((-1229) . T)) 
-((-3330 (((-3 $ "failed") $ $) 12)) (-3089 (($ $) NIL) (($ $ $) 9)) (* (($ (-930) $) NIL) (($ (-779) $) 16) (($ (-572) $) 26))) 
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+(-13 (-382 |t#1|) (-10 -7 (-6 -4457))) 
+(((-34) . T) ((-102) -2818 (|has| |#1| (-1113)) (|has| |#1| (-860))) ((-623 (-872)) -2818 (|has| |#1| (-1113)) (|has| |#1| (-860)) (|has| |#1| (-623 (-872)))) ((-152 |#1|) . T) ((-624 (-546)) |has| |#1| (-624 (-546))) ((-294 #0=(-574) |#1|) . T) ((-294 (-1248 (-574)) $) . T) ((-296 #0# |#1|) . T) ((-317 |#1|) -12 (|has| |#1| (-317 |#1|)) (|has| |#1| (-1113))) ((-382 |#1|) . T) ((-499 |#1|) . T) ((-614 #0# |#1|) . T) ((-524 |#1| |#1|) -12 (|has| |#1| (-317 |#1|)) (|has| |#1| (-1113))) ((-661 |#1|) . T) ((-860) |has| |#1| (-860)) ((-1113) -2818 (|has| |#1| (-1113)) (|has| |#1| (-860))) ((-1231) . T)) 
+((-2950 (((-3 $ "failed") $ $) 12)) (-3094 (($ $) NIL) (($ $ $) 9)) (* (($ (-932) $) NIL) (($ (-781) $) 16) (($ (-574) $) 26))) 
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 NIL 
-(-10 -8 (-15 -3089 (|#1| |#1| |#1|)) (-15 -3089 (|#1| |#1|)) (-15 * (|#1| (-572) |#1|)) (-15 -3330 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-779) |#1|)) (-15 * (|#1| (-930) |#1|))) 
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+((-2849 (((-112) $ $) 7)) (-2908 (((-112) $) 17)) (-2950 (((-3 $ "failed") $ $) 20)) (-3670 (($) 18 T CONST)) (-2568 (((-1172) $) 10)) (-3966 (((-1133) $) 11)) (-2943 (((-872) $) 12)) (-2923 (((-112) $ $) 9)) (-2134 (($) 19 T CONST)) (-2982 (((-112) $ $) 6)) (-3094 (($ $) 23) (($ $ $) 22)) (-3078 (($ $ $) 15)) (* (($ (-932) $) 14) (($ (-781) $) 16) (($ (-574) $) 24))) 
 (((-21) (-141)) (T -21)) 
-((-3089 (*1 *1 *1) (-4 *1 (-21))) (-3089 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-132) (-654 (-572)) (-10 -8 (-15 -3089 ($ $)) (-15 -3089 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-621 (-870)) . T) ((-654 (-572)) . T) ((-1111) . T)) 
-((-2697 (((-112) $) 10)) (-3281 (($) 15)) (* (($ (-930) $) 14) (($ (-779) $) 19))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-779) |#1|)) (-15 -2697 ((-112) |#1|)) (-15 -3281 (|#1|)) (-15 * (|#1| (-930) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-779) |#1|)) (-15 -2697 ((-112) |#1|)) (-15 -3281 (|#1|)) (-15 * (|#1| (-930) |#1|))) 
-((-2846 (((-112) $ $) 7)) (-2697 (((-112) $) 17)) (-3281 (($) 18 T CONST)) (-4347 (((-1170) $) 10)) (-3964 (((-1131) $) 11)) (-2940 (((-870) $) 12)) (-4379 (((-112) $ $) 9)) (-2131 (($) 19 T CONST)) (-2978 (((-112) $ $) 6)) (-3075 (($ $ $) 15)) (* (($ (-930) $) 14) (($ (-779) $) 16))) 
+((-3094 (*1 *1 *1) (-4 *1 (-21))) (-3094 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-132) (-656 (-574)) (-10 -8 (-15 -3094 ($ $)) (-15 -3094 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-623 (-872)) . T) ((-656 (-574)) . T) ((-1113) . T)) 
+((-2908 (((-112) $) 10)) (-3670 (($) 15)) (* (($ (-932) $) 14) (($ (-781) $) 19))) 
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+NIL 
+(-10 -8 (-15 * (|#1| (-781) |#1|)) (-15 -2908 ((-112) |#1|)) (-15 -3670 (|#1|)) (-15 * (|#1| (-932) |#1|))) 
+((-2849 (((-112) $ $) 7)) (-2908 (((-112) $) 17)) (-3670 (($) 18 T CONST)) (-2568 (((-1172) $) 10)) (-3966 (((-1133) $) 11)) (-2943 (((-872) $) 12)) (-2923 (((-112) $ $) 9)) (-2134 (($) 19 T CONST)) (-2982 (((-112) $ $) 6)) (-3078 (($ $ $) 15)) (* (($ (-932) $) 14) (($ (-781) $) 16))) 
 (((-23) (-141)) (T -23)) 
-((-2131 (*1 *1) (-4 *1 (-23))) (-3281 (*1 *1) (-4 *1 (-23))) (-2697 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-779))))) 
-(-13 (-25) (-10 -8 (-15 (-2131) ($) -1705) (-15 -3281 ($) -1705) (-15 -2697 ((-112) $)) (-15 * ($ (-779) $)))) 
-(((-25) . T) ((-102) . T) ((-621 (-870)) . T) ((-1111) . T)) 
-((* (($ (-930) $) 10))) 
-(((-24 |#1|) (-10 -8 (-15 * (|#1| (-930) |#1|))) (-25)) (T -24)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-930) |#1|))) 
-((-2846 (((-112) $ $) 7)) (-4347 (((-1170) $) 10)) (-3964 (((-1131) $) 11)) (-2940 (((-870) $) 12)) (-4379 (((-112) $ $) 9)) (-2978 (((-112) $ $) 6)) (-3075 (($ $ $) 15)) (* (($ (-930) $) 14))) 
+((-2134 (*1 *1) (-4 *1 (-23))) (-3670 (*1 *1) (-4 *1 (-23))) (-2908 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-112)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-781))))) 
+(-13 (-25) (-10 -8 (-15 (-2134) ($) -1707) (-15 -3670 ($) -1707) (-15 -2908 ((-112) $)) (-15 * ($ (-781) $)))) 
+(((-25) . T) ((-102) . T) ((-623 (-872)) . T) ((-1113) . T)) 
+((* (($ (-932) $) 10))) 
+(((-24 |#1|) (-10 -8 (-15 * (|#1| (-932) |#1|))) (-25)) (T -24)) 
+NIL 
+(-10 -8 (-15 * (|#1| (-932) |#1|))) 
+((-2849 (((-112) $ $) 7)) (-2568 (((-1172) $) 10)) (-3966 (((-1133) $) 11)) (-2943 (((-872) $) 12)) (-2923 (((-112) $ $) 9)) (-2982 (((-112) $ $) 6)) (-3078 (($ $ $) 15)) (* (($ (-932) $) 14))) 
 (((-25) (-141)) (T -25)) 
-((-3075 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-930))))) 
-(-13 (-1111) (-10 -8 (-15 -3075 ($ $ $)) (-15 * ($ (-930) $)))) 
-(((-102) . T) ((-621 (-870)) . T) ((-1111) . T)) 
-((-2345 (((-652 $) (-961 $)) 32) (((-652 $) (-1184 $)) 16) (((-652 $) (-1184 $) (-1188)) 20)) (-4164 (($ (-961 $)) 30) (($ (-1184 $)) 11) (($ (-1184 $) (-1188)) 60)) (-2901 (((-652 $) (-961 $)) 33) (((-652 $) (-1184 $)) 18) (((-652 $) (-1184 $) (-1188)) 19)) (-1821 (($ (-961 $)) 31) (($ (-1184 $)) 13) (($ (-1184 $) (-1188)) NIL))) 
-(((-26 |#1|) (-10 -8 (-15 -2345 ((-652 |#1|) (-1184 |#1|) (-1188))) (-15 -2345 ((-652 |#1|) (-1184 |#1|))) (-15 -2345 ((-652 |#1|) (-961 |#1|))) (-15 -4164 (|#1| (-1184 |#1|) (-1188))) (-15 -4164 (|#1| (-1184 |#1|))) (-15 -4164 (|#1| (-961 |#1|))) (-15 -2901 ((-652 |#1|) (-1184 |#1|) (-1188))) (-15 -2901 ((-652 |#1|) (-1184 |#1|))) (-15 -2901 ((-652 |#1|) (-961 |#1|))) (-15 -1821 (|#1| (-1184 |#1|) (-1188))) (-15 -1821 (|#1| (-1184 |#1|))) (-15 -1821 (|#1| (-961 |#1|)))) (-27)) (T -26)) 
-NIL 
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+((-3078 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-932))))) 
+(-13 (-1113) (-10 -8 (-15 -3078 ($ $ $)) (-15 * ($ (-932) $)))) 
+(((-102) . T) ((-623 (-872)) . T) ((-1113) . T)) 
+((-2656 (((-654 $) (-963 $)) 32) (((-654 $) (-1186 $)) 16) (((-654 $) (-1186 $) (-1190)) 20)) (-1397 (($ (-963 $)) 30) (($ (-1186 $)) 11) (($ (-1186 $) (-1190)) 60)) (-3072 (((-654 $) (-963 $)) 33) (((-654 $) (-1186 $)) 18) (((-654 $) (-1186 $) (-1190)) 19)) (-1413 (($ (-963 $)) 31) (($ (-1186 $)) 13) (($ (-1186 $) (-1190)) NIL))) 
+(((-26 |#1|) (-10 -8 (-15 -2656 ((-654 |#1|) (-1186 |#1|) (-1190))) (-15 -2656 ((-654 |#1|) (-1186 |#1|))) (-15 -2656 ((-654 |#1|) (-963 |#1|))) (-15 -1397 (|#1| (-1186 |#1|) (-1190))) (-15 -1397 (|#1| (-1186 |#1|))) (-15 -1397 (|#1| (-963 |#1|))) (-15 -3072 ((-654 |#1|) (-1186 |#1|) (-1190))) (-15 -3072 ((-654 |#1|) (-1186 |#1|))) (-15 -3072 ((-654 |#1|) (-963 |#1|))) (-15 -1413 (|#1| (-1186 |#1|) (-1190))) (-15 -1413 (|#1| (-1186 |#1|))) (-15 -1413 (|#1| (-963 |#1|)))) (-27)) (T -26)) 
+NIL 
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 (((-27) (-141)) (T -27)) 
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-NIL 
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 (((-93) (-141)) (T -93)) 
 NIL 
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 NIL 
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 NIL 
 (((-98) (-141)) (T -98)) 
 NIL 
-(-13 (-10 -7 (-6 -4454) (-6 (-4456 "*")) (-6 -4455) (-6 -4451) (-6 -4449) (-6 -4448) (-6 -4447) (-6 -4452) (-6 -4446) (-6 -4445) (-6 -4444) (-6 -4443) (-6 -4442) (-6 -4450) (-6 -4453) (-6 |NullSquare|) (-6 |JacobiIdentity|) (-6 -4441))) 
-((-2846 (((-112) $ $) NIL)) (-3281 (($) NIL T CONST)) (-2062 (((-3 $ "failed") $) NIL)) (-1886 (((-112) $) NIL)) (-2980 (($ (-1 |#1| |#1|)) 27) (($ (-1 |#1| |#1|) (-1 |#1| |#1|)) 26) (($ (-1 |#1| |#1| (-572))) 24)) (-4347 (((-1170) $) NIL)) (-1322 (($ $) 16)) (-3964 (((-1131) $) NIL)) (-2196 ((|#1| $ |#1|) 13)) (-1516 (($ $ $) NIL)) (-4326 (($ $ $) NIL)) (-2940 (((-870) $) 22)) (-4379 (((-112) $ $) NIL)) (-2143 (($) 8 T CONST)) (-2978 (((-112) $ $) 10)) (-3106 (($ $ $) NIL)) (** (($ $ (-930)) 32) (($ $ (-779)) NIL) (($ $ (-572)) 18)) (* (($ $ $) 33))) 
-(((-99 |#1|) (-13 (-481) (-292 |#1| |#1|) (-10 -8 (-15 -2980 ($ (-1 |#1| |#1|))) (-15 -2980 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -2980 ($ (-1 |#1| |#1| (-572)))))) (-1060)) (T -99)) 
-((-2980 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1060)) (-5 *1 (-99 *3)))) (-2980 (*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1060)) (-5 *1 (-99 *3)))) (-2980 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-572))) (-4 *3 (-1060)) (-5 *1 (-99 *3))))) 
-(-13 (-481) (-292 |#1| |#1|) (-10 -8 (-15 -2980 ($ (-1 |#1| |#1|))) (-15 -2980 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -2980 ($ (-1 |#1| |#1| (-572)))))) 
-((-3609 (((-426 |#2|) |#2| (-652 |#2|)) 10) (((-426 |#2|) |#2| |#2|) 11))) 
-(((-100 |#1| |#2|) (-10 -7 (-15 -3609 ((-426 |#2|) |#2| |#2|)) (-15 -3609 ((-426 |#2|) |#2| (-652 |#2|)))) (-13 (-460) (-148)) (-1255 |#1|)) (T -100)) 
-((-3609 (*1 *2 *3 *4) (-12 (-5 *4 (-652 *3)) (-4 *3 (-1255 *5)) (-4 *5 (-13 (-460) (-148))) (-5 *2 (-426 *3)) (-5 *1 (-100 *5 *3)))) (-3609 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-460) (-148))) (-5 *2 (-426 *3)) (-5 *1 (-100 *4 *3)) (-4 *3 (-1255 *4))))) 
-(-10 -7 (-15 -3609 ((-426 |#2|) |#2| |#2|)) (-15 -3609 ((-426 |#2|) |#2| (-652 |#2|)))) 
-((-2846 (((-112) $ $) 10))) 
-(((-101 |#1|) (-10 -8 (-15 -2846 ((-112) |#1| |#1|))) (-102)) (T -101)) 
-NIL 
-(-10 -8 (-15 -2846 ((-112) |#1| |#1|))) 
-((-2846 (((-112) $ $) 7)) (-2978 (((-112) $ $) 6))) 
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+((-2849 (((-112) $ $) NIL)) (-3670 (($) NIL T CONST)) (-1950 (((-3 $ "failed") $) NIL)) (-3965 (((-112) $) NIL)) (-2513 (($ (-1 |#1| |#1|)) 27) (($ (-1 |#1| |#1|) (-1 |#1| |#1|)) 26) (($ (-1 |#1| |#1| (-574))) 24)) (-2568 (((-1172) $) NIL)) (-1324 (($ $) 16)) (-3966 (((-1133) $) NIL)) (-2200 ((|#1| $ |#1|) 13)) (-1514 (($ $ $) NIL)) (-3647 (($ $ $) NIL)) (-2943 (((-872) $) 22)) (-2923 (((-112) $ $) NIL)) (-2146 (($) 8 T CONST)) (-2982 (((-112) $ $) 10)) (-3107 (($ $ $) NIL)) (** (($ $ (-932)) 32) (($ $ (-781)) NIL) (($ $ (-574)) 18)) (* (($ $ $) 33))) 
+(((-99 |#1|) (-13 (-483) (-294 |#1| |#1|) (-10 -8 (-15 -2513 ($ (-1 |#1| |#1|))) (-15 -2513 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -2513 ($ (-1 |#1| |#1| (-574)))))) (-1062)) (T -99)) 
+((-2513 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1062)) (-5 *1 (-99 *3)))) (-2513 (*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1062)) (-5 *1 (-99 *3)))) (-2513 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-574))) (-4 *3 (-1062)) (-5 *1 (-99 *3))))) 
+(-13 (-483) (-294 |#1| |#1|) (-10 -8 (-15 -2513 ($ (-1 |#1| |#1|))) (-15 -2513 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -2513 ($ (-1 |#1| |#1| (-574)))))) 
+((-4028 (((-428 |#2|) |#2| (-654 |#2|)) 10) (((-428 |#2|) |#2| |#2|) 11))) 
+(((-100 |#1| |#2|) (-10 -7 (-15 -4028 ((-428 |#2|) |#2| |#2|)) (-15 -4028 ((-428 |#2|) |#2| (-654 |#2|)))) (-13 (-462) (-148)) (-1257 |#1|)) (T -100)) 
+((-4028 (*1 *2 *3 *4) (-12 (-5 *4 (-654 *3)) (-4 *3 (-1257 *5)) (-4 *5 (-13 (-462) (-148))) (-5 *2 (-428 *3)) (-5 *1 (-100 *5 *3)))) (-4028 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-462) (-148))) (-5 *2 (-428 *3)) (-5 *1 (-100 *4 *3)) (-4 *3 (-1257 *4))))) 
+(-10 -7 (-15 -4028 ((-428 |#2|) |#2| |#2|)) (-15 -4028 ((-428 |#2|) |#2| (-654 |#2|)))) 
+((-2849 (((-112) $ $) 10))) 
+(((-101 |#1|) (-10 -8 (-15 -2849 ((-112) |#1| |#1|))) (-102)) (T -101)) 
+NIL 
+(-10 -8 (-15 -2849 ((-112) |#1| |#1|))) 
+((-2849 (((-112) $ $) 7)) (-2982 (((-112) $ $) 6))) 
 (((-102) (-141)) (T -102)) 
-((-2846 (*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) (-2978 (*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112))))) 
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-((-2746 ((|#3| |#2| |#2|) 34)) (-2607 ((|#1| |#2| |#2|) 51 (|has| |#1| (-6 (-4456 "*"))))) (-2951 ((|#3| |#2| |#2|) 36)) (-2970 ((|#1| |#2|) 54 (|has| |#1| (-6 (-4456 "*")))))) 
-(((-104 |#1| |#2| |#3| |#4| |#5|) (-10 -7 (-15 -2746 (|#3| |#2| |#2|)) (-15 -2951 (|#3| |#2| |#2|)) (IF (|has| |#1| (-6 (-4456 "*"))) (PROGN (-15 -2607 (|#1| |#2| |#2|)) (-15 -2970 (|#1| |#2|))) |%noBranch|)) (-1060) (-1255 |#1|) (-695 |#1| |#4| |#5|) (-380 |#1|) (-380 |#1|)) (T -104)) 
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-(-10 -7 (-15 -2746 (|#3| |#2| |#2|)) (-15 -2951 (|#3| |#2| |#2|)) (IF (|has| |#1| (-6 (-4456 "*"))) (PROGN (-15 -2607 (|#1| |#2| |#2|)) (-15 -2970 (|#1| |#2|))) |%noBranch|)) 
-((-2846 (((-112) $ $) NIL)) (-4347 (((-1170) $) NIL)) (-3964 (((-1131) $) NIL)) (-2940 (((-870) $) NIL)) (-4367 (((-652 (-1188))) 37)) (-1581 (((-2 (|:| |zeros| (-1168 (-227))) (|:| |ones| (-1168 (-227))) (|:| |singularities| (-1168 (-227)))) (-1188)) 39)) (-4379 (((-112) $ $) NIL)) (-2978 (((-112) $ $) NIL))) 
-(((-105) (-13 (-1111) (-10 -7 (-15 -4367 ((-652 (-1188)))) (-15 -1581 ((-2 (|:| |zeros| (-1168 (-227))) (|:| |ones| (-1168 (-227))) (|:| |singularities| (-1168 (-227)))) (-1188))) (-6 -4454)))) (T -105)) 
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-((-2022 (($ (-652 |#2|)) 11))) 
-(((-106 |#1| |#2|) (-10 -8 (-15 -2022 (|#1| (-652 |#2|)))) (-107 |#2|) (-1229)) (T -106)) 
-NIL 
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-(((-107 |#1|) (-141) (-1229)) (T -107)) 
-((-2022 (*1 *1 *2) (-12 (-5 *2 (-652 *3)) (-4 *3 (-1229)) (-4 *1 (-107 *3)))) (-3378 (*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1229)))) (-2036 (*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1229)))) (-1651 (*1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1229))))) 
-(-13 (-497 |t#1|) (-10 -8 (-6 -4455) (-15 -2022 ($ (-652 |t#1|))) (-15 -3378 (|t#1| $)) (-15 -2036 ($ |t#1| $)) (-15 -1651 (|t#1| $)))) 
-(((-34) . T) ((-102) |has| |#1| (-1111)) ((-621 (-870)) -2813 (|has| |#1| (-1111)) (|has| |#1| (-621 (-870)))) ((-315 |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-497 |#1|) . T) ((-522 |#1| |#1|) -12 (|has| |#1| (-315 |#1|)) (|has| |#1| (-1111))) ((-1111) |has| |#1| (-1111)) ((-1229) . T)) 
-((-2846 (((-112) $ $) NIL)) (-2697 (((-112) $) NIL)) (-2689 (((-572) $) NIL (|has| (-572) (-313)))) (-2072 (((-2 (|:| -3161 $) (|:| -4441 $) (|:| |associate| $)) $) NIL)) (-3009 (($ $) NIL)) (-4334 (((-112) $) NIL)) (-3330 (((-3 $ "failed") $ $) NIL)) (-2603 (((-426 (-1184 $)) (-1184 $)) NIL (|has| (-572) (-918)))) (-3517 (($ $) NIL)) (-2287 (((-426 $) $) NIL)) (-3643 (((-3 (-652 (-1184 $)) "failed") (-652 (-1184 $)) (-1184 $)) NIL (|has| (-572) (-918)))) (-4217 (((-112) $ $) NIL)) (-2840 (((-572) $) NIL (|has| (-572) (-828)))) (-3281 (($) NIL T CONST)) (-1695 (((-3 (-572) "failed") $) NIL) (((-3 (-1188) "failed") $) NIL (|has| (-572) (-1049 (-1188)))) (((-3 (-415 (-572)) "failed") $) NIL (|has| (-572) (-1049 (-572)))) (((-3 (-572) "failed") $) NIL (|has| (-572) (-1049 (-572))))) (-2204 (((-572) $) NIL) (((-1188) $) NIL (|has| (-572) (-1049 (-1188)))) (((-415 (-572)) $) NIL (|has| (-572) (-1049 (-572)))) (((-572) $) NIL (|has| (-572) (-1049 (-572))))) (-2780 (($ $ $) NIL)) (-2993 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-NIL 
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-NIL 
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-NIL 
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+(((-1231) . 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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+(((-195) (-797)) (T -195)) 
+NIL 
+(-797) 
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+NIL 
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+(((-197) (-797)) (T -197)) 
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-NIL 
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-(((-273) (-847)) (T -273)) 
-NIL 
-(-847) 
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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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-((-2997 (*1 *1) (-5 *1 (-485)))) 
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+NIL 
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+NIL 
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+((-3001 (*1 *1) (-5 *1 (-487)))) 
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+((-1796 (*1 *2 *1) (-12 (-5 *2 (-1148)) (-5 *1 (-488)))) (-1809 (*1 *2 *1) (-12 (-5 *2 (-1148)) (-5 *1 (-488))))) 
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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 
 (-57 |#1| |#4| |#5|) 
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(-227)) (|:| |relerr| (-227)))) (|:| -1907 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1168 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1910 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (-5 *1 (-567)))) (-2180 (*1 *1 *2) (-12 (-5 *2 (-652 (-2 (|:| -3690 (-2 (|:| |var| (-1188)) (|:| |fn| (-322 (-227))) (|:| -1910 (-1105 (-851 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| 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-NIL 
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-NIL 
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-NIL 
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-1909 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1170 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2967 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-569)))) (-1765 (*1 *2 *1) (-12 (-5 *2 (-654 (-2 (|:| |var| (-1190)) (|:| |fn| (-324 (-227))) (|:| -2967 (-1107 (-853 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-569)))) (-3863 (*1 *2) (-12 (-5 *2 (-1286)) 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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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 (((-854) (-141)) (T -854)) 
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 NIL 
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-(((-102) . T) ((-621 (-870)) . T) ((-734) . T) ((-865) . T) ((-858) . T) ((-1123) . T) ((-1111) . T)) 
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+(-13 (-867) (-736)) 
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 NIL 
-(-10 -8 (-15 -2700 (|#1| |#1|)) (-15 -2840 ((-572) |#1|)) (-15 -1623 ((-112) |#1|)) (-15 -3074 ((-112) |#1|))) 
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-(((-856) (-141)) (T -856)) 
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-((-3654 (($ $ $) 12)) (-2427 (($ $ $) 11)) (-4379 (((-112) $ $) 9)) (-3039 (((-112) $ $) 15)) (-3014 (((-112) $ $) 13)) (-3026 (((-112) $ $) 16))) 
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-NIL 
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 (((-858) (-141)) (T -858)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-102) . T) ((-111 |#3| |#3|) . T) ((-132) . T) ((-621 (-870)) . T) ((-315 |#3|) -12 (|has| |#3| (-315 |#3|)) (|has| |#3| (-1111))) ((-497 |#3|) . T) ((-522 |#3| |#3|) -12 (|has| |#3| (-315 |#3|)) (|has| |#3| (-1111))) ((-654 (-572)) . T) ((-654 |#3|) . T) ((-656 |#3|) . T) ((-648 |#3|) |has| |#3| (-174)) ((-725 |#3|) |has| |#3| (-174)) ((-1062 |#3|) . T) ((-1067 |#3|) . T) ((-1111) . T) ((-1229) . T)) 
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-((-2785 (*1 *1 *2) (-12 (-5 *2 (-697 *5)) (-4 *5 (-1060)) (-5 *1 (-1065 *3 *4 *5)) (-14 *3 (-779)) (-14 *4 (-779))))) 
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-NIL 
-(-13 (-21) (-1062 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-621 (-870)) . T) ((-654 (-572)) . T) ((-1062 |#1|) . T) ((-1111) . T)) 
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-(((-1069) (-141)) (T -1069)) 
-NIL 
-(-13 (-21) (-1123)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-102) . T) ((-132) . T) ((-621 (-870)) . T) ((-654 (-572)) . T) ((-1123) . T) ((-1111) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-(((-1113 |#1|) (-433 |#1|) (-1111)) (T -1113)) 
-NIL 
-(-433 |#1|) 
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-(((-1114 |#1| |#2| |#3| |#4| |#5|) (-141) (-1111) (-1111) (-1111) (-1111) (-1111)) (T -1114)) 
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-(((-102) . T) ((-621 (-870)) . T) ((-626 (-652 $)) . T) ((-626 |#1|) . T) ((-626 |#2|) . T) ((-626 |#3|) . T) ((-626 |#4|) . T) ((-626 |#5|) . T) ((-292 (-572) $) . T) ((-292 (-652 (-572)) $) . T) ((-1111) . T) ((-1229) . T)) 
-((-2846 (((-112) $ $) NIL)) (-1475 (((-112) $) NIL)) (-4003 (((-1188) $) NIL)) (-3842 (((-112) $) NIL)) (-3246 (((-1170) $) NIL)) (-4412 (((-112) $) NIL)) (-3893 (((-112) $) NIL)) (-2201 (((-112) $) NIL)) (-4347 (((-1170) $) NIL)) (-3347 (((-112) $) NIL)) (-4024 (((-572) $) NIL)) (-3964 (((-1131) $) NIL)) (-2465 (((-112) $) NIL)) (-2379 (((-227) $) NIL)) (-1443 (((-870) $) NIL)) (-4121 (((-112) $ $) NIL)) (-2196 (($ $ (-572)) NIL) (($ $ (-652 (-572))) NIL)) (-4291 (((-652 $) $) NIL)) (-1835 (($ (-1170)) NIL) (($ (-1188)) NIL) (($ (-572)) NIL) (($ (-227)) NIL) (($ (-870)) NIL) (($ (-652 $)) NIL)) (-2940 (((-870) $) NIL)) (-4278 (($ $) NIL)) (-2878 (($ $) NIL)) (-4379 (((-112) $ $) NIL)) (-3967 (((-112) $) NIL)) (-2978 (((-112) $ $) NIL)) (-2860 (((-572) $) NIL))) 
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-NIL 
-(-1114 (-1170) (-1188) (-572) (-227) (-870)) 
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-NIL 
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+NIL 
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+NIL 
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T) ((-656 |#2|) |has| |#1| (-370)) ((-656 $) . T) ((-648 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-648 |#1|) |has| |#1| (-174)) ((-648 |#2|) |has| |#1| (-370)) ((-648 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-647 #3#) -12 (|has| |#1| (-370)) (|has| |#2| (-647 (-572)))) ((-647 |#2|) |has| |#1| (-370)) ((-725 #1#) -2813 (|has| |#1| (-370)) (|has| |#1| (-38 (-415 (-572))))) ((-725 |#1|) |has| |#1| (-174)) ((-725 |#2|) |has| |#1| (-370)) ((-725 $) -2813 (|has| |#1| (-564)) (|has| |#1| (-370))) ((-734) . 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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 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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"WFFINTBS" 3186662 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1287 3183655 3184082 3184544 "WEIER" 3185323 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1286 3182701 3183151 3183193 "VSPACE" 3183329 NIL VSPACE (NIL T) -9 NIL 3183403 NIL) (-1285 3182539 3182566 3182657 "VSPACE-" 3182662 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1284 3182348 3182390 3182458 "VOID" 3182493 T VOID (NIL) -8 NIL NIL NIL) (-1283 3180484 3180843 3181249 "VIEW" 3181964 T VIEW (NIL) -7 NIL NIL NIL) (-1282 3176908 3177547 3178284 "VIEWDEF" 3179769 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1281 3166212 3168456 3170629 "VIEW3D" 3174757 T VIEW3D (NIL) -8 NIL NIL NIL) (-1280 3158463 3160123 3161702 "VIEW2D" 3164655 T VIEW2D (NIL) -8 NIL NIL NIL) (-1279 3153816 3158233 3158325 "VECTOR" 3158406 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1278 3152393 3152652 3152970 "VECTOR2" 3153546 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1277 3145835 3150144 3150187 "VECTCAT" 3151182 NIL VECTCAT (NIL T) -9 NIL 3151769 NIL) (-1276 3144849 3145103 3145493 "VECTCAT-" 3145498 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1275 3144303 3144500 3144620 "VARIABLE" 3144764 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1274 3144236 3144241 3144271 "UTYPE" 3144276 T UTYPE (NIL) -9 NIL NIL NIL) (-1273 3143066 3143220 3143482 "UTSODETL" 3144062 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1272 3140506 3140966 3141490 "UTSODE" 3142607 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1271 3132344 3138132 3138621 "UTS" 3140075 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1270 3123131 3128500 3128543 "UTSCAT" 3129655 NIL UTSCAT (NIL T) -9 NIL 3130413 NIL) (-1269 3120479 3121201 3122190 "UTSCAT-" 3122195 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1268 3120106 3120149 3120282 "UTS2" 3120430 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1267 3114332 3116944 3116987 "URAGG" 3119057 NIL URAGG (NIL T) -9 NIL 3119780 NIL) (-1266 3111271 3112134 3113257 "URAGG-" 3113262 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1265 3106980 3109906 3110371 "UPXSSING" 3110935 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1264 3099046 3106227 3106500 "UPXS" 3106765 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1263 3092119 3098950 3099022 "UPXSCONS" 3099027 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1262 3081770 3088565 3088627 "UPXSCCA" 3089201 NIL UPXSCCA (NIL T T) -9 NIL 3089434 NIL) (-1261 3081408 3081493 3081667 "UPXSCCA-" 3081672 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1260 3070911 3077479 3077522 "UPXSCAT" 3078170 NIL UPXSCAT (NIL T) -9 NIL 3078779 NIL) (-1259 3070341 3070420 3070599 "UPXS2" 3070826 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1258 3068995 3069248 3069599 "UPSQFREE" 3070084 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1257 3062420 3065479 3065534 "UPSCAT" 3066614 NIL UPSCAT (NIL T T) -9 NIL 3067379 NIL) (-1256 3061624 3061831 3062158 "UPSCAT-" 3062163 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1255 3047120 3054977 3055020 "UPOLYC" 3057121 NIL UPOLYC (NIL T) -9 NIL 3058342 NIL) (-1254 3038448 3040874 3044021 "UPOLYC-" 3044026 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1253 3038075 3038118 3038251 "UPOLYC2" 3038399 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3029797 3037758 3037887 "UP" 3037994 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1251 3029136 3029243 3029407 "UPMP" 3029686 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1250 3028689 3028770 3028909 "UPDIVP" 3029049 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1249 3027257 3027506 3027822 "UPDECOMP" 3028438 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1248 3026488 3026600 3026786 "UPCDEN" 3027141 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1247 3026007 3026076 3026225 "UP2" 3026413 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1246 3024474 3025211 3025488 "UNISEG" 3025765 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1245 3023689 3023816 3024021 "UNISEG2" 3024317 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1244 3022749 3022929 3023155 "UNIFACT" 3023505 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1243 3006510 3021926 3022177 "ULS" 3022556 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1242 2994373 3006414 3006486 "ULSCONS" 3006491 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1241 2976073 2988197 2988259 "ULSCCAT" 2988897 NIL ULSCCAT (NIL T T) -9 NIL 2989186 NIL) (-1240 2975123 2975368 2975756 "ULSCCAT-" 2975761 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1239 2964410 2970892 2970935 "ULSCAT" 2971798 NIL ULSCAT (NIL T) -9 NIL 2972529 NIL) (-1238 2963840 2963919 2964098 "ULS2" 2964325 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1237 2962959 2963469 2963576 "UINT8" 2963687 T UINT8 (NIL) -8 NIL NIL 2963772) (-1236 2962077 2962587 2962694 "UINT64" 2962805 T UINT64 (NIL) -8 NIL NIL 2962890) (-1235 2961195 2961705 2961812 "UINT32" 2961923 T UINT32 (NIL) -8 NIL NIL 2962008) (-1234 2960313 2960823 2960930 "UINT16" 2961041 T UINT16 (NIL) -8 NIL NIL 2961126) (-1233 2958616 2959573 2959603 "UFD" 2959815 T UFD (NIL) -9 NIL 2959929 NIL) (-1232 2958410 2958456 2958551 "UFD-" 2958556 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1231 2957492 2957675 2957891 "UDVO" 2958216 T UDVO (NIL) -7 NIL NIL NIL) (-1230 2955308 2955717 2956188 "UDPO" 2957056 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1229 2955241 2955246 2955276 "TYPE" 2955281 T TYPE (NIL) -9 NIL NIL NIL) (-1228 2955001 2955196 2955227 "TYPEAST" 2955232 T TYPEAST (NIL) -8 NIL NIL NIL) (-1227 2953972 2954174 2954414 "TWOFACT" 2954795 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1226 2952995 2953381 2953616 "TUPLE" 2953772 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1225 2950686 2951205 2951744 "TUBETOOL" 2952478 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1224 2949535 2949740 2949981 "TUBE" 2950479 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1223 2944264 2948507 2948790 "TS" 2949287 NIL TS (NIL T) -8 NIL NIL NIL) (-1222 2932904 2937023 2937120 "TSETCAT" 2942389 NIL TSETCAT (NIL T T T T) -9 NIL 2943920 NIL) (-1221 2927636 2929236 2931127 "TSETCAT-" 2931132 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1220 2922275 2923122 2924051 "TRMANIP" 2926772 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1219 2921716 2921779 2921942 "TRIMAT" 2922207 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1218 2919582 2919819 2920176 "TRIGMNIP" 2921465 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1217 2919102 2919215 2919245 "TRIGCAT" 2919458 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1216 2918771 2918850 2918991 "TRIGCAT-" 2918996 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1215 2915616 2917629 2917910 "TREE" 2918525 NIL TREE (NIL T) -8 NIL NIL NIL) (-1214 2914890 2915418 2915448 "TRANFUN" 2915483 T TRANFUN (NIL) -9 NIL 2915549 NIL) (-1213 2914169 2914360 2914640 "TRANFUN-" 2914645 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1212 2913973 2914005 2914066 "TOPSP" 2914130 T TOPSP (NIL) -7 NIL NIL NIL) (-1211 2913321 2913436 2913590 "TOOLSIGN" 2913854 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1210 2911955 2912498 2912737 "TEXTFILE" 2913104 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1209 2909867 2910408 2910837 "TEX" 2911548 T TEX (NIL) -8 NIL NIL NIL) (-1208 2909648 2909679 2909751 "TEX1" 2909830 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1207 2909296 2909359 2909449 "TEMUTL" 2909580 T TEMUTL (NIL) -7 NIL NIL NIL) (-1206 2907450 2907730 2908055 "TBCMPPK" 2909019 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1205 2899227 2905610 2905666 "TBAGG" 2906066 NIL TBAGG (NIL T T) -9 NIL 2906277 NIL) (-1204 2894297 2895785 2897539 "TBAGG-" 2897544 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1203 2893681 2893788 2893933 "TANEXP" 2894186 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1202 2893192 2893456 2893546 "TALGOP" 2893626 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1201 2886582 2893049 2893142 "TABLE" 2893147 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1200 2885994 2886093 2886231 "TABLEAU" 2886479 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1199 2880602 2881822 2883070 "TABLBUMP" 2884780 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1198 2879824 2879971 2880152 "SYSTEM" 2880443 T SYSTEM (NIL) -8 NIL NIL NIL) (-1197 2876283 2876982 2877765 "SYSSOLP" 2879075 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1196 2876081 2876238 2876269 "SYSPTR" 2876274 T SYSPTR (NIL) -8 NIL NIL NIL) (-1195 2875117 2875622 2875741 "SYSNNI" 2875927 NIL SYSNNI (NIL NIL) -8 NIL NIL 2876012) (-1194 2874416 2874875 2874954 "SYSINT" 2875014 NIL SYSINT (NIL NIL) -8 NIL NIL 2875059) (-1193 2870748 2871694 2872404 "SYNTAX" 2873728 T SYNTAX (NIL) -8 NIL NIL NIL) (-1192 2867906 2868508 2869140 "SYMTAB" 2870138 T SYMTAB (NIL) -8 NIL NIL NIL) (-1191 2863155 2864057 2865040 "SYMS" 2866945 T SYMS (NIL) -8 NIL NIL NIL) (-1190 2860390 2862613 2862843 "SYMPOLY" 2862960 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1189 2859907 2859982 2860105 "SYMFUNC" 2860302 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1188 2855927 2857219 2858032 "SYMBOL" 2859116 T SYMBOL (NIL) -8 NIL NIL NIL) (-1187 2849466 2851155 2852875 "SWITCH" 2854229 T SWITCH (NIL) -8 NIL NIL NIL) (-1186 2842700 2848287 2848590 "SUTS" 2849221 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1185 2834766 2841947 2842220 "SUPXS" 2842485 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2826436 2834384 2834510 "SUP" 2834675 NIL SUP (NIL T) -8 NIL NIL NIL) (-1183 2825595 2825722 2825939 "SUPFRACF" 2826304 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1182 2825216 2825275 2825388 "SUP2" 2825530 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1181 2823664 2823938 2824294 "SUMRF" 2824915 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1180 2822999 2823065 2823257 "SUMFS" 2823585 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1179 2806795 2822176 2822427 "SULS" 2822806 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1178 2806397 2806617 2806687 "SUCHTAST" 2806747 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1177 2805692 2805922 2806062 "SUCH" 2806305 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1176 2799559 2800598 2801557 "SUBSPACE" 2804780 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1175 2798989 2799079 2799243 "SUBRESP" 2799447 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1174 2792357 2793654 2794965 "STTF" 2797725 NIL STTF (NIL T) -7 NIL NIL NIL) (-1173 2786530 2787650 2788797 "STTFNC" 2791257 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1172 2777843 2779712 2781506 "STTAYLOR" 2784771 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1171 2770973 2777707 2777790 "STRTBL" 2777795 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1170 2766337 2770928 2770959 "STRING" 2770964 T STRING (NIL) -8 NIL NIL NIL) (-1169 2761166 2765680 2765710 "STRICAT" 2765769 T STRICAT (NIL) -9 NIL 2765831 NIL) (-1168 2753919 2758785 2759396 "STREAM" 2760590 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1167 2753429 2753506 2753650 "STREAM3" 2753836 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1166 2752411 2752594 2752829 "STREAM2" 2753242 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1165 2752099 2752151 2752244 "STREAM1" 2752353 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1164 2751115 2751296 2751527 "STINPROD" 2751915 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1163 2750667 2750877 2750907 "STEP" 2750987 T STEP (NIL) -9 NIL 2751065 NIL) (-1162 2749854 2750156 2750304 "STEPAST" 2750541 T STEPAST (NIL) -8 NIL NIL NIL) (-1161 2743286 2749753 2749830 "STBL" 2749835 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1160 2738381 2742477 2742520 "STAGG" 2742673 NIL STAGG (NIL T) -9 NIL 2742762 NIL) (-1159 2736083 2736685 2737557 "STAGG-" 2737562 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1158 2734230 2735853 2735945 "STACK" 2736026 NIL STACK (NIL T) -8 NIL NIL NIL) (-1157 2726925 2732371 2732827 "SREGSET" 2733860 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1156 2719350 2720719 2722232 "SRDCMPK" 2725531 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1155 2712235 2716760 2716790 "SRAGG" 2718093 T SRAGG (NIL) -9 NIL 2718701 NIL) (-1154 2711252 2711507 2711886 "SRAGG-" 2711891 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1153 2705623 2710199 2710620 "SQMATRIX" 2710878 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1152 2699308 2702341 2703068 "SPLTREE" 2704968 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1151 2695271 2695964 2696610 "SPLNODE" 2698734 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1150 2694318 2694551 2694581 "SPFCAT" 2695025 T SPFCAT (NIL) -9 NIL NIL NIL) (-1149 2693055 2693265 2693529 "SPECOUT" 2694076 T SPECOUT (NIL) -7 NIL NIL NIL) (-1148 2684165 2686037 2686067 "SPADXPT" 2690743 T SPADXPT (NIL) -9 NIL 2692907 NIL) (-1147 2683926 2683966 2684035 "SPADPRSR" 2684118 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1146 2681975 2683881 2683912 "SPADAST" 2683917 T SPADAST (NIL) -8 NIL NIL NIL) (-1145 2673920 2675693 2675736 "SPACEC" 2680109 NIL SPACEC (NIL T) -9 NIL 2681925 NIL) (-1144 2672050 2673852 2673901 "SPACE3" 2673906 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1143 2670802 2670973 2671264 "SORTPAK" 2671855 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1142 2668894 2669197 2669609 "SOLVETRA" 2670466 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1141 2667944 2668166 2668427 "SOLVESER" 2668667 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1140 2663248 2664136 2665131 "SOLVERAD" 2666996 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1139 2659063 2659672 2660401 "SOLVEFOR" 2662615 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1138 2653333 2658412 2658509 "SNTSCAT" 2658514 NIL SNTSCAT (NIL T T T T) -9 NIL 2658584 NIL) (-1137 2647439 2651656 2652047 "SMTS" 2653023 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1136 2642035 2647327 2647404 "SMP" 2647409 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1135 2640194 2640495 2640893 "SMITH" 2641732 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1134 2632747 2637033 2637136 "SMATCAT" 2638487 NIL SMATCAT (NIL NIL T T T) -9 NIL 2639037 NIL) (-1133 2629465 2630350 2631608 "SMATCAT-" 2631613 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1132 2627131 2628701 2628744 "SKAGG" 2629005 NIL SKAGG (NIL T) -9 NIL 2629140 NIL) (-1131 2623407 2626604 2626788 "SINT" 2626940 T SINT (NIL) -8 NIL NIL 2627102) (-1130 2623179 2623217 2623283 "SIMPAN" 2623363 T SIMPAN (NIL) -7 NIL NIL NIL) (-1129 2622458 2622714 2622854 "SIG" 2623061 T SIG (NIL) -8 NIL NIL NIL) (-1128 2621296 2621517 2621792 "SIGNRF" 2622217 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1127 2620129 2620280 2620564 "SIGNEF" 2621125 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1126 2619435 2619712 2619836 "SIGAST" 2620027 T SIGAST (NIL) -8 NIL NIL NIL) (-1125 2617125 2617579 2618085 "SHP" 2618976 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1124 2610840 2617026 2617102 "SHDP" 2617107 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1123 2610413 2610605 2610635 "SGROUP" 2610728 T SGROUP (NIL) -9 NIL 2610790 NIL) (-1122 2610271 2610297 2610370 "SGROUP-" 2610375 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1121 2607062 2607760 2608483 "SGCF" 2609570 T SGCF (NIL) -7 NIL NIL NIL) (-1120 2601430 2606509 2606606 "SFRTCAT" 2606611 NIL SFRTCAT (NIL T T T T) -9 NIL 2606650 NIL) (-1119 2594851 2595869 2597005 "SFRGCD" 2600413 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1118 2587977 2589050 2590236 "SFQCMPK" 2593784 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1117 2587597 2587686 2587797 "SFORT" 2587918 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1116 2586715 2587437 2587558 "SEXOF" 2587563 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1115 2585822 2586596 2586664 "SEX" 2586669 T SEX (NIL) -8 NIL NIL NIL) (-1114 2581603 2582318 2582413 "SEXCAT" 2585035 NIL SEXCAT (NIL T T T T T) -9 NIL 2585595 NIL) (-1113 2578756 2581537 2581585 "SET" 2581590 NIL SET (NIL T) -8 NIL NIL NIL) (-1112 2576980 2577469 2577774 "SETMN" 2578497 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1111 2576476 2576628 2576658 "SETCAT" 2576834 T SETCAT (NIL) -9 NIL 2576944 NIL) (-1110 2576168 2576246 2576376 "SETCAT-" 2576381 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1109 2572529 2574629 2574672 "SETAGG" 2575542 NIL SETAGG (NIL T) -9 NIL 2575882 NIL) (-1108 2571987 2572103 2572340 "SETAGG-" 2572345 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1107 2571430 2571683 2571784 "SEQAST" 2571908 T SEQAST (NIL) -8 NIL NIL NIL) (-1106 2570629 2570923 2570984 "SEGXCAT" 2571270 NIL SEGXCAT (NIL T T) -9 NIL 2571390 NIL) (-1105 2569635 2570295 2570477 "SEG" 2570482 NIL SEG (NIL T) -8 NIL NIL NIL) (-1104 2568614 2568828 2568871 "SEGCAT" 2569393 NIL SEGCAT (NIL T) -9 NIL 2569614 NIL) (-1103 2567546 2567977 2568185 "SEGBIND" 2568441 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1102 2567167 2567226 2567339 "SEGBIND2" 2567481 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1101 2566740 2566968 2567045 "SEGAST" 2567112 T SEGAST (NIL) -8 NIL NIL NIL) (-1100 2565959 2566085 2566289 "SEG2" 2566584 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1099 2565369 2565894 2565941 "SDVAR" 2565946 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1098 2557807 2565139 2565269 "SDPOL" 2565274 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1097 2556400 2556666 2556985 "SCPKG" 2557522 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1096 2555564 2555736 2555928 "SCOPE" 2556230 T SCOPE (NIL) -8 NIL NIL NIL) (-1095 2554784 2554918 2555097 "SCACHE" 2555419 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1094 2554430 2554616 2554646 "SASTCAT" 2554651 T SASTCAT (NIL) -9 NIL 2554664 NIL) (-1093 2553917 2554265 2554341 "SAOS" 2554376 T SAOS (NIL) -8 NIL NIL NIL) (-1092 2553482 2553517 2553690 "SAERFFC" 2553876 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1091 2547332 2553379 2553459 "SAE" 2553464 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1090 2546925 2546960 2547119 "SAEFACT" 2547291 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1089 2545246 2545560 2545961 "RURPK" 2546591 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1088 2543883 2544189 2544494 "RULESET" 2545080 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1087 2541106 2541636 2542094 "RULE" 2543564 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1086 2540718 2540900 2540983 "RULECOLD" 2541058 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1085 2540508 2540536 2540607 "RTVALUE" 2540669 T RTVALUE (NIL) -8 NIL NIL NIL) (-1084 2539979 2540225 2540319 "RSTRCAST" 2540436 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1083 2534827 2535622 2536542 "RSETGCD" 2539178 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1082 2524057 2529136 2529233 "RSETCAT" 2533352 NIL RSETCAT (NIL T T T T) -9 NIL 2534449 NIL) (-1081 2521984 2522523 2523347 "RSETCAT-" 2523352 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1080 2514370 2515746 2517266 "RSDCMPK" 2520583 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1079 2512349 2512816 2512890 "RRCC" 2513976 NIL RRCC (NIL T T) -9 NIL 2514320 NIL) (-1078 2511700 2511874 2512153 "RRCC-" 2512158 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1077 2511143 2511396 2511497 "RPTAST" 2511621 T RPTAST (NIL) -8 NIL NIL NIL) (-1076 2484859 2494307 2494374 "RPOLCAT" 2505040 NIL RPOLCAT (NIL T T T) -9 NIL 2508200 NIL) (-1075 2476357 2478697 2481819 "RPOLCAT-" 2481824 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1074 2467288 2474568 2475050 "ROUTINE" 2475897 T ROUTINE (NIL) -8 NIL NIL NIL) (-1073 2464035 2466914 2467054 "ROMAN" 2467170 T ROMAN (NIL) -8 NIL NIL NIL) (-1072 2462279 2462895 2463155 "ROIRC" 2463840 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1071 2458511 2460795 2460825 "RNS" 2461129 T RNS (NIL) -9 NIL 2461403 NIL) (-1070 2457020 2457403 2457937 "RNS-" 2458012 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1069 2456423 2456831 2456861 "RNG" 2456866 T RNG (NIL) -9 NIL 2456887 NIL) (-1068 2455426 2455788 2455990 "RNGBIND" 2456274 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1067 2454825 2455213 2455256 "RMODULE" 2455261 NIL RMODULE (NIL T) -9 NIL 2455288 NIL) (-1066 2453661 2453755 2454091 "RMCAT2" 2454726 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1065 2450511 2453007 2453304 "RMATRIX" 2453423 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1064 2443338 2445598 2445713 "RMATCAT" 2449072 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2450054 NIL) (-1063 2442713 2442860 2443167 "RMATCAT-" 2443172 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1062 2442114 2442335 2442378 "RLINSET" 2442572 NIL RLINSET (NIL T) -9 NIL 2442663 NIL) (-1061 2441681 2441756 2441884 "RINTERP" 2442033 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1060 2440739 2441293 2441323 "RING" 2441379 T RING (NIL) -9 NIL 2441471 NIL) (-1059 2440531 2440575 2440672 "RING-" 2440677 NIL RING- (NIL T) -8 NIL NIL NIL) (-1058 2439372 2439609 2439867 "RIDIST" 2440295 T RIDIST (NIL) -7 NIL NIL NIL) (-1057 2430661 2438840 2439046 "RGCHAIN" 2439220 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1056 2430011 2430417 2430458 "RGBCSPC" 2430516 NIL RGBCSPC (NIL T) -9 NIL 2430568 NIL) (-1055 2429169 2429550 2429591 "RGBCMDL" 2429823 NIL RGBCMDL (NIL T) -9 NIL 2429937 NIL) (-1054 2426163 2426777 2427447 "RF" 2428533 NIL RF (NIL T) -7 NIL NIL NIL) (-1053 2425809 2425872 2425975 "RFFACTOR" 2426094 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1052 2425534 2425569 2425666 "RFFACT" 2425768 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1051 2423651 2424015 2424397 "RFDIST" 2425174 T RFDIST (NIL) -7 NIL NIL NIL) (-1050 2423104 2423196 2423359 "RETSOL" 2423553 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1049 2422740 2422820 2422863 "RETRACT" 2422996 NIL RETRACT (NIL T) -9 NIL 2423083 NIL) (-1048 2422589 2422614 2422701 "RETRACT-" 2422706 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1047 2422191 2422411 2422481 "RETAST" 2422541 T RETAST (NIL) -8 NIL NIL NIL) (-1046 2414929 2421844 2421971 "RESULT" 2422086 T RESULT (NIL) -8 NIL NIL NIL) (-1045 2413520 2414198 2414397 "RESRING" 2414832 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1044 2413156 2413205 2413303 "RESLATC" 2413457 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1043 2412861 2412896 2413003 "REPSQ" 2413115 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1042 2410283 2410863 2411465 "REP" 2412281 T REP (NIL) -7 NIL NIL NIL) (-1041 2409980 2410015 2410126 "REPDB" 2410242 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1040 2403880 2405269 2406492 "REP2" 2408792 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1039 2400257 2400938 2401746 "REP1" 2403107 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1038 2392953 2398398 2398854 "REGSET" 2399887 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1037 2391718 2392101 2392351 "REF" 2392738 NIL REF (NIL T) -8 NIL NIL NIL) (-1036 2391095 2391198 2391365 "REDORDER" 2391602 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1035 2387063 2390308 2390535 "RECLOS" 2390923 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1034 2386115 2386296 2386511 "REALSOLV" 2386870 T REALSOLV (NIL) -7 NIL NIL NIL) (-1033 2385961 2386002 2386032 "REAL" 2386037 T REAL (NIL) -9 NIL 2386072 NIL) (-1032 2382444 2383246 2384130 "REAL0Q" 2385126 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1031 2378045 2379033 2380094 "REAL0" 2381425 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1030 2377516 2377762 2377856 "RDUCEAST" 2377973 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1029 2376921 2376993 2377200 "RDIV" 2377438 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1028 2375989 2376163 2376376 "RDIST" 2376743 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1027 2374586 2374873 2375245 "RDETRS" 2375697 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1026 2372398 2372852 2373390 "RDETR" 2374128 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1025 2371023 2371301 2371698 "RDEEFS" 2372114 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1024 2369532 2369838 2370263 "RDEEF" 2370711 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1023 2363593 2366513 2366543 "RCFIELD" 2367838 T RCFIELD (NIL) -9 NIL 2368569 NIL) (-1022 2361657 2362161 2362857 "RCFIELD-" 2362932 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1021 2357926 2359758 2359801 "RCAGG" 2360885 NIL RCAGG (NIL T) -9 NIL 2361350 NIL) (-1020 2357554 2357648 2357811 "RCAGG-" 2357816 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1019 2356889 2357001 2357166 "RATRET" 2357438 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1018 2356442 2356509 2356630 "RATFACT" 2356817 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1017 2355750 2355870 2356022 "RANDSRC" 2356312 T RANDSRC (NIL) -7 NIL NIL NIL) (-1016 2355484 2355528 2355601 "RADUTIL" 2355699 T RADUTIL (NIL) -7 NIL NIL NIL) (-1015 2348505 2354315 2354626 "RADIX" 2355207 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1014 2340021 2348347 2348477 "RADFF" 2348482 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1013 2339668 2339743 2339773 "RADCAT" 2339933 T RADCAT (NIL) -9 NIL NIL NIL) (-1012 2339450 2339498 2339598 "RADCAT-" 2339603 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1011 2337548 2339220 2339312 "QUEUE" 2339393 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1010 2333996 2337481 2337529 "QUAT" 2337534 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1009 2333627 2333670 2333801 "QUATCT2" 2333947 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1008 2326850 2330285 2330327 "QUATCAT" 2331118 NIL QUATCAT (NIL T) -9 NIL 2331884 NIL) (-1007 2322989 2324026 2325416 "QUATCAT-" 2325512 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1006 2320454 2322065 2322108 "QUAGG" 2322489 NIL QUAGG (NIL T) -9 NIL 2322664 NIL) (-1005 2320056 2320276 2320346 "QQUTAST" 2320406 T QQUTAST (NIL) -8 NIL NIL NIL) (-1004 2319069 2319569 2319734 "QFORM" 2319937 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1003 2309903 2315231 2315273 "QFCAT" 2315941 NIL QFCAT (NIL T) -9 NIL 2316942 NIL) (-1002 2305248 2306511 2308185 "QFCAT-" 2308281 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2304879 2304922 2305053 "QFCAT2" 2305199 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1000 2304334 2304444 2304576 "QEQUAT" 2304769 T QEQUAT (NIL) -8 NIL NIL NIL) (-999 2297480 2298553 2299737 "QCMPACK" 2303267 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-998 2295029 2295477 2295905 "QALGSET" 2297135 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-997 2294274 2294448 2294680 "QALGSET2" 2294849 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-996 2292964 2293188 2293505 "PWFFINTB" 2294047 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-995 2291146 2291314 2291668 "PUSHVAR" 2292778 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-994 2287064 2288118 2288159 "PTRANFN" 2290043 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-993 2285466 2285757 2286079 "PTPACK" 2286775 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-992 2285098 2285155 2285264 "PTFUNC2" 2285403 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-991 2279543 2283940 2283981 "PTCAT" 2284277 NIL PTCAT (NIL T) -9 NIL 2284430 NIL) (-990 2279201 2279236 2279360 "PSQFR" 2279502 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-989 2277796 2278094 2278428 "PSEUDLIN" 2278899 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-988 2264559 2266930 2269254 "PSETPK" 2275556 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-987 2257577 2260317 2260413 "PSETCAT" 2263434 NIL PSETCAT (NIL T T T T) -9 NIL 2264248 NIL) (-986 2255413 2256047 2256868 "PSETCAT-" 2256873 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-985 2254762 2254927 2254955 "PSCURVE" 2255223 T PSCURVE (NIL) -9 NIL 2255390 NIL) (-984 2250760 2252276 2252341 "PSCAT" 2253185 NIL PSCAT (NIL T T T) -9 NIL 2253425 NIL) (-983 2249823 2250039 2250439 "PSCAT-" 2250444 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-982 2248182 2248892 2249155 "PRTITION" 2249580 T PRTITION (NIL) -8 NIL NIL NIL) (-981 2247657 2247903 2247995 "PRTDAST" 2248110 T PRTDAST (NIL) -8 NIL NIL NIL) (-980 2236747 2238961 2241149 "PRS" 2245519 NIL PRS (NIL T T) -7 NIL NIL NIL) (-979 2234558 2236097 2236137 "PRQAGG" 2236320 NIL PRQAGG (NIL T) -9 NIL 2236422 NIL) (-978 2233894 2234199 2234227 "PROPLOG" 2234366 T PROPLOG (NIL) -9 NIL 2234481 NIL) (-977 2233498 2233555 2233678 "PROPFUN2" 2233817 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-976 2232813 2232934 2233106 "PROPFUN1" 2233359 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-975 2230994 2231560 2231857 "PROPFRML" 2232549 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-974 2230463 2230570 2230698 "PROPERTY" 2230886 T PROPERTY (NIL) -8 NIL NIL NIL) (-973 2224521 2228629 2229449 "PRODUCT" 2229689 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-972 2221799 2223979 2224213 "PR" 2224332 NIL PR (NIL T T) -8 NIL NIL NIL) (-971 2221595 2221627 2221686 "PRINT" 2221760 T PRINT (NIL) -7 NIL NIL NIL) (-970 2220935 2221052 2221204 "PRIMES" 2221475 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-969 2219000 2219401 2219867 "PRIMELT" 2220514 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-968 2218729 2218778 2218806 "PRIMCAT" 2218930 T PRIMCAT (NIL) -9 NIL NIL NIL) (-967 2214844 2218667 2218712 "PRIMARR" 2218717 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-966 2213851 2214029 2214257 "PRIMARR2" 2214662 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-965 2213494 2213550 2213661 "PREASSOC" 2213789 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-964 2212969 2213102 2213130 "PPCURVE" 2213335 T PPCURVE (NIL) -9 NIL 2213471 NIL) (-963 2212564 2212764 2212847 "PORTNUM" 2212906 T PORTNUM (NIL) -8 NIL NIL NIL) (-962 2209923 2210322 2210914 "POLYROOT" 2212145 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-961 2204016 2209527 2209687 "POLY" 2209796 NIL POLY (NIL T) -8 NIL NIL NIL) (-960 2203399 2203457 2203691 "POLYLIFT" 2203952 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-959 2199674 2200123 2200752 "POLYCATQ" 2202944 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-958 2186256 2191473 2191538 "POLYCAT" 2195052 NIL POLYCAT (NIL T T T) -9 NIL 2196930 NIL) (-957 2179483 2181407 2183871 "POLYCAT-" 2183876 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-956 2179070 2179138 2179258 "POLY2UP" 2179409 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-955 2178702 2178759 2178868 "POLY2" 2179007 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-954 2177387 2177626 2177902 "POLUTIL" 2178476 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-953 2175742 2176019 2176350 "POLTOPOL" 2177109 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-952 2171207 2175678 2175724 "POINT" 2175729 NIL POINT (NIL T) -8 NIL NIL NIL) (-951 2169394 2169751 2170126 "PNTHEORY" 2170852 T PNTHEORY (NIL) -7 NIL NIL NIL) (-950 2167852 2168149 2168548 "PMTOOLS" 2169092 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-949 2167445 2167523 2167640 "PMSYM" 2167768 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-948 2166953 2167022 2167197 "PMQFCAT" 2167370 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-947 2166308 2166418 2166574 "PMPRED" 2166830 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-946 2165701 2165787 2165949 "PMPREDFS" 2166209 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-945 2164365 2164573 2164951 "PMPLCAT" 2165463 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-944 2163897 2163976 2164128 "PMLSAGG" 2164280 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-943 2163370 2163446 2163628 "PMKERNEL" 2163815 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-942 2162987 2163062 2163175 "PMINS" 2163289 NIL PMINS (NIL T) -7 NIL NIL NIL) (-941 2162429 2162498 2162707 "PMFS" 2162912 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-940 2161657 2161775 2161980 "PMDOWN" 2162306 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-939 2160824 2160982 2161163 "PMASS" 2161496 T PMASS (NIL) -7 NIL NIL NIL) (-938 2160097 2160207 2160370 "PMASSFS" 2160711 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-937 2159752 2159820 2159914 "PLOTTOOL" 2160023 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-936 2154359 2155563 2156711 "PLOT" 2158624 T PLOT (NIL) -8 NIL NIL NIL) (-935 2150163 2151207 2152128 "PLOT3D" 2153458 T PLOT3D (NIL) -8 NIL NIL NIL) (-934 2149075 2149252 2149487 "PLOT1" 2149967 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-933 2124466 2129141 2133992 "PLEQN" 2144341 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-932 2123784 2123906 2124086 "PINTERP" 2124331 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-931 2123477 2123524 2123627 "PINTERPA" 2123731 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-930 2122693 2123241 2123328 "PI" 2123368 T PI (NIL) -8 NIL NIL 2123435) (-929 2120990 2121965 2121993 "PID" 2122175 T PID (NIL) -9 NIL 2122309 NIL) (-928 2120741 2120778 2120853 "PICOERCE" 2120947 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-927 2120061 2120200 2120376 "PGROEB" 2120597 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-926 2115648 2116462 2117367 "PGE" 2119176 T PGE (NIL) -7 NIL NIL NIL) (-925 2113771 2114018 2114384 "PGCD" 2115365 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-924 2113109 2113212 2113373 "PFRPAC" 2113655 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-923 2109749 2111657 2112010 "PFR" 2112788 NIL PFR (NIL T) -8 NIL NIL NIL) (-922 2108138 2108382 2108707 "PFOTOOLS" 2109496 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-921 2106671 2106910 2107261 "PFOQ" 2107895 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-920 2105172 2105384 2105740 "PFO" 2106455 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-919 2101725 2105061 2105130 "PF" 2105135 NIL PF (NIL NIL) -8 NIL NIL NIL) (-918 2099059 2100330 2100358 "PFECAT" 2100943 T PFECAT (NIL) -9 NIL 2101327 NIL) (-917 2098504 2098658 2098872 "PFECAT-" 2098877 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-916 2097107 2097359 2097660 "PFBRU" 2098253 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-915 2094973 2095325 2095757 "PFBR" 2096758 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-914 2091019 2092485 2093132 "PERM" 2094359 NIL PERM (NIL T) -8 NIL NIL NIL) (-913 2086253 2087226 2088096 "PERMGRP" 2090182 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-912 2084372 2085332 2085373 "PERMCAT" 2085773 NIL PERMCAT (NIL T) -9 NIL 2086071 NIL) (-911 2084025 2084066 2084190 "PERMAN" 2084325 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-910 2081513 2083690 2083812 "PENDTREE" 2083936 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-909 2079537 2080305 2080346 "PDRING" 2081003 NIL PDRING (NIL T) -9 NIL 2081289 NIL) (-908 2078640 2078858 2079220 "PDRING-" 2079225 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-907 2075855 2076633 2077301 "PDEPROB" 2077992 T PDEPROB (NIL) -8 NIL NIL NIL) (-906 2073400 2073904 2074459 "PDEPACK" 2075320 T PDEPACK (NIL) -7 NIL NIL NIL) (-905 2072312 2072502 2072753 "PDECOMP" 2073199 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-904 2069891 2070734 2070762 "PDECAT" 2071549 T PDECAT (NIL) -9 NIL 2072262 NIL) (-903 2069642 2069675 2069765 "PCOMP" 2069852 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-902 2067820 2068443 2068740 "PBWLB" 2069371 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-901 2060293 2061893 2063231 "PATTERN" 2066503 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-900 2059925 2059982 2060091 "PATTERN2" 2060230 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-899 2057682 2058070 2058527 "PATTERN1" 2059514 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-898 2055050 2055631 2056112 "PATRES" 2057247 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-897 2054614 2054681 2054813 "PATRES2" 2054977 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-896 2052497 2052902 2053309 "PATMATCH" 2054281 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-895 2052007 2052216 2052257 "PATMAB" 2052364 NIL PATMAB (NIL T) -9 NIL 2052447 NIL) (-894 2050525 2050861 2051119 "PATLRES" 2051812 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-893 2050071 2050194 2050235 "PATAB" 2050240 NIL PATAB (NIL T) -9 NIL 2050412 NIL) (-892 2048253 2048648 2049071 "PARTPERM" 2049668 T PARTPERM (NIL) -7 NIL NIL NIL) (-891 2047874 2047937 2048039 "PARSURF" 2048184 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-890 2047506 2047563 2047672 "PARSU2" 2047811 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-889 2047270 2047310 2047377 "PARSER" 2047459 T PARSER (NIL) -7 NIL NIL NIL) (-888 2046891 2046954 2047056 "PARSCURV" 2047201 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-887 2046523 2046580 2046689 "PARSC2" 2046828 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-886 2046162 2046220 2046317 "PARPCURV" 2046459 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-885 2045794 2045851 2045960 "PARPC2" 2046099 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-884 2044855 2045167 2045349 "PARAMAST" 2045632 T PARAMAST (NIL) -8 NIL NIL NIL) (-883 2044375 2044461 2044580 "PAN2EXPR" 2044756 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-882 2043152 2043496 2043724 "PALETTE" 2044167 T PALETTE (NIL) -8 NIL NIL NIL) (-881 2041545 2042157 2042517 "PAIR" 2042838 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-880 2035324 2040802 2040997 "PADICRC" 2041399 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-879 2028448 2034668 2034853 "PADICRAT" 2035171 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-878 2026763 2028385 2028430 "PADIC" 2028435 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-877 2023873 2025437 2025477 "PADICCT" 2026058 NIL PADICCT (NIL NIL) -9 NIL 2026340 NIL) (-876 2022830 2023030 2023298 "PADEPAC" 2023660 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-875 2022042 2022175 2022381 "PADE" 2022692 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-874 2020429 2021250 2021530 "OWP" 2021846 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-873 2019922 2020135 2020232 "OVERSET" 2020352 T OVERSET (NIL) -8 NIL NIL NIL) (-872 2018968 2019527 2019699 "OVAR" 2019790 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-871 2018232 2018353 2018514 "OUT" 2018827 T OUT (NIL) -7 NIL NIL NIL) (-870 2007104 2009341 2011541 "OUTFORM" 2016052 T OUTFORM (NIL) -8 NIL NIL NIL) (-869 2006440 2006701 2006828 "OUTBFILE" 2006997 T OUTBFILE (NIL) -8 NIL NIL NIL) (-868 2005747 2005912 2005940 "OUTBCON" 2006258 T OUTBCON (NIL) -9 NIL 2006424 NIL) (-867 2005348 2005460 2005617 "OUTBCON-" 2005622 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-866 2004728 2005077 2005166 "OSI" 2005279 T OSI (NIL) -8 NIL NIL NIL) (-865 2004258 2004596 2004624 "OSGROUP" 2004629 T OSGROUP (NIL) -9 NIL 2004651 NIL) (-864 2003003 2003230 2003515 "ORTHPOL" 2004005 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-863 2000554 2002838 2002959 "OREUP" 2002964 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-862 1997957 2000245 2000372 "ORESUP" 2000496 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-861 1995485 1995985 1996546 "OREPCTO" 1997446 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-860 1989171 1991372 1991413 "OREPCAT" 1993761 NIL OREPCAT (NIL T) -9 NIL 1994865 NIL) (-859 1986318 1987100 1988158 "OREPCAT-" 1988163 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-858 1985469 1985767 1985795 "ORDSET" 1986104 T ORDSET (NIL) -9 NIL 1986268 NIL) (-857 1984900 1985048 1985272 "ORDSET-" 1985277 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-856 1983465 1984256 1984284 "ORDRING" 1984486 T ORDRING (NIL) -9 NIL 1984611 NIL) (-855 1983110 1983204 1983348 "ORDRING-" 1983353 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-854 1982490 1982953 1982981 "ORDMON" 1982986 T ORDMON (NIL) -9 NIL 1983007 NIL) (-853 1981652 1981799 1981994 "ORDFUNS" 1982339 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-852 1980990 1981409 1981437 "ORDFIN" 1981502 T ORDFIN (NIL) -9 NIL 1981576 NIL) (-851 1977549 1979576 1979985 "ORDCOMP" 1980614 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-850 1976815 1976942 1977128 "ORDCOMP2" 1977409 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-849 1973396 1974306 1975120 "OPTPROB" 1976021 T OPTPROB (NIL) -8 NIL NIL NIL) (-848 1970198 1970837 1971541 "OPTPACK" 1972712 T OPTPACK (NIL) -7 NIL NIL NIL) (-847 1967885 1968651 1968679 "OPTCAT" 1969498 T OPTCAT (NIL) -9 NIL 1970148 NIL) (-846 1967269 1967562 1967667 "OPSIG" 1967800 T OPSIG (NIL) -8 NIL NIL NIL) (-845 1967037 1967076 1967142 "OPQUERY" 1967223 T OPQUERY (NIL) -7 NIL NIL NIL) (-844 1964168 1965348 1965852 "OP" 1966566 NIL OP (NIL T) -8 NIL NIL NIL) (-843 1963542 1963768 1963809 "OPERCAT" 1964021 NIL OPERCAT (NIL T) -9 NIL 1964118 NIL) (-842 1963297 1963353 1963470 "OPERCAT-" 1963475 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-841 1960110 1962094 1962463 "ONECOMP" 1962961 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-840 1959415 1959530 1959704 "ONECOMP2" 1959982 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-839 1958834 1958940 1959070 "OMSERVER" 1959305 T OMSERVER (NIL) -7 NIL NIL NIL) (-838 1955696 1958274 1958314 "OMSAGG" 1958375 NIL OMSAGG (NIL T) -9 NIL 1958439 NIL) (-837 1954319 1954582 1954864 "OMPKG" 1955434 T OMPKG (NIL) -7 NIL NIL NIL) (-836 1953749 1953852 1953880 "OM" 1954179 T OM (NIL) -9 NIL NIL NIL) (-835 1952296 1953298 1953467 "OMLO" 1953630 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-834 1951256 1951403 1951623 "OMEXPR" 1952122 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-833 1950547 1950802 1950938 "OMERR" 1951140 T OMERR (NIL) -8 NIL NIL NIL) (-832 1949698 1949968 1950128 "OMERRK" 1950407 T OMERRK (NIL) -8 NIL NIL NIL) (-831 1949149 1949375 1949483 "OMENC" 1949610 T OMENC (NIL) -8 NIL NIL NIL) (-830 1943044 1944229 1945400 "OMDEV" 1947998 T OMDEV (NIL) -8 NIL NIL NIL) (-829 1942113 1942284 1942478 "OMCONN" 1942870 T OMCONN (NIL) -8 NIL NIL NIL) (-828 1940634 1941610 1941638 "OINTDOM" 1941643 T OINTDOM (NIL) -9 NIL 1941664 NIL) (-827 1937972 1939322 1939659 "OFMONOID" 1940329 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-826 1937383 1937909 1937954 "ODVAR" 1937959 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-825 1934806 1937128 1937283 "ODR" 1937288 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-824 1927298 1934582 1934708 "ODPOL" 1934713 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-823 1920983 1927170 1927275 "ODP" 1927280 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-822 1919749 1919964 1920239 "ODETOOLS" 1920757 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-821 1916716 1917374 1918090 "ODESYS" 1919082 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-820 1911598 1912506 1913531 "ODERTRIC" 1915791 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-819 1911024 1911106 1911300 "ODERED" 1911510 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-818 1907912 1908460 1909137 "ODERAT" 1910447 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-817 1904871 1905336 1905933 "ODEPRRIC" 1907441 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-816 1902814 1903410 1903896 "ODEPROB" 1904405 T ODEPROB (NIL) -8 NIL NIL NIL) (-815 1899334 1899819 1900466 "ODEPRIM" 1902293 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-814 1898583 1898685 1898945 "ODEPAL" 1899226 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-813 1894745 1895536 1896400 "ODEPACK" 1897739 T ODEPACK (NIL) -7 NIL NIL NIL) (-812 1893806 1893913 1894135 "ODEINT" 1894634 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-811 1887907 1889332 1890779 "ODEIFTBL" 1892379 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-810 1883305 1884091 1885043 "ODEEF" 1887066 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-809 1882654 1882743 1882966 "ODECONST" 1883210 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-808 1880779 1881440 1881468 "ODECAT" 1882073 T ODECAT (NIL) -9 NIL 1882604 NIL) (-807 1877634 1880484 1880606 "OCT" 1880689 NIL OCT (NIL T) -8 NIL NIL NIL) (-806 1877272 1877315 1877442 "OCTCT2" 1877585 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-805 1871883 1874318 1874358 "OC" 1875455 NIL OC (NIL T) -9 NIL 1876313 NIL) (-804 1869110 1869858 1870848 "OC-" 1870942 NIL OC- (NIL T T) -8 NIL NIL NIL) (-803 1868462 1868930 1868958 "OCAMON" 1868963 T OCAMON (NIL) -9 NIL 1868984 NIL) (-802 1867993 1868334 1868362 "OASGP" 1868367 T OASGP (NIL) -9 NIL 1868387 NIL) (-801 1867254 1867743 1867771 "OAMONS" 1867811 T OAMONS (NIL) -9 NIL 1867854 NIL) (-800 1866668 1867101 1867129 "OAMON" 1867134 T OAMON (NIL) -9 NIL 1867154 NIL) (-799 1865926 1866444 1866472 "OAGROUP" 1866477 T OAGROUP (NIL) -9 NIL 1866497 NIL) (-798 1865616 1865666 1865754 "NUMTUBE" 1865870 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-797 1859189 1860707 1862243 "NUMQUAD" 1864100 T NUMQUAD (NIL) -7 NIL NIL NIL) (-796 1854945 1855933 1856958 "NUMODE" 1858184 T NUMODE (NIL) -7 NIL NIL NIL) (-795 1852300 1853180 1853208 "NUMINT" 1854131 T NUMINT (NIL) -9 NIL 1854895 NIL) (-794 1851248 1851445 1851663 "NUMFMT" 1852102 T NUMFMT (NIL) -7 NIL NIL NIL) (-793 1837607 1840552 1843084 "NUMERIC" 1848755 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-792 1831977 1837056 1837151 "NTSCAT" 1837156 NIL NTSCAT (NIL T T T T) -9 NIL 1837195 NIL) (-791 1831171 1831336 1831529 "NTPOLFN" 1831816 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-790 1819159 1827996 1828808 "NSUP" 1830392 NIL NSUP (NIL T) -8 NIL NIL NIL) (-789 1818791 1818848 1818957 "NSUP2" 1819096 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-788 1808928 1818565 1818698 "NSMP" 1818703 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-787 1807360 1807661 1808018 "NREP" 1808616 NIL NREP (NIL T) -7 NIL NIL NIL) (-786 1805951 1806203 1806561 "NPCOEF" 1807103 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-785 1805017 1805132 1805348 "NORMRETR" 1805832 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-784 1803058 1803348 1803757 "NORMPK" 1804725 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-783 1802743 1802771 1802895 "NORMMA" 1803024 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-782 1802543 1802700 1802729 "NONE" 1802734 T NONE (NIL) -8 NIL NIL NIL) (-781 1802332 1802361 1802430 "NONE1" 1802507 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-780 1801829 1801891 1802070 "NODE1" 1802264 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-779 1800110 1800961 1801216 "NNI" 1801563 T NNI (NIL) -8 NIL NIL 1801798) (-778 1798530 1798843 1799207 "NLINSOL" 1799778 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-777 1794771 1795766 1796665 "NIPROB" 1797651 T NIPROB (NIL) -8 NIL NIL NIL) (-776 1793528 1793762 1794064 "NFINTBAS" 1794533 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-775 1792702 1793178 1793219 "NETCLT" 1793391 NIL NETCLT (NIL T) -9 NIL 1793473 NIL) (-774 1791410 1791641 1791922 "NCODIV" 1792470 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-773 1791172 1791209 1791284 "NCNTFRAC" 1791367 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-772 1789352 1789716 1790136 "NCEP" 1790797 NIL NCEP (NIL T) -7 NIL NIL NIL) (-771 1788203 1788976 1789004 "NASRING" 1789114 T NASRING (NIL) -9 NIL 1789194 NIL) (-770 1787998 1788042 1788136 "NASRING-" 1788141 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-769 1787105 1787630 1787658 "NARNG" 1787775 T NARNG (NIL) -9 NIL 1787866 NIL) (-768 1786797 1786864 1786998 "NARNG-" 1787003 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-767 1785676 1785883 1786118 "NAGSP" 1786582 T NAGSP (NIL) -7 NIL NIL NIL) (-766 1776948 1778632 1780305 "NAGS" 1784023 T NAGS (NIL) -7 NIL NIL NIL) (-765 1775496 1775804 1776135 "NAGF07" 1776637 T NAGF07 (NIL) -7 NIL NIL NIL) (-764 1770034 1771325 1772632 "NAGF04" 1774209 T NAGF04 (NIL) -7 NIL NIL NIL) (-763 1763002 1764616 1766249 "NAGF02" 1768421 T NAGF02 (NIL) -7 NIL NIL NIL) (-762 1758226 1759326 1760443 "NAGF01" 1761905 T NAGF01 (NIL) -7 NIL NIL NIL) (-761 1751854 1753420 1755005 "NAGE04" 1756661 T NAGE04 (NIL) -7 NIL NIL NIL) (-760 1743023 1745144 1747274 "NAGE02" 1749744 T NAGE02 (NIL) -7 NIL NIL NIL) (-759 1738976 1739923 1740887 "NAGE01" 1742079 T NAGE01 (NIL) -7 NIL NIL NIL) (-758 1736771 1737305 1737863 "NAGD03" 1738438 T NAGD03 (NIL) -7 NIL NIL NIL) (-757 1728521 1730449 1732403 "NAGD02" 1734837 T NAGD02 (NIL) -7 NIL NIL NIL) (-756 1722332 1723757 1725197 "NAGD01" 1727101 T NAGD01 (NIL) -7 NIL NIL NIL) (-755 1718541 1719363 1720200 "NAGC06" 1721515 T NAGC06 (NIL) -7 NIL NIL NIL) (-754 1717006 1717338 1717694 "NAGC05" 1718205 T NAGC05 (NIL) -7 NIL NIL NIL) (-753 1716382 1716501 1716645 "NAGC02" 1716882 T NAGC02 (NIL) -7 NIL NIL NIL) (-752 1715341 1715924 1715964 "NAALG" 1716043 NIL NAALG (NIL T) -9 NIL 1716104 NIL) (-751 1715176 1715205 1715295 "NAALG-" 1715300 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-750 1709126 1710234 1711421 "MULTSQFR" 1714072 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-749 1708445 1708520 1708704 "MULTFACT" 1709038 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-748 1701169 1705082 1705135 "MTSCAT" 1706205 NIL MTSCAT (NIL T T) -9 NIL 1706720 NIL) (-747 1700881 1700935 1701027 "MTHING" 1701109 NIL MTHING (NIL T) -7 NIL NIL NIL) (-746 1700673 1700706 1700766 "MSYSCMD" 1700841 T MSYSCMD (NIL) -7 NIL NIL NIL) (-745 1696755 1699428 1699748 "MSET" 1700386 NIL MSET (NIL T) -8 NIL NIL NIL) (-744 1693824 1696316 1696357 "MSETAGG" 1696362 NIL MSETAGG (NIL T) -9 NIL 1696396 NIL) (-743 1689666 1691203 1691948 "MRING" 1693124 NIL MRING (NIL T T) -8 NIL NIL NIL) (-742 1689232 1689299 1689430 "MRF2" 1689593 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-741 1688850 1688885 1689029 "MRATFAC" 1689191 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-740 1686462 1686757 1687188 "MPRFF" 1688555 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-739 1680670 1686316 1686413 "MPOLY" 1686418 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-738 1680160 1680195 1680403 "MPCPF" 1680629 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-737 1679674 1679717 1679901 "MPC3" 1680111 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-736 1678869 1678950 1679171 "MPC2" 1679589 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-735 1677170 1677507 1677897 "MONOTOOL" 1678529 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-734 1676395 1676712 1676740 "MONOID" 1676959 T MONOID (NIL) -9 NIL 1677106 NIL) (-733 1675941 1676060 1676241 "MONOID-" 1676246 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-732 1666120 1672161 1672220 "MONOGEN" 1672894 NIL MONOGEN (NIL T T) -9 NIL 1673350 NIL) (-731 1663338 1664073 1665073 "MONOGEN-" 1665192 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-730 1662171 1662617 1662645 "MONADWU" 1663037 T MONADWU (NIL) -9 NIL 1663275 NIL) (-729 1661543 1661702 1661950 "MONADWU-" 1661955 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-728 1660902 1661146 1661174 "MONAD" 1661381 T MONAD (NIL) -9 NIL 1661493 NIL) (-727 1660587 1660665 1660797 "MONAD-" 1660802 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-726 1658876 1659500 1659779 "MOEBIUS" 1660340 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-725 1658154 1658558 1658598 "MODULE" 1658603 NIL MODULE (NIL T) -9 NIL 1658642 NIL) (-724 1657722 1657818 1658008 "MODULE-" 1658013 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-723 1655402 1656086 1656413 "MODRING" 1657546 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652346 1653507 1654028 "MODOP" 1654931 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-721 1650934 1651413 1651690 "MODMONOM" 1652209 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-720 1640889 1649225 1649639 "MODMON" 1650571 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-719 1638045 1639733 1640009 "MODFIELD" 1640764 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-718 1637022 1637326 1637516 "MMLFORM" 1637875 T MMLFORM (NIL) -8 NIL NIL NIL) (-717 1636548 1636591 1636770 "MMAP" 1636973 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-716 1634627 1635394 1635435 "MLO" 1635858 NIL MLO (NIL T) -9 NIL 1636100 NIL) (-715 1631993 1632509 1633111 "MLIFT" 1634108 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-714 1631384 1631468 1631622 "MKUCFUNC" 1631904 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-713 1630983 1631053 1631176 "MKRECORD" 1631307 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-712 1630030 1630192 1630420 "MKFUNC" 1630794 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-711 1629418 1629522 1629678 "MKFLCFN" 1629913 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-710 1628695 1628797 1628982 "MKBCFUNC" 1629311 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-709 1625370 1628249 1628385 "MINT" 1628579 T MINT (NIL) -8 NIL NIL NIL) (-708 1624182 1624425 1624702 "MHROWRED" 1625125 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-707 1619562 1622717 1623122 "MFLOAT" 1623797 T MFLOAT (NIL) -8 NIL NIL NIL) (-706 1618919 1618995 1619166 "MFINFACT" 1619474 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-705 1615234 1616082 1616966 "MESH" 1618055 T MESH (NIL) -7 NIL NIL NIL) (-704 1613624 1613936 1614289 "MDDFACT" 1614921 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-703 1610419 1612783 1612824 "MDAGG" 1613079 NIL MDAGG (NIL T) -9 NIL 1613222 NIL) (-702 1600066 1609712 1609919 "MCMPLX" 1610232 T MCMPLX (NIL) -8 NIL NIL NIL) (-701 1599203 1599349 1599550 "MCDEN" 1599915 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-700 1597093 1597363 1597743 "MCALCFN" 1598933 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-699 1596018 1596258 1596491 "MAYBE" 1596899 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-698 1593630 1594153 1594715 "MATSTOR" 1595489 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-697 1589587 1593002 1593250 "MATRIX" 1593415 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-696 1585353 1586060 1586796 "MATLIN" 1588944 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-695 1575459 1578645 1578722 "MATCAT" 1583602 NIL MATCAT (NIL T T T) -9 NIL 1585019 NIL) (-694 1571815 1572836 1574192 "MATCAT-" 1574197 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-693 1570409 1570562 1570895 "MATCAT2" 1571650 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-692 1568521 1568845 1569229 "MAPPKG3" 1570084 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-691 1567502 1567675 1567897 "MAPPKG2" 1568345 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-690 1566001 1566285 1566612 "MAPPKG1" 1567208 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-689 1565080 1565407 1565584 "MAPPAST" 1565844 T MAPPAST (NIL) -8 NIL NIL NIL) (-688 1564691 1564749 1564872 "MAPHACK3" 1565016 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-687 1564283 1564344 1564458 "MAPHACK2" 1564623 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-686 1563721 1563824 1563966 "MAPHACK1" 1564174 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-685 1561800 1562421 1562725 "MAGMA" 1563449 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-684 1561279 1561524 1561615 "MACROAST" 1561729 T MACROAST (NIL) -8 NIL NIL NIL) (-683 1557697 1559518 1559979 "M3D" 1560851 NIL M3D (NIL T) -8 NIL NIL NIL) (-682 1551772 1556036 1556077 "LZSTAGG" 1556859 NIL LZSTAGG (NIL T) -9 NIL 1557154 NIL) (-681 1547730 1548903 1550360 "LZSTAGG-" 1550365 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-680 1544817 1545621 1546108 "LWORD" 1547275 NIL LWORD (NIL T) -8 NIL NIL NIL) (-679 1544393 1544621 1544696 "LSTAST" 1544762 T LSTAST (NIL) -8 NIL NIL NIL) (-678 1537470 1544164 1544298 "LSQM" 1544303 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-677 1536694 1536833 1537061 "LSPP" 1537325 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-676 1534506 1534807 1535263 "LSMP" 1536383 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-675 1531285 1531959 1532689 "LSMP1" 1533808 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-674 1525131 1530422 1530463 "LSAGG" 1530525 NIL LSAGG (NIL T) -9 NIL 1530603 NIL) (-673 1521826 1522750 1523963 "LSAGG-" 1523968 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-672 1519425 1520970 1521219 "LPOLY" 1521621 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-671 1519007 1519092 1519215 "LPEFRAC" 1519334 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-670 1517328 1518101 1518354 "LO" 1518839 NIL LO (NIL T T T) -8 NIL NIL NIL) (-669 1516980 1517092 1517120 "LOGIC" 1517231 T LOGIC (NIL) -9 NIL 1517312 NIL) (-668 1516842 1516865 1516936 "LOGIC-" 1516941 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-667 1516035 1516175 1516368 "LODOOPS" 1516698 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-666 1513458 1515951 1516017 "LODO" 1516022 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-665 1511996 1512231 1512584 "LODOF" 1513205 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-664 1508200 1510631 1510672 "LODOCAT" 1511110 NIL LODOCAT (NIL T) -9 NIL 1511321 NIL) (-663 1507933 1507991 1508118 "LODOCAT-" 1508123 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-662 1505253 1507774 1507892 "LODO2" 1507897 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-661 1502688 1505190 1505235 "LODO1" 1505240 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-660 1501569 1501734 1502039 "LODEEF" 1502511 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-659 1496872 1499763 1499804 "LNAGG" 1500666 NIL LNAGG (NIL T) -9 NIL 1501101 NIL) (-658 1496019 1496233 1496575 "LNAGG-" 1496580 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-657 1492155 1492944 1493583 "LMOPS" 1495434 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-656 1491558 1491946 1491987 "LMODULE" 1491992 NIL LMODULE (NIL T) -9 NIL 1492018 NIL) (-655 1488756 1491203 1491326 "LMDICT" 1491468 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-654 1488162 1488383 1488424 "LLINSET" 1488615 NIL LLINSET (NIL T) -9 NIL 1488706 NIL) (-653 1487861 1488070 1488130 "LITERAL" 1488135 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-652 1481024 1486795 1487099 "LIST" 1487590 NIL LIST (NIL T) -8 NIL NIL NIL) (-651 1480549 1480623 1480762 "LIST3" 1480944 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-650 1479556 1479734 1479962 "LIST2" 1480367 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-649 1477690 1478002 1478401 "LIST2MAP" 1479203 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-648 1477286 1477523 1477564 "LINSET" 1477569 NIL LINSET (NIL T) -9 NIL 1477603 NIL) (-647 1476015 1476548 1476589 "LINEXP" 1476940 NIL LINEXP (NIL T) -9 NIL 1477131 NIL) (-646 1474592 1474852 1475163 "LINDEP" 1475767 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-645 1471359 1472078 1472855 "LIMITRF" 1473847 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-644 1469662 1469958 1470367 "LIMITPS" 1471054 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-643 1464090 1469173 1469401 "LIE" 1469483 NIL LIE (NIL T T) -8 NIL NIL NIL) (-642 1463038 1463507 1463547 "LIECAT" 1463687 NIL LIECAT (NIL T) -9 NIL 1463838 NIL) (-641 1462879 1462906 1462994 "LIECAT-" 1462999 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-640 1455466 1462419 1462575 "LIB" 1462743 T LIB (NIL) -8 NIL NIL NIL) (-639 1451101 1451984 1452919 "LGROBP" 1454583 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-638 1449099 1449373 1449723 "LF" 1450822 NIL LF (NIL T T) -7 NIL NIL NIL) (-637 1447939 1448631 1448659 "LFCAT" 1448866 T LFCAT (NIL) -9 NIL 1449005 NIL) (-636 1444841 1445471 1446159 "LEXTRIPK" 1447303 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-635 1441585 1442411 1442914 "LEXP" 1444421 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-634 1441061 1441306 1441398 "LETAST" 1441513 T LETAST (NIL) -8 NIL NIL NIL) (-633 1439459 1439772 1440173 "LEADCDET" 1440743 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-632 1438649 1438723 1438952 "LAZM3PK" 1439380 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-631 1433566 1436726 1437264 "LAUPOL" 1438161 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-630 1433145 1433189 1433350 "LAPLACE" 1433516 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-629 1431084 1432246 1432497 "LA" 1432978 NIL LA (NIL T T T) -8 NIL NIL NIL) (-628 1430078 1430662 1430703 "LALG" 1430765 NIL LALG (NIL T) -9 NIL 1430824 NIL) (-627 1429792 1429851 1429987 "LALG-" 1429992 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-626 1429627 1429651 1429692 "KVTFROM" 1429754 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-625 1428550 1428994 1429179 "KTVLOGIC" 1429462 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-624 1428385 1428409 1428450 "KRCFROM" 1428512 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-623 1427289 1427476 1427775 "KOVACIC" 1428185 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-622 1427124 1427148 1427189 "KONVERT" 1427251 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-621 1426959 1426983 1427024 "KOERCE" 1427086 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-620 1424790 1425552 1425929 "KERNEL" 1426615 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-619 1424286 1424367 1424499 "KERNEL2" 1424704 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-618 1418056 1422825 1422879 "KDAGG" 1423256 NIL KDAGG (NIL T T) -9 NIL 1423462 NIL) (-617 1417585 1417709 1417914 "KDAGG-" 1417919 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1410733 1417246 1417401 "KAFILE" 1417463 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-615 1405161 1410244 1410472 "JORDAN" 1410554 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-614 1404540 1404810 1404931 "JOINAST" 1405060 T JOINAST (NIL) -8 NIL NIL NIL) (-613 1404386 1404445 1404500 "JAVACODE" 1404505 T JAVACODE (NIL) -8 NIL NIL NIL) (-612 1400638 1402591 1402645 "IXAGG" 1403574 NIL IXAGG (NIL T T) -9 NIL 1404033 NIL) (-611 1399557 1399863 1400282 "IXAGG-" 1400287 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-610 1395087 1399479 1399538 "IVECTOR" 1399543 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-609 1393853 1394090 1394356 "ITUPLE" 1394854 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-608 1392355 1392532 1392827 "ITRIGMNP" 1393675 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-607 1391100 1391304 1391587 "ITFUN3" 1392131 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-606 1390732 1390789 1390898 "ITFUN2" 1391037 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-605 1389891 1390212 1390386 "ITFORM" 1390578 T ITFORM (NIL) -8 NIL NIL NIL) (-604 1387852 1388911 1389189 "ITAYLOR" 1389646 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-603 1376797 1381989 1383152 "ISUPS" 1386722 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-602 1375901 1376041 1376277 "ISUMP" 1376644 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-601 1371276 1375846 1375887 "ISTRING" 1375892 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-600 1370752 1370997 1371089 "ISAST" 1371204 T ISAST (NIL) -8 NIL NIL NIL) (-599 1369961 1370043 1370259 "IRURPK" 1370666 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-598 1368897 1369098 1369338 "IRSN" 1369741 T IRSN (NIL) -7 NIL NIL NIL) (-597 1366968 1367323 1367752 "IRRF2F" 1368535 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-596 1366715 1366753 1366829 "IRREDFFX" 1366924 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-595 1365330 1365589 1365888 "IROOT" 1366448 NIL IROOT (NIL T) -7 NIL NIL NIL) (-594 1361934 1363014 1363706 "IR" 1364670 NIL IR (NIL T) -8 NIL NIL NIL) (-593 1361139 1361427 1361578 "IRFORM" 1361803 T IRFORM (NIL) -8 NIL NIL NIL) (-592 1358752 1359247 1359813 "IR2" 1360617 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-591 1357852 1357965 1358179 "IR2F" 1358635 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-590 1357643 1357677 1357737 "IPRNTPK" 1357812 T IPRNTPK (NIL) -7 NIL NIL NIL) (-589 1354224 1357532 1357601 "IPF" 1357606 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-588 1352551 1354149 1354206 "IPADIC" 1354211 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-587 1351863 1352111 1352241 "IP4ADDR" 1352441 T IP4ADDR (NIL) -8 NIL NIL NIL) (-586 1351237 1351492 1351624 "IOMODE" 1351751 T IOMODE (NIL) -8 NIL NIL NIL) (-585 1350310 1350834 1350961 "IOBFILE" 1351130 T IOBFILE (NIL) -8 NIL NIL NIL) (-584 1349798 1350214 1350242 "IOBCON" 1350247 T IOBCON (NIL) -9 NIL 1350268 NIL) (-583 1349309 1349367 1349550 "INVLAPLA" 1349734 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-582 1338957 1341311 1343697 "INTTR" 1346973 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-581 1335292 1336034 1336899 "INTTOOLS" 1338142 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-580 1334878 1334969 1335086 "INTSLPE" 1335195 T INTSLPE (NIL) -7 NIL NIL NIL) (-579 1332831 1334801 1334860 "INTRVL" 1334865 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-578 1330433 1330945 1331520 "INTRF" 1332316 NIL INTRF (NIL T) -7 NIL NIL NIL) (-577 1329844 1329941 1330083 "INTRET" 1330331 NIL INTRET (NIL T) -7 NIL NIL NIL) (-576 1327841 1328230 1328700 "INTRAT" 1329452 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-575 1325104 1325687 1326306 "INTPM" 1327326 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-574 1321849 1322448 1323186 "INTPAF" 1324490 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-573 1317028 1317990 1319041 "INTPACK" 1320818 T INTPACK (NIL) -7 NIL NIL NIL) (-572 1313926 1316825 1316934 "INT" 1316939 T INT (NIL) -8 NIL NIL NIL) (-571 1313178 1313330 1313538 "INTHERTR" 1313768 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-570 1312617 1312697 1312885 "INTHERAL" 1313092 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-569 1310463 1310906 1311363 "INTHEORY" 1312180 T INTHEORY (NIL) -7 NIL NIL NIL) (-568 1301869 1303490 1305262 "INTG0" 1308815 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-567 1282442 1287232 1292042 "INTFTBL" 1297079 T INTFTBL (NIL) -8 NIL NIL NIL) (-566 1281691 1281829 1282002 "INTFACT" 1282301 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-565 1279118 1279564 1280121 "INTEF" 1281245 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-564 1277485 1278224 1278252 "INTDOM" 1278553 T INTDOM (NIL) -9 NIL 1278760 NIL) (-563 1276854 1277028 1277270 "INTDOM-" 1277275 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-562 1273242 1275170 1275224 "INTCAT" 1276023 NIL INTCAT (NIL T) -9 NIL 1276344 NIL) (-561 1272714 1272817 1272945 "INTBIT" 1273134 T INTBIT (NIL) -7 NIL NIL NIL) (-560 1271413 1271567 1271874 "INTALG" 1272559 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-559 1270896 1270986 1271143 "INTAF" 1271317 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-558 1264239 1270706 1270846 "INTABL" 1270851 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-557 1263572 1264038 1264103 "INT8" 1264137 T INT8 (NIL) -8 NIL NIL 1264182) (-556 1262904 1263370 1263435 "INT64" 1263469 T INT64 (NIL) -8 NIL NIL 1263514) (-555 1262236 1262702 1262767 "INT32" 1262801 T INT32 (NIL) -8 NIL NIL 1262846) (-554 1261568 1262034 1262099 "INT16" 1262133 T INT16 (NIL) -8 NIL NIL 1262178) (-553 1256376 1259142 1259170 "INS" 1260104 T INS (NIL) -9 NIL 1260769 NIL) (-552 1253616 1254387 1255361 "INS-" 1255434 NIL INS- (NIL T) -8 NIL NIL NIL) (-551 1252391 1252618 1252916 "INPSIGN" 1253369 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-550 1251509 1251626 1251823 "INPRODPF" 1252271 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-549 1250403 1250520 1250757 "INPRODFF" 1251389 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-548 1249403 1249555 1249815 "INNMFACT" 1250239 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-547 1248600 1248697 1248885 "INMODGCD" 1249302 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-546 1247108 1247353 1247677 "INFSP" 1248345 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-545 1246292 1246409 1246592 "INFPROD0" 1246988 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-544 1243147 1244357 1244872 "INFORM" 1245785 T INFORM (NIL) -8 NIL NIL NIL) (-543 1242757 1242817 1242915 "INFORM1" 1243082 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-542 1242280 1242369 1242483 "INFINITY" 1242663 T INFINITY (NIL) -7 NIL NIL NIL) (-541 1241456 1242000 1242101 "INETCLTS" 1242199 T INETCLTS (NIL) -8 NIL NIL NIL) (-540 1240072 1240322 1240643 "INEP" 1241204 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-539 1239321 1239969 1240034 "INDE" 1240039 NIL INDE (NIL T) -8 NIL NIL NIL) (-538 1238885 1238953 1239070 "INCRMAPS" 1239248 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-537 1237703 1238154 1238360 "INBFILE" 1238699 T INBFILE (NIL) -8 NIL NIL NIL) (-536 1233002 1233939 1234883 "INBFF" 1236791 NIL INBFF (NIL T) -7 NIL NIL NIL) (-535 1231910 1232179 1232207 "INBCON" 1232720 T INBCON (NIL) -9 NIL 1232986 NIL) (-534 1231162 1231385 1231661 "INBCON-" 1231666 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-533 1230641 1230886 1230977 "INAST" 1231091 T INAST (NIL) -8 NIL NIL NIL) (-532 1230068 1230320 1230426 "IMPTAST" 1230555 T IMPTAST (NIL) -8 NIL NIL NIL) (-531 1226514 1229912 1230016 "IMATRIX" 1230021 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-530 1225222 1225345 1225661 "IMATQF" 1226370 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-529 1223442 1223669 1224006 "IMATLIN" 1224978 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-528 1218020 1223366 1223424 "ILIST" 1223429 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-527 1215925 1217880 1217993 "IIARRAY2" 1217998 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-526 1211323 1215836 1215900 "IFF" 1215905 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-525 1210670 1210940 1211056 "IFAST" 1211227 T IFAST (NIL) -8 NIL NIL NIL) (-524 1205665 1209962 1210150 "IFARRAY" 1210527 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-523 1204845 1205569 1205642 "IFAMON" 1205647 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-522 1204429 1204494 1204548 "IEVALAB" 1204755 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-521 1204104 1204172 1204332 "IEVALAB-" 1204337 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-520 1203735 1204018 1204081 "IDPO" 1204086 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-519 1202985 1203624 1203699 "IDPOAMS" 1203704 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-518 1202292 1202874 1202949 "IDPOAM" 1202954 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-517 1201351 1201627 1201680 "IDPC" 1202093 NIL IDPC (NIL T T) -9 NIL 1202242 NIL) (-516 1200820 1201243 1201316 "IDPAM" 1201321 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-515 1200196 1200712 1200785 "IDPAG" 1200790 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-514 1199841 1200032 1200107 "IDENT" 1200141 T IDENT (NIL) -8 NIL NIL NIL) (-513 1196096 1196944 1197839 "IDECOMP" 1198998 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-512 1188933 1190019 1191066 "IDEAL" 1195132 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-511 1188093 1188205 1188405 "ICDEN" 1188817 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-510 1187164 1187573 1187720 "ICARD" 1187966 T ICARD (NIL) -8 NIL NIL NIL) (-509 1185224 1185537 1185942 "IBPTOOLS" 1186841 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-508 1180831 1184844 1184957 "IBITS" 1185143 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-507 1177554 1178130 1178825 "IBATOOL" 1180248 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-506 1175333 1175795 1176328 "IBACHIN" 1177089 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-505 1173162 1175179 1175282 "IARRAY2" 1175287 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-504 1169268 1173088 1173145 "IARRAY1" 1173150 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-503 1163306 1167680 1168161 "IAN" 1168807 T IAN (NIL) -8 NIL NIL NIL) (-502 1162817 1162874 1163047 "IALGFACT" 1163243 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-501 1162345 1162458 1162486 "HYPCAT" 1162693 T HYPCAT (NIL) -9 NIL NIL NIL) (-500 1161883 1162000 1162186 "HYPCAT-" 1162191 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-499 1161478 1161678 1161761 "HOSTNAME" 1161820 T HOSTNAME (NIL) -8 NIL NIL NIL) (-498 1161323 1161360 1161401 "HOMOTOP" 1161406 NIL HOMOTOP (NIL T) -9 NIL 1161439 NIL) (-497 1157955 1159333 1159374 "HOAGG" 1160355 NIL HOAGG (NIL T) -9 NIL 1161034 NIL) (-496 1156549 1156948 1157474 "HOAGG-" 1157479 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-495 1150458 1156142 1156292 "HEXADEC" 1156419 T HEXADEC (NIL) -8 NIL NIL NIL) (-494 1149206 1149428 1149691 "HEUGCD" 1150235 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-493 1148282 1149043 1149173 "HELLFDIV" 1149178 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-492 1146461 1148059 1148147 "HEAP" 1148226 NIL HEAP (NIL T) -8 NIL NIL NIL) (-491 1145724 1146013 1146147 "HEADAST" 1146347 T HEADAST (NIL) -8 NIL NIL NIL) (-490 1139453 1145639 1145701 "HDP" 1145706 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-489 1133352 1139088 1139240 "HDMP" 1139354 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-488 1132676 1132816 1132980 "HB" 1133208 T HB (NIL) -7 NIL NIL NIL) (-487 1126062 1132522 1132626 "HASHTBL" 1132631 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-486 1125538 1125783 1125875 "HASAST" 1125990 T HASAST (NIL) -8 NIL NIL NIL) (-485 1123316 1125160 1125342 "HACKPI" 1125376 T HACKPI (NIL) -8 NIL NIL NIL) (-484 1118984 1123169 1123282 "GTSET" 1123287 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-483 1112399 1118862 1118960 "GSTBL" 1118965 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-482 1104677 1111430 1111695 "GSERIES" 1112190 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-481 1103818 1104235 1104263 "GROUP" 1104466 T GROUP (NIL) -9 NIL 1104600 NIL) (-480 1103184 1103343 1103594 "GROUP-" 1103599 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-479 1101551 1101872 1102259 "GROEBSOL" 1102861 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-478 1100465 1100753 1100804 "GRMOD" 1101333 NIL GRMOD (NIL T T) -9 NIL 1101501 NIL) (-477 1100233 1100269 1100397 "GRMOD-" 1100402 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-476 1095523 1096587 1097587 "GRIMAGE" 1099253 T GRIMAGE (NIL) -8 NIL NIL NIL) (-475 1093989 1094250 1094574 "GRDEF" 1095219 T GRDEF (NIL) -7 NIL NIL NIL) (-474 1093433 1093549 1093690 "GRAY" 1093868 T GRAY (NIL) -7 NIL NIL NIL) (-473 1092620 1093026 1093077 "GRALG" 1093230 NIL GRALG (NIL T T) -9 NIL 1093323 NIL) (-472 1092281 1092354 1092517 "GRALG-" 1092522 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-471 1089058 1091866 1092044 "GPOLSET" 1092188 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-470 1088412 1088469 1088727 "GOSPER" 1088995 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-469 1084144 1084850 1085376 "GMODPOL" 1088111 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-468 1083149 1083333 1083571 "GHENSEL" 1083956 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-467 1077305 1078148 1079168 "GENUPS" 1082233 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-466 1077002 1077053 1077142 "GENUFACT" 1077248 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-465 1076414 1076491 1076656 "GENPGCD" 1076920 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-464 1075888 1075923 1076136 "GENMFACT" 1076373 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-463 1074454 1074711 1075018 "GENEEZ" 1075631 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-462 1068513 1074065 1074227 "GDMP" 1074377 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-461 1057856 1062284 1063390 "GCNAALG" 1067496 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-460 1056183 1057045 1057073 "GCDDOM" 1057328 T GCDDOM (NIL) -9 NIL 1057485 NIL) (-459 1055653 1055780 1055995 "GCDDOM-" 1056000 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-458 1054325 1054510 1054814 "GB" 1055432 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-457 1042941 1045271 1047663 "GBINTERN" 1052016 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-456 1040778 1041070 1041491 "GBF" 1042616 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-455 1039559 1039724 1039991 "GBEUCLID" 1040594 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-454 1038908 1039033 1039182 "GAUSSFAC" 1039430 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-453 1037275 1037577 1037891 "GALUTIL" 1038627 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-452 1035583 1035857 1036181 "GALPOLYU" 1037002 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-451 1032948 1033238 1033645 "GALFACTU" 1035280 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-450 1024754 1026253 1027861 "GALFACT" 1031380 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-449 1022142 1022800 1022828 "FVFUN" 1023984 T FVFUN (NIL) -9 NIL 1024704 NIL) (-448 1021408 1021590 1021618 "FVC" 1021909 T FVC (NIL) -9 NIL 1022092 NIL) (-447 1021051 1021233 1021301 "FUNDESC" 1021360 T FUNDESC (NIL) -8 NIL NIL NIL) (-446 1020666 1020848 1020929 "FUNCTION" 1021003 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-445 1018410 1018988 1019454 "FT" 1020220 T FT (NIL) -8 NIL NIL NIL) (-444 1017201 1017711 1017914 "FTEM" 1018227 T FTEM (NIL) -8 NIL NIL NIL) (-443 1015492 1015781 1016178 "FSUPFACT" 1016892 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-442 1013889 1014178 1014510 "FST" 1015180 T FST (NIL) -8 NIL NIL NIL) (-441 1013088 1013194 1013382 "FSRED" 1013771 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-440 1011787 1012043 1012390 "FSPRMELT" 1012803 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-439 1009093 1009531 1010017 "FSPECF" 1011350 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-438 990465 998936 998977 "FS" 1002861 NIL FS (NIL T) -9 NIL 1005150 NIL) (-437 979108 982101 986158 "FS-" 986458 NIL FS- (NIL T T) -8 NIL NIL NIL) (-436 978636 978690 978860 "FSINT" 979049 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-435 976928 977629 977932 "FSERIES" 978415 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-434 975970 976086 976310 "FSCINT" 976808 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-433 972178 974914 974955 "FSAGG" 975325 NIL FSAGG (NIL T) -9 NIL 975584 NIL) (-432 969940 970541 971337 "FSAGG-" 971432 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-431 968982 969125 969352 "FSAGG2" 969793 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-430 966664 966944 967491 "FS2UPS" 968700 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-429 966298 966341 966470 "FS2" 966615 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-428 965176 965347 965649 "FS2EXPXP" 966123 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-427 964602 964717 964869 "FRUTIL" 965056 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-426 956015 960097 961455 "FR" 963276 NIL FR (NIL T) -8 NIL NIL NIL) (-425 951029 953704 953744 "FRNAALG" 955064 NIL FRNAALG (NIL T) -9 NIL 955662 NIL) (-424 946702 947778 949053 "FRNAALG-" 949803 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-423 946340 946383 946510 "FRNAAF2" 946653 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-422 944715 945189 945485 "FRMOD" 946152 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-421 942458 943090 943408 "FRIDEAL" 944506 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-420 941649 941736 942027 "FRIDEAL2" 942365 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-419 940782 941196 941237 "FRETRCT" 941242 NIL FRETRCT (NIL T) -9 NIL 941418 NIL) (-418 939894 940125 940476 "FRETRCT-" 940481 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-417 936982 938192 938251 "FRAMALG" 939133 NIL FRAMALG (NIL T T) -9 NIL 939425 NIL) (-416 935116 935571 936201 "FRAMALG-" 936424 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-415 928946 934589 934866 "FRAC" 934871 NIL FRAC (NIL T) -8 NIL NIL NIL) (-414 928582 928639 928746 "FRAC2" 928883 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-413 928218 928275 928382 "FR2" 928519 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-412 922731 925624 925652 "FPS" 926771 T FPS (NIL) -9 NIL 927328 NIL) (-411 922180 922289 922453 "FPS-" 922599 NIL FPS- (NIL T) -8 NIL NIL NIL) (-410 919482 921151 921179 "FPC" 921404 T FPC (NIL) -9 NIL 921546 NIL) (-409 919275 919315 919412 "FPC-" 919417 NIL FPC- (NIL T) -8 NIL NIL NIL) (-408 918065 918763 918804 "FPATMAB" 918809 NIL FPATMAB (NIL T) -9 NIL 918961 NIL) (-407 915738 916241 916667 "FPARFRAC" 917702 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-406 911132 911630 912312 "FORTRAN" 915170 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-405 908848 909348 909887 "FORT" 910613 T FORT (NIL) -7 NIL NIL NIL) (-404 906524 907086 907114 "FORTFN" 908174 T FORTFN (NIL) -9 NIL 908798 NIL) (-403 906288 906338 906366 "FORTCAT" 906425 T FORTCAT (NIL) -9 NIL 906487 NIL) (-402 904394 904904 905294 "FORMULA" 905918 T FORMULA (NIL) -8 NIL NIL NIL) (-401 904182 904212 904281 "FORMULA1" 904358 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-400 903705 903757 903930 "FORDER" 904124 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-399 902801 902965 903158 "FOP" 903532 T FOP (NIL) -7 NIL NIL NIL) (-398 901382 902081 902255 "FNLA" 902683 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-397 900111 900526 900554 "FNCAT" 901014 T FNCAT (NIL) -9 NIL 901274 NIL) (-396 899650 900070 900098 "FNAME" 900103 T FNAME (NIL) -8 NIL NIL NIL) (-395 898213 899176 899204 "FMTC" 899209 T FMTC (NIL) -9 NIL 899245 NIL) (-394 896959 898149 898195 "FMONOID" 898200 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-393 893787 894955 894996 "FMONCAT" 896213 NIL FMONCAT (NIL T) -9 NIL 896818 NIL) (-392 892979 893529 893678 "FM" 893683 NIL FM (NIL T T) -8 NIL NIL NIL) (-391 890403 891049 891077 "FMFUN" 892221 T FMFUN (NIL) -9 NIL 892929 NIL) (-390 889672 889853 889881 "FMC" 890171 T FMC (NIL) -9 NIL 890353 NIL) (-389 886751 887611 887665 "FMCAT" 888860 NIL FMCAT (NIL T T) -9 NIL 889355 NIL) (-388 885617 886517 886617 "FM1" 886696 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-387 883391 883807 884301 "FLOATRP" 885168 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-386 876969 881120 881741 "FLOAT" 882790 T FLOAT (NIL) -8 NIL NIL NIL) (-385 874407 874907 875485 "FLOATCP" 876436 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-384 873254 874013 874054 "FLINEXP" 874059 NIL FLINEXP (NIL T) -9 NIL 874152 NIL) (-383 872186 872483 872891 "FLINEXP-" 872896 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-382 871262 871406 871630 "FLASORT" 872038 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-381 868378 869246 869298 "FLALG" 870525 NIL FLALG (NIL T T) -9 NIL 870992 NIL) (-380 862082 865834 865875 "FLAGG" 867137 NIL FLAGG (NIL T) -9 NIL 867789 NIL) (-379 860808 861147 861637 "FLAGG-" 861642 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-378 859850 859993 860220 "FLAGG2" 860661 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-377 856701 857709 857768 "FINRALG" 858896 NIL FINRALG (NIL T T) -9 NIL 859404 NIL) (-376 855861 856090 856429 "FINRALG-" 856434 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-375 855241 855480 855508 "FINITE" 855704 T FINITE (NIL) -9 NIL 855811 NIL) (-374 847598 849785 849825 "FINAALG" 853492 NIL FINAALG (NIL T) -9 NIL 854945 NIL) (-373 842930 843980 845124 "FINAALG-" 846503 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-372 842298 842685 842788 "FILE" 842860 NIL FILE (NIL T) -8 NIL NIL NIL) (-371 840956 841294 841348 "FILECAT" 842032 NIL FILECAT (NIL T T) -9 NIL 842248 NIL) (-370 838672 840200 840228 "FIELD" 840268 T FIELD (NIL) -9 NIL 840348 NIL) (-369 837292 837677 838188 "FIELD-" 838193 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-368 835142 835927 836274 "FGROUP" 836978 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-367 834232 834396 834616 "FGLMICPK" 834974 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-366 830064 834157 834214 "FFX" 834219 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-365 829665 829726 829861 "FFSLPE" 829997 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-364 825655 826437 827233 "FFPOLY" 828901 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-363 825159 825195 825404 "FFPOLY2" 825613 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-362 821005 825078 825141 "FFP" 825146 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-361 816403 820916 820980 "FF" 820985 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-360 811529 815746 815936 "FFNBX" 816257 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-359 806457 810664 810922 "FFNBP" 811383 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-358 801090 805741 805952 "FFNB" 806290 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-357 799922 800120 800435 "FFINTBAS" 800887 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-356 795961 798182 798210 "FFIELDC" 798830 T FFIELDC (NIL) -9 NIL 799206 NIL) (-355 794623 794994 795491 "FFIELDC-" 795496 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-354 794192 794238 794362 "FFHOM" 794565 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-353 791887 792374 792891 "FFF" 793707 NIL FFF (NIL T) -7 NIL NIL NIL) (-352 787505 791629 791730 "FFCGX" 791830 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-351 783127 787237 787344 "FFCGP" 787448 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-350 778310 782854 782962 "FFCG" 783063 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-349 759347 768532 768618 "FFCAT" 773783 NIL FFCAT (NIL T T T) -9 NIL 775234 NIL) (-348 754544 755592 756906 "FFCAT-" 758136 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-347 753955 753998 754233 "FFCAT2" 754495 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 743278 746927 748147 "FEXPR" 752807 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-345 742240 742675 742716 "FEVALAB" 742800 NIL FEVALAB (NIL T) -9 NIL 743061 NIL) (-344 741399 741609 741947 "FEVALAB-" 741952 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-343 739965 740782 740985 "FDIV" 741298 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-342 736985 737726 737841 "FDIVCAT" 739409 NIL FDIVCAT (NIL T T T T) -9 NIL 739846 NIL) (-341 736747 736774 736944 "FDIVCAT-" 736949 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-340 735967 736054 736331 "FDIV2" 736654 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734941 735262 735464 "FCTRDATA" 735785 T FCTRDATA (NIL) -8 NIL NIL NIL) (-338 733627 733886 734175 "FCPAK1" 734672 T FCPAK1 (NIL) -7 NIL NIL NIL) (-337 732726 733127 733268 "FCOMP" 733518 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-336 716431 719876 723414 "FC" 729208 T FC (NIL) -8 NIL NIL NIL) (-335 708737 712765 712805 "FAXF" 714607 NIL FAXF (NIL T) -9 NIL 715299 NIL) (-334 706014 706671 707496 "FAXF-" 707961 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-333 701066 705390 705566 "FARRAY" 705871 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-332 695960 698027 698080 "FAMR" 699103 NIL FAMR (NIL T T) -9 NIL 699563 NIL) (-331 694850 695152 695587 "FAMR-" 695592 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-330 694019 694772 694825 "FAMONOID" 694830 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-329 691805 692515 692568 "FAMONC" 693509 NIL FAMONC (NIL T T) -9 NIL 693895 NIL) (-328 690469 691559 691696 "FAGROUP" 691701 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-327 688264 688583 688986 "FACUTIL" 690150 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-326 687363 687548 687770 "FACTFUNC" 688074 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-325 679785 686666 686865 "EXPUPXS" 687219 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-324 677268 677808 678394 "EXPRTUBE" 679219 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-323 673539 674131 674861 "EXPRODE" 676607 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-322 659258 672188 672617 "EXPR" 673143 NIL EXPR (NIL T) -8 NIL NIL NIL) (-321 653812 654399 655205 "EXPR2UPS" 658556 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-320 653444 653501 653610 "EXPR2" 653749 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-319 644697 652595 652886 "EXPEXPAN" 653280 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-318 644497 644654 644683 "EXIT" 644688 T EXIT (NIL) -8 NIL NIL NIL) (-317 643977 644221 644312 "EXITAST" 644426 T EXITAST (NIL) -8 NIL NIL NIL) (-316 643604 643666 643779 "EVALCYC" 643909 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-315 643145 643263 643304 "EVALAB" 643474 NIL EVALAB (NIL T) -9 NIL 643578 NIL) (-314 642626 642748 642969 "EVALAB-" 642974 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-313 639994 641296 641324 "EUCDOM" 641879 T EUCDOM (NIL) -9 NIL 642229 NIL) (-312 638399 638841 639431 "EUCDOM-" 639436 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-311 625938 628697 631447 "ESTOOLS" 635669 T ESTOOLS (NIL) -7 NIL NIL NIL) (-310 625570 625627 625736 "ESTOOLS2" 625875 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-309 625321 625363 625443 "ESTOOLS1" 625522 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-308 619358 620966 620994 "ES" 623762 T ES (NIL) -9 NIL 625172 NIL) (-307 614305 615592 617409 "ES-" 617573 NIL ES- (NIL T) -8 NIL NIL NIL) (-306 610679 611440 612220 "ESCONT" 613545 T ESCONT (NIL) -7 NIL NIL NIL) (-305 610424 610456 610538 "ESCONT1" 610641 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-304 610099 610149 610249 "ES2" 610368 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-303 609729 609787 609896 "ES1" 610035 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-302 608945 609074 609250 "ERROR" 609573 T ERROR (NIL) -7 NIL NIL NIL) (-301 602337 608804 608895 "EQTBL" 608900 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-300 594840 597651 599100 "EQ" 600921 NIL -2075 (NIL T) -8 NIL NIL NIL) (-299 594472 594529 594638 "EQ2" 594777 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-298 589763 590810 591903 "EP" 593411 NIL EP (NIL T) -7 NIL NIL NIL) (-297 588363 588654 588960 "ENV" 589477 T ENV (NIL) -8 NIL NIL NIL) (-296 587457 588011 588039 "ENTIRER" 588044 T ENTIRER (NIL) -9 NIL 588090 NIL) (-295 584151 585639 586000 "EMR" 587265 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-294 583281 583466 583520 "ELTAGG" 583900 NIL ELTAGG (NIL T T) -9 NIL 584111 NIL) (-293 583000 583062 583203 "ELTAGG-" 583208 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-292 582764 582793 582847 "ELTAB" 582931 NIL ELTAB (NIL T T) -9 NIL 582983 NIL) (-291 581890 582036 582235 "ELFUTS" 582615 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-290 581632 581688 581716 "ELEMFUN" 581821 T ELEMFUN (NIL) -9 NIL NIL NIL) (-289 581502 581523 581591 "ELEMFUN-" 581596 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-288 576316 579572 579613 "ELAGG" 580553 NIL ELAGG (NIL T) -9 NIL 581016 NIL) (-287 574601 575035 575698 "ELAGG-" 575703 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-286 573913 574050 574206 "ELABOR" 574465 T ELABOR (NIL) -8 NIL NIL NIL) (-285 572574 572853 573147 "ELABEXPR" 573639 T ELABEXPR (NIL) -8 NIL NIL NIL) (-284 565438 567241 568068 "EFUPXS" 571850 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-283 558888 560689 561499 "EFULS" 564714 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-282 556373 556731 557203 "EFSTRUC" 558520 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-281 546164 547730 549278 "EF" 554888 NIL EF (NIL T T) -7 NIL NIL NIL) (-280 545238 545649 545798 "EAB" 546035 T EAB (NIL) -8 NIL NIL NIL) (-279 544420 545197 545225 "E04UCFA" 545230 T E04UCFA (NIL) -8 NIL NIL NIL) (-278 543602 544379 544407 "E04NAFA" 544412 T E04NAFA (NIL) -8 NIL NIL NIL) (-277 542784 543561 543589 "E04MBFA" 543594 T E04MBFA (NIL) -8 NIL NIL NIL) (-276 541966 542743 542771 "E04JAFA" 542776 T E04JAFA (NIL) -8 NIL NIL NIL) (-275 541150 541925 541953 "E04GCFA" 541958 T E04GCFA (NIL) -8 NIL NIL NIL) (-274 540334 541109 541137 "E04FDFA" 541142 T E04FDFA (NIL) -8 NIL NIL NIL) (-273 539516 540293 540321 "E04DGFA" 540326 T E04DGFA (NIL) -8 NIL NIL NIL) (-272 533689 535041 536405 "E04AGNT" 538172 T E04AGNT (NIL) -7 NIL NIL NIL) (-271 532369 532875 532915 "DVARCAT" 533390 NIL DVARCAT (NIL T) -9 NIL 533589 NIL) (-270 531573 531785 532099 "DVARCAT-" 532104 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-269 524621 531372 531501 "DSMP" 531506 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-268 519402 520566 521634 "DROPT" 523573 T DROPT (NIL) -8 NIL NIL NIL) (-267 519067 519126 519224 "DROPT1" 519337 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-266 514182 515308 516445 "DROPT0" 517950 T DROPT0 (NIL) -7 NIL NIL NIL) (-265 512527 512852 513238 "DRAWPT" 513816 T DRAWPT (NIL) -7 NIL NIL NIL) (-264 507114 508037 509116 "DRAW" 511501 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 506747 506800 506918 "DRAWHACK" 507055 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-262 505478 505747 506038 "DRAWCX" 506476 T DRAWCX (NIL) -7 NIL NIL NIL) (-261 504993 505062 505213 "DRAWCURV" 505404 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-260 495461 497423 499538 "DRAWCFUN" 502898 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-259 492225 494154 494195 "DQAGG" 494824 NIL DQAGG (NIL T) -9 NIL 495098 NIL) (-258 480162 486720 486803 "DPOLCAT" 488655 NIL DPOLCAT (NIL T T T T) -9 NIL 489200 NIL) (-257 474999 476347 478305 "DPOLCAT-" 478310 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-256 468308 474860 474958 "DPMO" 474963 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-255 461520 468088 468255 "DPMM" 468260 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-254 461090 461304 461393 "DOMTMPLT" 461451 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-253 460523 460892 460972 "DOMCTOR" 461030 T DOMCTOR (NIL) -8 NIL NIL NIL) (-252 459735 460003 460154 "DOMAIN" 460392 T DOMAIN (NIL) -8 NIL NIL NIL) (-251 453634 459370 459522 "DMP" 459636 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-250 453234 453290 453434 "DLP" 453572 NIL DLP (NIL T) -7 NIL NIL NIL) (-249 447056 452561 452751 "DLIST" 453076 NIL DLIST (NIL T) -8 NIL NIL NIL) (-248 443853 445909 445950 "DLAGG" 446500 NIL DLAGG (NIL T) -9 NIL 446730 NIL) (-247 442529 443193 443221 "DIVRING" 443313 T DIVRING (NIL) -9 NIL 443396 NIL) (-246 441766 441956 442256 "DIVRING-" 442261 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-245 439868 440225 440631 "DISPLAY" 441380 T DISPLAY (NIL) -7 NIL NIL NIL) (-244 433617 439782 439845 "DIRPROD" 439850 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-243 432465 432668 432933 "DIRPROD2" 433410 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-242 420976 427122 427175 "DIRPCAT" 427585 NIL DIRPCAT (NIL NIL T) -9 NIL 428425 NIL) (-241 418080 418784 419745 "DIRPCAT-" 420082 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-240 417367 417527 417713 "DIOSP" 417914 T DIOSP (NIL) -7 NIL NIL NIL) (-239 414022 416279 416320 "DIOPS" 416754 NIL DIOPS (NIL T) -9 NIL 416983 NIL) (-238 413571 413685 413876 "DIOPS-" 413881 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-237 412460 413088 413116 "DIFRING" 413235 T DIFRING (NIL) -9 NIL 413318 NIL) (-236 412105 412183 412335 "DIFRING-" 412340 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-235 411813 411858 411899 "DIFFDOM" 412020 NIL DIFFDOM (NIL T) -9 NIL 412088 NIL) (-234 411666 411690 411774 "DIFFDOM-" 411779 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 409345 410617 410658 "DIFEXT" 411021 NIL DIFEXT (NIL T) -9 NIL 411315 NIL) (-232 407630 408058 408724 "DIFEXT-" 408729 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 404905 407162 407203 "DIAGG" 407208 NIL DIAGG (NIL T) -9 NIL 407228 NIL) (-230 404289 404446 404698 "DIAGG-" 404703 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 399706 403248 403525 "DHMATRIX" 404058 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 395318 396227 397237 "DFSFUN" 398716 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 390398 394249 394561 "DFLOAT" 395026 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 388661 388942 389331 "DFINTTLS" 390106 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 385690 386682 387082 "DERHAM" 388327 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 383491 385465 385554 "DEQUEUE" 385634 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 382745 382878 383061 "DEGRED" 383353 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 379175 379920 380766 "DEFINTRF" 381973 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 376730 377199 377791 "DEFINTEF" 378694 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 376080 376350 376465 "DEFAST" 376635 T DEFAST (NIL) -8 NIL NIL NIL) (-219 369989 375673 375823 "DECIMAL" 375950 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 367501 367959 368465 "DDFACT" 369533 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 367097 367140 367291 "DBLRESP" 367452 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 364965 365327 365688 "DBASE" 366863 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 364207 364445 364591 "DATAARY" 364864 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 363313 364166 364194 "D03FAFA" 364199 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 362420 363272 363300 "D03EEFA" 363305 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 360370 360836 361325 "D03AGNT" 361951 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 359659 360329 360357 "D02EJFA" 360362 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 358948 359618 359646 "D02CJFA" 359651 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 358237 358907 358935 "D02BHFA" 358940 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 357526 358196 358224 "D02BBFA" 358229 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 350723 352312 353918 "D02AGNT" 355940 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 348491 349014 349560 "D01WGTS" 350197 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 347558 348450 348478 "D01TRNS" 348483 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 346626 347517 347545 "D01GBFA" 347550 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 345694 346585 346613 "D01FCFA" 346618 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 344762 345653 345681 "D01ASFA" 345686 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 343830 344721 344749 "D01AQFA" 344754 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 342898 343789 343817 "D01APFA" 343822 T D01APFA (NIL) -8 NIL NIL NIL) (-199 341966 342857 342885 "D01ANFA" 342890 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 341034 341925 341953 "D01AMFA" 341958 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 340102 340993 341021 "D01ALFA" 341026 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 339170 340061 340089 "D01AKFA" 340094 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 338238 339129 339157 "D01AJFA" 339162 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 331533 333086 334647 "D01AGNT" 336697 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 330870 330998 331150 "CYCLOTOM" 331401 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 327603 328318 329045 "CYCLES" 330163 T CYCLES (NIL) -7 NIL NIL NIL) (-191 326915 327049 327220 "CVMP" 327464 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 324756 325014 325383 "CTRIGMNP" 326643 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 324192 324550 324623 "CTOR" 324703 T CTOR (NIL) -8 NIL NIL NIL) (-188 323701 323923 324024 "CTORKIND" 324111 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 322992 323308 323336 "CTORCAT" 323518 T CTORCAT (NIL) -9 NIL 323631 NIL) (-186 322590 322701 322860 "CTORCAT-" 322865 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 322052 322264 322372 "CTORCALL" 322514 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 321426 321525 321678 "CSTTOOLS" 321949 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 317225 317882 318640 "CRFP" 320738 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 316700 316946 317038 "CRCEAST" 317153 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 315747 315932 316160 "CRAPACK" 316504 NIL 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\ No newline at end of file
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+NIL 
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+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
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T T) -9 NIL 3215701 NIL) (-1301 3210253 3212394 3212782 "XPBWPOLY" 3213535 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1300 3205948 3208243 3208285 "XF" 3208906 NIL XF (NIL T) -9 NIL 3209306 NIL) (-1299 3205569 3205657 3205826 "XF-" 3205831 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1298 3200765 3202054 3202109 "XFALG" 3204281 NIL XFALG (NIL T T) -9 NIL 3205070 NIL) (-1297 3199898 3200002 3200207 "XEXPPKG" 3200657 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1296 3198007 3199748 3199844 "XDPOLY" 3199849 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1295 3196814 3197414 3197457 "XALG" 3197462 NIL XALG (NIL T) -9 NIL 3197573 NIL) (-1294 3190256 3194791 3195285 "WUTSET" 3196406 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1293 3188512 3189308 3189631 "WP" 3190067 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1292 3188114 3188334 3188404 "WHILEAST" 3188464 T WHILEAST (NIL) -8 NIL NIL NIL) (-1291 3187586 3187831 3187925 "WHEREAST" 3188042 T WHEREAST (NIL) -8 NIL NIL NIL) (-1290 3186472 3186670 3186965 "WFFINTBS" 3187383 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1289 3184376 3184803 3185265 "WEIER" 3186044 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1288 3183422 3183872 3183914 "VSPACE" 3184050 NIL VSPACE (NIL T) -9 NIL 3184124 NIL) (-1287 3183260 3183287 3183378 "VSPACE-" 3183383 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1286 3183069 3183111 3183179 "VOID" 3183214 T VOID (NIL) -8 NIL NIL NIL) (-1285 3181205 3181564 3181970 "VIEW" 3182685 T VIEW (NIL) -7 NIL NIL NIL) (-1284 3177629 3178268 3179005 "VIEWDEF" 3180490 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1283 3166933 3169177 3171350 "VIEW3D" 3175478 T VIEW3D (NIL) -8 NIL NIL NIL) (-1282 3159184 3160844 3162423 "VIEW2D" 3165376 T VIEW2D (NIL) -8 NIL NIL NIL) (-1281 3154537 3158954 3159046 "VECTOR" 3159127 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1280 3153114 3153373 3153691 "VECTOR2" 3154267 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1279 3146556 3150865 3150908 "VECTCAT" 3151903 NIL VECTCAT (NIL T) -9 NIL 3152490 NIL) (-1278 3145570 3145824 3146214 "VECTCAT-" 3146219 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1277 3145024 3145221 3145341 "VARIABLE" 3145485 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1276 3144957 3144962 3144992 "UTYPE" 3144997 T UTYPE (NIL) -9 NIL NIL NIL) (-1275 3143787 3143941 3144203 "UTSODETL" 3144783 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1274 3141227 3141687 3142211 "UTSODE" 3143328 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1273 3133065 3138853 3139342 "UTS" 3140796 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1272 3123852 3129221 3129264 "UTSCAT" 3130376 NIL UTSCAT (NIL T) -9 NIL 3131134 NIL) (-1271 3121200 3121922 3122911 "UTSCAT-" 3122916 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1270 3120827 3120870 3121003 "UTS2" 3121151 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1269 3115053 3117665 3117708 "URAGG" 3119778 NIL URAGG (NIL T) -9 NIL 3120501 NIL) (-1268 3111992 3112855 3113978 "URAGG-" 3113983 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1267 3107701 3110627 3111092 "UPXSSING" 3111656 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1266 3099767 3106948 3107221 "UPXS" 3107486 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1265 3092840 3099671 3099743 "UPXSCONS" 3099748 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1264 3082491 3089286 3089348 "UPXSCCA" 3089922 NIL UPXSCCA (NIL T T) -9 NIL 3090155 NIL) (-1263 3082129 3082214 3082388 "UPXSCCA-" 3082393 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1262 3071632 3078200 3078243 "UPXSCAT" 3078891 NIL UPXSCAT (NIL T) -9 NIL 3079500 NIL) (-1261 3071062 3071141 3071320 "UPXS2" 3071547 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1260 3069716 3069969 3070320 "UPSQFREE" 3070805 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1259 3063141 3066200 3066255 "UPSCAT" 3067335 NIL UPSCAT (NIL T T) -9 NIL 3068100 NIL) (-1258 3062345 3062552 3062879 "UPSCAT-" 3062884 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1257 3047841 3055698 3055741 "UPOLYC" 3057842 NIL UPOLYC (NIL T) -9 NIL 3059063 NIL) (-1256 3039169 3041595 3044742 "UPOLYC-" 3044747 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1255 3038796 3038839 3038972 "UPOLYC2" 3039120 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1254 3030518 3038479 3038608 "UP" 3038715 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1253 3029857 3029964 3030128 "UPMP" 3030407 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1252 3029410 3029491 3029630 "UPDIVP" 3029770 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1251 3027978 3028227 3028543 "UPDECOMP" 3029159 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1250 3027209 3027321 3027507 "UPCDEN" 3027862 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1249 3026728 3026797 3026946 "UP2" 3027134 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1248 3025195 3025932 3026209 "UNISEG" 3026486 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1247 3024410 3024537 3024742 "UNISEG2" 3025038 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1246 3023470 3023650 3023876 "UNIFACT" 3024226 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1245 3007231 3022647 3022898 "ULS" 3023277 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1244 2995094 3007135 3007207 "ULSCONS" 3007212 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1243 2976794 2988918 2988980 "ULSCCAT" 2989618 NIL ULSCCAT (NIL T T) -9 NIL 2989907 NIL) (-1242 2975844 2976089 2976477 "ULSCCAT-" 2976482 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1241 2965131 2971613 2971656 "ULSCAT" 2972519 NIL ULSCAT (NIL T) -9 NIL 2973250 NIL) (-1240 2964561 2964640 2964819 "ULS2" 2965046 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1239 2963680 2964190 2964297 "UINT8" 2964408 T UINT8 (NIL) -8 NIL NIL 2964493) (-1238 2962798 2963308 2963415 "UINT64" 2963526 T UINT64 (NIL) -8 NIL NIL 2963611) (-1237 2961916 2962426 2962533 "UINT32" 2962644 T UINT32 (NIL) -8 NIL NIL 2962729) (-1236 2961034 2961544 2961651 "UINT16" 2961762 T UINT16 (NIL) -8 NIL NIL 2961847) (-1235 2959337 2960294 2960324 "UFD" 2960536 T UFD (NIL) -9 NIL 2960650 NIL) (-1234 2959131 2959177 2959272 "UFD-" 2959277 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1233 2958213 2958396 2958612 "UDVO" 2958937 T UDVO (NIL) -7 NIL NIL NIL) (-1232 2956029 2956438 2956909 "UDPO" 2957777 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1231 2955962 2955967 2955997 "TYPE" 2956002 T TYPE (NIL) -9 NIL NIL NIL) (-1230 2955722 2955917 2955948 "TYPEAST" 2955953 T TYPEAST (NIL) -8 NIL NIL NIL) (-1229 2954693 2954895 2955135 "TWOFACT" 2955516 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1228 2953716 2954102 2954337 "TUPLE" 2954493 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1227 2951407 2951926 2952465 "TUBETOOL" 2953199 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1226 2950256 2950461 2950702 "TUBE" 2951200 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1225 2944985 2949228 2949511 "TS" 2950008 NIL TS (NIL T) -8 NIL NIL NIL) (-1224 2933625 2937744 2937841 "TSETCAT" 2943110 NIL TSETCAT (NIL T T T T) -9 NIL 2944641 NIL) (-1223 2928357 2929957 2931848 "TSETCAT-" 2931853 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1222 2922996 2923843 2924772 "TRMANIP" 2927493 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1221 2922437 2922500 2922663 "TRIMAT" 2922928 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1220 2920303 2920540 2920897 "TRIGMNIP" 2922186 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1219 2919823 2919936 2919966 "TRIGCAT" 2920179 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1218 2919492 2919571 2919712 "TRIGCAT-" 2919717 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1217 2916337 2918350 2918631 "TREE" 2919246 NIL TREE (NIL T) -8 NIL NIL NIL) (-1216 2915611 2916139 2916169 "TRANFUN" 2916204 T TRANFUN (NIL) -9 NIL 2916270 NIL) (-1215 2914890 2915081 2915361 "TRANFUN-" 2915366 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1214 2914694 2914726 2914787 "TOPSP" 2914851 T TOPSP (NIL) -7 NIL NIL NIL) (-1213 2914042 2914157 2914311 "TOOLSIGN" 2914575 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1212 2912676 2913219 2913458 "TEXTFILE" 2913825 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1211 2910588 2911129 2911558 "TEX" 2912269 T TEX (NIL) -8 NIL NIL NIL) (-1210 2910369 2910400 2910472 "TEX1" 2910551 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1209 2910017 2910080 2910170 "TEMUTL" 2910301 T TEMUTL (NIL) -7 NIL NIL NIL) (-1208 2908171 2908451 2908776 "TBCMPPK" 2909740 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1207 2899948 2906331 2906387 "TBAGG" 2906787 NIL TBAGG (NIL T T) -9 NIL 2906998 NIL) (-1206 2895018 2896506 2898260 "TBAGG-" 2898265 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1205 2894402 2894509 2894654 "TANEXP" 2894907 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1204 2893913 2894177 2894267 "TALGOP" 2894347 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1203 2887303 2893770 2893863 "TABLE" 2893868 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1202 2886715 2886814 2886952 "TABLEAU" 2887200 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1201 2881323 2882543 2883791 "TABLBUMP" 2885501 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1200 2880545 2880692 2880873 "SYSTEM" 2881164 T SYSTEM (NIL) -8 NIL NIL NIL) (-1199 2877004 2877703 2878486 "SYSSOLP" 2879796 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1198 2876802 2876959 2876990 "SYSPTR" 2876995 T SYSPTR (NIL) -8 NIL NIL NIL) (-1197 2875838 2876343 2876462 "SYSNNI" 2876648 NIL SYSNNI (NIL NIL) -8 NIL NIL 2876733) (-1196 2875137 2875596 2875675 "SYSINT" 2875735 NIL SYSINT (NIL NIL) -8 NIL NIL 2875780) (-1195 2871469 2872415 2873125 "SYNTAX" 2874449 T SYNTAX (NIL) -8 NIL NIL NIL) (-1194 2868627 2869229 2869861 "SYMTAB" 2870859 T SYMTAB (NIL) -8 NIL NIL NIL) (-1193 2863876 2864778 2865761 "SYMS" 2867666 T SYMS (NIL) -8 NIL NIL NIL) (-1192 2861111 2863334 2863564 "SYMPOLY" 2863681 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1191 2860628 2860703 2860826 "SYMFUNC" 2861023 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1190 2856648 2857940 2858753 "SYMBOL" 2859837 T SYMBOL (NIL) -8 NIL NIL NIL) (-1189 2850187 2851876 2853596 "SWITCH" 2854950 T SWITCH (NIL) -8 NIL NIL NIL) (-1188 2843421 2849008 2849311 "SUTS" 2849942 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2835487 2842668 2842941 "SUPXS" 2843206 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1186 2827157 2835105 2835231 "SUP" 2835396 NIL SUP (NIL T) -8 NIL NIL NIL) (-1185 2826316 2826443 2826660 "SUPFRACF" 2827025 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1184 2825937 2825996 2826109 "SUP2" 2826251 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1183 2824385 2824659 2825015 "SUMRF" 2825636 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1182 2823720 2823786 2823978 "SUMFS" 2824306 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1181 2807516 2822897 2823148 "SULS" 2823527 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1180 2807118 2807338 2807408 "SUCHTAST" 2807468 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1179 2806413 2806643 2806783 "SUCH" 2807026 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1178 2800280 2801319 2802278 "SUBSPACE" 2805501 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1177 2799710 2799800 2799964 "SUBRESP" 2800168 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1176 2793078 2794375 2795686 "STTF" 2798446 NIL STTF (NIL T) -7 NIL NIL NIL) (-1175 2787251 2788371 2789518 "STTFNC" 2791978 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1174 2778564 2780433 2782227 "STTAYLOR" 2785492 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1173 2771694 2778428 2778511 "STRTBL" 2778516 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1172 2767058 2771649 2771680 "STRING" 2771685 T STRING (NIL) -8 NIL NIL NIL) (-1171 2761887 2766401 2766431 "STRICAT" 2766490 T STRICAT (NIL) -9 NIL 2766552 NIL) (-1170 2754640 2759506 2760117 "STREAM" 2761311 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1169 2754150 2754227 2754371 "STREAM3" 2754557 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1168 2753132 2753315 2753550 "STREAM2" 2753963 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1167 2752820 2752872 2752965 "STREAM1" 2753074 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1166 2751836 2752017 2752248 "STINPROD" 2752636 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1165 2751388 2751598 2751628 "STEP" 2751708 T STEP (NIL) -9 NIL 2751786 NIL) (-1164 2750575 2750877 2751025 "STEPAST" 2751262 T STEPAST (NIL) -8 NIL NIL NIL) (-1163 2744007 2750474 2750551 "STBL" 2750556 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1162 2739102 2743198 2743241 "STAGG" 2743394 NIL STAGG (NIL T) -9 NIL 2743483 NIL) (-1161 2736804 2737406 2738278 "STAGG-" 2738283 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1160 2734951 2736574 2736666 "STACK" 2736747 NIL STACK (NIL T) -8 NIL NIL NIL) (-1159 2727646 2733092 2733548 "SREGSET" 2734581 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1158 2720071 2721440 2722953 "SRDCMPK" 2726252 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1157 2712956 2717481 2717511 "SRAGG" 2718814 T SRAGG (NIL) -9 NIL 2719422 NIL) (-1156 2711973 2712228 2712607 "SRAGG-" 2712612 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1155 2706344 2710920 2711341 "SQMATRIX" 2711599 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1154 2700029 2703062 2703789 "SPLTREE" 2705689 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1153 2695992 2696685 2697331 "SPLNODE" 2699455 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1152 2695039 2695272 2695302 "SPFCAT" 2695746 T SPFCAT (NIL) -9 NIL NIL NIL) (-1151 2693776 2693986 2694250 "SPECOUT" 2694797 T SPECOUT (NIL) -7 NIL NIL NIL) (-1150 2684886 2686758 2686788 "SPADXPT" 2691464 T SPADXPT (NIL) -9 NIL 2693628 NIL) (-1149 2684647 2684687 2684756 "SPADPRSR" 2684839 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1148 2682696 2684602 2684633 "SPADAST" 2684638 T SPADAST (NIL) -8 NIL NIL NIL) (-1147 2674641 2676414 2676457 "SPACEC" 2680830 NIL SPACEC (NIL T) -9 NIL 2682646 NIL) (-1146 2672771 2674573 2674622 "SPACE3" 2674627 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1145 2671523 2671694 2671985 "SORTPAK" 2672576 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1144 2669615 2669918 2670330 "SOLVETRA" 2671187 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1143 2668665 2668887 2669148 "SOLVESER" 2669388 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1142 2663969 2664857 2665852 "SOLVERAD" 2667717 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1141 2659784 2660393 2661122 "SOLVEFOR" 2663336 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1140 2654054 2659133 2659230 "SNTSCAT" 2659235 NIL SNTSCAT (NIL T T T T) -9 NIL 2659305 NIL) (-1139 2648160 2652377 2652768 "SMTS" 2653744 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1138 2642756 2648048 2648125 "SMP" 2648130 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1137 2640915 2641216 2641614 "SMITH" 2642453 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1136 2633468 2637754 2637857 "SMATCAT" 2639208 NIL SMATCAT (NIL NIL T T T) -9 NIL 2639758 NIL) (-1135 2630186 2631071 2632329 "SMATCAT-" 2632334 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1134 2627852 2629422 2629465 "SKAGG" 2629726 NIL SKAGG (NIL T) -9 NIL 2629861 NIL) (-1133 2624128 2627325 2627509 "SINT" 2627661 T SINT (NIL) -8 NIL NIL 2627823) (-1132 2623900 2623938 2624004 "SIMPAN" 2624084 T SIMPAN (NIL) -7 NIL NIL NIL) (-1131 2623179 2623435 2623575 "SIG" 2623782 T SIG (NIL) -8 NIL NIL NIL) (-1130 2622017 2622238 2622513 "SIGNRF" 2622938 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1129 2620850 2621001 2621285 "SIGNEF" 2621846 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1128 2620156 2620433 2620557 "SIGAST" 2620748 T SIGAST (NIL) -8 NIL NIL NIL) (-1127 2617846 2618300 2618806 "SHP" 2619697 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1126 2611561 2617747 2617823 "SHDP" 2617828 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1125 2611134 2611326 2611356 "SGROUP" 2611449 T SGROUP (NIL) -9 NIL 2611511 NIL) (-1124 2610992 2611018 2611091 "SGROUP-" 2611096 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1123 2607783 2608481 2609204 "SGCF" 2610291 T SGCF (NIL) -7 NIL NIL NIL) (-1122 2602151 2607230 2607327 "SFRTCAT" 2607332 NIL SFRTCAT (NIL T T T T) -9 NIL 2607371 NIL) (-1121 2595572 2596590 2597726 "SFRGCD" 2601134 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1120 2588698 2589771 2590957 "SFQCMPK" 2594505 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1119 2588318 2588407 2588518 "SFORT" 2588639 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1118 2587436 2588158 2588279 "SEXOF" 2588284 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1117 2586543 2587317 2587385 "SEX" 2587390 T SEX (NIL) -8 NIL NIL NIL) (-1116 2582324 2583039 2583134 "SEXCAT" 2585756 NIL SEXCAT (NIL T T T T T) -9 NIL 2586316 NIL) (-1115 2579477 2582258 2582306 "SET" 2582311 NIL SET (NIL T) -8 NIL NIL NIL) (-1114 2577701 2578190 2578495 "SETMN" 2579218 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1113 2577197 2577349 2577379 "SETCAT" 2577555 T SETCAT (NIL) -9 NIL 2577665 NIL) (-1112 2576889 2576967 2577097 "SETCAT-" 2577102 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1111 2573250 2575350 2575393 "SETAGG" 2576263 NIL SETAGG (NIL T) -9 NIL 2576603 NIL) (-1110 2572708 2572824 2573061 "SETAGG-" 2573066 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1109 2572151 2572404 2572505 "SEQAST" 2572629 T SEQAST (NIL) -8 NIL NIL NIL) (-1108 2571350 2571644 2571705 "SEGXCAT" 2571991 NIL SEGXCAT (NIL T T) -9 NIL 2572111 NIL) (-1107 2570356 2571016 2571198 "SEG" 2571203 NIL SEG (NIL T) -8 NIL NIL NIL) (-1106 2569335 2569549 2569592 "SEGCAT" 2570114 NIL SEGCAT (NIL T) -9 NIL 2570335 NIL) (-1105 2568267 2568698 2568906 "SEGBIND" 2569162 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1104 2567888 2567947 2568060 "SEGBIND2" 2568202 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1103 2567461 2567689 2567766 "SEGAST" 2567833 T SEGAST (NIL) -8 NIL NIL NIL) (-1102 2566680 2566806 2567010 "SEG2" 2567305 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1101 2566090 2566615 2566662 "SDVAR" 2566667 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1100 2558528 2565860 2565990 "SDPOL" 2565995 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1099 2557121 2557387 2557706 "SCPKG" 2558243 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1098 2556285 2556457 2556649 "SCOPE" 2556951 T SCOPE (NIL) -8 NIL NIL NIL) (-1097 2555505 2555639 2555818 "SCACHE" 2556140 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1096 2555151 2555337 2555367 "SASTCAT" 2555372 T SASTCAT (NIL) -9 NIL 2555385 NIL) (-1095 2554638 2554986 2555062 "SAOS" 2555097 T SAOS (NIL) -8 NIL NIL NIL) (-1094 2554203 2554238 2554411 "SAERFFC" 2554597 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1093 2548053 2554100 2554180 "SAE" 2554185 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1092 2547646 2547681 2547840 "SAEFACT" 2548012 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1091 2545967 2546281 2546682 "RURPK" 2547312 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1090 2544604 2544910 2545215 "RULESET" 2545801 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1089 2541827 2542357 2542815 "RULE" 2544285 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1088 2541439 2541621 2541704 "RULECOLD" 2541779 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1087 2541229 2541257 2541328 "RTVALUE" 2541390 T RTVALUE (NIL) -8 NIL NIL NIL) (-1086 2540700 2540946 2541040 "RSTRCAST" 2541157 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1085 2535548 2536343 2537263 "RSETGCD" 2539899 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1084 2524778 2529857 2529954 "RSETCAT" 2534073 NIL RSETCAT (NIL T T T T) -9 NIL 2535170 NIL) (-1083 2522705 2523244 2524068 "RSETCAT-" 2524073 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1082 2515091 2516467 2517987 "RSDCMPK" 2521304 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1081 2513070 2513537 2513611 "RRCC" 2514697 NIL RRCC (NIL T T) -9 NIL 2515041 NIL) (-1080 2512421 2512595 2512874 "RRCC-" 2512879 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1079 2511864 2512117 2512218 "RPTAST" 2512342 T RPTAST (NIL) -8 NIL NIL NIL) (-1078 2485580 2495028 2495095 "RPOLCAT" 2505761 NIL RPOLCAT (NIL T T T) -9 NIL 2508921 NIL) (-1077 2477078 2479418 2482540 "RPOLCAT-" 2482545 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1076 2468009 2475289 2475771 "ROUTINE" 2476618 T ROUTINE (NIL) -8 NIL NIL NIL) (-1075 2464756 2467635 2467775 "ROMAN" 2467891 T ROMAN (NIL) -8 NIL NIL NIL) (-1074 2463000 2463616 2463876 "ROIRC" 2464561 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1073 2459232 2461516 2461546 "RNS" 2461850 T RNS (NIL) -9 NIL 2462124 NIL) (-1072 2457741 2458124 2458658 "RNS-" 2458733 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1071 2457144 2457552 2457582 "RNG" 2457587 T RNG (NIL) -9 NIL 2457608 NIL) (-1070 2456147 2456509 2456711 "RNGBIND" 2456995 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1069 2455546 2455934 2455977 "RMODULE" 2455982 NIL RMODULE (NIL T) -9 NIL 2456009 NIL) (-1068 2454382 2454476 2454812 "RMCAT2" 2455447 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1067 2451232 2453728 2454025 "RMATRIX" 2454144 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1066 2444059 2446319 2446434 "RMATCAT" 2449793 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2450775 NIL) (-1065 2443434 2443581 2443888 "RMATCAT-" 2443893 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1064 2442835 2443056 2443099 "RLINSET" 2443293 NIL RLINSET (NIL T) -9 NIL 2443384 NIL) (-1063 2442402 2442477 2442605 "RINTERP" 2442754 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1062 2441460 2442014 2442044 "RING" 2442100 T RING (NIL) -9 NIL 2442192 NIL) (-1061 2441252 2441296 2441393 "RING-" 2441398 NIL RING- (NIL T) -8 NIL NIL NIL) (-1060 2440093 2440330 2440588 "RIDIST" 2441016 T RIDIST (NIL) -7 NIL NIL NIL) (-1059 2431382 2439561 2439767 "RGCHAIN" 2439941 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1058 2430732 2431138 2431179 "RGBCSPC" 2431237 NIL RGBCSPC (NIL T) -9 NIL 2431289 NIL) (-1057 2429890 2430271 2430312 "RGBCMDL" 2430544 NIL RGBCMDL (NIL T) -9 NIL 2430658 NIL) (-1056 2426884 2427498 2428168 "RF" 2429254 NIL RF (NIL T) -7 NIL NIL NIL) (-1055 2426530 2426593 2426696 "RFFACTOR" 2426815 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1054 2426255 2426290 2426387 "RFFACT" 2426489 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1053 2424372 2424736 2425118 "RFDIST" 2425895 T RFDIST (NIL) -7 NIL NIL NIL) (-1052 2423825 2423917 2424080 "RETSOL" 2424274 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1051 2423461 2423541 2423584 "RETRACT" 2423717 NIL RETRACT (NIL T) -9 NIL 2423804 NIL) (-1050 2423310 2423335 2423422 "RETRACT-" 2423427 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1049 2422912 2423132 2423202 "RETAST" 2423262 T RETAST (NIL) -8 NIL NIL NIL) (-1048 2415650 2422565 2422692 "RESULT" 2422807 T RESULT (NIL) -8 NIL NIL NIL) (-1047 2414241 2414919 2415118 "RESRING" 2415553 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1046 2413877 2413926 2414024 "RESLATC" 2414178 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1045 2413582 2413617 2413724 "REPSQ" 2413836 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1044 2411004 2411584 2412186 "REP" 2413002 T REP (NIL) -7 NIL NIL NIL) (-1043 2410701 2410736 2410847 "REPDB" 2410963 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1042 2404601 2405990 2407213 "REP2" 2409513 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1041 2400978 2401659 2402467 "REP1" 2403828 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1040 2393674 2399119 2399575 "REGSET" 2400608 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1039 2392439 2392822 2393072 "REF" 2393459 NIL REF (NIL T) -8 NIL NIL NIL) (-1038 2391816 2391919 2392086 "REDORDER" 2392323 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1037 2387784 2391029 2391256 "RECLOS" 2391644 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1036 2386836 2387017 2387232 "REALSOLV" 2387591 T REALSOLV (NIL) -7 NIL NIL NIL) (-1035 2386682 2386723 2386753 "REAL" 2386758 T REAL (NIL) -9 NIL 2386793 NIL) (-1034 2383165 2383967 2384851 "REAL0Q" 2385847 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1033 2378766 2379754 2380815 "REAL0" 2382146 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1032 2378237 2378483 2378577 "RDUCEAST" 2378694 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1031 2377642 2377714 2377921 "RDIV" 2378159 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1030 2376710 2376884 2377097 "RDIST" 2377464 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1029 2375307 2375594 2375966 "RDETRS" 2376418 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1028 2373119 2373573 2374111 "RDETR" 2374849 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1027 2371744 2372022 2372419 "RDEEFS" 2372835 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1026 2370253 2370559 2370984 "RDEEF" 2371432 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1025 2364314 2367234 2367264 "RCFIELD" 2368559 T RCFIELD (NIL) -9 NIL 2369290 NIL) (-1024 2362378 2362882 2363578 "RCFIELD-" 2363653 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1023 2358647 2360479 2360522 "RCAGG" 2361606 NIL RCAGG (NIL T) -9 NIL 2362071 NIL) (-1022 2358275 2358369 2358532 "RCAGG-" 2358537 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1021 2357610 2357722 2357887 "RATRET" 2358159 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1020 2357163 2357230 2357351 "RATFACT" 2357538 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1019 2356471 2356591 2356743 "RANDSRC" 2357033 T RANDSRC (NIL) -7 NIL NIL NIL) (-1018 2356205 2356249 2356322 "RADUTIL" 2356420 T RADUTIL (NIL) -7 NIL NIL NIL) (-1017 2349226 2355036 2355347 "RADIX" 2355928 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1016 2340742 2349068 2349198 "RADFF" 2349203 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1015 2340389 2340464 2340494 "RADCAT" 2340654 T RADCAT (NIL) -9 NIL NIL NIL) (-1014 2340171 2340219 2340319 "RADCAT-" 2340324 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1013 2338269 2339941 2340033 "QUEUE" 2340114 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1012 2334717 2338202 2338250 "QUAT" 2338255 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1011 2334348 2334391 2334522 "QUATCT2" 2334668 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1010 2327571 2331006 2331048 "QUATCAT" 2331839 NIL QUATCAT (NIL T) -9 NIL 2332605 NIL) (-1009 2323710 2324747 2326137 "QUATCAT-" 2326233 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1008 2321175 2322786 2322829 "QUAGG" 2323210 NIL QUAGG (NIL T) -9 NIL 2323385 NIL) (-1007 2320777 2320997 2321067 "QQUTAST" 2321127 T QQUTAST (NIL) -8 NIL NIL NIL) (-1006 2319790 2320290 2320455 "QFORM" 2320658 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1005 2310624 2315952 2315994 "QFCAT" 2316662 NIL QFCAT (NIL T) -9 NIL 2317663 NIL) (-1004 2305969 2307232 2308906 "QFCAT-" 2309002 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1003 2305600 2305643 2305774 "QFCAT2" 2305920 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1002 2305055 2305165 2305297 "QEQUAT" 2305490 T QEQUAT (NIL) -8 NIL NIL NIL) (-1001 2298181 2299254 2300440 "QCMPACK" 2303988 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1000 2295719 2296167 2296597 "QALGSET" 2297836 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-999 2294957 2295133 2295367 "QALGSET2" 2295537 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-998 2293647 2293871 2294188 "PWFFINTB" 2294730 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-997 2291829 2291997 2292351 "PUSHVAR" 2293461 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-996 2287747 2288801 2288842 "PTRANFN" 2290726 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-995 2286149 2286440 2286762 "PTPACK" 2287458 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-994 2285781 2285838 2285947 "PTFUNC2" 2286086 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-993 2280226 2284623 2284664 "PTCAT" 2284960 NIL PTCAT (NIL T) -9 NIL 2285113 NIL) (-992 2279884 2279919 2280043 "PSQFR" 2280185 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-991 2278479 2278777 2279111 "PSEUDLIN" 2279582 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-990 2265242 2267613 2269937 "PSETPK" 2276239 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-989 2258260 2261000 2261096 "PSETCAT" 2264117 NIL PSETCAT (NIL T T T T) -9 NIL 2264931 NIL) (-988 2256096 2256730 2257551 "PSETCAT-" 2257556 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-987 2255445 2255610 2255638 "PSCURVE" 2255906 T PSCURVE (NIL) -9 NIL 2256073 NIL) (-986 2251443 2252959 2253024 "PSCAT" 2253868 NIL PSCAT (NIL T T T) -9 NIL 2254108 NIL) (-985 2250506 2250722 2251122 "PSCAT-" 2251127 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-984 2248865 2249575 2249838 "PRTITION" 2250263 T PRTITION (NIL) -8 NIL NIL NIL) (-983 2248340 2248586 2248678 "PRTDAST" 2248793 T PRTDAST (NIL) -8 NIL NIL NIL) (-982 2237430 2239644 2241832 "PRS" 2246202 NIL PRS (NIL T T) -7 NIL NIL NIL) (-981 2235241 2236780 2236820 "PRQAGG" 2237003 NIL PRQAGG (NIL T) -9 NIL 2237105 NIL) (-980 2234577 2234882 2234910 "PROPLOG" 2235049 T PROPLOG (NIL) -9 NIL 2235164 NIL) (-979 2234181 2234238 2234361 "PROPFUN2" 2234500 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-978 2233496 2233617 2233789 "PROPFUN1" 2234042 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-977 2231677 2232243 2232540 "PROPFRML" 2233232 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-976 2231146 2231253 2231381 "PROPERTY" 2231569 T PROPERTY (NIL) -8 NIL NIL NIL) (-975 2225204 2229312 2230132 "PRODUCT" 2230372 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-974 2222482 2224662 2224896 "PR" 2225015 NIL PR (NIL T T) -8 NIL NIL NIL) (-973 2222278 2222310 2222369 "PRINT" 2222443 T PRINT (NIL) -7 NIL NIL NIL) (-972 2221618 2221735 2221887 "PRIMES" 2222158 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-971 2219683 2220084 2220550 "PRIMELT" 2221197 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-970 2219412 2219461 2219489 "PRIMCAT" 2219613 T PRIMCAT (NIL) -9 NIL NIL NIL) (-969 2215527 2219350 2219395 "PRIMARR" 2219400 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-968 2214534 2214712 2214940 "PRIMARR2" 2215345 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-967 2214177 2214233 2214344 "PREASSOC" 2214472 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-966 2213652 2213785 2213813 "PPCURVE" 2214018 T PPCURVE (NIL) -9 NIL 2214154 NIL) (-965 2213247 2213447 2213530 "PORTNUM" 2213589 T PORTNUM (NIL) -8 NIL NIL NIL) (-964 2210606 2211005 2211597 "POLYROOT" 2212828 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-963 2204699 2210210 2210370 "POLY" 2210479 NIL POLY (NIL T) -8 NIL NIL NIL) (-962 2204082 2204140 2204374 "POLYLIFT" 2204635 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-961 2200357 2200806 2201435 "POLYCATQ" 2203627 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-960 2186939 2192156 2192221 "POLYCAT" 2195735 NIL POLYCAT (NIL T T T) -9 NIL 2197613 NIL) (-959 2180166 2182090 2184554 "POLYCAT-" 2184559 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-958 2179753 2179821 2179941 "POLY2UP" 2180092 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-957 2179385 2179442 2179551 "POLY2" 2179690 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-956 2178070 2178309 2178585 "POLUTIL" 2179159 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-955 2176425 2176702 2177033 "POLTOPOL" 2177792 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-954 2171890 2176361 2176407 "POINT" 2176412 NIL POINT (NIL T) -8 NIL NIL NIL) (-953 2170077 2170434 2170809 "PNTHEORY" 2171535 T PNTHEORY (NIL) -7 NIL NIL NIL) (-952 2168535 2168832 2169231 "PMTOOLS" 2169775 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-951 2168128 2168206 2168323 "PMSYM" 2168451 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-950 2167636 2167705 2167880 "PMQFCAT" 2168053 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-949 2166991 2167101 2167257 "PMPRED" 2167513 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-948 2166384 2166470 2166632 "PMPREDFS" 2166892 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-947 2165048 2165256 2165634 "PMPLCAT" 2166146 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-946 2164580 2164659 2164811 "PMLSAGG" 2164963 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-945 2164053 2164129 2164311 "PMKERNEL" 2164498 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-944 2163670 2163745 2163858 "PMINS" 2163972 NIL PMINS (NIL T) -7 NIL NIL NIL) (-943 2163112 2163181 2163390 "PMFS" 2163595 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-942 2162340 2162458 2162663 "PMDOWN" 2162989 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-941 2161507 2161665 2161846 "PMASS" 2162179 T PMASS (NIL) -7 NIL NIL NIL) (-940 2160780 2160890 2161053 "PMASSFS" 2161394 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-939 2160435 2160503 2160597 "PLOTTOOL" 2160706 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-938 2155042 2156246 2157394 "PLOT" 2159307 T PLOT (NIL) -8 NIL NIL NIL) (-937 2150846 2151890 2152811 "PLOT3D" 2154141 T PLOT3D (NIL) -8 NIL NIL NIL) (-936 2149758 2149935 2150170 "PLOT1" 2150650 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-935 2125149 2129824 2134675 "PLEQN" 2145024 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-934 2124467 2124589 2124769 "PINTERP" 2125014 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-933 2124160 2124207 2124310 "PINTERPA" 2124414 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-932 2123376 2123924 2124011 "PI" 2124051 T PI (NIL) -8 NIL NIL 2124118) (-931 2121673 2122648 2122676 "PID" 2122858 T PID (NIL) -9 NIL 2122992 NIL) (-930 2121424 2121461 2121536 "PICOERCE" 2121630 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-929 2120744 2120883 2121059 "PGROEB" 2121280 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-928 2116331 2117145 2118050 "PGE" 2119859 T PGE (NIL) -7 NIL NIL NIL) (-927 2114454 2114701 2115067 "PGCD" 2116048 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-926 2113792 2113895 2114056 "PFRPAC" 2114338 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-925 2110432 2112340 2112693 "PFR" 2113471 NIL PFR (NIL T) -8 NIL NIL NIL) (-924 2108821 2109065 2109390 "PFOTOOLS" 2110179 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-923 2107354 2107593 2107944 "PFOQ" 2108578 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-922 2105855 2106067 2106423 "PFO" 2107138 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-921 2102408 2105744 2105813 "PF" 2105818 NIL PF (NIL NIL) -8 NIL NIL NIL) (-920 2099742 2101013 2101041 "PFECAT" 2101626 T PFECAT (NIL) -9 NIL 2102010 NIL) (-919 2099187 2099341 2099555 "PFECAT-" 2099560 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-918 2097790 2098042 2098343 "PFBRU" 2098936 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-917 2095656 2096008 2096440 "PFBR" 2097441 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-916 2091702 2093168 2093815 "PERM" 2095042 NIL PERM (NIL T) -8 NIL NIL NIL) (-915 2086936 2087909 2088779 "PERMGRP" 2090865 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-914 2085055 2086015 2086056 "PERMCAT" 2086456 NIL PERMCAT (NIL T) -9 NIL 2086754 NIL) (-913 2084708 2084749 2084873 "PERMAN" 2085008 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-912 2082196 2084373 2084495 "PENDTREE" 2084619 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-911 2080220 2080988 2081029 "PDRING" 2081686 NIL PDRING (NIL T) -9 NIL 2081972 NIL) (-910 2079323 2079541 2079903 "PDRING-" 2079908 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-909 2076538 2077316 2077984 "PDEPROB" 2078675 T PDEPROB (NIL) -8 NIL NIL NIL) (-908 2074083 2074587 2075142 "PDEPACK" 2076003 T PDEPACK (NIL) -7 NIL NIL NIL) (-907 2072995 2073185 2073436 "PDECOMP" 2073882 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-906 2070574 2071417 2071445 "PDECAT" 2072232 T PDECAT (NIL) -9 NIL 2072945 NIL) (-905 2070325 2070358 2070448 "PCOMP" 2070535 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-904 2068503 2069126 2069423 "PBWLB" 2070054 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-903 2060976 2062576 2063914 "PATTERN" 2067186 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-902 2060608 2060665 2060774 "PATTERN2" 2060913 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-901 2058365 2058753 2059210 "PATTERN1" 2060197 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-900 2055733 2056314 2056795 "PATRES" 2057930 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-899 2055297 2055364 2055496 "PATRES2" 2055660 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-898 2053180 2053585 2053992 "PATMATCH" 2054964 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-897 2052690 2052899 2052940 "PATMAB" 2053047 NIL PATMAB (NIL T) -9 NIL 2053130 NIL) (-896 2051208 2051544 2051802 "PATLRES" 2052495 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-895 2050754 2050877 2050918 "PATAB" 2050923 NIL PATAB (NIL T) -9 NIL 2051095 NIL) (-894 2048936 2049331 2049754 "PARTPERM" 2050351 T PARTPERM (NIL) -7 NIL NIL NIL) (-893 2048557 2048620 2048722 "PARSURF" 2048867 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-892 2048189 2048246 2048355 "PARSU2" 2048494 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-891 2047953 2047993 2048060 "PARSER" 2048142 T PARSER (NIL) -7 NIL NIL NIL) (-890 2047574 2047637 2047739 "PARSCURV" 2047884 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-889 2047206 2047263 2047372 "PARSC2" 2047511 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-888 2046845 2046903 2047000 "PARPCURV" 2047142 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-887 2046477 2046534 2046643 "PARPC2" 2046782 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-886 2045538 2045850 2046032 "PARAMAST" 2046315 T PARAMAST (NIL) -8 NIL NIL NIL) (-885 2045058 2045144 2045263 "PAN2EXPR" 2045439 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-884 2043835 2044179 2044407 "PALETTE" 2044850 T PALETTE (NIL) -8 NIL NIL NIL) (-883 2042228 2042840 2043200 "PAIR" 2043521 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-882 2036007 2041485 2041680 "PADICRC" 2042082 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-881 2029131 2035351 2035536 "PADICRAT" 2035854 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-880 2027446 2029068 2029113 "PADIC" 2029118 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-879 2024556 2026120 2026160 "PADICCT" 2026741 NIL PADICCT (NIL NIL) -9 NIL 2027023 NIL) (-878 2023513 2023713 2023981 "PADEPAC" 2024343 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-877 2022725 2022858 2023064 "PADE" 2023375 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-876 2021112 2021933 2022213 "OWP" 2022529 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-875 2020605 2020818 2020915 "OVERSET" 2021035 T OVERSET (NIL) -8 NIL NIL NIL) (-874 2019651 2020210 2020382 "OVAR" 2020473 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-873 2018915 2019036 2019197 "OUT" 2019510 T OUT (NIL) -7 NIL NIL NIL) (-872 2007787 2010024 2012224 "OUTFORM" 2016735 T OUTFORM (NIL) -8 NIL NIL NIL) (-871 2007123 2007384 2007511 "OUTBFILE" 2007680 T OUTBFILE (NIL) -8 NIL NIL NIL) (-870 2006430 2006595 2006623 "OUTBCON" 2006941 T OUTBCON (NIL) -9 NIL 2007107 NIL) (-869 2006031 2006143 2006300 "OUTBCON-" 2006305 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-868 2005411 2005760 2005849 "OSI" 2005962 T OSI (NIL) -8 NIL NIL NIL) (-867 2004941 2005279 2005307 "OSGROUP" 2005312 T OSGROUP (NIL) -9 NIL 2005334 NIL) (-866 2003686 2003913 2004198 "ORTHPOL" 2004688 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-865 2001237 2003521 2003642 "OREUP" 2003647 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-864 1998640 2000928 2001055 "ORESUP" 2001179 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-863 1996168 1996668 1997229 "OREPCTO" 1998129 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-862 1989854 1992055 1992096 "OREPCAT" 1994444 NIL OREPCAT (NIL T) -9 NIL 1995548 NIL) (-861 1987001 1987783 1988841 "OREPCAT-" 1988846 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-860 1986152 1986450 1986478 "ORDSET" 1986787 T ORDSET (NIL) -9 NIL 1986951 NIL) (-859 1985583 1985731 1985955 "ORDSET-" 1985960 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-858 1984148 1984939 1984967 "ORDRING" 1985169 T ORDRING (NIL) -9 NIL 1985294 NIL) (-857 1983793 1983887 1984031 "ORDRING-" 1984036 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-856 1983173 1983636 1983664 "ORDMON" 1983669 T ORDMON (NIL) -9 NIL 1983690 NIL) (-855 1982335 1982482 1982677 "ORDFUNS" 1983022 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-854 1981673 1982092 1982120 "ORDFIN" 1982185 T ORDFIN (NIL) -9 NIL 1982259 NIL) (-853 1978232 1980259 1980668 "ORDCOMP" 1981297 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-852 1977498 1977625 1977811 "ORDCOMP2" 1978092 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-851 1974079 1974989 1975803 "OPTPROB" 1976704 T OPTPROB (NIL) -8 NIL NIL NIL) (-850 1970881 1971520 1972224 "OPTPACK" 1973395 T OPTPACK (NIL) -7 NIL NIL NIL) (-849 1968568 1969334 1969362 "OPTCAT" 1970181 T OPTCAT (NIL) -9 NIL 1970831 NIL) (-848 1967952 1968245 1968350 "OPSIG" 1968483 T OPSIG (NIL) -8 NIL NIL NIL) (-847 1967720 1967759 1967825 "OPQUERY" 1967906 T OPQUERY (NIL) -7 NIL NIL NIL) (-846 1964851 1966031 1966535 "OP" 1967249 NIL OP (NIL T) -8 NIL NIL NIL) (-845 1964225 1964451 1964492 "OPERCAT" 1964704 NIL OPERCAT (NIL T) -9 NIL 1964801 NIL) (-844 1963980 1964036 1964153 "OPERCAT-" 1964158 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-843 1960793 1962777 1963146 "ONECOMP" 1963644 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-842 1960098 1960213 1960387 "ONECOMP2" 1960665 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1959517 1959623 1959753 "OMSERVER" 1959988 T OMSERVER (NIL) -7 NIL NIL NIL) (-840 1956379 1958957 1958997 "OMSAGG" 1959058 NIL OMSAGG (NIL T) -9 NIL 1959122 NIL) (-839 1955002 1955265 1955547 "OMPKG" 1956117 T OMPKG (NIL) -7 NIL NIL NIL) (-838 1954432 1954535 1954563 "OM" 1954862 T OM (NIL) -9 NIL NIL NIL) (-837 1952979 1953981 1954150 "OMLO" 1954313 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-836 1951939 1952086 1952306 "OMEXPR" 1952805 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-835 1951230 1951485 1951621 "OMERR" 1951823 T OMERR (NIL) -8 NIL NIL NIL) (-834 1950381 1950651 1950811 "OMERRK" 1951090 T OMERRK (NIL) -8 NIL NIL NIL) (-833 1949832 1950058 1950166 "OMENC" 1950293 T OMENC (NIL) -8 NIL NIL NIL) (-832 1943727 1944912 1946083 "OMDEV" 1948681 T OMDEV (NIL) -8 NIL NIL NIL) (-831 1942796 1942967 1943161 "OMCONN" 1943553 T OMCONN (NIL) -8 NIL NIL NIL) (-830 1941317 1942293 1942321 "OINTDOM" 1942326 T OINTDOM (NIL) -9 NIL 1942347 NIL) (-829 1938655 1940005 1940342 "OFMONOID" 1941012 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-828 1938066 1938592 1938637 "ODVAR" 1938642 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-827 1935489 1937811 1937966 "ODR" 1937971 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-826 1927981 1935265 1935391 "ODPOL" 1935396 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-825 1921666 1927853 1927958 "ODP" 1927963 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-824 1920432 1920647 1920922 "ODETOOLS" 1921440 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-823 1917399 1918057 1918773 "ODESYS" 1919765 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-822 1912281 1913189 1914214 "ODERTRIC" 1916474 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-821 1911707 1911789 1911983 "ODERED" 1912193 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-820 1908595 1909143 1909820 "ODERAT" 1911130 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-819 1905554 1906019 1906616 "ODEPRRIC" 1908124 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-818 1903497 1904093 1904579 "ODEPROB" 1905088 T ODEPROB (NIL) -8 NIL NIL NIL) (-817 1900017 1900502 1901149 "ODEPRIM" 1902976 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-816 1899266 1899368 1899628 "ODEPAL" 1899909 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-815 1895428 1896219 1897083 "ODEPACK" 1898422 T ODEPACK (NIL) -7 NIL NIL NIL) (-814 1894489 1894596 1894818 "ODEINT" 1895317 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-813 1888590 1890015 1891462 "ODEIFTBL" 1893062 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-812 1883988 1884774 1885726 "ODEEF" 1887749 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-811 1883337 1883426 1883649 "ODECONST" 1883893 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-810 1881462 1882123 1882151 "ODECAT" 1882756 T ODECAT (NIL) -9 NIL 1883287 NIL) (-809 1878317 1881167 1881289 "OCT" 1881372 NIL OCT (NIL T) -8 NIL NIL NIL) (-808 1877955 1877998 1878125 "OCTCT2" 1878268 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-807 1872566 1875001 1875041 "OC" 1876138 NIL OC (NIL T) -9 NIL 1876996 NIL) (-806 1869793 1870541 1871531 "OC-" 1871625 NIL OC- (NIL T T) -8 NIL NIL NIL) (-805 1869145 1869613 1869641 "OCAMON" 1869646 T OCAMON (NIL) -9 NIL 1869667 NIL) (-804 1868676 1869017 1869045 "OASGP" 1869050 T OASGP (NIL) -9 NIL 1869070 NIL) (-803 1867937 1868426 1868454 "OAMONS" 1868494 T OAMONS (NIL) -9 NIL 1868537 NIL) (-802 1867351 1867784 1867812 "OAMON" 1867817 T OAMON (NIL) -9 NIL 1867837 NIL) (-801 1866609 1867127 1867155 "OAGROUP" 1867160 T OAGROUP (NIL) -9 NIL 1867180 NIL) (-800 1866299 1866349 1866437 "NUMTUBE" 1866553 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-799 1859872 1861390 1862926 "NUMQUAD" 1864783 T NUMQUAD (NIL) -7 NIL NIL NIL) (-798 1855628 1856616 1857641 "NUMODE" 1858867 T NUMODE (NIL) -7 NIL NIL NIL) (-797 1852983 1853863 1853891 "NUMINT" 1854814 T NUMINT (NIL) -9 NIL 1855578 NIL) (-796 1851931 1852128 1852346 "NUMFMT" 1852785 T NUMFMT (NIL) -7 NIL NIL NIL) (-795 1838290 1841235 1843767 "NUMERIC" 1849438 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-794 1832660 1837739 1837834 "NTSCAT" 1837839 NIL NTSCAT (NIL T T T T) -9 NIL 1837878 NIL) (-793 1831854 1832019 1832212 "NTPOLFN" 1832499 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-792 1819842 1828679 1829491 "NSUP" 1831075 NIL NSUP (NIL T) -8 NIL NIL NIL) (-791 1819474 1819531 1819640 "NSUP2" 1819779 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-790 1809611 1819248 1819381 "NSMP" 1819386 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-789 1808043 1808344 1808701 "NREP" 1809299 NIL NREP (NIL T) -7 NIL NIL NIL) (-788 1806634 1806886 1807244 "NPCOEF" 1807786 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-787 1805700 1805815 1806031 "NORMRETR" 1806515 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-786 1803741 1804031 1804440 "NORMPK" 1805408 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-785 1803426 1803454 1803578 "NORMMA" 1803707 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-784 1803226 1803383 1803412 "NONE" 1803417 T NONE (NIL) -8 NIL NIL NIL) (-783 1803015 1803044 1803113 "NONE1" 1803190 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-782 1802512 1802574 1802753 "NODE1" 1802947 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-781 1800793 1801644 1801899 "NNI" 1802246 T NNI (NIL) -8 NIL NIL 1802481) (-780 1799213 1799526 1799890 "NLINSOL" 1800461 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-779 1795454 1796449 1797348 "NIPROB" 1798334 T NIPROB (NIL) -8 NIL NIL NIL) (-778 1794211 1794445 1794747 "NFINTBAS" 1795216 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-777 1793385 1793861 1793902 "NETCLT" 1794074 NIL NETCLT (NIL T) -9 NIL 1794156 NIL) (-776 1792093 1792324 1792605 "NCODIV" 1793153 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-775 1791855 1791892 1791967 "NCNTFRAC" 1792050 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-774 1790035 1790399 1790819 "NCEP" 1791480 NIL NCEP (NIL T) -7 NIL NIL NIL) (-773 1788886 1789659 1789687 "NASRING" 1789797 T NASRING (NIL) -9 NIL 1789877 NIL) (-772 1788681 1788725 1788819 "NASRING-" 1788824 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-771 1787788 1788313 1788341 "NARNG" 1788458 T NARNG (NIL) -9 NIL 1788549 NIL) (-770 1787480 1787547 1787681 "NARNG-" 1787686 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-769 1786359 1786566 1786801 "NAGSP" 1787265 T NAGSP (NIL) -7 NIL NIL NIL) (-768 1777631 1779315 1780988 "NAGS" 1784706 T NAGS (NIL) -7 NIL NIL NIL) (-767 1776179 1776487 1776818 "NAGF07" 1777320 T NAGF07 (NIL) -7 NIL NIL NIL) (-766 1770717 1772008 1773315 "NAGF04" 1774892 T NAGF04 (NIL) -7 NIL NIL NIL) (-765 1763685 1765299 1766932 "NAGF02" 1769104 T NAGF02 (NIL) -7 NIL NIL NIL) (-764 1758909 1760009 1761126 "NAGF01" 1762588 T NAGF01 (NIL) -7 NIL NIL NIL) (-763 1752537 1754103 1755688 "NAGE04" 1757344 T NAGE04 (NIL) -7 NIL NIL NIL) (-762 1743706 1745827 1747957 "NAGE02" 1750427 T NAGE02 (NIL) -7 NIL NIL NIL) (-761 1739659 1740606 1741570 "NAGE01" 1742762 T NAGE01 (NIL) -7 NIL NIL NIL) (-760 1737454 1737988 1738546 "NAGD03" 1739121 T NAGD03 (NIL) -7 NIL NIL NIL) (-759 1729204 1731132 1733086 "NAGD02" 1735520 T NAGD02 (NIL) -7 NIL NIL NIL) (-758 1723015 1724440 1725880 "NAGD01" 1727784 T NAGD01 (NIL) -7 NIL NIL NIL) (-757 1719224 1720046 1720883 "NAGC06" 1722198 T NAGC06 (NIL) -7 NIL NIL NIL) (-756 1717689 1718021 1718377 "NAGC05" 1718888 T NAGC05 (NIL) -7 NIL NIL NIL) (-755 1717065 1717184 1717328 "NAGC02" 1717565 T NAGC02 (NIL) -7 NIL NIL NIL) (-754 1716024 1716607 1716647 "NAALG" 1716726 NIL NAALG (NIL T) -9 NIL 1716787 NIL) (-753 1715859 1715888 1715978 "NAALG-" 1715983 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-752 1709809 1710917 1712104 "MULTSQFR" 1714755 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-751 1709128 1709203 1709387 "MULTFACT" 1709721 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-750 1701852 1705765 1705818 "MTSCAT" 1706888 NIL MTSCAT (NIL T T) -9 NIL 1707403 NIL) (-749 1701564 1701618 1701710 "MTHING" 1701792 NIL MTHING (NIL T) -7 NIL NIL NIL) (-748 1701356 1701389 1701449 "MSYSCMD" 1701524 T MSYSCMD (NIL) -7 NIL NIL NIL) (-747 1697438 1700111 1700431 "MSET" 1701069 NIL MSET (NIL T) -8 NIL NIL NIL) (-746 1694507 1696999 1697040 "MSETAGG" 1697045 NIL MSETAGG (NIL T) -9 NIL 1697079 NIL) (-745 1690349 1691886 1692631 "MRING" 1693807 NIL MRING (NIL T T) -8 NIL NIL NIL) (-744 1689915 1689982 1690113 "MRF2" 1690276 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-743 1689533 1689568 1689712 "MRATFAC" 1689874 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-742 1687145 1687440 1687871 "MPRFF" 1689238 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-741 1681353 1686999 1687096 "MPOLY" 1687101 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-740 1680843 1680878 1681086 "MPCPF" 1681312 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-739 1680357 1680400 1680584 "MPC3" 1680794 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1679552 1679633 1679854 "MPC2" 1680272 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-737 1677853 1678190 1678580 "MONOTOOL" 1679212 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-736 1677078 1677395 1677423 "MONOID" 1677642 T MONOID (NIL) -9 NIL 1677789 NIL) (-735 1676624 1676743 1676924 "MONOID-" 1676929 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-734 1666803 1672844 1672903 "MONOGEN" 1673577 NIL MONOGEN (NIL T T) -9 NIL 1674033 NIL) (-733 1664021 1664756 1665756 "MONOGEN-" 1665875 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-732 1662854 1663300 1663328 "MONADWU" 1663720 T MONADWU (NIL) -9 NIL 1663958 NIL) (-731 1662226 1662385 1662633 "MONADWU-" 1662638 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-730 1661585 1661829 1661857 "MONAD" 1662064 T MONAD (NIL) -9 NIL 1662176 NIL) (-729 1661270 1661348 1661480 "MONAD-" 1661485 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-728 1659559 1660183 1660462 "MOEBIUS" 1661023 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-727 1658837 1659241 1659281 "MODULE" 1659286 NIL MODULE (NIL T) -9 NIL 1659325 NIL) (-726 1658405 1658501 1658691 "MODULE-" 1658696 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-725 1656085 1656769 1657096 "MODRING" 1658229 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-724 1653029 1654190 1654711 "MODOP" 1655614 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-723 1651617 1652096 1652373 "MODMONOM" 1652892 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-722 1641572 1649908 1650322 "MODMON" 1651254 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-721 1638728 1640416 1640692 "MODFIELD" 1641447 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1637705 1638009 1638199 "MMLFORM" 1638558 T MMLFORM (NIL) -8 NIL NIL NIL) (-719 1637231 1637274 1637453 "MMAP" 1637656 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-718 1635310 1636077 1636118 "MLO" 1636541 NIL MLO (NIL T) -9 NIL 1636783 NIL) (-717 1632676 1633192 1633794 "MLIFT" 1634791 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-716 1632067 1632151 1632305 "MKUCFUNC" 1632587 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-715 1631666 1631736 1631859 "MKRECORD" 1631990 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-714 1630713 1630875 1631103 "MKFUNC" 1631477 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-713 1630101 1630205 1630361 "MKFLCFN" 1630596 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-712 1629378 1629480 1629665 "MKBCFUNC" 1629994 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-711 1626053 1628932 1629068 "MINT" 1629262 T MINT (NIL) -8 NIL NIL NIL) (-710 1624865 1625108 1625385 "MHROWRED" 1625808 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-709 1620245 1623400 1623805 "MFLOAT" 1624480 T MFLOAT (NIL) -8 NIL NIL NIL) (-708 1619602 1619678 1619849 "MFINFACT" 1620157 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-707 1615917 1616765 1617649 "MESH" 1618738 T MESH (NIL) -7 NIL NIL NIL) (-706 1614307 1614619 1614972 "MDDFACT" 1615604 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-705 1611102 1613466 1613507 "MDAGG" 1613762 NIL MDAGG (NIL T) -9 NIL 1613905 NIL) (-704 1600749 1610395 1610602 "MCMPLX" 1610915 T MCMPLX (NIL) -8 NIL NIL NIL) (-703 1599886 1600032 1600233 "MCDEN" 1600598 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-702 1597776 1598046 1598426 "MCALCFN" 1599616 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-701 1596701 1596941 1597174 "MAYBE" 1597582 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-700 1594313 1594836 1595398 "MATSTOR" 1596172 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-699 1590270 1593685 1593933 "MATRIX" 1594098 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-698 1586036 1586743 1587479 "MATLIN" 1589627 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-697 1576142 1579328 1579405 "MATCAT" 1584285 NIL MATCAT (NIL T T T) -9 NIL 1585702 NIL) (-696 1572498 1573519 1574875 "MATCAT-" 1574880 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-695 1571092 1571245 1571578 "MATCAT2" 1572333 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-694 1569204 1569528 1569912 "MAPPKG3" 1570767 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-693 1568185 1568358 1568580 "MAPPKG2" 1569028 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-692 1566684 1566968 1567295 "MAPPKG1" 1567891 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-691 1565763 1566090 1566267 "MAPPAST" 1566527 T MAPPAST (NIL) -8 NIL NIL NIL) (-690 1565374 1565432 1565555 "MAPHACK3" 1565699 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-689 1564966 1565027 1565141 "MAPHACK2" 1565306 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-688 1564404 1564507 1564649 "MAPHACK1" 1564857 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-687 1562483 1563104 1563408 "MAGMA" 1564132 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-686 1561962 1562207 1562298 "MACROAST" 1562412 T MACROAST (NIL) -8 NIL NIL NIL) (-685 1558380 1560201 1560662 "M3D" 1561534 NIL M3D (NIL T) -8 NIL NIL NIL) (-684 1552455 1556719 1556760 "LZSTAGG" 1557542 NIL LZSTAGG (NIL T) -9 NIL 1557837 NIL) (-683 1548413 1549586 1551043 "LZSTAGG-" 1551048 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-682 1545500 1546304 1546791 "LWORD" 1547958 NIL LWORD (NIL T) -8 NIL NIL NIL) (-681 1545076 1545304 1545379 "LSTAST" 1545445 T LSTAST (NIL) -8 NIL NIL NIL) (-680 1538153 1544847 1544981 "LSQM" 1544986 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-679 1537377 1537516 1537744 "LSPP" 1538008 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-678 1535189 1535490 1535946 "LSMP" 1537066 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-677 1531968 1532642 1533372 "LSMP1" 1534491 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-676 1525814 1531105 1531146 "LSAGG" 1531208 NIL LSAGG (NIL T) -9 NIL 1531286 NIL) (-675 1522509 1523433 1524646 "LSAGG-" 1524651 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-674 1520108 1521653 1521902 "LPOLY" 1522304 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-673 1519690 1519775 1519898 "LPEFRAC" 1520017 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-672 1518011 1518784 1519037 "LO" 1519522 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1517663 1517775 1517803 "LOGIC" 1517914 T LOGIC (NIL) -9 NIL 1517995 NIL) (-670 1517525 1517548 1517619 "LOGIC-" 1517624 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-669 1516718 1516858 1517051 "LODOOPS" 1517381 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-668 1514141 1516634 1516700 "LODO" 1516705 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-667 1512679 1512914 1513267 "LODOF" 1513888 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-666 1508883 1511314 1511355 "LODOCAT" 1511793 NIL LODOCAT (NIL T) -9 NIL 1512004 NIL) (-665 1508616 1508674 1508801 "LODOCAT-" 1508806 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-664 1505936 1508457 1508575 "LODO2" 1508580 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-663 1503371 1505873 1505918 "LODO1" 1505923 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-662 1502252 1502417 1502722 "LODEEF" 1503194 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-661 1497555 1500446 1500487 "LNAGG" 1501349 NIL LNAGG (NIL T) -9 NIL 1501784 NIL) (-660 1496702 1496916 1497258 "LNAGG-" 1497263 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-659 1492838 1493627 1494266 "LMOPS" 1496117 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-658 1492241 1492629 1492670 "LMODULE" 1492675 NIL LMODULE (NIL T) -9 NIL 1492701 NIL) (-657 1489439 1491886 1492009 "LMDICT" 1492151 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-656 1488845 1489066 1489107 "LLINSET" 1489298 NIL LLINSET (NIL T) -9 NIL 1489389 NIL) (-655 1488544 1488753 1488813 "LITERAL" 1488818 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-654 1481707 1487478 1487782 "LIST" 1488273 NIL LIST (NIL T) -8 NIL NIL NIL) (-653 1481232 1481306 1481445 "LIST3" 1481627 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-652 1480239 1480417 1480645 "LIST2" 1481050 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-651 1478373 1478685 1479084 "LIST2MAP" 1479886 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-650 1477969 1478206 1478247 "LINSET" 1478252 NIL LINSET (NIL T) -9 NIL 1478286 NIL) (-649 1476698 1477231 1477272 "LINEXP" 1477623 NIL LINEXP (NIL T) -9 NIL 1477814 NIL) (-648 1475275 1475535 1475846 "LINDEP" 1476450 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-647 1472042 1472761 1473538 "LIMITRF" 1474530 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-646 1470345 1470641 1471050 "LIMITPS" 1471737 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-645 1464773 1469856 1470084 "LIE" 1470166 NIL LIE (NIL T T) -8 NIL NIL NIL) (-644 1463721 1464190 1464230 "LIECAT" 1464370 NIL LIECAT (NIL T) -9 NIL 1464521 NIL) (-643 1463562 1463589 1463677 "LIECAT-" 1463682 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-642 1456149 1463102 1463258 "LIB" 1463426 T LIB (NIL) -8 NIL NIL NIL) (-641 1451784 1452667 1453602 "LGROBP" 1455266 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-640 1449782 1450056 1450406 "LF" 1451505 NIL LF (NIL T T) -7 NIL NIL NIL) (-639 1448622 1449314 1449342 "LFCAT" 1449549 T LFCAT (NIL) -9 NIL 1449688 NIL) (-638 1445524 1446154 1446842 "LEXTRIPK" 1447986 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-637 1442268 1443094 1443597 "LEXP" 1445104 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-636 1441744 1441989 1442081 "LETAST" 1442196 T LETAST (NIL) -8 NIL NIL NIL) (-635 1440142 1440455 1440856 "LEADCDET" 1441426 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-634 1439332 1439406 1439635 "LAZM3PK" 1440063 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-633 1434249 1437409 1437947 "LAUPOL" 1438844 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-632 1433828 1433872 1434033 "LAPLACE" 1434199 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-631 1431767 1432929 1433180 "LA" 1433661 NIL LA (NIL T T T) -8 NIL NIL NIL) (-630 1430761 1431345 1431386 "LALG" 1431448 NIL LALG (NIL T) -9 NIL 1431507 NIL) (-629 1430475 1430534 1430670 "LALG-" 1430675 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-628 1430310 1430334 1430375 "KVTFROM" 1430437 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-627 1429233 1429677 1429862 "KTVLOGIC" 1430145 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-626 1429068 1429092 1429133 "KRCFROM" 1429195 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-625 1427972 1428159 1428458 "KOVACIC" 1428868 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-624 1427807 1427831 1427872 "KONVERT" 1427934 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-623 1427642 1427666 1427707 "KOERCE" 1427769 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-622 1425473 1426235 1426612 "KERNEL" 1427298 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-621 1424969 1425050 1425182 "KERNEL2" 1425387 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-620 1418739 1423508 1423562 "KDAGG" 1423939 NIL KDAGG (NIL T T) -9 NIL 1424145 NIL) (-619 1418268 1418392 1418597 "KDAGG-" 1418602 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-618 1411416 1417929 1418084 "KAFILE" 1418146 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-617 1405844 1410927 1411155 "JORDAN" 1411237 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-616 1405223 1405493 1405614 "JOINAST" 1405743 T JOINAST (NIL) -8 NIL NIL NIL) (-615 1405069 1405128 1405183 "JAVACODE" 1405188 T JAVACODE (NIL) -8 NIL NIL NIL) (-614 1401321 1403274 1403328 "IXAGG" 1404257 NIL IXAGG (NIL T T) -9 NIL 1404716 NIL) (-613 1400240 1400546 1400965 "IXAGG-" 1400970 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-612 1395770 1400162 1400221 "IVECTOR" 1400226 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-611 1394536 1394773 1395039 "ITUPLE" 1395537 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-610 1393038 1393215 1393510 "ITRIGMNP" 1394358 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-609 1391783 1391987 1392270 "ITFUN3" 1392814 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-608 1391415 1391472 1391581 "ITFUN2" 1391720 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-607 1390574 1390895 1391069 "ITFORM" 1391261 T ITFORM (NIL) -8 NIL NIL NIL) (-606 1388535 1389594 1389872 "ITAYLOR" 1390329 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-605 1377480 1382672 1383835 "ISUPS" 1387405 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-604 1376584 1376724 1376960 "ISUMP" 1377327 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-603 1371959 1376529 1376570 "ISTRING" 1376575 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-602 1371435 1371680 1371772 "ISAST" 1371887 T ISAST (NIL) -8 NIL NIL NIL) (-601 1370644 1370726 1370942 "IRURPK" 1371349 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-600 1369580 1369781 1370021 "IRSN" 1370424 T IRSN (NIL) -7 NIL NIL NIL) (-599 1367651 1368006 1368435 "IRRF2F" 1369218 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-598 1367398 1367436 1367512 "IRREDFFX" 1367607 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-597 1366013 1366272 1366571 "IROOT" 1367131 NIL IROOT (NIL T) -7 NIL NIL NIL) (-596 1362617 1363697 1364389 "IR" 1365353 NIL IR (NIL T) -8 NIL NIL NIL) (-595 1361822 1362110 1362261 "IRFORM" 1362486 T IRFORM (NIL) -8 NIL NIL NIL) (-594 1359435 1359930 1360496 "IR2" 1361300 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-593 1358535 1358648 1358862 "IR2F" 1359318 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-592 1358326 1358360 1358420 "IPRNTPK" 1358495 T IPRNTPK (NIL) -7 NIL NIL NIL) (-591 1354907 1358215 1358284 "IPF" 1358289 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-590 1353234 1354832 1354889 "IPADIC" 1354894 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-589 1352546 1352794 1352924 "IP4ADDR" 1353124 T IP4ADDR (NIL) -8 NIL NIL NIL) (-588 1351920 1352175 1352307 "IOMODE" 1352434 T IOMODE (NIL) -8 NIL NIL NIL) (-587 1350993 1351517 1351644 "IOBFILE" 1351813 T IOBFILE (NIL) -8 NIL NIL NIL) (-586 1350481 1350897 1350925 "IOBCON" 1350930 T IOBCON (NIL) -9 NIL 1350951 NIL) (-585 1349992 1350050 1350233 "INVLAPLA" 1350417 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-584 1339640 1341994 1344380 "INTTR" 1347656 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-583 1335975 1336717 1337582 "INTTOOLS" 1338825 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-582 1335561 1335652 1335769 "INTSLPE" 1335878 T INTSLPE (NIL) -7 NIL NIL NIL) (-581 1333514 1335484 1335543 "INTRVL" 1335548 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-580 1331116 1331628 1332203 "INTRF" 1332999 NIL INTRF (NIL T) -7 NIL NIL NIL) (-579 1330527 1330624 1330766 "INTRET" 1331014 NIL INTRET (NIL T) -7 NIL NIL NIL) (-578 1328524 1328913 1329383 "INTRAT" 1330135 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-577 1325787 1326370 1326989 "INTPM" 1328009 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-576 1322532 1323131 1323869 "INTPAF" 1325173 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-575 1317711 1318673 1319724 "INTPACK" 1321501 T INTPACK (NIL) -7 NIL NIL NIL) (-574 1314609 1317508 1317617 "INT" 1317622 T INT (NIL) -8 NIL NIL NIL) (-573 1313861 1314013 1314221 "INTHERTR" 1314451 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-572 1313300 1313380 1313568 "INTHERAL" 1313775 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-571 1311146 1311589 1312046 "INTHEORY" 1312863 T INTHEORY (NIL) -7 NIL NIL NIL) (-570 1302552 1304173 1305945 "INTG0" 1309498 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-569 1283125 1287915 1292725 "INTFTBL" 1297762 T INTFTBL (NIL) -8 NIL NIL NIL) (-568 1282374 1282512 1282685 "INTFACT" 1282984 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-567 1279801 1280247 1280804 "INTEF" 1281928 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-566 1278168 1278907 1278935 "INTDOM" 1279236 T INTDOM (NIL) -9 NIL 1279443 NIL) (-565 1277537 1277711 1277953 "INTDOM-" 1277958 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-564 1273925 1275853 1275907 "INTCAT" 1276706 NIL INTCAT (NIL T) -9 NIL 1277027 NIL) (-563 1273397 1273500 1273628 "INTBIT" 1273817 T INTBIT (NIL) -7 NIL NIL NIL) (-562 1272096 1272250 1272557 "INTALG" 1273242 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-561 1271579 1271669 1271826 "INTAF" 1272000 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-560 1264922 1271389 1271529 "INTABL" 1271534 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-559 1264255 1264721 1264786 "INT8" 1264820 T INT8 (NIL) -8 NIL NIL 1264865) (-558 1263587 1264053 1264118 "INT64" 1264152 T INT64 (NIL) -8 NIL NIL 1264197) (-557 1262919 1263385 1263450 "INT32" 1263484 T INT32 (NIL) -8 NIL NIL 1263529) (-556 1262251 1262717 1262782 "INT16" 1262816 T INT16 (NIL) -8 NIL NIL 1262861) (-555 1257059 1259825 1259853 "INS" 1260787 T INS (NIL) -9 NIL 1261452 NIL) (-554 1254299 1255070 1256044 "INS-" 1256117 NIL INS- (NIL T) -8 NIL NIL NIL) (-553 1253074 1253301 1253599 "INPSIGN" 1254052 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-552 1252192 1252309 1252506 "INPRODPF" 1252954 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-551 1251086 1251203 1251440 "INPRODFF" 1252072 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-550 1250086 1250238 1250498 "INNMFACT" 1250922 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-549 1249283 1249380 1249568 "INMODGCD" 1249985 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-548 1247791 1248036 1248360 "INFSP" 1249028 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-547 1246975 1247092 1247275 "INFPROD0" 1247671 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-546 1243830 1245040 1245555 "INFORM" 1246468 T INFORM (NIL) -8 NIL NIL NIL) (-545 1243440 1243500 1243598 "INFORM1" 1243765 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-544 1242963 1243052 1243166 "INFINITY" 1243346 T INFINITY (NIL) -7 NIL NIL NIL) (-543 1242139 1242683 1242784 "INETCLTS" 1242882 T INETCLTS (NIL) -8 NIL NIL NIL) (-542 1240755 1241005 1241326 "INEP" 1241887 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-541 1240004 1240652 1240717 "INDE" 1240722 NIL INDE (NIL T) -8 NIL NIL NIL) (-540 1239568 1239636 1239753 "INCRMAPS" 1239931 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-539 1238386 1238837 1239043 "INBFILE" 1239382 T INBFILE (NIL) -8 NIL NIL NIL) (-538 1233685 1234622 1235566 "INBFF" 1237474 NIL INBFF (NIL T) -7 NIL NIL NIL) (-537 1232593 1232862 1232890 "INBCON" 1233403 T INBCON (NIL) -9 NIL 1233669 NIL) (-536 1231845 1232068 1232344 "INBCON-" 1232349 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-535 1231324 1231569 1231660 "INAST" 1231774 T INAST (NIL) -8 NIL NIL NIL) (-534 1230751 1231003 1231109 "IMPTAST" 1231238 T IMPTAST (NIL) -8 NIL NIL NIL) (-533 1227197 1230595 1230699 "IMATRIX" 1230704 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-532 1225905 1226028 1226344 "IMATQF" 1227053 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-531 1224125 1224352 1224689 "IMATLIN" 1225661 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-530 1218703 1224049 1224107 "ILIST" 1224112 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-529 1216608 1218563 1218676 "IIARRAY2" 1218681 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-528 1212006 1216519 1216583 "IFF" 1216588 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-527 1211353 1211623 1211739 "IFAST" 1211910 T IFAST (NIL) -8 NIL NIL NIL) (-526 1206348 1210645 1210833 "IFARRAY" 1211210 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-525 1205528 1206252 1206325 "IFAMON" 1206330 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-524 1205112 1205177 1205231 "IEVALAB" 1205438 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-523 1204787 1204855 1205015 "IEVALAB-" 1205020 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-522 1204418 1204701 1204764 "IDPO" 1204769 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1203668 1204307 1204382 "IDPOAMS" 1204387 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-520 1202975 1203557 1203632 "IDPOAM" 1203637 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-519 1202034 1202310 1202363 "IDPC" 1202776 NIL IDPC (NIL T T) -9 NIL 1202925 NIL) (-518 1201503 1201926 1201999 "IDPAM" 1202004 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-517 1200879 1201395 1201468 "IDPAG" 1201473 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-516 1200524 1200715 1200790 "IDENT" 1200824 T IDENT (NIL) -8 NIL NIL NIL) (-515 1196779 1197627 1198522 "IDECOMP" 1199681 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-514 1189616 1190702 1191749 "IDEAL" 1195815 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-513 1188776 1188888 1189088 "ICDEN" 1189500 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-512 1187847 1188256 1188403 "ICARD" 1188649 T ICARD (NIL) -8 NIL NIL NIL) (-511 1185907 1186220 1186625 "IBPTOOLS" 1187524 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-510 1181514 1185527 1185640 "IBITS" 1185826 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-509 1178237 1178813 1179508 "IBATOOL" 1180931 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-508 1176016 1176478 1177011 "IBACHIN" 1177772 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-507 1173845 1175862 1175965 "IARRAY2" 1175970 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-506 1169951 1173771 1173828 "IARRAY1" 1173833 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-505 1163989 1168363 1168844 "IAN" 1169490 T IAN (NIL) -8 NIL NIL NIL) (-504 1163500 1163557 1163730 "IALGFACT" 1163926 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-503 1163028 1163141 1163169 "HYPCAT" 1163376 T HYPCAT (NIL) -9 NIL NIL NIL) (-502 1162566 1162683 1162869 "HYPCAT-" 1162874 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-501 1162161 1162361 1162444 "HOSTNAME" 1162503 T HOSTNAME (NIL) -8 NIL NIL NIL) (-500 1162006 1162043 1162084 "HOMOTOP" 1162089 NIL HOMOTOP (NIL T) -9 NIL 1162122 NIL) (-499 1158638 1160016 1160057 "HOAGG" 1161038 NIL HOAGG (NIL T) -9 NIL 1161717 NIL) (-498 1157232 1157631 1158157 "HOAGG-" 1158162 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-497 1151141 1156825 1156975 "HEXADEC" 1157102 T HEXADEC (NIL) -8 NIL NIL NIL) (-496 1149889 1150111 1150374 "HEUGCD" 1150918 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-495 1148965 1149726 1149856 "HELLFDIV" 1149861 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-494 1147144 1148742 1148830 "HEAP" 1148909 NIL HEAP (NIL T) -8 NIL NIL NIL) (-493 1146407 1146696 1146830 "HEADAST" 1147030 T HEADAST (NIL) -8 NIL NIL NIL) (-492 1140136 1146322 1146384 "HDP" 1146389 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-491 1134035 1139771 1139923 "HDMP" 1140037 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-490 1133359 1133499 1133663 "HB" 1133891 T HB (NIL) -7 NIL NIL NIL) (-489 1126745 1133205 1133309 "HASHTBL" 1133314 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-488 1126221 1126466 1126558 "HASAST" 1126673 T HASAST (NIL) -8 NIL NIL NIL) (-487 1123999 1125843 1126025 "HACKPI" 1126059 T HACKPI (NIL) -8 NIL NIL NIL) (-486 1119667 1123852 1123965 "GTSET" 1123970 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-485 1113082 1119545 1119643 "GSTBL" 1119648 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-484 1105360 1112113 1112378 "GSERIES" 1112873 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-483 1104501 1104918 1104946 "GROUP" 1105149 T GROUP (NIL) -9 NIL 1105283 NIL) (-482 1103867 1104026 1104277 "GROUP-" 1104282 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-481 1102234 1102555 1102942 "GROEBSOL" 1103544 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-480 1101148 1101436 1101487 "GRMOD" 1102016 NIL GRMOD (NIL T T) -9 NIL 1102184 NIL) (-479 1100916 1100952 1101080 "GRMOD-" 1101085 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-478 1096206 1097270 1098270 "GRIMAGE" 1099936 T GRIMAGE (NIL) -8 NIL NIL NIL) (-477 1094672 1094933 1095257 "GRDEF" 1095902 T GRDEF (NIL) -7 NIL NIL NIL) (-476 1094116 1094232 1094373 "GRAY" 1094551 T GRAY (NIL) -7 NIL NIL NIL) (-475 1093303 1093709 1093760 "GRALG" 1093913 NIL GRALG (NIL T T) -9 NIL 1094006 NIL) (-474 1092964 1093037 1093200 "GRALG-" 1093205 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-473 1089741 1092549 1092727 "GPOLSET" 1092871 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-472 1089095 1089152 1089410 "GOSPER" 1089678 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-471 1084827 1085533 1086059 "GMODPOL" 1088794 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-470 1083832 1084016 1084254 "GHENSEL" 1084639 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-469 1077988 1078831 1079851 "GENUPS" 1082916 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-468 1077685 1077736 1077825 "GENUFACT" 1077931 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-467 1077097 1077174 1077339 "GENPGCD" 1077603 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-466 1076571 1076606 1076819 "GENMFACT" 1077056 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-465 1075137 1075394 1075701 "GENEEZ" 1076314 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-464 1069196 1074748 1074910 "GDMP" 1075060 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-463 1058539 1062967 1064073 "GCNAALG" 1068179 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-462 1056866 1057728 1057756 "GCDDOM" 1058011 T GCDDOM (NIL) -9 NIL 1058168 NIL) (-461 1056336 1056463 1056678 "GCDDOM-" 1056683 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-460 1055008 1055193 1055497 "GB" 1056115 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-459 1043624 1045954 1048346 "GBINTERN" 1052699 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-458 1041461 1041753 1042174 "GBF" 1043299 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-457 1040242 1040407 1040674 "GBEUCLID" 1041277 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-456 1039591 1039716 1039865 "GAUSSFAC" 1040113 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-455 1037958 1038260 1038574 "GALUTIL" 1039310 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-454 1036266 1036540 1036864 "GALPOLYU" 1037685 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-453 1033631 1033921 1034328 "GALFACTU" 1035963 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-452 1025437 1026936 1028544 "GALFACT" 1032063 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-451 1022825 1023483 1023511 "FVFUN" 1024667 T FVFUN (NIL) -9 NIL 1025387 NIL) (-450 1022091 1022273 1022301 "FVC" 1022592 T FVC (NIL) -9 NIL 1022775 NIL) (-449 1021734 1021916 1021984 "FUNDESC" 1022043 T FUNDESC (NIL) -8 NIL NIL NIL) (-448 1021349 1021531 1021612 "FUNCTION" 1021686 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-447 1019093 1019671 1020137 "FT" 1020903 T FT (NIL) -8 NIL NIL NIL) (-446 1017884 1018394 1018597 "FTEM" 1018910 T FTEM (NIL) -8 NIL NIL NIL) (-445 1016175 1016464 1016861 "FSUPFACT" 1017575 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-444 1014572 1014861 1015193 "FST" 1015863 T FST (NIL) -8 NIL NIL NIL) (-443 1013771 1013877 1014065 "FSRED" 1014454 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-442 1012470 1012726 1013073 "FSPRMELT" 1013486 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-441 1009776 1010214 1010700 "FSPECF" 1012033 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-440 991148 999619 999660 "FS" 1003544 NIL FS (NIL T) -9 NIL 1005833 NIL) (-439 979791 982784 986841 "FS-" 987141 NIL FS- (NIL T T) -8 NIL NIL NIL) (-438 979319 979373 979543 "FSINT" 979732 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-437 977611 978312 978615 "FSERIES" 979098 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-436 976653 976769 976993 "FSCINT" 977491 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-435 972861 975597 975638 "FSAGG" 976008 NIL FSAGG (NIL T) -9 NIL 976267 NIL) (-434 970623 971224 972020 "FSAGG-" 972115 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-433 969665 969808 970035 "FSAGG2" 970476 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-432 967347 967627 968174 "FS2UPS" 969383 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-431 966981 967024 967153 "FS2" 967298 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-430 965859 966030 966332 "FS2EXPXP" 966806 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-429 965285 965400 965552 "FRUTIL" 965739 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-428 956698 960780 962138 "FR" 963959 NIL FR (NIL T) -8 NIL NIL NIL) (-427 951712 954387 954427 "FRNAALG" 955747 NIL FRNAALG (NIL T) -9 NIL 956345 NIL) (-426 947385 948461 949736 "FRNAALG-" 950486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-425 947023 947066 947193 "FRNAAF2" 947336 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-424 945398 945872 946168 "FRMOD" 946835 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-423 943141 943773 944091 "FRIDEAL" 945189 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-422 942332 942419 942710 "FRIDEAL2" 943048 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-421 941465 941879 941920 "FRETRCT" 941925 NIL FRETRCT (NIL T) -9 NIL 942101 NIL) (-420 940577 940808 941159 "FRETRCT-" 941164 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-419 937665 938875 938934 "FRAMALG" 939816 NIL FRAMALG (NIL T T) -9 NIL 940108 NIL) (-418 935799 936254 936884 "FRAMALG-" 937107 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-417 929629 935272 935549 "FRAC" 935554 NIL FRAC (NIL T) -8 NIL NIL NIL) (-416 929265 929322 929429 "FRAC2" 929566 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-415 928901 928958 929065 "FR2" 929202 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-414 923414 926307 926335 "FPS" 927454 T FPS (NIL) -9 NIL 928011 NIL) (-413 922863 922972 923136 "FPS-" 923282 NIL FPS- (NIL T) -8 NIL NIL NIL) (-412 920165 921834 921862 "FPC" 922087 T FPC (NIL) -9 NIL 922229 NIL) (-411 919958 919998 920095 "FPC-" 920100 NIL FPC- (NIL T) -8 NIL NIL NIL) (-410 918748 919446 919487 "FPATMAB" 919492 NIL FPATMAB (NIL T) -9 NIL 919644 NIL) (-409 916421 916924 917350 "FPARFRAC" 918385 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-408 911815 912313 912995 "FORTRAN" 915853 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-407 909531 910031 910570 "FORT" 911296 T FORT (NIL) -7 NIL NIL NIL) (-406 907207 907769 907797 "FORTFN" 908857 T FORTFN (NIL) -9 NIL 909481 NIL) (-405 906971 907021 907049 "FORTCAT" 907108 T FORTCAT (NIL) -9 NIL 907170 NIL) (-404 905077 905587 905977 "FORMULA" 906601 T FORMULA (NIL) -8 NIL NIL NIL) (-403 904865 904895 904964 "FORMULA1" 905041 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-402 904388 904440 904613 "FORDER" 904807 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-401 903484 903648 903841 "FOP" 904215 T FOP (NIL) -7 NIL NIL NIL) (-400 902065 902764 902938 "FNLA" 903366 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-399 900794 901209 901237 "FNCAT" 901697 T FNCAT (NIL) -9 NIL 901957 NIL) (-398 900333 900753 900781 "FNAME" 900786 T FNAME (NIL) -8 NIL NIL NIL) (-397 898896 899859 899887 "FMTC" 899892 T FMTC (NIL) -9 NIL 899928 NIL) (-396 897642 898832 898878 "FMONOID" 898883 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-395 894470 895638 895679 "FMONCAT" 896896 NIL FMONCAT (NIL T) -9 NIL 897501 NIL) (-394 893662 894212 894361 "FM" 894366 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 891086 891732 891760 "FMFUN" 892904 T FMFUN (NIL) -9 NIL 893612 NIL) (-392 890355 890536 890564 "FMC" 890854 T FMC (NIL) -9 NIL 891036 NIL) (-391 887434 888294 888348 "FMCAT" 889543 NIL FMCAT (NIL T T) -9 NIL 890038 NIL) (-390 886300 887200 887300 "FM1" 887379 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-389 884074 884490 884984 "FLOATRP" 885851 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-388 877652 881803 882424 "FLOAT" 883473 T FLOAT (NIL) -8 NIL NIL NIL) (-387 875090 875590 876168 "FLOATCP" 877119 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-386 873937 874696 874737 "FLINEXP" 874742 NIL FLINEXP (NIL T) -9 NIL 874835 NIL) (-385 872869 873166 873574 "FLINEXP-" 873579 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-384 871945 872089 872313 "FLASORT" 872721 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-383 869061 869929 869981 "FLALG" 871208 NIL FLALG (NIL T T) -9 NIL 871675 NIL) (-382 862765 866517 866558 "FLAGG" 867820 NIL FLAGG (NIL T) -9 NIL 868472 NIL) (-381 861491 861830 862320 "FLAGG-" 862325 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-380 860533 860676 860903 "FLAGG2" 861344 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-379 857384 858392 858451 "FINRALG" 859579 NIL FINRALG (NIL T T) -9 NIL 860087 NIL) (-378 856544 856773 857112 "FINRALG-" 857117 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-377 855924 856163 856191 "FINITE" 856387 T FINITE (NIL) -9 NIL 856494 NIL) (-376 848281 850468 850508 "FINAALG" 854175 NIL FINAALG (NIL T) -9 NIL 855628 NIL) (-375 843613 844663 845807 "FINAALG-" 847186 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-374 842981 843368 843471 "FILE" 843543 NIL FILE (NIL T) -8 NIL NIL NIL) (-373 841639 841977 842031 "FILECAT" 842715 NIL FILECAT (NIL T T) -9 NIL 842931 NIL) (-372 839355 840883 840911 "FIELD" 840951 T FIELD (NIL) -9 NIL 841031 NIL) (-371 837975 838360 838871 "FIELD-" 838876 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-370 835825 836610 836957 "FGROUP" 837661 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-369 834915 835079 835299 "FGLMICPK" 835657 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-368 830747 834840 834897 "FFX" 834902 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-367 830348 830409 830544 "FFSLPE" 830680 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-366 826338 827120 827916 "FFPOLY" 829584 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-365 825842 825878 826087 "FFPOLY2" 826296 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-364 821688 825761 825824 "FFP" 825829 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-363 817086 821599 821663 "FF" 821668 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-362 812212 816429 816619 "FFNBX" 816940 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-361 807140 811347 811605 "FFNBP" 812066 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-360 801773 806424 806635 "FFNB" 806973 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-359 800605 800803 801118 "FFINTBAS" 801570 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-358 796644 798865 798893 "FFIELDC" 799513 T FFIELDC (NIL) -9 NIL 799889 NIL) (-357 795306 795677 796174 "FFIELDC-" 796179 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-356 794875 794921 795045 "FFHOM" 795248 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-355 792570 793057 793574 "FFF" 794390 NIL FFF (NIL T) -7 NIL NIL NIL) (-354 788188 792312 792413 "FFCGX" 792513 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-353 783810 787920 788027 "FFCGP" 788131 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-352 778993 783537 783645 "FFCG" 783746 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-351 760030 769215 769301 "FFCAT" 774466 NIL FFCAT (NIL T T T) -9 NIL 775917 NIL) (-350 755227 756275 757589 "FFCAT-" 758819 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-349 754638 754681 754916 "FFCAT2" 755178 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-348 743961 747610 748830 "FEXPR" 753490 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-347 742923 743358 743399 "FEVALAB" 743483 NIL FEVALAB (NIL T) -9 NIL 743744 NIL) (-346 742082 742292 742630 "FEVALAB-" 742635 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-345 740648 741465 741668 "FDIV" 741981 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-344 737668 738409 738524 "FDIVCAT" 740092 NIL FDIVCAT (NIL T T T T) -9 NIL 740529 NIL) (-343 737430 737457 737627 "FDIVCAT-" 737632 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-342 736650 736737 737014 "FDIV2" 737337 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 735624 735945 736147 "FCTRDATA" 736468 T FCTRDATA (NIL) -8 NIL NIL NIL) (-340 734310 734569 734858 "FCPAK1" 735355 T FCPAK1 (NIL) -7 NIL NIL NIL) (-339 733409 733810 733951 "FCOMP" 734201 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-338 717114 720559 724097 "FC" 729891 T FC (NIL) -8 NIL NIL NIL) (-337 709420 713448 713488 "FAXF" 715290 NIL FAXF (NIL T) -9 NIL 715982 NIL) (-336 706697 707354 708179 "FAXF-" 708644 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-335 701749 706073 706249 "FARRAY" 706554 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-334 696643 698710 698763 "FAMR" 699786 NIL FAMR (NIL T T) -9 NIL 700246 NIL) (-333 695533 695835 696270 "FAMR-" 696275 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-332 694702 695455 695508 "FAMONOID" 695513 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-331 692488 693198 693251 "FAMONC" 694192 NIL FAMONC (NIL T T) -9 NIL 694578 NIL) (-330 691152 692242 692379 "FAGROUP" 692384 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-329 688947 689266 689669 "FACUTIL" 690833 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-328 688046 688231 688453 "FACTFUNC" 688757 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-327 680468 687349 687548 "EXPUPXS" 687902 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-326 677951 678491 679077 "EXPRTUBE" 679902 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-325 674222 674814 675544 "EXPRODE" 677290 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-324 659941 672871 673300 "EXPR" 673826 NIL EXPR (NIL T) -8 NIL NIL NIL) (-323 654495 655082 655888 "EXPR2UPS" 659239 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-322 654127 654184 654293 "EXPR2" 654432 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-321 645380 653278 653569 "EXPEXPAN" 653963 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-320 645180 645337 645366 "EXIT" 645371 T EXIT (NIL) -8 NIL NIL NIL) (-319 644660 644904 644995 "EXITAST" 645109 T EXITAST (NIL) -8 NIL NIL NIL) (-318 644287 644349 644462 "EVALCYC" 644592 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-317 643828 643946 643987 "EVALAB" 644157 NIL EVALAB (NIL T) -9 NIL 644261 NIL) (-316 643309 643431 643652 "EVALAB-" 643657 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-315 640677 641979 642007 "EUCDOM" 642562 T EUCDOM (NIL) -9 NIL 642912 NIL) (-314 639082 639524 640114 "EUCDOM-" 640119 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-313 626621 629380 632130 "ESTOOLS" 636352 T ESTOOLS (NIL) -7 NIL NIL NIL) (-312 626253 626310 626419 "ESTOOLS2" 626558 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-311 626004 626046 626126 "ESTOOLS1" 626205 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-310 620041 621649 621677 "ES" 624445 T ES (NIL) -9 NIL 625855 NIL) (-309 614988 616275 618092 "ES-" 618256 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 611362 612123 612903 "ESCONT" 614228 T ESCONT (NIL) -7 NIL NIL NIL) (-307 611107 611139 611221 "ESCONT1" 611324 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-306 610782 610832 610932 "ES2" 611051 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-305 610412 610470 610579 "ES1" 610718 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-304 609628 609757 609933 "ERROR" 610256 T ERROR (NIL) -7 NIL NIL NIL) (-303 603020 609487 609578 "EQTBL" 609583 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-302 595523 598334 599783 "EQ" 601604 NIL -2078 (NIL T) -8 NIL NIL NIL) (-301 595155 595212 595321 "EQ2" 595460 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-300 590446 591493 592586 "EP" 594094 NIL EP (NIL T) -7 NIL NIL NIL) (-299 589046 589337 589643 "ENV" 590160 T ENV (NIL) -8 NIL NIL NIL) (-298 588140 588694 588722 "ENTIRER" 588727 T ENTIRER (NIL) -9 NIL 588773 NIL) (-297 584834 586322 586683 "EMR" 587948 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-296 583964 584149 584203 "ELTAGG" 584583 NIL ELTAGG (NIL T T) -9 NIL 584794 NIL) (-295 583683 583745 583886 "ELTAGG-" 583891 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-294 583447 583476 583530 "ELTAB" 583614 NIL ELTAB (NIL T T) -9 NIL 583666 NIL) (-293 582573 582719 582918 "ELFUTS" 583298 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-292 582315 582371 582399 "ELEMFUN" 582504 T ELEMFUN (NIL) -9 NIL NIL NIL) (-291 582185 582206 582274 "ELEMFUN-" 582279 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-290 576999 580255 580296 "ELAGG" 581236 NIL ELAGG (NIL T) -9 NIL 581699 NIL) (-289 575284 575718 576381 "ELAGG-" 576386 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-288 574596 574733 574889 "ELABOR" 575148 T ELABOR (NIL) -8 NIL NIL NIL) (-287 573257 573536 573830 "ELABEXPR" 574322 T ELABEXPR (NIL) -8 NIL NIL NIL) (-286 566121 567924 568751 "EFUPXS" 572533 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-285 559571 561372 562182 "EFULS" 565397 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-284 557056 557414 557886 "EFSTRUC" 559203 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-283 546847 548413 549961 "EF" 555571 NIL EF (NIL T T) -7 NIL NIL NIL) (-282 545921 546332 546481 "EAB" 546718 T EAB (NIL) -8 NIL NIL NIL) (-281 545103 545880 545908 "E04UCFA" 545913 T E04UCFA (NIL) -8 NIL NIL NIL) (-280 544285 545062 545090 "E04NAFA" 545095 T E04NAFA (NIL) -8 NIL NIL NIL) (-279 543467 544244 544272 "E04MBFA" 544277 T E04MBFA (NIL) -8 NIL NIL NIL) (-278 542649 543426 543454 "E04JAFA" 543459 T E04JAFA (NIL) -8 NIL NIL NIL) (-277 541833 542608 542636 "E04GCFA" 542641 T E04GCFA (NIL) -8 NIL NIL NIL) (-276 541017 541792 541820 "E04FDFA" 541825 T E04FDFA (NIL) -8 NIL NIL NIL) (-275 540199 540976 541004 "E04DGFA" 541009 T E04DGFA (NIL) -8 NIL NIL NIL) (-274 534372 535724 537088 "E04AGNT" 538855 T E04AGNT (NIL) -7 NIL NIL NIL) (-273 533052 533558 533598 "DVARCAT" 534073 NIL DVARCAT (NIL T) -9 NIL 534272 NIL) (-272 532256 532468 532782 "DVARCAT-" 532787 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-271 525304 532055 532184 "DSMP" 532189 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-270 520085 521249 522317 "DROPT" 524256 T DROPT (NIL) -8 NIL NIL NIL) (-269 519750 519809 519907 "DROPT1" 520020 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 514865 515991 517128 "DROPT0" 518633 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 513210 513535 513921 "DRAWPT" 514499 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 507797 508720 509799 "DRAW" 512184 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 507430 507483 507601 "DRAWHACK" 507738 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 506161 506430 506721 "DRAWCX" 507159 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 505676 505745 505896 "DRAWCURV" 506087 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 496144 498106 500221 "DRAWCFUN" 503581 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 492908 494837 494878 "DQAGG" 495507 NIL DQAGG (NIL T) -9 NIL 495781 NIL) (-260 480845 487403 487486 "DPOLCAT" 489338 NIL DPOLCAT (NIL T T T T) -9 NIL 489883 NIL) (-259 475682 477030 478988 "DPOLCAT-" 478993 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 468991 475543 475641 "DPMO" 475646 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 462203 468771 468938 "DPMM" 468943 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 461773 461987 462076 "DOMTMPLT" 462134 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 461206 461575 461655 "DOMCTOR" 461713 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 460418 460686 460837 "DOMAIN" 461075 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 454317 460053 460205 "DMP" 460319 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 453917 453973 454117 "DLP" 454255 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 447739 453244 453434 "DLIST" 453759 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 444536 446592 446633 "DLAGG" 447183 NIL DLAGG (NIL T) -9 NIL 447413 NIL) (-249 443212 443876 443904 "DIVRING" 443996 T DIVRING (NIL) -9 NIL 444079 NIL) (-248 442449 442639 442939 "DIVRING-" 442944 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 440551 440908 441314 "DISPLAY" 442063 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 434300 440465 440528 "DIRPROD" 440533 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 433148 433351 433616 "DIRPROD2" 434093 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 421659 427805 427858 "DIRPCAT" 428268 NIL DIRPCAT (NIL NIL T) -9 NIL 429108 NIL) (-243 418763 419467 420428 "DIRPCAT-" 420765 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 418050 418210 418396 "DIOSP" 418597 T DIOSP (NIL) -7 NIL NIL NIL) (-241 414705 416962 417003 "DIOPS" 417437 NIL DIOPS (NIL T) -9 NIL 417666 NIL) (-240 414254 414368 414559 "DIOPS-" 414564 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 413143 413771 413799 "DIFRING" 413918 T DIFRING (NIL) -9 NIL 414001 NIL) (-238 412788 412866 413018 "DIFRING-" 413023 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-237 412460 412534 412562 "DIFFSPC" 412681 T DIFFSPC (NIL) -9 NIL 412756 NIL) (-236 412105 412183 412335 "DIFFSPC-" 412340 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 411813 411858 411899 "DIFFDOM" 412020 NIL DIFFDOM (NIL T) -9 NIL 412088 NIL) (-234 411666 411690 411774 "DIFFDOM-" 411779 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 409345 410617 410658 "DIFEXT" 411021 NIL DIFEXT (NIL T) -9 NIL 411315 NIL) (-232 407630 408058 408724 "DIFEXT-" 408729 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 404905 407162 407203 "DIAGG" 407208 NIL DIAGG (NIL T) -9 NIL 407228 NIL) (-230 404289 404446 404698 "DIAGG-" 404703 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 399706 403248 403525 "DHMATRIX" 404058 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 395318 396227 397237 "DFSFUN" 398716 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 390398 394249 394561 "DFLOAT" 395026 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 388661 388942 389331 "DFINTTLS" 390106 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 385690 386682 387082 "DERHAM" 388327 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 383491 385465 385554 "DEQUEUE" 385634 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 382745 382878 383061 "DEGRED" 383353 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 379175 379920 380766 "DEFINTRF" 381973 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 376730 377199 377791 "DEFINTEF" 378694 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 376080 376350 376465 "DEFAST" 376635 T DEFAST (NIL) -8 NIL NIL NIL) (-219 369989 375673 375823 "DECIMAL" 375950 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 367501 367959 368465 "DDFACT" 369533 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 367097 367140 367291 "DBLRESP" 367452 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 364965 365327 365688 "DBASE" 366863 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 364207 364445 364591 "DATAARY" 364864 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 363313 364166 364194 "D03FAFA" 364199 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 362420 363272 363300 "D03EEFA" 363305 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 360370 360836 361325 "D03AGNT" 361951 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 359659 360329 360357 "D02EJFA" 360362 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 358948 359618 359646 "D02CJFA" 359651 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 358237 358907 358935 "D02BHFA" 358940 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 357526 358196 358224 "D02BBFA" 358229 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 350723 352312 353918 "D02AGNT" 355940 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 348491 349014 349560 "D01WGTS" 350197 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 347558 348450 348478 "D01TRNS" 348483 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 346626 347517 347545 "D01GBFA" 347550 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 345694 346585 346613 "D01FCFA" 346618 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 344762 345653 345681 "D01ASFA" 345686 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 343830 344721 344749 "D01AQFA" 344754 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 342898 343789 343817 "D01APFA" 343822 T D01APFA (NIL) -8 NIL NIL NIL) (-199 341966 342857 342885 "D01ANFA" 342890 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 341034 341925 341953 "D01AMFA" 341958 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 340102 340993 341021 "D01ALFA" 341026 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 339170 340061 340089 "D01AKFA" 340094 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 338238 339129 339157 "D01AJFA" 339162 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 331533 333086 334647 "D01AGNT" 336697 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 330870 330998 331150 "CYCLOTOM" 331401 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 327603 328318 329045 "CYCLES" 330163 T CYCLES (NIL) -7 NIL NIL NIL) (-191 326915 327049 327220 "CVMP" 327464 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 324756 325014 325383 "CTRIGMNP" 326643 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 324192 324550 324623 "CTOR" 324703 T CTOR (NIL) -8 NIL NIL NIL) (-188 323701 323923 324024 "CTORKIND" 324111 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 322992 323308 323336 "CTORCAT" 323518 T CTORCAT (NIL) -9 NIL 323631 NIL) (-186 322590 322701 322860 "CTORCAT-" 322865 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 322052 322264 322372 "CTORCALL" 322514 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 321426 321525 321678 "CSTTOOLS" 321949 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 317225 317882 318640 "CRFP" 320738 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 316700 316946 317038 "CRCEAST" 317153 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 315747 315932 316160 "CRAPACK" 316504 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 315131 315232 315436 "CPMATCH" 315623 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 314856 314884 314990 "CPIMA" 315097 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 311204 311876 312595 "COORDSYS" 314191 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 310616 310737 310879 "CONTOUR" 311082 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 306507 308619 309111 "CONTFRAC" 310156 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 306387 306408 306436 "CONDUIT" 306473 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 305475 306029 306057 "COMRING" 306062 T COMRING (NIL) -9 NIL 306114 NIL) (-173 304529 304833 305017 "COMPPROP" 305311 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 304190 304225 304353 "COMPLPAT" 304488 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 294392 303999 304108 "COMPLEX" 304113 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 294028 294085 294192 "COMPLEX2" 294329 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 293367 293488 293648 "COMPILER" 293888 T COMPILER (NIL) -8 NIL NIL NIL) (-168 293085 293120 293218 "COMPFACT" 293326 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276977 287061 287101 "COMPCAT" 288105 NIL COMPCAT (NIL T) -9 NIL 289453 NIL) (-166 266267 269256 272963 "COMPCAT-" 273319 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265996 266024 266127 "COMMUPC" 266233 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265790 265824 265883 "COMMONOP" 265957 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 265346 265541 265628 "COMM" 265723 T COMM (NIL) -8 NIL NIL NIL) (-162 264922 265150 265225 "COMMAAST" 265291 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 264171 264365 264393 "COMBOPC" 264731 T COMBOPC (NIL) -9 NIL 264906 NIL) (-160 263067 263277 263519 "COMBINAT" 263961 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 259524 260098 260725 "COMBF" 262489 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 258282 258640 258875 "COLOR" 259309 T COLOR (NIL) -8 NIL NIL NIL) (-157 257758 258003 258095 "COLONAST" 258210 T COLONAST (NIL) -8 NIL NIL NIL) (-156 257398 257445 257570 "CMPLXRT" 257705 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256846 257098 257197 "CLLCTAST" 257319 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 252348 253376 254456 "CLIP" 255786 T CLIP (NIL) -7 NIL NIL NIL) (-153 250689 251449 251689 "CLIF" 252175 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246864 248835 248876 "CLAGG" 249805 NIL CLAGG (NIL T) -9 NIL 250341 NIL) (-151 245286 245743 246326 "CLAGG-" 246331 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244830 244915 245055 "CINTSLPE" 245195 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 242331 242802 243350 "CHVAR" 244358 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 241505 242059 242087 "CHARZ" 242092 T CHARZ (NIL) -9 NIL 242107 NIL) (-147 241259 241299 241377 "CHARPOL" 241459 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 240317 240904 240932 "CHARNZ" 240979 T CHARNZ (NIL) -9 NIL 241035 NIL) (-145 238223 238971 239324 "CHAR" 239984 T CHAR (NIL) -8 NIL NIL NIL) (-144 237949 238010 238038 "CFCAT" 238149 T CFCAT (NIL) -9 NIL NIL NIL) (-143 237190 237301 237484 "CDEN" 237833 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 233155 236343 236623 "CCLASS" 236930 T CCLASS (NIL) -8 NIL NIL NIL) (-141 232406 232563 232740 "CATEGORY" 232998 T -10 (NIL) -8 NIL NIL NIL) (-140 231979 232325 232373 "CATCTOR" 232378 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 231430 231682 231780 "CATAST" 231901 T CATAST (NIL) -8 NIL NIL NIL) (-138 230906 231151 231243 "CASEAST" 231358 T CASEAST (NIL) -8 NIL NIL NIL) (-137 226044 227063 227807 "CARTEN" 230218 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 225152 225300 225521 "CARTEN2" 225891 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223468 224302 224559 "CARD" 224915 T CARD (NIL) -8 NIL NIL NIL) (-134 223044 223272 223347 "CAPSLAST" 223413 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 222548 222756 222784 "CACHSET" 222916 T CACHSET (NIL) -9 NIL 222994 NIL) (-132 222018 222340 222368 "CABMON" 222418 T CABMON (NIL) -9 NIL 222474 NIL) (-131 221491 221722 221832 "BYTEORD" 221928 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 220468 221020 221162 "BYTE" 221325 T BYTE (NIL) -8 NIL NIL 221447) (-129 215818 219973 220145 "BYTEBUF" 220316 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 213327 215510 215617 "BTREE" 215744 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 210776 212975 213097 "BTOURN" 213237 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 208146 210246 210287 "BTCAT" 210355 NIL BTCAT (NIL T) -9 NIL 210432 NIL) (-125 207813 207893 208042 "BTCAT-" 208047 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 203192 207072 207100 "BTAGG" 207214 T BTAGG (NIL) -9 NIL 207324 NIL) (-123 202682 202807 203013 "BTAGG-" 203018 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 199677 201960 202175 "BSTREE" 202499 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 198815 198941 199125 "BRILL" 199533 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 195467 197541 197582 "BRAGG" 198231 NIL BRAGG (NIL T) -9 NIL 198489 NIL) (-119 193996 194402 194957 "BRAGG-" 194962 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 187120 193340 193525 "BPADICRT" 193843 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 185435 187057 187102 "BPADIC" 187107 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 185133 185163 185277 "BOUNDZRO" 185399 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 180361 181559 182471 "BOP" 184241 T BOP (NIL) -8 NIL NIL NIL) (-114 178142 178546 179021 "BOP1" 179919 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 177843 177904 177932 "BOOLE" 178043 T BOOLE (NIL) -9 NIL 178125 NIL) (-112 176668 177417 177566 "BOOLEAN" 177714 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175947 176351 176405 "BMODULE" 176410 NIL BMODULE (NIL T T) -9 NIL 176475 NIL) (-110 171748 175745 175818 "BITS" 175894 T BITS (NIL) -8 NIL NIL NIL) (-109 171169 171288 171428 "BINDING" 171628 T BINDING (NIL) -8 NIL NIL NIL) (-108 165081 170764 170913 "BINARY" 171040 T BINARY (NIL) -8 NIL NIL NIL) (-107 162861 164336 164377 "BGAGG" 164637 NIL BGAGG (NIL T) -9 NIL 164774 NIL) (-106 162692 162724 162815 "BGAGG-" 162820 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161763 162076 162281 "BFUNCT" 162507 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160453 160631 160919 "BEZOUT" 161587 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156922 159305 159635 "BBTREE" 160156 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156656 156709 156737 "BASTYPE" 156856 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156508 156537 156610 "BASTYPE-" 156615 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155942 156018 156170 "BALFACT" 156419 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154798 155357 155543 "AUTOMOR" 155787 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154524 154529 154555 "ATTREG" 154560 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152776 153221 153573 "ATTRBUT" 154190 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152384 152604 152670 "ATTRAST" 152728 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151920 152033 152059 "ATRIG" 152260 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151729 151770 151857 "ATRIG-" 151862 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151374 151560 151586 "ASTCAT" 151591 T ASTCAT (NIL) -9 NIL 151621 NIL) (-92 151101 151160 151279 "ASTCAT-" 151284 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149250 150877 150965 "ASTACK" 151044 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147755 148052 148417 "ASSOCEQ" 148932 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146787 147414 147538 "ASP9" 147662 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146550 146735 146774 "ASP8" 146779 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145418 146155 146297 "ASP80" 146439 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144316 145053 145185 "ASP7" 145317 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143270 143993 144111 "ASP78" 144229 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142239 142950 143067 "ASP77" 143184 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141151 141877 142008 "ASP74" 142139 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 140051 140786 140918 "ASP73" 141050 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139155 139877 139977 "ASP6" 139982 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 138102 138832 138950 "ASP55" 139068 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 137051 137776 137895 "ASP50" 138014 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 136139 136752 136862 "ASP4" 136972 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135227 135840 135950 "ASP49" 136060 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 134011 134766 134934 "ASP42" 135116 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132788 133544 133714 "ASP41" 133898 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131738 132465 132583 "ASP35" 132701 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131503 131686 131725 "ASP34" 131730 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131240 131307 131383 "ASP33" 131458 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 130134 130875 131007 "ASP31" 131139 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129899 130082 130121 "ASP30" 130126 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129634 129703 129779 "ASP29" 129854 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129399 129582 129621 "ASP28" 129626 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129164 129347 129386 "ASP27" 129391 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128248 128862 128973 "ASP24" 129084 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127325 128050 128162 "ASP20" 128167 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126413 127026 127136 "ASP1" 127246 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125356 126087 126206 "ASP19" 126325 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 125093 125160 125236 "ASP12" 125311 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123945 124692 124836 "ASP10" 124980 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121796 123789 123880 "ARRAY2" 123885 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117561 121444 121558 "ARRAY1" 121713 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116593 116766 116987 "ARRAY12" 117384 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110905 112823 112898 "ARR2CAT" 115528 NIL ARR2CAT (NIL T T T) -9 NIL 116286 NIL) (-56 108339 109083 110037 "ARR2CAT-" 110042 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107656 107966 108091 "ARITY" 108232 T ARITY (NIL) -8 NIL NIL NIL) (-54 106432 106584 106883 "APPRULE" 107492 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 106083 106131 106250 "APPLYORE" 106378 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 105437 105676 105796 "ANY" 105981 T ANY (NIL) -8 NIL NIL NIL) (-51 104715 104838 104995 "ANY1" 105311 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 102245 103152 103479 "ANTISYM" 104439 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101737 101952 102048 "ANON" 102167 T ANON (NIL) -8 NIL NIL NIL) (-48 95915 100276 100730 "AN" 101301 T AN (NIL) -8 NIL NIL NIL) (-47 91813 93201 93252 "AMR" 94000 NIL AMR (NIL T T) -9 NIL 94600 NIL) (-46 90925 91146 91509 "AMR-" 91514 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 75364 90842 90903 "ALIST" 90908 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 72169 74958 75127 "ALGSC" 75282 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68725 69279 69886 "ALGPKG" 71609 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 68002 68103 68287 "ALGMFACT" 68611 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 64037 64616 65210 "ALGMANIP" 67586 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55304 63663 63813 "ALGFF" 63970 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54500 54631 54810 "ALGFACT" 55162 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53441 54041 54079 "ALGEBRA" 54084 NIL ALGEBRA (NIL T) -9 NIL 54125 NIL) (-37 53159 53218 53350 "ALGEBRA-" 53355 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35222 51131 51183 "ALAGG" 51319 NIL ALAGG (NIL T T) -9 NIL 51480 NIL) (-35 34758 34871 34897 "AHYP" 35098 T AHYP (NIL) -9 NIL NIL NIL) (-34 33689 33937 33963 "AGG" 34462 T AGG (NIL) -9 NIL 34741 NIL) (-33 33123 33285 33499 "AGG-" 33504 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30929 31352 31757 "AF" 32765 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30409 30654 30744 "ADDAST" 30857 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29677 29936 30092 "ACPLOT" 30271 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26678 26716 "ACFS" 27323 NIL ACFS (NIL T) -9 NIL 27562 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 3da0023a..1ff049a1 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,13218 +1,13254 @@
 
-(732665 . 3485510918)        
-(((*1 *1 *2)
-  (-12 (-5 *2 (-1294 (-1188) *3)) (-4 *3 (-1060)) (-5 *1 (-1301 *3))))
- ((*1 *1 *2)
-  (-12 (-5 *2 (-1294 *3 *4)) (-4 *3 (-858)) (-4 *4 (-1060))
-   (-5 *1 (-1303 *3 *4))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-572)) (-5 *1 (-936))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-830)) (-5 *1 (-829))))) 
-(((*1 *2 *3 *3 *1)
-  (-12 (-4 *4 (-460)) (-4 *5 (-801)) (-4 *6 (-858))
-   (-4 *3 (-1076 *4 *5 *6)) (-5 *2 (-3 *3 (-652 *1)))
-   (-4 *1 (-1082 *4 *5 *6 *3))))) 
+(732799 . 3485633351)        
+(((*1 *1 *2) (-12 (-5 *2 (-654 (-872))) (-5 *1 (-872))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-370)) (-4 *5 (-380 *4)) (-4 *6 (-380 *4))
-   (-5 *2 (-779)) (-5 *1 (-529 *4 *5 *6 *3)) (-4 *3 (-695 *4 *5 *6))))
- ((*1 *2 *1)
-  (-12 (-4 *1 (-695 *3 *4 *5)) (-4 *3 (-1060)) (-4 *4 (-380 *3))
-   (-4 *5 (-380 *3)) (-4 *3 (-564)) (-5 *2 (-779))))
+  (-12 (-5 *3 (-1190)) (-5 *2 (-546)) (-5 *1 (-545 *4))
+   (-4 *4 (-1231))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-666 *2)) (-4 *2 (-1062))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-564)) (-4 *4 (-174)) (-4 *5 (-380 *4))
-   (-4 *6 (-380 *4)) (-5 *2 (-779)) (-5 *1 (-696 *4 *5 *6 *3))
-   (-4 *3 (-695 *4 *5 *6))))
+  (-12 (-4 *4 (-566)) (-4 *4 (-174)) (-4 *5 (-382 *4))
+   (-4 *6 (-382 *4)) (-5 *2 (-2 (|:| |adjMat| *3) (|:| |detMat| *4)))
+   (-5 *1 (-698 *4 *5 *6 *3)) (-4 *3 (-697 *4 *5 *6))))
+ ((*1 *1 *1 *1)
+  (-12 (-4 *2 (-174)) (-4 *2 (-1062)) (-5 *1 (-724 *2 *3))
+   (-4 *3 (-658 *2))))
+ ((*1 *1 *1)
+  (-12 (-4 *2 (-174)) (-4 *2 (-1062)) (-5 *1 (-724 *2 *3))
+   (-4 *3 (-658 *2))))
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-846 *2)) (-4 *2 (-174)) (-4 *2 (-1062))))
+ ((*1 *1 *1) (-12 (-5 *1 (-846 *2)) (-4 *2 (-174)) (-4 *2 (-1062))))) 
+(((*1 *2 *1 *1)
+  (-12
+   (-5 *2
+    (-2 (|:| -2800 *3) (|:| |coef1| (-792 *3)) (|:| |coef2| (-792 *3))))
+   (-5 *1 (-792 *3)) (-4 *3 (-566)) (-4 *3 (-1062))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-654 *3)) (-4 *3 (-1113)) (-5 *1 (-747 *3))))
+ ((*1 *1 *2) (-12 (-5 *1 (-747 *2)) (-4 *2 (-1113))))
+ ((*1 *1) (-12 (-5 *1 (-747 *2)) (-4 *2 (-1113))))) 
+(((*1 *1 *2 *3 *4)
+  (-12 (-5 *3 (-574)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime"))
+   (-5 *1 (-428 *2)) (-4 *2 (-566))))) 
+(((*1 *1 *1) (-4 *1 (-144)))
+ ((*1 *2 *2)
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-            (|:| |endPointContinuity|
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-                  (|:| |lowerSingular|
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-                  (|:| |upperSingular|
-                       "There is a singularity at the upper end point")
-                  (|:| |bothSingular|
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-                  (|:| |notEvaluated|
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-            (|:| |singularitiesStream|
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-                  (|:| |notEvaluated|
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-            (|:| -1910
-                 (-3 (|:| |finite| "The range is finite")
-                  (|:| |lowerInfinite|
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-                  (|:| |upperInfinite| "The top of range is infinite")
-                  (|:| |bothInfinite|
-                       "Both top and bottom points are infinite")
-                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+                  (|:| |upperSingular|
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+                  (|:| |bothSingular|
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+                  (|:| |notEvaluated|
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+                  (|:| |lowerInfinite|
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+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
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+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+     (|:| |notEvaluated| "Range not yet evaluated")))
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 (((*1 *2 *3)
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+     (|:| |lowerSingular|
+          "There is a singularity at the lower end point")
+     (|:| |upperSingular|
+          "There is a singularity at the upper end point")
+     (|:| |bothSingular| "There are singularities at both end points")
+     (|:| |notEvaluated| "End point continuity not yet evaluated")))
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-           (-2
-            (|:| |endPointContinuity|
-                 (-3 (|:| |continuous| "Continuous at the end points")
-                  (|:| |lowerSingular|
-                       "There is a singularity at the lower end point")
-                  (|:| |upperSingular|
-                       "There is a singularity at the upper end point")
-                  (|:| |bothSingular|
-                       "There are singularities at both end points")
-                  (|:| |notEvaluated|
-                       "End point continuity not yet evaluated")))
-            (|:| |singularitiesStream|
-                 (-3 (|:| |str| (-1168 (-227)))
-                  (|:| |notEvaluated|
-                       "Internal singularities not yet evaluated")))
-            (|:| -1910
-                 (-3 (|:| |finite| "The range is finite")
-                  (|:| |lowerInfinite|
-                       "The bottom of range is infinite")
-                  (|:| |upperInfinite| "The top of range is infinite")
-                  (|:| |bothInfinite|
-                       "Both top and bottom points are infinite")
-                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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+            (|:| -2967 (-1107 (-853 (-227)))) (|:| |abserr| (-227))
+            (|:| |relerr| (-227))))
+      (|:| -1909
+           (-2
+            (|:| |endPointContinuity|
+                 (-3 (|:| |continuous| "Continuous at the end points")
+                  (|:| |lowerSingular|
+                       "There is a singularity at the lower end point")
+                  (|:| |upperSingular|
+                       "There is a singularity at the upper end point")
+                  (|:| |bothSingular|
+                       "There are singularities at both end points")
+                  (|:| |notEvaluated|
+                       "End point continuity not yet evaluated")))
+            (|:| |singularitiesStream|
+                 (-3 (|:| |str| (-1170 (-227)))
+                  (|:| |notEvaluated|
+                       "Internal singularities not yet evaluated")))
+            (|:| -2967
+                 (-3 (|:| |finite| "The range is finite")
+                  (|:| |lowerInfinite|
+                       "The bottom of range is infinite")
+                  (|:| |upperInfinite| "The top of range is infinite")
+                  (|:| |bothInfinite|
+                       "Both top and bottom points are infinite")
+                  (|:| |notEvaluated| "Range not yet evaluated"))))))))
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3)
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  ((*1 *2 *3 *4)
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-(((*1 *2 *3 *4 *4 *5)
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-(((*1 *2 *3 *3 *4)
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-(((*1 *2)
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-   (-5 *1 (-1231))))) 
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-   (-5 *1 (-32 *4 *2))))) 
-(((*1 *2 *3 *2)
-  (-12 (-5 *2 (-930)) (-5 *3 (-652 (-268))) (-5 *1 (-266))))
- ((*1 *1 *2) (-12 (-5 *2 (-930)) (-5 *1 (-268))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-572)) (-5 *1 (-569))))) 
+  (-12 (-5 *4 (-1190)) (-4 *5 (-13 (-566) (-1051 (-574)) (-148)))
+   (-5 *2 (-596 (-417 (-963 *5)))) (-5 *1 (-580 *5))
+   (-5 *3 (-417 (-963 *5)))))) 
 (((*1 *2 *3)
   (|partial| -12
       (-5 *3
-       (-2 (|:| |var| (-1188)) (|:| |fn| (-322 (-227)))
-        (|:| -1910 (-1105 (-851 (-227)))) (|:| |abserr| (-227))
+       (-2 (|:| |var| (-1190)) (|:| |fn| (-324 (-227)))
+        (|:| -2967 (-1107 (-853 (-227)))) (|:| |abserr| (-227))
         (|:| |relerr| (-227))))
       (-5 *2
        (-2
@@ -13227,430 +13263,397 @@
               (|:| |notEvaluated|
                    "End point continuity not yet evaluated")))
         (|:| |singularitiesStream|
-             (-3 (|:| |str| (-1168 (-227)))
+             (-3 (|:| |str| (-1170 (-227)))
               (|:| |notEvaluated|
                    "Internal singularities not yet evaluated")))
-        (|:| -1910
+        (|:| -2967
              (-3 (|:| |finite| "The range is finite")
               (|:| |lowerInfinite| "The bottom of range is infinite")
               (|:| |upperInfinite| "The top of range is infinite")
               (|:| |bothInfinite|
                    "Both top and bottom points are infinite")
               (|:| |notEvaluated| "Range not yet evaluated")))))
-      (-5 *1 (-567))))) 
+      (-5 *1 (-569))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-358)) (-4 *4 (-337 *3)) (-4 *5 (-1257 *4))
+   (-5 *1 (-787 *3 *4 *5 *2 *6)) (-4 *2 (-1257 *5)) (-14 *6 (-932))))
+ ((*1 *1 *1 *2)
+  (-12 (-5 *2 (-781)) (-4 *1 (-1300 *3)) (-4 *3 (-372)) (-4 *3 (-377))))
+ ((*1 *1 *1) (-12 (-4 *1 (-1300 *2)) (-4 *2 (-372)) (-4 *2 (-377))))) 
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+(((*1 *1 *2)
+  (-12 (-5 *2 (-1155 *3 *4)) (-14 *3 (-932)) (-4 *4 (-372))
+   (-5 *1 (-1006 *3 *4))))) 
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+(((*1 *2 *1) (-12 (-4 *1 (-1134 *2)) (-4 *2 (-1231))))) 
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 (((*1 *2 *3)
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-(((*1 *2 *1)
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 (((*1 *2 *3)
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-(((*1 *2 *3 *4)
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+  (-12 (-4 *4 (-566)) (-5 *2 (-781)) (-5 *1 (-43 *4 *3))
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-  (-12 (-5 *3 (-572)) (-5 *4 (-697 (-227))) (-5 *5 (-227))
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-(((*1 *2 *3 *4)
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- ((*1 *2 *3 *4)
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-   (-5 *1 (-700 *5 *6 *3 *4)) (-4 *3 (-380 *6))
-   (-4 *4 (-13 (-380 *5) (-10 -7 (-6 -4454))))))) 
+    (-2 (|:| |dpolys| (-654 (-253 *5 *6)))
+     (|:| |coords| (-654 (-574)))))
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+(((*1 *1) (-5 *1 (-299)))) 
+(((*1 *2 *3 *3)
+  (-12 (-4 *4 (-462)) (-4 *3 (-803)) (-4 *5 (-860)) (-5 *2 (-112))
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+(((*1 *1 *2 *2 *2)
+  (-12 (-5 *1 (-229 *2)) (-4 *2 (-13 (-372) (-1216)))))
+ ((*1 *1 *1 *2) (-12 (-5 *1 (-728 *2)) (-4 *2 (-372))))
+ ((*1 *1 *2) (-12 (-5 *1 (-728 *2)) (-4 *2 (-372))))
+ ((*1 *2 *1 *3 *4 *4)
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+  (-12 (-5 *1 (-605 *2)) (-4 *2 (-38 (-417 (-574)))) (-4 *2 (-1062))))) 
+(((*1 *2 *3)
+  (-12 (-5 *3 (-1190)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-712 *4 *5 *6 *7))
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+   (-4 *7 (-1231))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-654 (-872))) (-5 *1 (-338))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |var| (-1188)) (|:| |fn| (-322 (-227)))
-     (|:| -1910 (-1105 (-851 (-227)))) (|:| |abserr| (-227))
+    (-2 (|:| |var| (-1190)) (|:| |fn| (-324 (-227)))
+     (|:| -2967 (-1107 (-853 (-227)))) (|:| |abserr| (-227))
      (|:| |relerr| (-227))))
    (-5 *2
     (-2
@@ -13665,3026 +13668,3013 @@
            (|:| |notEvaluated|
                 "End point continuity not yet evaluated")))
      (|:| |singularitiesStream|
-          (-3 (|:| |str| (-1168 (-227)))
+          (-3 (|:| |str| (-1170 (-227)))
            (|:| |notEvaluated|
                 "Internal singularities not yet evaluated")))
-     (|:| -1910
+     (|:| -2967
           (-3 (|:| |finite| "The range is finite")
            (|:| |lowerInfinite| "The bottom of range is infinite")
            (|:| |upperInfinite| "The top of range is infinite")
            (|:| |bothInfinite|
                 "Both top and bottom points are infinite")
            (|:| |notEvaluated| "Range not yet evaluated")))))
-   (-5 *1 (-567))))) 
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-        (|:| |%term|
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 (((*1 *2 *1)
-  (-12 (-4 *1 (-329 *3 *4)) (-4 *3 (-1111)) (-4 *4 (-132))
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-   (-5 *1 (-743 *3 *4)) (-4 *3 (-1060)) (-4 *4 (-734))))
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 (((*1 *2 *3 *3 *3)
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+      (-5 *3 (-417 *5))))) 
 (((*1 *2 *3)
-  (-12
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-(((*1 *1) (-5 *1 (-586)))) 
+  (-12 (-5 *3 (-1281 *4)) (-4 *4 (-358)) (-5 *2 (-1186 *4))
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+  (-12 (-5 *3 (-227)) (-5 *4 (-574))
+   (-5 *5 (-3 (|:| |fn| (-398)) (|:| |fp| (-64 G)))) (-5 *2 (-1048))
+   (-5 *1 (-758))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1279 (-322 (-227))))
-   (-5 *2
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-(((*1 *2 *2) (|partial| -12 (-4 *1 (-994 *2)) (-4 *2 (-1214))))) 
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+  (-12 (-5 *3 (-227)) (-5 *4 (-574)) (-5 *5 (-1172))
+   (-5 *6 (-3 (|:| |fn| (-398)) (|:| |fp| (-82 PDEF))))
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 (((*1 *2 *3 *4)
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  ((*1 *2 *3 *4)
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-  (-12 (-4 *2 (-13 (-370) (-856))) (-5 *1 (-183 *2 *3))
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+          (-2 (|:| |var| (-1190)) (|:| |fn| (-324 (-227)))
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+           (|:| |relerr| (-227))))
+     (|:| -1909
+          (-2
+           (|:| |endPointContinuity|
+                (-3 (|:| |continuous| "Continuous at the end points")
+                 (|:| |lowerSingular|
+                      "There is a singularity at the lower end point")
+                 (|:| |upperSingular|
+                      "There is a singularity at the upper end point")
+                 (|:| |bothSingular|
+                      "There are singularities at both end points")
+                 (|:| |notEvaluated|
+                      "End point continuity not yet evaluated")))
+           (|:| |singularitiesStream|
+                (-3 (|:| |str| (-1170 (-227)))
+                 (|:| |notEvaluated|
+                      "Internal singularities not yet evaluated")))
+           (|:| -2967
+                (-3 (|:| |finite| "The range is finite")
+                 (|:| |lowerInfinite|
+                      "The bottom of range is infinite")
+                 (|:| |upperInfinite| "The top of range is infinite")
+                 (|:| |bothInfinite|
+                      "Both top and bottom points are infinite")
+                 (|:| |notEvaluated| "Range not yet evaluated")))))))
+   (-5 *1 (-569))))
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+   (-5 *2
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+          (-2 (|:| |xinit| (-227)) (|:| |xend| (-227))
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+           (|:| |intvals| (-654 (-227))) (|:| |g| (-324 (-227)))
+           (|:| |abserr| (-227)) (|:| |relerr| (-227))))
+     (|:| -1909
+          (-2 (|:| |stiffness| (-388)) (|:| |stability| (-388))
+           (|:| |expense| (-388)) (|:| |accuracy| (-388))
+           (|:| |intermediateResults| (-388))))))
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+ ((*1 *1)
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+(((*1 *2 *3 *2)
+  (-12 (-5 *3 (-932)) (-5 *1 (-1043 *2))
+   (-4 *2 (-13 (-1113) (-10 -8 (-15 -3078 ($ $ $)))))))) 
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-(((*1 *2 *1)
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-(((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1246 (-572))) (-4 *1 (-288 *3)) (-4 *3 (-1229))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-572)) (-4 *1 (-288 *3)) (-4 *3 (-1229))))) 
+    (-3 (|:| |overq| (-1186 (-417 (-574))))
+     (|:| |overan| (-1186 (-48))) (|:| -3601 (-112))))
+   (-5 *1 (-445 *4 *5 *3)) (-4 *3 (-1257 *5))))) 
+(((*1 *2 *1 *1)
+  (-12 (-4 *3 (-566)) (-4 *3 (-1062))
+   (-5 *2 (-2 (|:| -3855 *1) (|:| -3435 *1))) (-4 *1 (-862 *3))))
+ ((*1 *2 *3 *3 *4)
+  (-12 (-5 *4 (-99 *5)) (-4 *5 (-566)) (-4 *5 (-1062))
+   (-5 *2 (-2 (|:| -3855 *3) (|:| -3435 *3))) (-5 *1 (-863 *5 *3))
+   (-4 *3 (-862 *5))))) 
+(((*1 *2 *3)
+  (-12
+   (-5 *3
+    (-2
+     (|:| |endPointContinuity|
+          (-3 (|:| |continuous| "Continuous at the end points")
+           (|:| |lowerSingular|
+                "There is a singularity at the lower end point")
+           (|:| |upperSingular|
+                "There is a singularity at the upper end point")
+           (|:| |bothSingular|
+                "There are singularities at both end points")
+           (|:| |notEvaluated|
+                "End point continuity not yet evaluated")))
+     (|:| |singularitiesStream|
+          (-3 (|:| |str| (-1170 (-227)))
+           (|:| |notEvaluated|
+                "Internal singularities not yet evaluated")))
+     (|:| -2967
+          (-3 (|:| |finite| "The range is finite")
+           (|:| |lowerInfinite| "The bottom of range is infinite")
+           (|:| |upperInfinite| "The top of range is infinite")
+           (|:| |bothInfinite|
+                "Both top and bottom points are infinite")
+           (|:| |notEvaluated| "Range not yet evaluated")))))
+   (-5 *2 (-1048)) (-5 *1 (-313))))) 
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 (((*1 *2 *1)
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@@ -16696,1625 +16686,1637 @@
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\ No newline at end of file