add spad parser library

5 files changed, 8784 insertions, 8774 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 1ed6dd1a..283ba313 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(2204743 . 3403927923)       
+(2205538 . 3404130410)       
 (-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."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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(\\spad{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(\\spad{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| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(\\spad{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(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . 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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}."))) 
@@ -46,23 +46,23 @@ 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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-4177 . T) (-4175 . T) (-4174 . T) ((-4182 "*") . T) (-4173 . T) (-4178 . T) (-4172 . T) (-3353 . T)) 
+((-4180 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4176 . T) (-4181 . T) (-4175 . T) (-3252 . T)) 
 NIL 
 (-30) 
 ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) 
 NIL 
 NIL 
-(-31 R -1696) 
+(-31 R -2184) 
 ((|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 -952) (QUOTE (-517))))) 
 (-32 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 -4180))) 
+((|HasAttribute| |#1| (QUOTE -4183))) 
 (-33) 
 ((|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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-34) 
 ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) 
@@ -70,7 +70,7 @@ NIL
 NIL 
 (-35 |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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-36 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) 
@@ -78,17 +78,17 @@ NIL
 NIL 
 (-37 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-38 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 
-(-39 -1696 UP UPUP -1734) 
+(-39 -2184 UP UPUP -3962) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-4173 |has| (-377 |#2|) (-333)) (-4178 |has| (-377 |#2|) (-333)) (-4172 |has| (-377 |#2|) (-333)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3807 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3807 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3807 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3807 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
-(-40 R -1696) 
+((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3763 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3763 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
+(-40 R -2184) 
 ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -400) (|devaluate| |#1|))))) 
@@ -102,23 +102,23 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-278)))) 
 (-43 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) 
-((-4177 |has| |#1| (-509)) (-4175 . T) (-4174 . T)) 
+((-4180 |has| |#1| (-509)) (-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) 
 (-44 |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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (-3807 (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))))) 
 (-45 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-46 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-47) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (LIST (QUOTE -952) (QUOTE (-517))))) 
 (-48) 
 ((|constructor| (NIL "This domain implements anonymous functions"))) 
@@ -126,7 +126,7 @@ NIL
 NIL 
 (-49 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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-50 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}."))) 
@@ -140,7 +140,7 @@ 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 
-(-53 |Base| R -1696) 
+(-53 |Base| R -2184) 
 ((|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 
@@ -150,7 +150,7 @@ NIL
 NIL 
 (-55 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"))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-56 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),{}...]}."))) 
@@ -158,65 +158,65 @@ NIL
 NIL 
 (-57 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}"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-58 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
-(-59 -1207) 
+(-59 -1211) 
 ((|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 
-(-60 -1207) 
+(-60 -1211) 
 ((|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 
-(-61 -1207) 
+(-61 -1211) 
 ((|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 
-(-62 -1207) 
+(-62 -1211) 
 ((|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 
-(-63 -1207) 
+(-63 -1211) 
 ((|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}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-64 -1207) 
+(-64 -1211) 
 ((|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 
-(-65 -1207) 
+(-65 -1211) 
 ((|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 
-(-66 -1207) 
+(-66 -1211) 
 ((|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 
-(-67 -1207) 
+(-67 -1211) 
 ((|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 
-(-68 -1207) 
+(-68 -1211) 
 ((|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 
-(-69 -1207) 
+(-69 -1211) 
 ((|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 
-(-70 -1207) 
+(-70 -1211) 
 ((|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 
-(-71 -1207) 
+(-71 -1211) 
 ((|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 
-(-72 -1207) 
+(-72 -1211) 
 ((|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 
@@ -228,55 +228,55 @@ 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 
-(-75 -1207) 
+(-75 -1211) 
 ((|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 
-(-76 -1207) 
+(-76 -1211) 
 ((|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 
-(-77 -1207) 
+(-77 -1211) 
 ((|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 
-(-78 -1207) 
+(-78 -1211) 
 ((|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 
-(-79 -1207) 
+(-79 -1211) 
 ((|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}")) (|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 
-(-80 -1207) 
+(-80 -1211) 
 ((|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 
-(-81 -1207) 
+(-81 -1211) 
 ((|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 
-(-82 -1207) 
+(-82 -1211) 
 ((|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 
-(-83 -1207) 
+(-83 -1211) 
 ((|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 
-(-84 -1207) 
+(-84 -1211) 
 ((|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 
-(-85 -1207) 
+(-85 -1211) 
 ((|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 
-(-86 -1207) 
+(-86 -1211) 
 ((|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 
-(-87 -1207) 
+(-87 -1211) 
 ((|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 
@@ -286,7 +286,7 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-333)))) 
 (-89 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-90 S) 
 ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) 
@@ -298,15 +298,15 @@ NIL
 NIL 
 (-92) 
 ((|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\"."))) 
-((-4180 . T)) 
+((-4183 . T)) 
 NIL 
 (-93) 
 ((|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."))) 
-((-4180 . T) ((-4182 "*") . T) (-4181 . T) (-4177 . T) (-4175 . T) (-4174 . T) (-4173 . T) (-4178 . T) (-4172 . T) (-4171 . T) (-4170 . T) (-4169 . T) (-4168 . T) (-4176 . T) (-4179 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4167 . T)) 
+((-4183 . T) ((-4185 "*") . T) (-4184 . T) (-4180 . T) (-4178 . T) (-4177 . T) (-4176 . T) (-4181 . T) (-4175 . T) (-4174 . T) (-4173 . T) (-4172 . T) (-4171 . T) (-4179 . T) (-4182 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4170 . T)) 
 NIL 
 (-94 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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-95 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{\\spad{pi}} is balanced with respect to \\spad{b}."))) 
@@ -322,15 +322,15 @@ NIL
 NIL 
 (-98 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-99 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 (-4182 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4185 "*")))) 
 (-100) 
 ((|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"))) 
-((-4180 . T)) 
+((-4183 . T)) 
 NIL 
 (-101 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."))) 
@@ -338,23 +338,23 @@ NIL
 NIL 
 (-102 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."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-103) 
 ((|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.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1049))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3807 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
 (-104) 
 ((|constructor| (NIL "This domain provides an implementation of binary files. Data is accessed one byte at a time as a small integer.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "\\spad{position!(f,{} i)} sets the current byte-position to \\spad{i}.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{f}.")) (|readIfCan!| (((|Union| (|SingleInteger|) "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
 NIL 
 NIL 
 (-105) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1003))) (-12 (|HasCategory| (-107) (QUOTE (-1003))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107)))))) 
 (-106 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}"))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
 (-107) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|implies| (($ $ $) "\\spad{implies(a,{}b)} returns the logical implication of Boolean \\spad{a} and \\spad{b}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical inclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of Boolean \\spad{a} and \\spad{b}.")) (|not| (($ $) "\\spad{not n} returns the negation of \\spad{n}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
@@ -368,25 +368,25 @@ NIL
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|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| (((|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!| (($ $ (|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| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|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.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|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}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) 
 NIL 
 NIL 
-(-110 -1696 UP) 
+(-110 -2184 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 
 (-111 |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}."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-112 |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}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-111 |#1|) (QUOTE (-831))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-937))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1049))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1073)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3807 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-111 |#1|) (QUOTE (-831))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-134))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-111 |#1|) (QUOTE (-937))) (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-1050))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-111 |#1|) (QUOTE (-207))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -111) (|devaluate| |#1|)) (LIST (QUOTE -111) (|devaluate| |#1|)))) (|HasCategory| (-111 |#1|) (QUOTE (-278))) (|HasCategory| (-111 |#1|) (QUOTE (-502))) (|HasCategory| (-111 |#1|) (QUOTE (-779))) (-3763 (|HasCategory| (-111 |#1|) (QUOTE (-752))) (|HasCategory| (-111 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-111 |#1|) (QUOTE (-831)))) (|HasCategory| (-111 |#1|) (QUOTE (-132))))) 
 (-113 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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4181))) 
+((|HasAttribute| |#1| (QUOTE -4184))) 
 (-114 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-115 UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) 
@@ -394,7 +394,7 @@ NIL
 NIL 
 (-116 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"))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-117 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
@@ -402,7 +402,7 @@ NIL
 NIL 
 (-118) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
 (-119 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -410,15 +410,15 @@ NIL
 NIL 
 (-120 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-121 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-122 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."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-123) 
 ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) 
@@ -430,20 +430,20 @@ NIL
 NIL 
 (-125) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) 
-(((-4182 "*") . T)) 
+(((-4185 "*") . T)) 
 NIL 
-(-126 |minix| -2806 S T$) 
+(-126 |minix| -2630 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-127 |minix| -2806 R) 
+(-127 |minix| -2630 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 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 
 (-128) 
 ((|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}."))) 
-((-4180 . T) (-4170 . T) (-4181 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3807 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
+((-4183 . T) (-4173 . T) (-4184 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-338))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
 (-129 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{\\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{\\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 
@@ -458,7 +458,7 @@ NIL
 NIL 
 (-132) 
 ((|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."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-133 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}."))) 
@@ -466,9 +466,9 @@ NIL
 NIL 
 (-134) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
-(-135 -1696 UP UPUP) 
+(-135 -2184 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 
@@ -479,14 +479,14 @@ NIL
 (-137 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 -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasAttribute| |#1| (QUOTE -4180))) 
+((|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasAttribute| |#1| (QUOTE -4183))) 
 (-138 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."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-139 |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."))) 
-((-4175 . T) (-4174 . T) (-4177 . T)) 
+((-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
 (-140) 
 ((|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."))) 
@@ -500,7 +500,7 @@ 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 
-(-143 R -1696) 
+(-143 R -2184) 
 ((|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 
@@ -527,10 +527,10 @@ NIL
 (-149 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 (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4176)) (|HasAttribute| |#2| (QUOTE -4179)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-918))) (|HasCategory| |#2| (QUOTE (-1095))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasAttribute| |#2| (QUOTE -4179)) (|HasAttribute| |#2| (QUOTE -4182)) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-150 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})"))) 
-((-4173 -3807 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4176 |has| |#1| (-6 -4176)) (-4179 |has| |#1| (-6 -4179)) (-3392 . T) (-3353 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 -3763 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4179 |has| |#1| (-6 -4179)) (-4182 |has| |#1| (-6 -4182)) (-3295 . T) (-3252 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-151 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."))) 
@@ -542,8 +542,8 @@ NIL
 NIL 
 (-153 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}."))) 
-((-4173 -3807 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4176 |has| |#1| (-6 -4176)) (-4179 |has| |#1| (-6 -4179)) (-3392 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1094))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-502))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-278))) (-3807 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-207))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-207))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4176)) (|HasAttribute| |#1| (QUOTE -4179)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073))))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-319))))) 
+((-4176 -3763 (|has| |#1| (-509)) (-12 (|has| |#1| (-278)) (|has| |#1| (-831)))) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4179 |has| |#1| (-6 -4179)) (-4182 |has| |#1| (-6 -4182)) (-3295 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-1095))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-1095)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-1095)))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-278))) (-3763 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-207))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-207))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-1095)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-831))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-333)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasAttribute| |#1| (QUOTE -4179)) (|HasAttribute| |#1| (QUOTE -4182)) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-319))))) 
 (-154 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 
@@ -554,11 +554,11 @@ NIL
 NIL 
 (-156) 
 ((|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."))) 
-(((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-157 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}."))) 
-(((-4182 "*") . T) (-4173 . T) (-4178 . T) (-4172 . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") . T) (-4176 . T) (-4181 . T) (-4175 . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-158 R) 
 ((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,{}b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,{}b)} is a function which will map the point \\spad{(lambda,{}mu,{}nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}."))) 
@@ -584,7 +584,7 @@ NIL
 ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) 
 NIL 
 NIL 
-(-164 R -1696) 
+(-164 R -2184) 
 ((|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 
@@ -688,19 +688,19 @@ NIL
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 
-(-190 -1696 UP UPUP R) 
+(-190 -2184 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 
-(-191 -1696 FP) 
+(-191 -2184 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 
 (-192) 
 ((|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.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1049))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3807 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
-(-193 R -1696) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+(-193 R -2184) 
 ((|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 
@@ -714,19 +714,19 @@ NIL
 NIL 
 (-196 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-197 |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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
-(-198 R -1696) 
+(-198 R -2184) 
 ((|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 
 (-199) 
 ((|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)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|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}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\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}."))) 
-((-3383 . T) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-200) 
 ((|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{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{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*\\%\\spad{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*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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)}.}"))) 
@@ -734,23 +734,23 @@ NIL
 NIL 
 (-201 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}"))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4182 "*"))) (|HasCategory| |#1| (QUOTE (-333)))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4185 "*"))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-202 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 
 (-203 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."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-204 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 -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207)))) 
+((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) 
 (-205 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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-206 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}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
@@ -758,36 +758,36 @@ NIL
 NIL 
 (-207) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-208 A S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4180))) 
+((|HasAttribute| |#1| (QUOTE -4183))) 
 (-209 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}."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-210) 
 ((|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 
-(-211 S -2806 R) 
+(-211 S -2630 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 (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4177)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1003)))) 
-(-212 -2806 R) 
+((|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (|HasAttribute| |#3| (QUOTE -4180)) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (QUOTE (-659))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1003)))) 
+(-212 -2630 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"))) 
-((-4174 |has| |#2| (-961)) (-4175 |has| |#2| (-961)) (-4177 |has| |#2| (-6 -4177)) ((-4182 "*") |has| |#2| (-156)) (-4180 . T) (-3353 . T)) 
+((-4177 |has| |#2| (-961)) (-4178 |has| |#2| (-961)) (-4180 |has| |#2| (-6 -4180)) ((-4185 "*") |has| |#2| (-156)) (-4183 . T) (-3252 . T)) 
 NIL 
-(-213 -2806 A B) 
+(-213 -2630 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 
-(-214 -2806 R) 
+(-214 -2630 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."))) 
-((-4174 |has| |#2| (-961)) (-4175 |has| |#2| (-961)) (-4177 |has| |#2| (-6 -4177)) ((-4182 "*") |has| |#2| (-156)) (-4180 . T)) 
-((|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777))) (-3807 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777)))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333)))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073))))) (|HasCategory| |#2| (QUOTE (-659))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-3807 (|HasCategory| |#2| (QUOTE (-961))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1003)))) (|HasAttribute| |#2| (QUOTE -4177)) (|HasCategory| |#2| (QUOTE (-123))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-25))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3807 (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-156)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-777)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1003))))) (-3807 (-12 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3807 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073))))))) 
+((-4177 |has| |#2| (-961)) (-4178 |has| |#2| (-961)) (-4180 |has| |#2| (-6 -4180)) ((-4185 "*") |has| |#2| (-156)) (-4183 . T)) 
+((|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777))) (-3763 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777)))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333)))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074))))) (|HasCategory| |#2| (QUOTE (-659))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-3763 (|HasCategory| |#2| (QUOTE (-961))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1003)))) (|HasAttribute| |#2| (QUOTE -4180)) (|HasCategory| |#2| (QUOTE (-123))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-25))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1003)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-961)))) (-3763 (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-156)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-777)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-1003))))) (-3763 (-12 (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-123))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-725))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-777))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074))))))) 
 (-215) 
 ((|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 
@@ -798,47 +798,47 @@ NIL
 NIL 
 (-217) 
 ((|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}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
-((-4173 . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-218 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."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-219 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}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-220 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 
 (-221 |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"))) 
-(((-4182 "*") |has| |#2| (-156)) (-4173 |has| |#2| (-509)) (-4178 |has| |#2| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-222) 
-((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: October 18,{} 2007. Basic Operations: Related Constructors: Type,{} OutputForm Also See: Type"))) 
+((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: November 13,{} 2007. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type")) (|reify| (((|Syntax|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 
 NIL 
 NIL 
 (-223 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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 (-224 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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(|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1073))))))) 
+((-4180 -3763 (-1651 (|has| |#3| (-961)) (|has| |#3| (-207))) (-1651 (|has| |#3| (-961)) (|has| |#3| (-822 (-1074)))) (|has| |#3| (-6 -4180)) (-1651 (|has| |#3| (-961)) (|has| |#3| (-579 (-517))))) (-4177 |has| |#3| (-961)) (-4178 |has| |#3| (-961)) ((-4185 "*") |has| |#3| (-156)) (-4183 . T)) 
+((|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777))) (-3763 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (QUOTE (-777)))) (|HasCategory| |#3| (QUOTE (-156))) (-3763 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-961)))) (-3763 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (-3763 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#3| (QUOTE (-207))) (-3763 (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#3| (QUOTE (-659))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-3763 (-12 (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517)))))) (-3763 (|HasCategory| |#3| (QUOTE (-961))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-1003)))) (-3763 (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-156)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-207)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-338)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-725)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-777)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-1003))))) (-3763 (|HasAttribute| |#3| (QUOTE -4180)) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074))))))) 
 (-225 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 
 ((|HasCategory| |#2| (QUOTE (-207)))) 
 (-226 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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
 (-227 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}."))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-228) 
 ((|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."))) 
@@ -878,8 +878,8 @@ NIL
 NIL 
 (-237 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"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#3| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-238 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 
@@ -924,11 +924,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|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 
-(-249 R -1696) 
+(-249 R -2184) 
 ((|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{\\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 
-(-250 R -1696) 
+(-250 R -2184) 
 ((|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{\\spad{ki}} was rewritten as \\spad{\\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 
@@ -946,7 +946,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003)))) 
 (-254 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}."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-255 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}."))) 
@@ -967,18 +967,18 @@ NIL
 (-259 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 -4181))) 
+((|HasAttribute| |#1| (QUOTE -4184))) 
 (-260 |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 
-(-261 S R |Mod| -3271 -3237 |exactQuo|) 
+(-261 S R |Mod| -1476 -2262 |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}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|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"))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-262) 
 ((|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."))) 
-((-4173 . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-263 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."))) 
@@ -990,21 +990,21 @@ NIL
 NIL 
 (-265 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."))) 
-((-4177 -3807 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4174 |has| |#1| (-961)) (-4175 |has| |#1| (-961))) 
-((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3807 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3807 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1015))) (-3807 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-21))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1003))))) 
+((-4180 -3763 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4177 |has| |#1| (-961)) (-4178 |has| |#1| (-961))) 
+((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-273))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442)))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-659))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-1015))) (-3763 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659)))) (|HasCategory| |#1| (QUOTE (-25))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-961)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-1003))))) 
 (-266 |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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
 (-267) 
 ((|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 
-(-268 -1696 S) 
+(-268 -2184 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 
-(-269 E -1696) 
+(-269 E -2184) 
 ((|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 
@@ -1042,7 +1042,7 @@ NIL
 NIL 
 (-278) 
 ((|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 \\spad{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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-279 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) 
@@ -1052,7 +1052,7 @@ NIL
 ((|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 
-(-281 -1696) 
+(-281 -2184) 
 ((|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 
@@ -1062,8 +1062,8 @@ NIL
 NIL 
 (-283 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))}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-1049))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-207))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -478) (QUOTE (-1073)) (LIST (QUOTE -1140) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -280) (LIST (QUOTE -1140) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (LIST (QUOTE -258) (LIST (QUOTE -1140) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1140) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-278))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-502))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-779))) (-3807 (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-752))) (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-779)))) (-12 (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))) (-3807 (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-132))) (-12 (|HasCategory| (-1140 |#1| |#2| |#3| |#4|) (QUOTE (-831))) (|HasCategory| $ (QUOTE (-132)))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
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 (-284 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 
@@ -1074,9 +1074,9 @@ NIL
 NIL 
 (-286 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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-(-287 R -1696) 
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+(-287 R -2184) 
 ((|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{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{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 
@@ -1086,8 +1086,8 @@ NIL
 NIL 
 (-289 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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+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
 (-290 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 
@@ -1098,7 +1098,7 @@ NIL
 NIL 
 (-292 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-724)))) 
 (-293 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{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| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
@@ -1114,19 +1114,19 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-296 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-297 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."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
-(-298 S -1696) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+(-298 S -2184) 
 ((|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 (-338)))) 
-(-299 -1696) 
+(-299 -2184) 
 ((|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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-300) 
 ((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) 
@@ -1144,54 +1144,54 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-304 S -1696 UP UPUP R) 
+(-304 S -2184 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 
-(-305 -1696 UP UPUP R) 
+(-305 -2184 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 
-(-306 -1696 UP UPUP R) 
+(-306 -2184 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
 (-307 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-308 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-309 |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{\\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.}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-349)))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (LIST (QUOTE -952) (QUOTE (-517))))) 
 (-310 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 
-(-311 S -1696 UP UPUP) 
+(-311 S -2184 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(\\spad{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}.") (($ (|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 (-338))) (|HasCategory| |#2| (QUOTE (-333)))) 
-(-312 -1696 UP UPUP) 
+(-312 -2184 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(\\spad{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}.") (($ (|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."))) 
-((-4173 |has| (-377 |#2|) (-333)) (-4178 |has| (-377 |#2|) (-333)) (-4172 |has| (-377 |#2|) (-333)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-313 |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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3807 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
 (-314 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-315 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-316 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 
@@ -1206,33 +1206,33 @@ NIL
 NIL 
 (-319) 
 ((|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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-320 R UP -1696) 
+(-320 R UP -2184) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-321 |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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3807 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
 (-322 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-323 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-324 |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}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3807 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-832 |#1|) (QUOTE (-134))) (|HasCategory| (-832 |#1|) (QUOTE (-338))) (|HasCategory| (-832 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-832 |#1|) (QUOTE (-132))) (|HasCategory| (-832 |#1|) (QUOTE (-338))))) 
 (-325 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
-(-326 -1696 GF) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+(-326 -2184 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 
@@ -1240,21 +1240,21 @@ NIL
 ((|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 
-(-328 -1696 FP FPP) 
+(-328 -2184 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
 (-329 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}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-338))))) 
 (-330 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 
 (-331 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-332 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1262,7 +1262,7 @@ NIL
 NIL 
 (-333) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-334 |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."))) 
@@ -1278,7 +1278,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-509)))) 
 (-337 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{\\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{\\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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-4177 |has| |#1| (-509)) (-4175 . T) (-4174 . T)) 
+((-4180 |has| |#1| (-509)) (-4178 . T) (-4177 . T)) 
 NIL 
 (-338) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) 
@@ -1290,7 +1290,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-340 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-341 S A R B) 
 ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) 
@@ -1299,14 +1299,14 @@ NIL
 (-342 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003)))) 
+((|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003)))) 
 (-343 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-4180 . T) (-3353 . T)) 
+((-4183 . T) (-3252 . T)) 
 NIL 
 (-344 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4175 . T) (-4174 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4178 . T) (-4177 . T)) 
 NIL 
 (-345 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."))) 
@@ -1318,7 +1318,7 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) 
 (-347 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}"))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-348 |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}."))) 
@@ -1326,7 +1326,7 @@ NIL
 NIL 
 (-349) 
 ((|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{\\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}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|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}."))) 
-((-4163 . T) (-4171 . T) (-3383 . T) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4166 . T) (-4174 . T) (-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-350 |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}."))) 
@@ -1334,23 +1334,23 @@ NIL
 NIL 
 (-351 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}"))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156)))) 
 (-352 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}."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
 (-353) 
 ((|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}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-354) 
 ((|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.}"))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-355 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."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156)))) 
 (-356 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1358,7 +1358,7 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-779)))) 
 (-357) 
 ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-358) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
@@ -1370,13 +1370,13 @@ NIL
 NIL 
 (-360 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
 (-361) 
 ((|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 
-(-362 -1696 UP UPUP R) 
+(-362 -2184 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 
@@ -1390,27 +1390,27 @@ NIL
 NIL 
 (-365) 
 ((|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."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-366) 
 ((|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.}"))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-367) 
 ((|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 
-(-368 -1207 |returnType| |arguments| |symbols|) 
+(-368 -1211 |returnType| |arguments| |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 
-(-369 -1696 UP) 
+(-369 -2184 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
 (-370 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-371 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
@@ -1418,15 +1418,15 @@ NIL
 NIL 
 (-372) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-373 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4163)) (|HasAttribute| |#1| (QUOTE -4171))) 
+((|HasAttribute| |#1| (QUOTE -4166)) (|HasAttribute| |#1| (QUOTE -4174))) 
 (-374) 
 ((|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\"."))) 
-((-3383 . T) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-375 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."))) 
@@ -1438,15 +1438,15 @@ NIL
 NIL 
 (-377 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."))) 
-((-4167 -12 (|has| |#1| (-6 -4178)) (|has| |#1| (-421)) (|has| |#1| (-6 -4167))) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4178)) (|HasAttribute| |#1| (QUOTE -4167)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+((-4170 -12 (|has| |#1| (-6 -4181)) (|has| |#1| (-421)) (|has| |#1| (-6 -4170))) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-502))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (-12 (|HasAttribute| |#1| (QUOTE -4181)) (|HasAttribute| |#1| (QUOTE -4170)) (|HasCategory| |#1| (QUOTE (-421)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-779)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-760))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-378 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 
 (-379 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-380 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
@@ -1460,11 +1460,11 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-383 R -1696 UP A) 
+(-383 R -2184 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
-(-384 R -1696 UP A |ibasis|) 
+(-384 R -2184 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) 
 NIL 
 ((|HasCategory| |#4| (LIST (QUOTE -952) (|devaluate| |#2|)))) 
@@ -1478,12 +1478,12 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-387 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to 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{\\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."))) 
-((-4177 |has| |#1| (-509)) (-4175 . T) (-4174 . T)) 
+((-4180 |has| |#1| (-509)) (-4178 . T) (-4177 . T)) 
 NIL 
 (-388 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."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1112))))) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -280) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -258) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-1113))))) 
 (-389 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 
@@ -1510,17 +1510,17 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-395 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-4180 . T) (-4170 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4173 . T) (-4184 . T) (-3252 . T)) 
 NIL 
-(-396 R -1696) 
+(-396 R -2184) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
 (-397 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) 
-((-4167 -12 (|has| |#1| (-6 -4167)) (|has| |#2| (-6 -4167))) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -4167)) (|HasAttribute| |#2| (QUOTE -4167)))) 
-(-398 R -1696) 
+((-4170 -12 (|has| |#1| (-6 -4170)) (|has| |#2| (-6 -4170))) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -4170)) (|HasAttribute| |#2| (QUOTE -4170)))) 
+(-398 R -2184) 
 ((|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 
@@ -1530,17 +1530,17 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) 
 (-400 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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) 
-((-4177 -3807 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) ((-4182 "*") |has| |#1| (-509)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-509)) (-4172 |has| |#1| (-509)) (-3353 . T)) 
+((-4180 -3763 (|has| |#1| (-961)) (|has| |#1| (-442))) (-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-509)) (-4175 |has| |#1| (-509)) (-3252 . T)) 
 NIL 
-(-401 R -1696) 
+(-401 R -2184) 
 ((|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 
-(-402 R -1696) 
+(-402 R -2184) 
 ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-403 R -1696) 
+(-403 R -2184) 
 ((|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 
@@ -1548,7 +1548,7 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-405 R -1696 UP) 
+(-405 R -2184 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 -952) (QUOTE (-47))))) 
@@ -1566,17 +1566,17 @@ NIL
 NIL 
 (-409) 
 ((|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}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-410) 
 ((|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.}"))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-411 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 
 NIL 
-(-412 R UP -1696) 
+(-412 R UP -2184) 
 ((|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 
 NIL 
@@ -1614,16 +1614,16 @@ NIL
 NIL 
 (-421) 
 ((|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}."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-422 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"))) 
-((-4177 |has| (-377 (-874 |#1|)) (-509)) (-4175 . T) (-4174 . T)) 
+((-4180 |has| (-377 (-874 |#1|)) (-509)) (-4178 . T) (-4177 . T)) 
 ((|HasCategory| (-377 (-874 |#1|)) (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-377 (-874 |#1|)) (QUOTE (-509)))) 
 (-423 |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"))) 
-(((-4182 "*") |has| |#2| (-156)) (-4173 |has| |#2| (-509)) (-4178 |has| |#2| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-424 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 
@@ -1650,7 +1650,7 @@ NIL
 NIL 
 (-430 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
 (-431 E V R P Q) 
 ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1658,7 +1658,7 @@ NIL
 NIL 
 (-432 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1003))) (-12 (|HasCategory| |#4| (QUOTE (-1003))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509)))) 
 (-433 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}."))) 
@@ -1688,7 +1688,7 @@ NIL
 ((|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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-440 |lv| -1696 R) 
+(-440 |lv| -2184 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1698,45 +1698,45 @@ NIL
 NIL 
 (-442) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-443 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
 (-444 |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."))) 
-((-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) 
+((-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) 
 (-445 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)}"))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1003))) (-12 (|HasCategory| |#4| (QUOTE (-1003))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338)))) 
 (-446) 
 ((|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{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-447 |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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
 (-448) 
 ((|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 
 (-449 |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"))) 
-(((-4182 "*") |has| |#2| (-156)) (-4173 |has| |#2| (-509)) (-4178 |has| |#2| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
-(-450 -2806 S) 
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 (-451 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
-(-452 -1696 UP UPUP R) 
+(-452 -2184 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 
@@ -1746,15 +1746,15 @@ NIL
 NIL 
 (-454) 
 ((|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.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1049))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3807 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
 (-455 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 -4180)) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) 
+((|HasAttribute| |#1| (QUOTE -4183)) (|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -557) (QUOTE (-787))))) 
 (-456 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-457 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
@@ -1764,33 +1764,33 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-459 -1696 UP |AlExt| |AlPol|) 
+(-459 -2184 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-460) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (LIST (QUOTE -952) (QUOTE (-517))))) 
 (-461 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-462 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."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-463 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 
-(-464 R UP -1696) 
+(-464 R UP -2184) 
 ((|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{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\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{\\spad{mi}} is given by \\spad{\\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{\\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{\\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-465 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| (-107) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-107) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-107) (QUOTE (-1003))) (-12 (|HasCategory| (-107) (QUOTE (-1003))) (|HasCategory| (-107) (LIST (QUOTE -280) (QUOTE (-107)))))) 
 (-466 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)}."))) 
@@ -1804,10 +1804,10 @@ NIL
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\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{\\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 
-(-469 -1696 |Expon| |VarSet| |DPoly|) 
+(-469 -2184 |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 -558) (QUOTE (-1073))))) 
+((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-1074))))) 
 (-470 |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 
@@ -1850,32 +1850,32 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-724)))) 
 (-480 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}"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-481 |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}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3807 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-530 |#1|) (QUOTE (-134))) (|HasCategory| (-530 |#1|) (QUOTE (-338))) (|HasCategory| (-530 |#1|) (QUOTE (-132))) (-3763 (|HasCategory| (-530 |#1|) (QUOTE (-132))) (|HasCategory| (-530 |#1|) (QUOTE (-338))))) 
 (-482 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-483 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."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-484 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 -4181))) 
+((|HasAttribute| |#3| (QUOTE -4184))) 
 (-485 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 -4181))) 
+((|HasAttribute| |#7| (QUOTE -4184))) 
 (-486 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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4182 "*"))) (|HasCategory| |#1| (QUOTE (-333)))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4185 "*"))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-487 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 
@@ -1888,7 +1888,7 @@ NIL
 ((|constructor| (NIL "converts entire exponents to OutputForm"))) 
 NIL 
 NIL 
-(-490 K -1696 |Par|) 
+(-490 K -2184 |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 
@@ -1908,7 +1908,7 @@ NIL
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-495 K -1696 |Par|) 
+(-495 K -2184 |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 
@@ -1938,17 +1938,17 @@ NIL
 NIL 
 (-502) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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."))) 
-((-4178 . T) (-4179 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4181 . T) (-4182 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-503 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
-(-504 R -1696) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
+(-504 R -2184) 
 ((|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 
-(-505 R0 -1696 UP UPUP R) 
+(-505 R0 -2184 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 
@@ -1958,7 +1958,7 @@ NIL
 NIL 
 (-507 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This 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."))) 
-((-3383 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3284 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-508 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."))) 
@@ -1966,9 +1966,9 @@ NIL
 NIL 
 (-509) 
 ((|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."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-510 R -1696) 
+(-510 R -2184) 
 ((|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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{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 
@@ -1980,7 +1980,7 @@ NIL
 ((|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 
-(-513 R -1696 L) 
+(-513 R -2184 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -593) (|devaluate| |#2|)))) 
@@ -1988,31 +1988,31 @@ NIL
 ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ^= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) 
 NIL 
 NIL 
-(-515 -1696 UP UPUP R) 
+(-515 -2184 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 
-(-516 -1696 UP) 
+(-516 -2184 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 
 (-517) 
 ((|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.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) 
-((-4162 . T) (-4168 . T) (-4172 . T) (-4167 . T) (-4178 . T) (-4179 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4165 . T) (-4171 . T) (-4175 . T) (-4170 . T) (-4181 . T) (-4182 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-518) 
 ((|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 
-(-519 R -1696 L) 
+(-519 R -2184 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -593) (|devaluate| |#2|)))) 
-(-520 R -1696) 
+(-520 R -2184) 
 ((|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 -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1037)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) 
-(-521 -1696 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1038)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-569))))) 
+(-521 -2184 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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{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 
@@ -2020,54 +2020,54 @@ NIL
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-523 -1696) 
+(-523 -2184) 
 ((|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,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 
 (-524 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."))) 
-((-3383 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3284 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-525) 
 ((|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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
 NIL 
 NIL 
-(-526 R -1696) 
+(-526 R -2184) 
 ((|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 -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) 
-(-527 -1696 UP) 
+((-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-256))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-256)))) (|HasCategory| |#1| (QUOTE (-509)))) 
+(-527 -2184 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' + +/[\\spad{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(+,{}[\\spad{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(+,{}[\\spad{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 
-(-528 R -1696) 
+(-528 R -2184) 
 ((|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 
 (-529 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-530 |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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) 
 (-531) 
 ((|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 
-(-532 R -1696) 
+(-532 R -2184) 
 ((|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 
-(-533 E -1696) 
+(-533 E -2184) 
 ((|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 
-(-534 -1696) 
+(-534 -2184) 
 ((|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}."))) 
-((-4175 . T) (-4174 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1073))))) 
+((-4178 . T) (-4177 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-1074))))) 
 (-535 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 
@@ -2090,19 +2090,19 @@ NIL
 NIL 
 (-540 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-3807 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3807 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3807 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-3763 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131)))))) (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (|HasCategory| (-131) (LIST (QUOTE -557) (QUOTE (-787)))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
 (-541 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 
 (-542 |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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073))))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (|HasCategory| (-517) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074))))))) 
 (-543 |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}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} 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.}"))) 
-((-4175 |has| |#1| (-509)) (-4174 |has| |#1| (-509)) ((-4182 "*") |has| |#1| (-509)) (-4173 |has| |#1| (-509)) (-4177 . T)) 
+((-4178 |has| |#1| (-509)) (-4177 |has| |#1| (-509)) ((-4185 "*") |has| |#1| (-509)) (-4176 |has| |#1| (-509)) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-509)))) 
 (-544 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),{}..]}."))) 
@@ -2112,7 +2112,7 @@ NIL
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) 
 NIL 
 NIL 
-(-546 R -1696 FG) 
+(-546 R -2184 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{\\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{\\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 
@@ -2122,31 +2122,31 @@ NIL
 NIL 
 (-548 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-549 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 -4181)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4180)) (|HasCategory| |#3| (QUOTE (-1003)))) 
+((|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (QUOTE (-779))) (|HasAttribute| |#1| (QUOTE -4183)) (|HasCategory| |#3| (QUOTE (-1003)))) 
 (-550 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-551 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4177 -3807 (-4035 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4175 . T) (-4174 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
+((-4180 -3763 (-1651 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
 (-552 |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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1056) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (QUOTE (-1056))) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#1|))))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#1|))))))) 
 (-553 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 
 (-554 |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}."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-555 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"))) 
@@ -2164,7 +2164,7 @@ NIL
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-559 -1696 UP) 
+(-559 -2184 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
@@ -2174,20 +2174,20 @@ NIL
 NIL 
 (-561 R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-562 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}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-777)))) 
-(-563 R -1696) 
+(-563 R -2184) 
 ((|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 
 (-564 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"))) 
-((-4175 . T) (-4174 . T) ((-4182 "*") . T) (-4173 . T) (-4177 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) 
+((-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4176 . T) (-4180 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) 
 (-565 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 
@@ -2198,7 +2198,7 @@ NIL
 NIL 
 (-567 |VarSet| R |Order|) 
 ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\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}}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-568 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\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}}."))) 
@@ -2208,30 +2208,30 @@ NIL
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-570 R -1696) 
+(-570 R -2184) 
 ((|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{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\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 
-(-571 |lv| -1696) 
+(-571 |lv| -2184) 
 ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) 
 NIL 
 NIL 
 (-572) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|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."))) 
-((-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1056) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (QUOTE (-1056))) (LIST (QUOTE |:|) (QUOTE -1257) (QUOTE (-51))))))) (-3807 (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003))))) 
+((-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003))))) 
 (-573 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-574 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4175 . T) (-4174 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4178 . T) (-4177 . T)) 
 NIL 
 (-575 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4177 -3807 (-4035 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4175 . T) (-4174 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
+((-4180 -3763 (-1651 (|has| |#2| (-337 |#1|)) (|has| |#1| (-509))) (-12 (|has| |#2| (-387 |#1|)) (|has| |#1| (-509)))) (-4178 . T) (-4177 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -337) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -387) (|devaluate| |#1|)))))) 
 (-576 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "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 
@@ -2243,10 +2243,10 @@ NIL
 (-578 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\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 
-((|HasCategory| |#1| (QUOTE (-333))) (-2630 (|HasCategory| |#1| (QUOTE (-333))))) 
+((|HasCategory| |#1| (QUOTE (-333))) (-2455 (|HasCategory| |#1| (QUOTE (-333))))) 
 (-579 R) 
 ((|constructor| (NIL "An extension ring 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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-580 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}."))) 
@@ -2262,11 +2262,11 @@ NIL
 NIL 
 (-583 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()} returns the empty list."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-584 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) 
 (-585 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) 
@@ -2279,22 +2279,22 @@ NIL
 (-587 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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 -4181))) 
+((|HasAttribute| |#1| (QUOTE -4184))) 
 (-588 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|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})}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
-(-589 R -1696 L) 
+(-589 R -2184 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 
 (-590 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}}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-591 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-592 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) 
@@ -2302,15 +2302,15 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-593 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}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-594 -1696 UP) 
+(-594 -2184 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)))) 
-(-595 A -2252) 
+(-595 A -1328) 
 ((|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}}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-596 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."))) 
@@ -2326,7 +2326,7 @@ NIL
 NIL 
 (-599 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}."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#1| (QUOTE (-723)))) 
 (-600 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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) 
@@ -2334,7 +2334,7 @@ NIL
 NIL 
 (-601 |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) (-4175 . T) (-4174 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-602 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}."))) 
@@ -2342,13 +2342,13 @@ NIL
 NIL 
 (-603 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}."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-604 -1696) 
+(-604 -2184) 
 ((|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 
-(-605 -1696 |Row| |Col| M) 
+(-605 -2184 |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 
@@ -2358,8 +2358,8 @@ NIL
 NIL 
 (-607 |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."))) 
-((-4177 . T) (-4180 . T) (-4174 . T) (-4175 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4182 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3807 (|HasAttribute| |#2| (QUOTE (-4182 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3807 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))))) (|HasCategory| |#2| (QUOTE (-156)))) 
+((-4180 . T) (-4183 . T) (-4177 . T) (-4178 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509))) (-3763 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-608 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
@@ -2370,12 +2370,12 @@ NIL
 NIL 
 (-610 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-611 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 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-612 |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 
@@ -2411,10 +2411,10 @@ NIL
 (-620 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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 (-4182 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) 
+((|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-509)))) 
 (-621 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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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"))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-622 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."))) 
@@ -2422,13 +2422,13 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509)))) 
 (-623 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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4182 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-509))) (|HasAttribute| |#1| (QUOTE (-4185 "*"))) (|HasCategory| |#1| (QUOTE (-333))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-624 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 
-(-625 S -1696 FLAF FLAS) 
+(-625 S -2184 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 
@@ -2438,11 +2438,11 @@ NIL
 NIL 
 (-627) 
 ((|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"))) 
-((-4173 . T) (-4178 |has| (-632) (-333)) (-4172 |has| (-632) (-333)) (-3392 . T) (-4179 |has| (-632) (-6 -4179)) (-4176 |has| (-632) (-6 -4176)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3807 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-937))) (|HasCategory| (-632) (QUOTE (-1094))) (-12 (|HasCategory| (-632) (QUOTE (-918))) (|HasCategory| (-632) (QUOTE (-1094)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-970))) (-12 (|HasCategory| (-632) (QUOTE (-970))) (|HasCategory| (-632) (QUOTE (-1094)))) (-3807 (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3807 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-831))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4179)) (|HasAttribute| (-632) (QUOTE -4176)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3807 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3807 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3807 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-319))))) 
+((-4176 . T) (-4181 |has| (-632) (-333)) (-4175 |has| (-632) (-333)) (-3295 . T) (-4182 |has| (-632) (-6 -4182)) (-4179 |has| (-632) (-6 -4179)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-632) (QUOTE (-134))) (|HasCategory| (-632) (QUOTE (-132))) (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-338))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-319))) (-3763 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (LIST (QUOTE -258) (QUOTE (-632)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -280) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-632)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-632) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-632) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-632) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-632) (QUOTE (-937))) (|HasCategory| (-632) (QUOTE (-1095))) (-12 (|HasCategory| (-632) (QUOTE (-918))) (|HasCategory| (-632) (QUOTE (-1095)))) (|HasCategory| (-632) (QUOTE (-502))) (|HasCategory| (-632) (QUOTE (-970))) (-12 (|HasCategory| (-632) (QUOTE (-970))) (|HasCategory| (-632) (QUOTE (-1095)))) (-3763 (|HasCategory| (-632) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (QUOTE (-278))) (-3763 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-319)))) (|HasCategory| (-632) (QUOTE (-831))) (-12 (|HasCategory| (-632) (QUOTE (-207))) (|HasCategory| (-632) (QUOTE (-333)))) (-12 (|HasCategory| (-632) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-632) (QUOTE (-333)))) (|HasCategory| (-632) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-632) (QUOTE (-779))) (|HasCategory| (-632) (QUOTE (-509))) (|HasAttribute| (-632) (QUOTE -4182)) (|HasAttribute| (-632) (QUOTE -4179)) (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-333))) (|HasCategory| (-632) (QUOTE (-831)))) (-12 (|HasCategory| (-632) (QUOTE (-319))) (|HasCategory| (-632) (QUOTE (-831))))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-509)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-132)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-632) (QUOTE (-278))) (|HasCategory| (-632) (QUOTE (-831)))) (|HasCategory| (-632) (QUOTE (-319))))) 
 (-628 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}."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
 (-629 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}."))) 
@@ -2452,13 +2452,13 @@ NIL
 ((|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 
-(-631 OV E -1696 PG) 
+(-631 OV E -2184 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 
 (-632) 
 ((|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|)) "\\spad{base()} returns the base of the model") (((|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}"))) 
-((-3383 . T) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3284 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-633 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."))) 
@@ -2466,7 +2466,7 @@ NIL
 NIL 
 (-634) 
 ((|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}"))) 
-((-4179 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4182 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-635 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"))) 
@@ -2488,7 +2488,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-640 S -2731 I) 
+(-640 S -2553 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 
@@ -2498,31 +2498,31 @@ NIL
 NIL 
 (-642 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)}.}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-643 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 
-(-644 R |Mod| -3271 -3237 |exactQuo|) 
+(-644 R |Mod| -1476 -2262 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-645 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(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"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4176 |has| |#1| (-333)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-319))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-646 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
 (-647 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) (-4177 . T)) 
+((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) 
-(-648 R |Mod| -3271 -3237 |exactQuo|) 
+(-648 R |Mod| -1476 -2262 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-649 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
@@ -2530,11 +2530,11 @@ NIL
 NIL 
 (-650 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
-(-651 -1696) 
+(-651 -2184) 
 ((|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]]}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-652 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."))) 
@@ -2558,7 +2558,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-657 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."))) 
-((-4173 |has| |#1| (-333)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 |has| |#1| (-333)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-658 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.")) (** (($ $ (|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."))) 
@@ -2568,7 +2568,7 @@ NIL
 ((|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.")) (** (($ $ (|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 
-(-660 -1696 UP) 
+(-660 -2184 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 
@@ -2586,8 +2586,8 @@ NIL
 NIL 
 (-664 |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."))) 
-(((-4182 "*") |has| |#2| (-156)) (-4173 |has| |#2| (-509)) (-4178 |has| |#2| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#2| (-156)) (-4176 |has| |#2| (-509)) (-4181 |has| |#2| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-789 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-665 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
@@ -2602,15 +2602,15 @@ NIL
 NIL 
 (-668 R M) 
 ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) 
-((-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) (-4177 . T)) 
+((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) 
 ((-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-669 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-4170 . T) (-4181 . T) (-3353 . T)) 
+((-4173 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-670 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}."))) 
-((-4180 . T) (-4170 . T) (-4181 . T)) 
+((-4183 . T) (-4173 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-671) 
 ((|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."))) 
@@ -2622,7 +2622,7 @@ NIL
 NIL 
 (-673 |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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
 (-674 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"))) 
@@ -2638,7 +2638,7 @@ NIL
 NIL 
 (-677 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}."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
 (-678) 
 ((|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}."))) 
@@ -2720,15 +2720,15 @@ NIL
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-698 -1696) 
+(-698 -2184) 
 ((|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 
-(-699 P -1696) 
+(-699 P -2184) 
 ((|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 
-(-700 UP -1696) 
+(-700 UP -2184) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\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 
@@ -2742,9 +2742,9 @@ NIL
 NIL 
 (-703) 
 ((|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."))) 
-(((-4182 "*") . T)) 
+(((-4185 "*") . T)) 
 NIL 
-(-704 R -1696) 
+(-704 R -2184) 
 ((|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 
@@ -2764,7 +2764,7 @@ NIL
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\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 
-(-709 -1696 |ExtF| |SUEx| |ExtP| |n|) 
+(-709 -2184 |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 
@@ -2778,23 +2778,23 @@ NIL
 NIL 
 (-712 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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
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+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
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 (-713 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 
 (-714 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)}"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4176 |has| |#1| (-333)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-715 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 -37) (LIST (QUOTE -377) (QUOTE (-517)))))) 
 (-716 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.}"))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
 (-717 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}."))) 
@@ -2846,25 +2846,25 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-338)))) 
 (-729 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,{}\\spad{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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-730 -3807 R OS S) 
+(-730 -3763 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
 (-731 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (-3807 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3807 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (-3763 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (|HasCategory| (-915 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) 
 (-732) 
 ((|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 
-(-733 R -1696 L) 
+(-733 R -2184 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{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-734 R -1696) 
+(-734 R -2184) 
 ((|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 
@@ -2872,7 +2872,7 @@ NIL
 ((|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 
-(-736 R -1696) 
+(-736 R -2184) 
 ((|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 
@@ -2880,11 +2880,11 @@ NIL
 ((|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 
-(-738 -1696 UP UPUP R) 
+(-738 -2184 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 
-(-739 -1696 UP L LQ) 
+(-739 -2184 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 
@@ -2892,41 +2892,41 @@ NIL
 ((|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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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 
-(-741 -1696 UP L LQ) 
+(-741 -2184 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^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{\\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{\\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 \\spad{ai}}} is \\spad{\\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 
-(-742 -1696 UP) 
+(-742 -2184 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 
-(-743 -1696 L UP A LO) 
+(-743 -2184 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 
-(-744 -1696 UP) 
+(-744 -2184 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{\\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 \\spad{ai}}} is \\spad{\\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)))) 
-(-745 -1696 LO) 
+(-745 -2184 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 
-(-746 -1696 LODO) 
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 ((|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(\\spad{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(\\spad{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 
-(-747 -2806 S |f|) 
+(-747 -2630 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}."))) 
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 ((|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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-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-750 (-1073)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-750 (-1073)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-750 (-1073)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-750 (-1073)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-750 (-1073)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-750 (-1074)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-750 (-1074)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-750 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-750 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-750 (-1074)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-749 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) 
-(((-4182 "*") |has| |#2| (-333)) (-4173 |has| |#2| (-333)) (-4178 |has| |#2| (-333)) (-4172 |has| |#2| (-333)) (-4177 . T) (-4175 . T) (-4174 . T)) 
+(((-4185 "*") |has| |#2| (-333)) (-4176 |has| |#2| (-333)) (-4181 |has| |#2| (-333)) (-4175 |has| |#2| (-333)) (-4180 . T) (-4178 . T) (-4177 . T)) 
 ((|HasCategory| |#2| (QUOTE (-333)))) 
 (-750 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}))."))) 
@@ -2938,7 +2938,7 @@ NIL
 NIL 
 (-752) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-753) 
 ((|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}"))) 
@@ -2966,7 +2966,7 @@ NIL
 NIL 
 (-759 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}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-207)))) 
 (-760) 
 ((|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."))) 
@@ -2978,7 +2978,7 @@ NIL
 NIL 
 (-762 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-4180 . T) (-4170 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4173 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-763) 
 ((|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."))) 
@@ -2990,11 +2990,11 @@ NIL
 NIL 
 (-765 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."))) 
-((-4177 |has| |#1| (-777))) 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3807 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
+((-4180 |has| |#1| (-777))) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
 (-766 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) (-4177 . T)) 
+((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134)))) 
 (-767) 
 ((|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)."))) 
@@ -3018,13 +3018,13 @@ NIL
 NIL 
 (-772 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."))) 
-((-4177 |has| |#1| (-777))) 
-((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3807 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3807 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
+((-4180 |has| |#1| (-777))) 
+((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-777))))) 
 (-773) 
 ((|constructor| (NIL "Ordered finite sets."))) 
 NIL 
 NIL 
-(-774 -2806 S) 
+(-774 -2630 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 
@@ -3038,7 +3038,7 @@ NIL
 NIL 
 (-777) 
 ((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-778 S) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) 
@@ -3054,19 +3054,19 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156)))) 
 (-781 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-782 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 (-333))) (|HasCategory| |#1| (QUOTE (-509)))) 
-(-783 R |sigma| -1330) 
+(-783 R |sigma| -2234) 
 ((|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."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-784 |x| R |sigma| -1330) 
+(-784 |x| R |sigma| -2234) 
 ((|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}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-333)))) 
 (-785 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..)}."))) 
@@ -3090,7 +3090,7 @@ NIL
 NIL 
 (-790 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) 
-((-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) (-4177 . T)) 
+((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-791 R PS UP) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
@@ -3102,20 +3102,20 @@ NIL
 NIL 
 (-793 |p|) 
 ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-794 |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)."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-795 |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)."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-794 |#1|) (QUOTE (-831))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-937))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1049))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1073)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3807 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-794 |#1|) (QUOTE (-831))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-134))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-794 |#1|) (QUOTE (-937))) (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-1050))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-794 |#1|) (QUOTE (-207))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -478) (QUOTE (-1074)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -280) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (LIST (QUOTE -258) (LIST (QUOTE -794) (|devaluate| |#1|)) (LIST (QUOTE -794) (|devaluate| |#1|)))) (|HasCategory| (-794 |#1|) (QUOTE (-278))) (|HasCategory| (-794 |#1|) (QUOTE (-502))) (|HasCategory| (-794 |#1|) (QUOTE (-779))) (-3763 (|HasCategory| (-794 |#1|) (QUOTE (-752))) (|HasCategory| (-794 |#1|) (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-794 |#1|) (QUOTE (-831)))) (|HasCategory| (-794 |#1|) (QUOTE (-132))))) 
 (-796 |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)}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3807 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-779))) (-3763 (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
 (-797) 
 ((|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 
@@ -3167,7 +3167,7 @@ NIL
 (-809 |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 
-((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073)))) (-12 (-2630 (|HasCategory| |#2| (QUOTE (-961)))) (-2630 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073)))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2630 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073))))))) 
+((|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (-12 (-2455 (|HasCategory| |#2| (QUOTE (-961)))) (-2455 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2455 (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074))))))) 
 (-810 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 
@@ -3176,7 +3176,7 @@ NIL
 ((|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 
-(-812 R -2731) 
+(-812 R -2553) 
 ((|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 
@@ -3200,7 +3200,7 @@ NIL
 ((|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 
-(-818 UP -1696) 
+(-818 UP -2184) 
 ((|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 
@@ -3218,7 +3218,7 @@ NIL
 NIL 
 (-822 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}."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-823 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}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
@@ -3230,7 +3230,7 @@ NIL
 NIL 
 (-825 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}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under 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."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
 (-826 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}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
@@ -3238,8 +3238,8 @@ NIL
 NIL 
 (-827 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|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."))) 
-((-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) 
+((-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-779))))) 
 (-828 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 \\spad{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 
@@ -3254,13 +3254,13 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-132)))) 
 (-831) 
 ((|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 \\spad{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}."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-832 |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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 ((|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-132))) (|HasCategory| $ (QUOTE (-338)))) 
-(-833 R0 -1696 UP UPUP R) 
+(-833 R0 -2184 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 
@@ -3274,7 +3274,7 @@ NIL
 NIL 
 (-836 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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-837 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."))) 
@@ -3288,7 +3288,7 @@ NIL
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{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 \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{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(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{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 
-(-840 -1696) 
+(-840 -2184) 
 ((|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 
@@ -3298,17 +3298,17 @@ NIL
 NIL 
 (-842) 
 ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-843) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4182 "*") . T)) 
+(((-4185 "*") . T)) 
 NIL 
-(-844 -1696 P) 
+(-844 -2184 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-845 |xx| -1696) 
+(-845 |xx| -2184) 
 ((|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 
@@ -3332,7 +3332,7 @@ NIL
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-851 R -1696) 
+(-851 R -2184) 
 ((|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| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
@@ -3344,7 +3344,7 @@ NIL
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-854 S R -1696) 
+(-854 S R -2184) 
 ((|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 
@@ -3364,11 +3364,11 @@ NIL
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -808) (|devaluate| |#1|)))) 
-(-859 R -1696 -2731) 
+(-859 R -2184 -2553) 
 ((|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 
-(-860 -2731) 
+(-860 -2553) 
 ((|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 
@@ -3390,8 +3390,8 @@ NIL
 NIL 
 (-865 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-866 |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 
@@ -3411,12 +3411,12 @@ NIL
 (-870 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 (-831))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#4| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#4| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#4| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-779)))) 
 (-871 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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
-(-872 E V R P -1696) 
+(-872 E V R P -2184) 
 ((|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 
@@ -3426,9 +3426,9 @@ NIL
 NIL 
 (-874 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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1073) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-1073) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-1073) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-1073) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-1073) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-875 E V R P -1696) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-1074) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-875 E V R P -2184) 
 ((|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)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-421)))) 
@@ -3446,13 +3446,13 @@ NIL
 NIL 
 (-879 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"))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
 (-880) 
 ((|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 
-(-881 -1696) 
+(-881 -2184) 
 ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{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 
@@ -3466,15 +3466,15 @@ NIL
 NIL 
 (-884 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}"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-123)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) 
 (-885 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"))) 
-((-4177 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) 
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+((-4180 -12 (|has| |#2| (-442)) (|has| |#1| (-442)))) 
+((-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-338)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-123))) (|HasCategory| |#2| (QUOTE (-123)))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-442)))) (-12 (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-659)))) (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725))))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-725))) (|HasCategory| |#2| (QUOTE (-725)))) (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-779)))))) 
 (-886 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}."))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-887 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}}"))) 
@@ -3490,7 +3490,7 @@ NIL
 NIL 
 (-890 |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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-891) 
 ((|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}."))) 
@@ -3502,7 +3502,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-509)))) 
 (-893 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."))) 
-((-4180 . T) (-3353 . T)) 
+((-4183 . T) (-3252 . T)) 
 NIL 
 (-894 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."))) 
@@ -3518,7 +3518,7 @@ NIL
 NIL 
 (-897 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| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|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}."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
 (-898 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) 
@@ -3536,7 +3536,7 @@ NIL
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-902 K R UP -1696) 
+(-902 K R UP -2184) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
@@ -3563,10 +3563,10 @@ NIL
 (-908 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 (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1049)))) 
+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-752))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-1050)))) 
 (-909 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}."))) 
-((-3353 . T) (-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3252 . T) (-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-910 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|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}."))) 
@@ -3574,7 +3574,7 @@ NIL
 NIL 
 (-911 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."))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-912 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}."))) 
@@ -3582,7 +3582,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-262)))) 
 (-913 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}."))) 
-((-4173 |has| |#1| (-262)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 |has| |#1| (-262)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-914 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}."))) 
@@ -3590,11 +3590,11 @@ NIL
 NIL 
 (-915 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.}"))) 
-((-4173 |has| |#1| (-262)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3807 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) 
+((-4176 |has| |#1| (-262)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-262))) (-3763 (|HasCategory| |#1| (QUOTE (-262))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -478) (QUOTE (-1074)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -258) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-502))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))))) 
 (-916 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
 (-917 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
@@ -3604,14 +3604,14 @@ NIL
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-919 -1696 UP UPUP |radicnd| |n|) 
+(-919 -2184 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-4173 |has| (-377 |#2|) (-333)) (-4178 |has| (-377 |#2|) (-333)) (-4172 |has| (-377 |#2|) (-333)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3807 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3807 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3807 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3807 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
+((-4176 |has| (-377 |#2|) (-333)) (-4181 |has| (-377 |#2|) (-333)) (-4175 |has| (-377 |#2|) (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-377 |#2|) (QUOTE (-132))) (|HasCategory| (-377 |#2|) (QUOTE (-134))) (|HasCategory| (-377 |#2|) (QUOTE (-319))) (|HasCategory| (-377 |#2|) (QUOTE (-333))) (-3763 (|HasCategory| (-377 |#2|) (QUOTE (-333))) (|HasCategory| (-377 |#2|) (QUOTE (-319)))) (|HasCategory| (-377 |#2|) (QUOTE (-338))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-338))) (-3763 (|HasCategory| (-377 |#2|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-12 (|HasCategory| (-377 |#2|) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-377 |#2|) (QUOTE (-207))) (|HasCategory| (-377 |#2|) (QUOTE (-333)))) (|HasCategory| (-377 |#2|) (QUOTE (-319))))) 
 (-920 |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.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1073)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1049))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1073)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3807 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-517) (QUOTE (-831))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-1074)))) (|HasCategory| (-517) (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-134))) (|HasCategory| (-517) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-937))) (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-1050))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| (-517) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| (-517) (QUOTE (-207))) (|HasCategory| (-517) (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| (-517) (LIST (QUOTE -478) (QUOTE (-1074)) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -280) (QUOTE (-517)))) (|HasCategory| (-517) (LIST (QUOTE -258) (QUOTE (-517)) (QUOTE (-517)))) (|HasCategory| (-517) (QUOTE (-278))) (|HasCategory| (-517) (QUOTE (-502))) (|HasCategory| (-517) (QUOTE (-779))) (-3763 (|HasCategory| (-517) (QUOTE (-752))) (|HasCategory| (-517) (QUOTE (-779)))) (|HasCategory| (-517) (LIST (QUOTE -579) (QUOTE (-517)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-517) (QUOTE (-831)))) (|HasCategory| (-517) (QUOTE (-132))))) 
 (-921) 
 ((|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 
@@ -3631,10 +3631,10 @@ NIL
 (-925 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 -4181)) (|HasCategory| |#2| (QUOTE (-1003)))) 
+((|HasAttribute| |#1| (QUOTE -4184)) (|HasCategory| |#2| (QUOTE (-1003)))) 
 (-926 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}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-927 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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) 
@@ -3642,21 +3642,21 @@ NIL
 NIL 
 (-928) 
 ((|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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) 
-((-4173 . T) (-4178 . T) (-4172 . T) (-4175 . T) (-4174 . T) ((-4182 "*") . T) (-4177 . T)) 
+((-4176 . T) (-4181 . T) (-4175 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4180 . T)) 
 NIL 
-(-929 R -1696) 
+(-929 R -2184) 
 ((|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 
-(-930 R -1696) 
+(-930 R -2184) 
 ((|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 
-(-931 -1696 UP) 
+(-931 -2184 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 
-(-932 -1696 UP) 
+(-932 -2184 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 
@@ -3686,9 +3686,9 @@ NIL
 NIL 
 (-939 |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"))) 
-((-4173 . T) (-4178 . T) (-4172 . T) (-4175 . T) (-4174 . T) ((-4182 "*") . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (-3807 (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) 
-(-940 -1696 L) 
+((-4176 . T) (-4181 . T) (-4175 . T) (-4178 . T) (-4177 . T) ((-4185 "*") . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (-3763 (|HasCategory| (-377 (-517)) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))))) 
+(-940 -2184 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{\\spad{fi}} must satisfy \\spad{op \\spad{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 
@@ -3698,12 +3698,12 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-1003)))) 
 (-942 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."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1003))) (-12 (|HasCategory| |#4| (QUOTE (-1003))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338)))) 
 (-943 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(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{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 \\spad{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 \\spad{ai}} and {\\em \\spad{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 (-4182 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-4185 "*")))) 
 (-944 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 
@@ -3724,14 +3724,14 @@ NIL
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-949 -1696 |Expon| |VarSet| |FPol| |LFPol|) 
+(-949 -2184 |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"))) 
-(((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-950) 
 ((|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.}"))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -1257) (QUOTE (-51))))))) (|HasCategory| (-1073) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) 
 (-951 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") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) 
 NIL 
@@ -3762,7 +3762,7 @@ NIL
 NIL 
 (-958 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| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-712 |#1| (-789 |#2|)) (QUOTE (-1003))) (|HasCategory| (-712 |#1| (-789 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -712) (|devaluate| |#1|) (LIST (QUOTE -789) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| (-789 |#2|) (QUOTE (-338)))) 
 (-959) 
 ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) 
@@ -3774,9 +3774,9 @@ NIL
 NIL 
 (-961) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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."))) 
-((-4177 . T)) 
+((-4180 . T)) 
 NIL 
-(-962 |xx| -1696) 
+(-962 |xx| -2184) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
@@ -3786,12 +3786,12 @@ NIL
 ((|HasCategory| |#4| (QUOTE (-278))) (|HasCategory| |#4| (QUOTE (-333))) (|HasCategory| |#4| (QUOTE (-509))) (|HasCategory| |#4| (QUOTE (-156)))) 
 (-964 |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"))) 
-((-4180 . T) (-3353 . T) (-4175 . T) (-4174 . T)) 
+((-4183 . T) (-3252 . T) (-4178 . T) (-4177 . T)) 
 NIL 
 (-965 |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.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-4180 . T) (-4175 . T) (-4174 . T)) 
-((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3807 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3807 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) 
+((-4183 . T) (-4178 . T) (-4177 . T)) 
+((|HasCategory| |#3| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (QUOTE (-278))) (|HasCategory| |#3| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-156))) (-3763 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))))) 
 (-966 |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 
@@ -3810,7 +3810,7 @@ NIL
 NIL 
 (-970) 
 ((|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."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-971 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
@@ -3818,19 +3818,19 @@ NIL
 NIL 
 (-972) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(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."))) 
-((-4168 . T) (-4172 . T) (-4167 . T) (-4178 . T) (-4179 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4171 . T) (-4175 . T) (-4170 . T) (-4181 . T) (-4182 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-973) 
 ((|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}"))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (QUOTE (-1073))) (LIST (QUOTE |:|) (QUOTE -1257) (QUOTE (-51))))))) (|HasCategory| (-1073) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1074))) (LIST (QUOTE |:|) (QUOTE -1266) (QUOTE (-51))))))) (|HasCategory| (-1074) (QUOTE (-779))) (|HasCategory| (-51) (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (QUOTE (-1003))) (|HasCategory| (-51) (QUOTE (-1003)))) (-12 (|HasCategory| (-51) (QUOTE (-1003))) (|HasCategory| (-51) (LIST (QUOTE -280) (QUOTE (-51)))))) 
 (-974 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1073))))) 
+((|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-502))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -909) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-1074))))) 
 (-975 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
 (-976 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}"))) 
@@ -3850,7 +3850,7 @@ NIL
 NIL 
 (-980 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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}."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
 (-981 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."))) 
@@ -3860,11 +3860,11 @@ NIL
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-983 |Base| R -1696) 
+(-983 |Base| R -2184) 
 ((|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 
-(-984 |Base| R -1696) 
+(-984 |Base| R -2184) 
 ((|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 
@@ -3878,8 +3878,8 @@ NIL
 NIL 
 (-987 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."))) 
-((-4173 |has| |#1| (-333)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073))))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) 
+((-4176 |has| |#1| (-333)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074))))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-319))))) 
 (-988 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 
@@ -3898,8 +3898,8 @@ NIL
 NIL 
 (-992 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"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-993 (-1073)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-993 (-1073)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-993 (-1073)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-993 (-1073)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-993 (-1073)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-993 (-1074)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-993 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 
@@ -3918,7 +3918,7 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-1003)))) 
 (-997 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|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{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\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."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-998 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
@@ -3926,7 +3926,7 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1003)))) 
 (-999 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
 (-1000 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
@@ -3934,7 +3934,7 @@ NIL
 NIL 
 (-1001 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
-((-4170 . T) (-3353 . T)) 
+((-4173 . T) (-3252 . T)) 
 NIL 
 (-1002 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
@@ -3950,8 +3950,8 @@ NIL
 NIL 
 (-1005 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)}}"))) 
-((-4180 . T) (-4170 . T) (-4181 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
+((-4183 . T) (-4173 . T) (-4184 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-779))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-338))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))))) 
 (-1006 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|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 
@@ -3978,7 +3978,7 @@ NIL
 NIL 
 (-1012 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.}"))) 
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 NIL 
 (-1013) 
 ((|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| (|Integer|)) (|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| (|Integer|)) (|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| (|Integer|))) "\\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 \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{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,{}\\spad{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 \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
@@ -3994,13 +3994,13 @@ NIL
 NIL 
 (-1016 |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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(LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-333)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-338)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-725)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-777)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#3| (QUOTE (-1003))))) (-3763 (-12 (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -952) (QUOTE (-517)))))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-123))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-156))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-207))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-333))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-338))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-725))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-777))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1003))) (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -280) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -822) (QUOTE (-1074))))))) 
 (-1017 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 (-421)))) 
-(-1018 R -1696) 
+(-1018 R -2184) 
 ((|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 
@@ -4014,19 +4014,19 @@ NIL
 NIL 
 (-1021) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|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."))) 
-((-4168 . T) (-4172 . T) (-4167 . T) (-4178 . T) (-4179 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4171 . T) (-4175 . T) (-4170 . T) (-4181 . T) (-4182 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-1022 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-4180 . T) (-4181 . T) (-3353 . T)) 
+((-4183 . T) (-4184 . T) (-3252 . T)) 
 NIL 
 (-1023 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-333))) (|HasAttribute| |#3| (QUOTE (-4182 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) 
+((|HasCategory| |#3| (QUOTE (-333))) (|HasAttribute| |#3| (QUOTE (-4185 "*"))) (|HasCategory| |#3| (QUOTE (-156)))) 
 (-1024 |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."))) 
-((-3353 . T) (-4180 . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-3252 . T) (-4183 . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 (-1025 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}."))) 
@@ -4034,17 +4034,17 @@ NIL
 NIL 
 (-1026 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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-1027 |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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
 (-1028 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}"))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-1029 UP -1696) 
+(-1029 UP -2184) 
 ((|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 
@@ -4073,580 +4073,584 @@ NIL
 NIL 
 NIL 
 (-1036) 
-((|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}."))) 
+((|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 
 (-1037) 
+((|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 
+(-1038) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1038 V C) 
+(-1039 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 
-(-1039 V C) 
+(-1040 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."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-1038 |#1| |#2|) (QUOTE (-1003))) (-12 (|HasCategory| (-1038 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1038) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1038 |#1| |#2|) (QUOTE (-1003))))) 
-(-1040 |ndim| R) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-1039 |#1| |#2|) (QUOTE (-1003))) (-12 (|HasCategory| (-1039 |#1| |#2|) (LIST (QUOTE -280) (LIST (QUOTE -1039) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1039 |#1| |#2|) (QUOTE (-1003))))) 
+(-1041 |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.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|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}."))) 
-((-4177 . T) (-4169 |has| |#2| (-6 (-4182 "*"))) (-4180 . T) (-4174 . T) (-4175 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4182 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (-3807 (|HasAttribute| |#2| (QUOTE (-4182 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3807 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))))) (|HasCategory| |#2| (QUOTE (-156)))) 
-(-1041 S) 
+((-4180 . T) (-4172 |has| |#2| (-6 (-4185 "*"))) (-4183 . T) (-4177 . T) (-4178 . T)) 
+((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (QUOTE (-278))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-333))) (-3763 (|HasAttribute| |#2| (QUOTE (-4185 "*"))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasCategory| |#2| (QUOTE (-207)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-207))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))))) (|HasCategory| |#2| (QUOTE (-156)))) 
+(-1042 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1042) 
+(-1043) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-1043 R E V P TS) 
+(-1044 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 
-(-1044 R E V P) 
+(-1045 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."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1003))) (-12 (|HasCategory| |#4| (QUOTE (-1003))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338)))) 
-(-1045 S) 
+(-1046 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}."))) 
-((-4180 . T) (-4181 . T)) 
+((-4183 . T) (-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
-(-1046 A S) 
+(-1047 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 
-(-1047 S) 
+(-1048 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})}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
-(-1048 |Key| |Ent| |dent|) 
+(-1049 |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."))) 
-((-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) 
-(-1049) 
+((-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003))))) 
+(-1050) 
 ((|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 
-(-1050 |Coef|) 
+(-1051 |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 
-(-1051 S) 
+(-1052 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 
-(-1052 A B) 
+(-1053 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 
-(-1053 A B C) 
+(-1054 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 
-(-1054 S) 
+(-1055 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}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
-((-4181 . T)) 
+((-4184 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-517) (QUOTE (-779)))) 
-(-1055) 
+(-1056) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-1056) 
+(-1057) 
 NIL 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3807 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
-(-1057 |Entry|) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| (-131) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| (-131) (QUOTE (-1003))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-3763 (-12 (|HasCategory| (-131) (QUOTE (-779))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))) (-12 (|HasCategory| (-131) (QUOTE (-1003))) (|HasCategory| (-131) (LIST (QUOTE -280) (QUOTE (-131))))))) 
+(-1058 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (QUOTE (-1056))) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#1|)))))) (|HasCategory| (-1056) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
-(-1058 A) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (QUOTE (-1057))) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#1|)))))) (|HasCategory| (-1057) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1003)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
+(-1059 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 1.")) (|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,{}\\spad{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 (-333))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) 
-(-1059 |Coef|) 
+(-1060 |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 
-(-1060 |Coef|) 
+(-1061 |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 
-(-1061 R UP) 
+(-1062 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 (-278)))) 
-(-1062 |n| R) 
+(-1063 |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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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,{}\\spad{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 
-(-1063 S1 S2) 
+(-1064 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 
-(-1064 |Coef| |var| |cen|) 
+(-1065 |Coef| |var| |cen|) 
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 ((|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 
-(-1066 R) 
+(-1067 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 
-(-1067 R S) 
+(-1068 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 
-(-1068 E OV R P) 
+(-1069 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 
-(-1069 R) 
+(-1070 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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4176 |has| |#1| (-333)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4178)) (|HasCategory| |#1| (QUOTE (-421))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
-(-1070 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#1| (QUOTE (-207))) (|HasAttribute| |#1| (QUOTE -4181)) (|HasCategory| |#1| (QUOTE (-421))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (|HasCategory| |#1| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))))) 
 (-1071 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
+(-1072 |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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
-(-1072) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
+(-1073) 
 ((|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 
-(-1073) 
+(-1074) 
 ((|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|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|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 
-(-1074 R) 
+(-1075 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{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1075 R) 
+(-1076 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-6 -4178)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-888) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4178))) 
-(-1076) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-6 -4181)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-421))) (-12 (|HasCategory| (-888) (QUOTE (-123))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasAttribute| |#1| (QUOTE -4181))) 
+(-1077) 
 ((|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 
-(-1077) 
+(-1078) 
 ((|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 
-(-1078) 
-((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) (|List| $)) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}.")) (|buildSyntax| (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|convert| (($ (|String|)) "\\spad{convert(s)} injects the string value \\spad{`s'} into the syntax domain") (($ (|Symbol|)) "\\spad{convert(s)} injects the symbol \\spad{`s'} into the syntax domain.") (($ (|DoubleFloat|)) "\\spad{convert(f)} injects the float value \\spad{`f'} into the syntax domain") (($ (|Integer|)) "\\spad{convert(i)} injects the integer value `i' into the syntax domain") (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
+(-1079) 
+((|constructor| (NIL "\\indented{1}{This domain provides a simple,{} general,{} and arguably} complete representation of Spad programs as objects of a term algebra built from ground terms of type boolean,{} integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity from a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} symbol,{} String,{} SExpression. See Also: SExpression.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The return value is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|buildSyntax| (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|convert| (($ (|String|)) "\\spad{convert(s)} injects the string value \\spad{`s'} into the syntax domain") (($ (|Symbol|)) "\\spad{convert(s)} injects the symbol \\spad{`s'} into the syntax domain.") (($ (|DoubleFloat|)) "\\spad{convert(f)} injects the float value \\spad{`f'} into the syntax domain") (($ (|Integer|)) "\\spad{convert(i)} injects the integer value `i' into the syntax domain") (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to syntax.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1079 R) 
+(-1080 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 
-(-1080 S) 
+(-1081 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 
-(-1081 S) 
+(-1082 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 
-(-1082 |Key| |Entry|) 
+(-1083 |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}"))) 
-((-4180 . T) (-4181 . T)) 
-((|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3435) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1257) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3807 (|HasCategory| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
-(-1083 R) 
+((-4183 . T) (-4184 . T)) 
+((|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (-12 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (LIST (QUOTE -280) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3342) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1266) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#2| (QUOTE (-1003))) (-3763 (|HasCategory| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1003)))) (-12 (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|))))) 
+(-1084 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{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1084 S |Key| |Entry|) 
+(-1085 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 
-(-1085 |Key| |Entry|) 
+(-1086 |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})}."))) 
-((-4181 . T) (-3353 . T)) 
+((-4184 . T) (-3252 . T)) 
 NIL 
-(-1086 |Key| |Entry|) 
+(-1087 |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 
-(-1087) 
+(-1088) 
 ((|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 
-(-1088 S) 
+(-1089 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 
-(-1089) 
+(-1090) 
 ((|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.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) 
 NIL 
 NIL 
-(-1090) 
+(-1091) 
 ((|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 
-(-1091 R) 
+(-1092 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 
-(-1092) 
+(-1093) 
 ((|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 
-(-1093 S) 
+(-1094 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1094) 
+(-1095) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1095 S) 
+(-1096 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#1| (QUOTE (-1003))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) 
-(-1096 S) 
+(-1097 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1097) 
+(-1098) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1098 R -1696) 
+(-1099 R -2184) 
 ((|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 
-(-1099 R |Row| |Col| M) 
+(-1100 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 
-(-1100 R -1696) 
+(-1101 R -2184) 
 ((|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 -558) (LIST (QUOTE -814) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -808) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -808) (|devaluate| |#1|))))) 
-(-1101 S R E V P) 
+(-1102 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 (-338)))) 
-(-1102 R E V P) 
+(-1103 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-1103 |Coef|) 
+(-1104 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-1104 |Curve|) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-509))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-333)))) 
+(-1105 |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 
-(-1105) 
+(-1106) 
 ((|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 
-(-1106 S) 
+(-1107 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")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787))))) 
-(-1107 -1696) 
+(-1108 -2184) 
 ((|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 
-(-1108) 
+(-1109) 
 ((|constructor| (NIL "The fundamental Type."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
-(-1109 S) 
+(-1110 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 < \\spad{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 < \\spad{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 (-779)))) 
-(-1110) 
+(-1111) 
 ((|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 
-(-1111 S) 
+(-1112 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 
-(-1112) 
+(-1113) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1113 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1114 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1114 |Coef|) 
+(-1115 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1115 S |Coef| UTS) 
+(-1116 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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|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 (-333)))) 
-(-1116 |Coef| UTS) 
+(-1117 |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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|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)}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-3353 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-3252 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1117 |Coef| UTS) 
+(-1118 |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)}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| (-517) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-134))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-134))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-517)) (|devaluate| |#1|))))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-937)))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-752)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-752)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779))))) (|HasCategory| |#2| (QUOTE (-831))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-502)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-278)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132))) (-3807 (|HasCategory| |#1| (QUOTE (-132))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-132))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3807 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -258) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -478) (QUOTE (-1073)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-752)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-779)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -280) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517))))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-1073)))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|)))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#1| (QUOTE (-132))) (-12 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-132)))))) 
-(-1118 |Coef| |var| |cen|) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
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(|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-502))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-278))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-132))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-132)))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-156)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333)))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-752))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-1050))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -258) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -280) (LIST (QUOTE -1147) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 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-37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|)))))) (-3763 (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-333)))) (-12 (|HasCategory| (-1147 |#1| |#2| |#3|) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-333)))) (|HasCategory| |#1| (QUOTE (-132))))) 
+(-1120 ZP) 
 ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) 
 NIL 
 NIL 
-(-1120 R S) 
+(-1121 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-777)))) 
-(-1121 S) 
+(-1122 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-777))) (|HasCategory| |#1| (QUOTE (-1003)))) 
-(-1122 |x| R |y| S) 
+(-1123 |x| R |y| S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-1123 R Q UP) 
+(-1124 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\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 
-(-1124 R UP) 
+(-1125 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 
-(-1125 R UP) 
+(-1126 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 
-(-1126 R U) 
+(-1127 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 
-(-1127 |x| R) 
+(-1128 |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| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) 
-(((-4182 "*") |has| |#2| (-156)) (-4173 |has| |#2| (-509)) (-4176 |has| |#2| (-333)) (-4178 |has| |#2| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1073)))) (-3807 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4178)) (|HasCategory| |#2| (QUOTE (-421))) (-3807 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3807 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
-(-1128 R PR S PS) 
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+((|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-509)))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-349)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-349))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -808) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -808) (QUOTE (-517))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-349)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -558) (LIST (QUOTE -814) (QUOTE (-517)))))) (-12 (|HasCategory| (-989) (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#2| (LIST (QUOTE -558) (QUOTE (-493))))) (|HasCategory| |#2| (QUOTE (-779))) (|HasCategory| |#2| (LIST (QUOTE -579) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| |#2| (QUOTE (-207))) (|HasAttribute| |#2| (QUOTE -4181)) (|HasCategory| |#2| (QUOTE (-421))) (-3763 (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-831)))) (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-831)))) (|HasCategory| |#2| (QUOTE (-132))))) 
+(-1129 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 
-(-1129 S R) 
+(-1130 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 -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1049)))) 
-(-1130 R) 
+((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333))) (|HasCategory| |#2| (QUOTE (-421))) (|HasCategory| |#2| (QUOTE (-509))) (|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (QUOTE (-1050)))) 
+(-1131 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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4176 |has| |#1| (-333)) (-4178 |has| |#1| (-6 -4178)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4179 |has| |#1| (-333)) (-4181 |has| |#1| (-6 -4181)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
-(-1131 S |Coef| |Expon|) 
+(-1132 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}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|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 -822) (QUOTE (-1073)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2256) (LIST (|devaluate| |#2|) (QUOTE (-1073)))))) 
-(-1132 |Coef| |Expon|) 
+((|HasCategory| |#2| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2182) (LIST (|devaluate| |#2|) (QUOTE (-1074)))))) 
+(-1133 |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}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1133 RC P) 
+(-1134 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1134 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(-1135 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) 
 NIL 
 NIL 
-(-1135 |Coef|) 
+(-1136 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1136 S |Coef| ULS) 
+(-1137 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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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 
-(-1137 |Coef| ULS) 
+(-1138 |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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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)}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1138 |Coef| ULS) 
+(-1139 |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)}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
-(-1139 |Coef| |var| |cen|) 
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+((|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
+(-1140 |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}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4178 |has| |#1| (-333)) (-4172 |has| |#1| (-333)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3807 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
-(-1140 R FE |var| |cen|) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4181 |has| |#1| (-333)) (-4175 |has| |#1| (-333)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517))) (|devaluate| |#1|))))) (|HasCategory| (-377 (-517)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (-3763 (|HasCategory| |#1| (QUOTE (-333))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
+(-1141 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))}."))) 
-(((-4182 "*") |has| (-1139 |#2| |#3| |#4|) (-156)) (-4173 |has| (-1139 |#2| |#3| |#4|) (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| (-1139 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1139 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1139 |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-421))) (-3807 (|HasCategory| (-1139 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1139 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1139 |#2| |#3| |#4|) (QUOTE (-509)))) 
-(-1141 A S) 
+(((-4185 "*") |has| (-1140 |#2| |#3| |#4|) (-156)) (-4176 |has| (-1140 |#2| |#3| |#4|) (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-132))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-156))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (QUOTE (-517)))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-333))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-421))) (-3763 (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (LIST (QUOTE -952) (LIST (QUOTE -377) (QUOTE (-517)))))) (|HasCategory| (-1140 |#2| |#3| |#4|) (QUOTE (-509)))) 
+(-1142 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -4181))) 
-(-1142 S) 
+((|HasAttribute| |#1| (QUOTE -4184))) 
+(-1143 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
-((-3353 . T)) 
+((-3252 . T)) 
 NIL 
-(-1143 |Coef1| |Coef2| UTS1 UTS2) 
+(-1144 |Coef1| |Coef2| UTS1 UTS2) 
 ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) 
 NIL 
 NIL 
-(-1144 S |Coef|) 
+(-1145 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-517)))) (|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasSignature| |#2| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4151) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1073))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) 
-(-1145 |Coef|) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#2| (QUOTE (-880))) (|HasCategory| |#2| (QUOTE (-1095))) (|HasSignature| |#2| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2863) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1074))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#2| (QUOTE (-333)))) 
+(-1146 |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."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1146 |Coef| |var| |cen|) 
+(-1147 |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|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|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}."))) 
-(((-4182 "*") |has| |#1| (-156)) (-4173 |has| |#1| (-509)) (-4174 . T) (-4175 . T) (-4177 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3807 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1073)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2256) (LIST (|devaluate| |#1|) (QUOTE (-1073)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3807 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -4151) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1073))))) (|HasSignature| |#1| (LIST (QUOTE -1364) (LIST (LIST (QUOTE -583) (QUOTE (-1073))) (|devaluate| |#1|))))))) 
-(-1147 |Coef| UTS) 
+(((-4185 "*") |has| |#1| (-156)) (-4176 |has| |#1| (-509)) (-4177 . T) (-4178 . T) (-4180 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#1| (QUOTE (-156))) (-3763 (|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-509)))) (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-134))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -822) (QUOTE (-1074)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-703)) (|devaluate| |#1|))))) (|HasCategory| (-703) (QUOTE (-1015))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-703))))) (|HasSignature| |#1| (LIST (QUOTE -2182) (LIST (|devaluate| |#1|) (QUOTE (-1074)))))) (|HasCategory| |#1| (QUOTE (-333))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-517)))) (|HasCategory| |#1| (QUOTE (-880))) (|HasCategory| |#1| (QUOTE (-1095))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasSignature| |#1| (LIST (QUOTE -2863) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1074))))) (|HasSignature| |#1| (LIST (QUOTE -1363) (LIST (LIST (QUOTE -583) (QUOTE (-1074))) (|devaluate| |#1|))))))) 
+(-1148 |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 
-(-1148 -1696 UP L UTS) 
+(-1149 -2184 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 (-509)))) 
-(-1149 |sym|) 
+(-1150 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1150 S R) 
+(-1151 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 (-918))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-659))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1151 R) 
+(-1152 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-4181 . T) (-4180 . T) (-3353 . T)) 
+((-4184 . T) (-4183 . T) (-3252 . T)) 
 NIL 
-(-1152 A B) 
+(-1153 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
-(-1153 R) 
+(-1154 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-4181 . T) (-4180 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3807 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3807 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
-(-1154) 
+((-4184 . T) (-4183 . T)) 
+((|HasCategory| |#1| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| (-517) (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003))) (-3763 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (QUOTE (-1003)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-659))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-918))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-779))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (LIST (QUOTE -280) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -557) (QUOTE (-787)))))) 
+(-1155) 
 ((|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,{}\\spad{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{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\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(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\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 
-(-1155) 
+(-1156) 
 ((|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 
-(-1156) 
+(-1157) 
 ((|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 
-(-1157) 
+(-1158) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{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 
-(-1158) 
+(-1159) 
 ((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1159 A S) 
+(-1160 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 
-(-1160 S) 
+(-1161 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}."))) 
-((-4175 . T) (-4174 . T)) 
+((-4178 . T) (-4177 . T)) 
 NIL 
-(-1161 R) 
+(-1162 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 
-(-1162 K R UP -1696) 
+(-1163 K R UP -2184) 
 ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) 
 NIL 
 NIL 
-(-1163 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1164 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) 
-((-4175 |has| |#1| (-156)) (-4174 |has| |#1| (-156)) (-4177 . T)) 
+((-4178 |has| |#1| (-156)) (-4177 |has| |#1| (-156)) (-4180 . T)) 
 ((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333)))) 
-(-1164 R E V P) 
+(-1165 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}}."))) 
-((-4181 . T) (-4180 . T)) 
+((-4184 . T) (-4183 . T)) 
 ((|HasCategory| |#4| (LIST (QUOTE -558) (QUOTE (-493)))) (|HasCategory| |#4| (QUOTE (-1003))) (-12 (|HasCategory| |#4| (QUOTE (-1003))) (|HasCategory| |#4| (LIST (QUOTE -280) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-509))) (|HasCategory| |#3| (QUOTE (-338)))) 
-(-1165 R) 
+(-1166 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})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) 
-((-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1166 |vl| R) 
+(-1167 |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."))) 
-((-4177 . T) (-4173 |has| |#2| (-6 -4173)) (-4175 . T) (-4174 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4173))) 
-(-1167 R |VarSet| XPOLY) 
+((-4180 . T) (-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4176))) 
+(-1168 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 
-(-1168 |vl| R) 
+(-1169 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-4173 |has| |#2| (-6 -4173)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+((-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
-(-1169 S -1696) 
+(-1170 S -2184) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-338))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-134)))) 
-(-1170 -1696) 
+(-1171 -2184) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
-((-4172 . T) (-4178 . T) (-4173 . T) ((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+((-4175 . T) (-4181 . T) (-4176 . T) ((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
-(-1171 |VarSet| R) 
+(-1172 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) 
-((-4173 |has| |#2| (-6 -4173)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4173))) 
-(-1172 |vl| R) 
+((-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasCategory| |#2| (LIST (QUOTE -650) (LIST (QUOTE -377) (QUOTE (-517))))) (|HasAttribute| |#2| (QUOTE -4176))) 
+(-1173 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-4173 |has| |#2| (-6 -4173)) (-4175 . T) (-4174 . T) (-4177 . T)) 
+((-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) 
 NIL 
-(-1173 R) 
+(-1174 R) 
 ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) 
-((-4173 |has| |#1| (-6 -4173)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4173))) 
-(-1174 R E) 
+((-4176 |has| |#1| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasAttribute| |#1| (QUOTE -4176))) 
+(-1175 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-4177 . T) (-4178 |has| |#1| (-6 -4178)) (-4173 |has| |#1| (-6 -4173)) (-4175 . T) (-4174 . T)) 
-((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4177)) (|HasAttribute| |#1| (QUOTE -4178)) (|HasAttribute| |#1| (QUOTE -4173))) 
-(-1175 |VarSet| R) 
+((-4180 . T) (-4181 |has| |#1| (-6 -4181)) (-4176 |has| |#1| (-6 -4176)) (-4178 . T) (-4177 . T)) 
+((|HasCategory| |#1| (QUOTE (-156))) (|HasCategory| |#1| (QUOTE (-333))) (|HasAttribute| |#1| (QUOTE -4180)) (|HasAttribute| |#1| (QUOTE -4181)) (|HasAttribute| |#1| (QUOTE -4176))) 
+(-1176 |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."))) 
-((-4173 |has| |#2| (-6 -4173)) (-4175 . T) (-4174 . T) (-4177 . T)) 
-((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4173))) 
-(-1176 A) 
+((-4176 |has| |#2| (-6 -4176)) (-4178 . T) (-4177 . T) (-4180 . T)) 
+((|HasCategory| |#2| (QUOTE (-156))) (|HasAttribute| |#2| (QUOTE -4176))) 
+(-1177 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 
-(-1177 R |ls| |ls2|) 
+(-1178 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 
-(-1178 R) 
+(-1179 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 
-(-1179 |p|) 
+(-1180 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4182 "*") . T) (-4174 . T) (-4175 . T) (-4177 . T)) 
+(((-4185 "*") . T) (-4177 . T) (-4178 . T) (-4180 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4668,4 +4672,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-1184 NIL 2204723 2204728 2204733 2204738) (-3 NIL 2204703 2204708 2204713 2204718) (-2 NIL 2204683 2204688 2204693 2204698) (-1 NIL 2204663 2204668 2204673 2204678) (0 NIL 2204643 2204648 2204653 2204658) (-1179 "ZMOD.spad" 2204452 2204465 2204581 2204638) (-1178 "ZLINDEP.spad" 2203496 2203507 2204442 2204447) (-1177 "ZDSOLVE.spad" 2193345 2193367 2203486 2203491) (-1176 "YSTREAM.spad" 2192838 2192849 2193335 2193340) (-1175 "XRPOLY.spad" 2192058 2192078 2192694 2192763) (-1174 "XPR.spad" 2189787 2189800 2191776 2191875) (-1173 "XPOLY.spad" 2189342 2189353 2189643 2189712) (-1172 "XPOLYC.spad" 2188659 2188675 2189268 2189337) (-1171 "XPBWPOLY.spad" 2187096 2187116 2188439 2188508) (-1170 "XF.spad" 2185557 2185572 2186998 2187091) (-1169 "XF.spad" 2183998 2184015 2185441 2185446) (-1168 "XFALG.spad" 2181022 2181038 2183924 2183993) (-1167 "XEXPPKG.spad" 2180273 2180299 2181012 2181017) (-1166 "XDPOLY.spad" 2179887 2179903 2180129 2180198) (-1165 "XALG.spad" 2179485 2179496 2179843 2179882) (-1164 "WUTSET.spad" 2175380 2175397 2179187 2179214) (-1163 "WP.spad" 2174394 2174438 2175238 2175305) (-1162 "WFFINTBS.spad" 2171957 2171979 2174384 2174389) (-1161 "WEIER.spad" 2170171 2170182 2171947 2171952) (-1160 "VSPACE.spad" 2169844 2169855 2170139 2170166) (-1159 "VSPACE.spad" 2169537 2169550 2169834 2169839) (-1158 "VOID.spad" 2169127 2169136 2169527 2169532) (-1157 "VIEW.spad" 2166749 2166758 2169117 2169122) (-1156 "VIEWDEF.spad" 2161946 2161955 2166739 2166744) (-1155 "VIEW3D.spad" 2145781 2145790 2161936 2161941) (-1154 "VIEW2D.spad" 2133518 2133527 2145771 2145776) (-1153 "VECTOR.spad" 2132195 2132206 2132446 2132473) (-1152 "VECTOR2.spad" 2130822 2130835 2132185 2132190) (-1151 "VECTCAT.spad" 2128710 2128721 2130778 2130817) (-1150 "VECTCAT.spad" 2126419 2126432 2128489 2128494) (-1149 "VARIABLE.spad" 2126199 2126214 2126409 2126414) (-1148 "UTSODETL.spad" 2125492 2125516 2126155 2126160) (-1147 "UTSODE.spad" 2123680 2123700 2125482 2125487) (-1146 "UTS.spad" 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2072583) (-1127 "UP.spad" 2069107 2069122 2069615 2069768) (-1126 "UPMP.spad" 2067997 2068010 2069097 2069102) (-1125 "UPDIVP.spad" 2067560 2067574 2067987 2067992) (-1124 "UPDECOMP.spad" 2065797 2065811 2067550 2067555) (-1123 "UPCDEN.spad" 2065004 2065020 2065787 2065792) (-1122 "UP2.spad" 2064366 2064387 2064994 2064999) (-1121 "UNISEG.spad" 2063719 2063730 2064285 2064290) (-1120 "UNISEG2.spad" 2063212 2063225 2063675 2063680) (-1119 "UNIFACT.spad" 2062313 2062325 2063202 2063207) (-1118 "ULS.spad" 2052872 2052900 2053965 2054394) (-1117 "ULSCONS.spad" 2046915 2046935 2047287 2047436) (-1116 "ULSCCAT.spad" 2044512 2044532 2046735 2046910) (-1115 "ULSCCAT.spad" 2042243 2042265 2044468 2044473) (-1114 "ULSCAT.spad" 2040459 2040475 2042089 2042238) (-1113 "ULS2.spad" 2039971 2040024 2040449 2040454) (-1112 "UFD.spad" 2039036 2039045 2039897 2039966) (-1111 "UFD.spad" 2038163 2038174 2039026 2039031) (-1110 "UDVO.spad" 2037010 2037019 2038153 2038158) (-1109 "UDPO.spad" 2034437 2034448 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1272325) (-734 "ODEEF.spad" 1265092 1265108 1269715 1269720) (-733 "ODECONST.spad" 1264611 1264629 1265082 1265087) (-732 "ODECAT.spad" 1263207 1263215 1264601 1264606) (-731 "OCT.spad" 1261354 1261364 1262070 1262109) (-730 "OCTCT2.spad" 1260998 1261019 1261344 1261349) (-729 "OC.spad" 1258772 1258782 1260954 1260993) (-728 "OC.spad" 1256272 1256284 1258456 1258461) (-727 "OCAMON.spad" 1256120 1256128 1256262 1256267) (-726 "OASGP.spad" 1255935 1255943 1256110 1256115) (-725 "OAMONS.spad" 1255455 1255463 1255925 1255930) (-724 "OAMON.spad" 1255316 1255324 1255445 1255450) (-723 "OAGROUP.spad" 1255178 1255186 1255306 1255311) (-722 "NUMTUBE.spad" 1254765 1254781 1255168 1255173) (-721 "NUMQUAD.spad" 1242627 1242635 1254755 1254760) (-720 "NUMODE.spad" 1233763 1233771 1242617 1242622) (-719 "NUMINT.spad" 1231321 1231329 1233753 1233758) (-718 "NUMFMT.spad" 1230161 1230169 1231311 1231316) (-717 "NUMERIC.spad" 1222234 1222244 1229967 1229972) (-716 "NTSCAT.spad" 1220724 1220740 1222190 1222229) (-715 "NTPOLFN.spad" 1220269 1220279 1220641 1220646) (-714 "NSUP.spad" 1213287 1213297 1217827 1217980) (-713 "NSUP2.spad" 1212679 1212691 1213277 1213282) (-712 "NSMP.spad" 1208878 1208897 1209186 1209313) (-711 "NREP.spad" 1207250 1207264 1208868 1208873) (-710 "NPCOEF.spad" 1206496 1206516 1207240 1207245) (-709 "NORMRETR.spad" 1206094 1206133 1206486 1206491) (-708 "NORMPK.spad" 1203996 1204015 1206084 1206089) (-707 "NORMMA.spad" 1203684 1203710 1203986 1203991) (-706 "NONE.spad" 1203425 1203433 1203674 1203679) (-705 "NONE1.spad" 1203101 1203111 1203415 1203420) (-704 "NODE1.spad" 1202570 1202586 1203091 1203096) (-703 "NNI.spad" 1201457 1201465 1202544 1202565) (-702 "NLINSOL.spad" 1200079 1200089 1201447 1201452) (-701 "NIPROB.spad" 1198562 1198570 1200069 1200074) (-700 "NFINTBAS.spad" 1196022 1196039 1198552 1198557) (-699 "NCODIV.spad" 1194220 1194236 1196012 1196017) (-698 "NCNTFRAC.spad" 1193862 1193876 1194210 1194215) (-697 "NCEP.spad" 1192022 1192036 1193852 1193857) (-696 "NASRING.spad" 1191618 1191626 1192012 1192017) (-695 "NASRING.spad" 1191212 1191222 1191608 1191613) (-694 "NARNG.spad" 1190556 1190564 1191202 1191207) (-693 "NARNG.spad" 1189898 1189908 1190546 1190551) (-692 "NAGSP.spad" 1188971 1188979 1189888 1189893) (-691 "NAGS.spad" 1178496 1178504 1188961 1188966) (-690 "NAGF07.spad" 1176889 1176897 1178486 1178491) (-689 "NAGF04.spad" 1171121 1171129 1176879 1176884) (-688 "NAGF02.spad" 1164930 1164938 1171111 1171116) (-687 "NAGF01.spad" 1160533 1160541 1164920 1164925) (-686 "NAGE04.spad" 1153993 1154001 1160523 1160528) (-685 "NAGE02.spad" 1144335 1144343 1153983 1153988) (-684 "NAGE01.spad" 1140219 1140227 1144325 1144330) (-683 "NAGD03.spad" 1138139 1138147 1140209 1140214) (-682 "NAGD02.spad" 1130670 1130678 1138129 1138134) (-681 "NAGD01.spad" 1124783 1124791 1130660 1130665) (-680 "NAGC06.spad" 1120570 1120578 1124773 1124778) (-679 "NAGC05.spad" 1119039 1119047 1120560 1120565) (-678 "NAGC02.spad" 1118294 1118302 1119029 1119034) (-677 "NAALG.spad" 1117829 1117839 1118262 1118289) (-676 "NAALG.spad" 1117384 1117396 1117819 1117824) (-675 "MULTSQFR.spad" 1114342 1114359 1117374 1117379) (-674 "MULTFACT.spad" 1113725 1113742 1114332 1114337) (-673 "MTSCAT.spad" 1111759 1111780 1113623 1113720) (-672 "MTHING.spad" 1111416 1111426 1111749 1111754) (-671 "MSYSCMD.spad" 1110850 1110858 1111406 1111411) (-670 "MSET.spad" 1108848 1108858 1110612 1110651) (-669 "MSETAGG.spad" 1108681 1108691 1108804 1108843) (-668 "MRING.spad" 1105652 1105664 1108389 1108456) (-667 "MRF2.spad" 1105220 1105234 1105642 1105647) (-666 "MRATFAC.spad" 1104766 1104783 1105210 1105215) (-665 "MPRFF.spad" 1102796 1102815 1104756 1104761) (-664 "MPOLY.spad" 1100234 1100249 1100593 1100720) (-663 "MPCPF.spad" 1099498 1099517 1100224 1100229) (-662 "MPC3.spad" 1099313 1099353 1099488 1099493) (-661 "MPC2.spad" 1098955 1098988 1099303 1099308) (-660 "MONOTOOL.spad" 1097290 1097307 1098945 1098950) (-659 "MONOID.spad" 1096464 1096472 1097280 1097285) (-658 "MONOID.spad" 1095636 1095646 1096454 1096459) (-657 "MONOGEN.spad" 1094382 1094395 1095496 1095631) (-656 "MONOGEN.spad" 1093150 1093165 1094266 1094271) (-655 "MONADWU.spad" 1091164 1091172 1093140 1093145) (-654 "MONADWU.spad" 1089176 1089186 1091154 1091159) (-653 "MONAD.spad" 1088320 1088328 1089166 1089171) (-652 "MONAD.spad" 1087462 1087472 1088310 1088315) (-651 "MOEBIUS.spad" 1086148 1086162 1087442 1087457) (-650 "MODULE.spad" 1086018 1086028 1086116 1086143) (-649 "MODULE.spad" 1085908 1085920 1086008 1086013) (-648 "MODRING.spad" 1085239 1085278 1085888 1085903) (-647 "MODOP.spad" 1083898 1083910 1085061 1085128) (-646 "MODMONOM.spad" 1083430 1083448 1083888 1083893) (-645 "MODMON.spad" 1080140 1080156 1080916 1081069) (-644 "MODFIELD.spad" 1079498 1079537 1080042 1080135) (-643 "MMAP.spad" 1079238 1079272 1079488 1079493) (-642 "MLO.spad" 1077665 1077675 1079194 1079233) (-641 "MLIFT.spad" 1076237 1076254 1077655 1077660) (-640 "MKUCFUNC.spad" 1075770 1075788 1076227 1076232) (-639 "MKRECORD.spad" 1075372 1075385 1075760 1075765) (-638 "MKFUNC.spad" 1074753 1074763 1075362 1075367) (-637 "MKFLCFN.spad" 1073709 1073719 1074743 1074748) (-636 "MKCHSET.spad" 1073485 1073495 1073699 1073704) (-635 "MKBCFUNC.spad" 1072970 1072988 1073475 1073480) (-634 "MINT.spad" 1072409 1072417 1072872 1072965) (-633 "MHROWRED.spad" 1070910 1070920 1072399 1072404) (-632 "MFLOAT.spad" 1069355 1069363 1070800 1070905) (-631 "MFINFACT.spad" 1068755 1068777 1069345 1069350) (-630 "MESH.spad" 1066487 1066495 1068745 1068750) (-629 "MDDFACT.spad" 1064680 1064690 1066477 1066482) (-628 "MDAGG.spad" 1063955 1063965 1064648 1064675) (-627 "MCMPLX.spad" 1059935 1059943 1060549 1060750) (-626 "MCDEN.spad" 1059143 1059155 1059925 1059930) (-625 "MCALCFN.spad" 1056245 1056271 1059133 1059138) (-624 "MATSTOR.spad" 1053521 1053531 1056235 1056240) (-623 "MATRIX.spad" 1052448 1052458 1052932 1052959) (-622 "MATLIN.spad" 1049774 1049798 1052332 1052337) (-621 "MATCAT.spad" 1041347 1041369 1049730 1049769) (-620 "MATCAT.spad" 1032804 1032828 1041189 1041194) (-619 "MATCAT2.spad" 1032072 1032120 1032794 1032799) (-618 "MAPPKG3.spad" 1030971 1030985 1032062 1032067) (-617 "MAPPKG2.spad" 1030305 1030317 1030961 1030966) (-616 "MAPPKG1.spad" 1029123 1029133 1030295 1030300) (-615 "MAPHACK3.spad" 1028931 1028945 1029113 1029118) (-614 "MAPHACK2.spad" 1028696 1028708 1028921 1028926) (-613 "MAPHACK1.spad" 1028326 1028336 1028686 1028691) (-612 "MAGMA.spad" 1026116 1026133 1028316 1028321) (-611 "M3D.spad" 1024037 1024047 1025719 1025724) (-610 "LZSTAGG.spad" 1021255 1021265 1024017 1024032) (-609 "LZSTAGG.spad" 1018481 1018493 1021245 1021250) (-608 "LWORD.spad" 1015186 1015203 1018471 1018476) (-607 "LSQM.spad" 1013470 1013484 1013868 1013919) (-606 "LSPP.spad" 1013003 1013020 1013460 1013465) (-605 "LSMP.spad" 1011843 1011871 1012993 1012998) (-604 "LSMP1.spad" 1009647 1009661 1011833 1011838) (-603 "LSAGG.spad" 1009304 1009314 1009603 1009642) (-602 "LSAGG.spad" 1008993 1009005 1009294 1009299) (-601 "LPOLY.spad" 1007947 1007966 1008849 1008918) (-600 "LPEFRAC.spad" 1007204 1007214 1007937 1007942) (-599 "LO.spad" 1006605 1006619 1007138 1007165) (-598 "LOGIC.spad" 1006207 1006215 1006595 1006600) (-597 "LOGIC.spad" 1005807 1005817 1006197 1006202) (-596 "LODOOPS.spad" 1004725 1004737 1005797 1005802) (-595 "LODO.spad" 1004111 1004127 1004407 1004446) (-594 "LODOF.spad" 1003155 1003172 1004068 1004073) (-593 "LODOCAT.spad" 1001813 1001823 1003111 1003150) (-592 "LODOCAT.spad" 1000469 1000481 1001769 1001774) (-591 "LODO2.spad" 999744 999756 1000151 1000190) (-590 "LODO1.spad" 999146 999156 999426 999465) (-589 "LODEEF.spad" 997918 997936 999136 999141) (-588 "LNAGG.spad" 993710 993720 997898 997913) (-587 "LNAGG.spad" 989476 989488 993666 993671) (-586 "LMOPS.spad" 986212 986229 989466 989471) (-585 "LMODULE.spad" 985854 985864 986202 986207) (-584 "LMDICT.spad" 985360 985370 985628 985655) (-583 "LIST.spad" 983078 983088 984507 984534) (-582 "LIST3.spad" 982369 982383 983068 983073) (-581 "LIST2.spad" 981009 981021 982359 982364) (-580 "LIST2MAP.spad" 977886 977898 980999 981004) (-579 "LINEXP.spad" 977318 977328 977866 977881) (-578 "LINDEP.spad" 976095 976107 977230 977235) (-577 "LIMITRF.spad" 974009 974019 976085 976090) (-576 "LIMITPS.spad" 972892 972905 973999 974004) (-575 "LIE.spad" 970906 970918 972182 972327) (-574 "LIECAT.spad" 970382 970392 970832 970901) (-573 "LIECAT.spad" 969886 969898 970338 970343) (-572 "LIB.spad" 968516 968524 969127 969142) (-571 "LGROBP.spad" 965869 965888 968506 968511) (-570 "LF.spad" 964788 964804 965859 965864) (-569 "LFCAT.spad" 963807 963815 964778 964783) (-568 "LEXTRIPK.spad" 959310 959325 963797 963802) (-567 "LEXP.spad" 957313 957340 959290 959305) (-566 "LEADCDET.spad" 955697 955714 957303 957308) (-565 "LAZM3PK.spad" 954401 954423 955687 955692) (-564 "LAUPOL.spad" 953092 953105 953996 954065) (-563 "LAPLACE.spad" 952665 952681 953082 953087) (-562 "LA.spad" 952105 952119 952587 952626) (-561 "LALG.spad" 951881 951891 952085 952100) (-560 "LALG.spad" 951665 951677 951871 951876) (-559 "KOVACIC.spad" 950378 950395 951655 951660) (-558 "KONVERT.spad" 950100 950110 950368 950373) (-557 "KOERCE.spad" 949837 949847 950090 950095) (-556 "KERNEL.spad" 948372 948382 949621 949626) (-555 "KERNEL2.spad" 948075 948087 948362 948367) (-554 "KDAGG.spad" 947166 947188 948043 948070) (-553 "KDAGG.spad" 946277 946301 947156 947161) (-552 "KAFILE.spad" 945389 945405 945624 945651) (-551 "JORDAN.spad" 943216 943228 944679 944824) (-550 "IXAGG.spad" 941329 941353 943196 943211) (-549 "IXAGG.spad" 939307 939333 941176 941181) (-548 "IVECTOR.spad" 938303 938318 938458 938485) (-547 "ITUPLE.spad" 937448 937458 938293 938298) (-546 "ITRIGMNP.spad" 936259 936278 937438 937443) (-545 "ITFUN3.spad" 935753 935767 936249 936254) (-544 "ITFUN2.spad" 935483 935495 935743 935748) (-543 "ITAYLOR.spad" 933275 933290 935319 935444) (-542 "ISUPS.spad" 925686 925701 932249 932346) (-541 "ISUMP.spad" 925183 925199 925676 925681) (-540 "ISTRING.spad" 924186 924199 924352 924379) (-539 "IRURPK.spad" 922899 922918 924176 924181) (-538 "IRSN.spad" 920859 920867 922889 922894) (-537 "IRRF2F.spad" 919334 919344 920815 920820) (-536 "IRREDFFX.spad" 918935 918946 919324 919329) (-535 "IROOT.spad" 917266 917276 918925 918930) (-534 "IR.spad" 915056 915070 917122 917149) (-533 "IR2.spad" 914076 914092 915046 915051) (-532 "IR2F.spad" 913276 913292 914066 914071) (-531 "IPRNTPK.spad" 913036 913044 913266 913271) (-530 "IPF.spad" 912601 912613 912841 912934) (-529 "IPADIC.spad" 912362 912388 912527 912596) (-528 "INVLAPLA.spad" 912007 912023 912352 912357) (-527 "INTTR.spad" 905253 905270 911997 912002) (-526 "INTTOOLS.spad" 902965 902981 904828 904833) (-525 "INTSLPE.spad" 902271 902279 902955 902960) (-524 "INTRVL.spad" 901837 901847 902185 902266) (-523 "INTRF.spad" 900201 900215 901827 901832) (-522 "INTRET.spad" 899633 899643 900191 900196) (-521 "INTRAT.spad" 898308 898325 899623 899628) (-520 "INTPM.spad" 896671 896687 897951 897956) (-519 "INTPAF.spad" 894439 894457 896603 896608) (-518 "INTPACK.spad" 884749 884757 894429 894434) (-517 "INT.spad" 884110 884118 884603 884744) (-516 "INTHERTR.spad" 883376 883393 884100 884105) (-515 "INTHERAL.spad" 883042 883066 883366 883371) (-514 "INTHEORY.spad" 879455 879463 883032 883037) (-513 "INTG0.spad" 872918 872936 879387 879392) (-512 "INTFTBL.spad" 866947 866955 872908 872913) (-511 "INTFACT.spad" 866006 866016 866937 866942) (-510 "INTEF.spad" 864321 864337 865996 866001) (-509 "INTDOM.spad" 862936 862944 864247 864316) (-508 "INTDOM.spad" 861613 861623 862926 862931) (-507 "INTCAT.spad" 859866 859876 861527 861608) (-506 "INTBIT.spad" 859369 859377 859856 859861) (-505 "INTALG.spad" 858551 858578 859359 859364) (-504 "INTAF.spad" 858043 858059 858541 858546) (-503 "INTABL.spad" 857123 857154 857286 857313) (-502 "INS.spad" 854519 854527 857025 857118) (-501 "INS.spad" 852001 852011 854509 854514) (-500 "INPSIGN.spad" 851435 851448 851991 851996) (-499 "INPRODPF.spad" 850501 850520 851425 851430) (-498 "INPRODFF.spad" 849559 849583 850491 850496) (-497 "INNMFACT.spad" 848530 848547 849549 849554) (-496 "INMODGCD.spad" 848014 848044 848520 848525) (-495 "INFSP.spad" 846299 846321 848004 848009) (-494 "INFPROD0.spad" 845349 845368 846289 846294) (-493 "INFORM.spad" 842617 842625 845339 845344) (-492 "INFORM1.spad" 842242 842252 842607 842612) (-491 "INFINITY.spad" 841794 841802 842232 842237) (-490 "INEP.spad" 840326 840348 841784 841789) (-489 "INDE.spad" 840232 840249 840316 840321) (-488 "INCRMAPS.spad" 839653 839663 840222 840227) (-487 "INBFF.spad" 835423 835434 839643 839648) (-486 "IMATRIX.spad" 834591 834617 835103 835130) (-485 "IMATQF.spad" 833685 833729 834547 834552) (-484 "IMATLIN.spad" 832290 832314 833641 833646) (-483 "ILIST.spad" 830946 830961 831473 831500) (-482 "IIARRAY2.spad" 830557 830595 830776 830803) (-481 "IFF.spad" 829967 829983 830238 830331) (-480 "IFARRAY.spad" 827677 827692 829373 829400) (-479 "IFAMON.spad" 827539 827556 827633 827638) (-478 "IEVALAB.spad" 826928 826940 827529 827534) (-477 "IEVALAB.spad" 826315 826329 826918 826923) (-476 "IDPO.spad" 826113 826125 826305 826310) (-475 "IDPOAMS.spad" 825869 825881 826103 826108) (-474 "IDPOAM.spad" 825589 825601 825859 825864) (-473 "IDPC.spad" 824523 824535 825579 825584) (-472 "IDPAM.spad" 824268 824280 824513 824518) (-471 "IDPAG.spad" 824015 824027 824258 824263) (-470 "IDECOMP.spad" 821252 821270 824005 824010) (-469 "IDEAL.spad" 816175 816214 821187 821192) (-468 "ICDEN.spad" 815326 815342 816165 816170) (-467 "ICARD.spad" 814515 814523 815316 815321) (-466 "IBPTOOLS.spad" 813108 813125 814505 814510) (-465 "IBITS.spad" 812365 812378 812802 812829) (-464 "IBATOOL.spad" 809240 809259 812355 812360) (-463 "IBACHIN.spad" 807727 807742 809230 809235) (-462 "IARRAY2.spad" 806938 806964 807557 807584) (-461 "IARRAY1.spad" 806206 806221 806344 806371) (-460 "IAN.spad" 804421 804429 806024 806117) (-459 "IALGFACT.spad" 804022 804055 804411 804416) (-458 "HYPCAT.spad" 803446 803454 804012 804017) (-457 "HYPCAT.spad" 802868 802878 803436 803441) (-456 "HOAGG.spad" 800126 800136 802848 802863) (-455 "HOAGG.spad" 797169 797181 799893 799898) (-454 "HEXADEC.spad" 795041 795049 795639 795732) (-453 "HEUGCD.spad" 794056 794067 795031 795036) (-452 "HELLFDIV.spad" 793646 793670 794046 794051) (-451 "HEAP.spad" 793261 793271 793476 793503) (-450 "HDP.spad" 785499 785515 785876 786005) (-449 "HDMP.spad" 782678 782693 783296 783423) (-448 "HB.spad" 780915 780923 782668 782673) (-447 "HASHTBL.spad" 779947 779978 780158 780185) (-446 "HACKPI.spad" 779430 779438 779849 779942) (-445 "GTSET.spad" 778425 778441 779132 779159) (-444 "GSTBL.spad" 777506 777541 777680 777695) (-443 "GSERIES.spad" 774673 774700 775638 775787) (-442 "GROUP.spad" 773847 773855 774653 774668) (-441 "GROUP.spad" 773029 773039 773837 773842) (-440 "GROEBSOL.spad" 771517 771538 773019 773024) (-439 "GRMOD.spad" 770088 770100 771507 771512) (-438 "GRMOD.spad" 768657 768671 770078 770083) (-437 "GRIMAGE.spad" 761262 761270 768647 768652) (-436 "GRDEF.spad" 759641 759649 761252 761257) (-435 "GRAY.spad" 758100 758108 759631 759636) (-434 "GRALG.spad" 757147 757159 758090 758095) (-433 "GRALG.spad" 756192 756206 757137 757142) (-432 "GPOLSET.spad" 755702 755725 755930 755957) (-431 "GOSPER.spad" 754967 754985 755692 755697) (-430 "GMODPOL.spad" 754105 754132 754935 754962) (-429 "GHENSEL.spad" 753174 753188 754095 754100) (-428 "GENUPS.spad" 749275 749288 753164 753169) (-427 "GENUFACT.spad" 748852 748862 749265 749270) (-426 "GENPGCD.spad" 748436 748453 748842 748847) (-425 "GENMFACT.spad" 747888 747907 748426 748431) (-424 "GENEEZ.spad" 745827 745840 747878 747883) (-423 "GDMP.spad" 742848 742865 743624 743751) (-422 "GCNAALG.spad" 736743 736770 742642 742709) (-421 "GCDDOM.spad" 735915 735923 736669 736738) (-420 "GCDDOM.spad" 735149 735159 735905 735910) (-419 "GB.spad" 732667 732705 735105 735110) (-418 "GBINTERN.spad" 728687 728725 732657 732662) (-417 "GBF.spad" 724444 724482 728677 728682) (-416 "GBEUCLID.spad" 722318 722356 724434 724439) (-415 "GAUSSFAC.spad" 721615 721623 722308 722313) (-414 "GALUTIL.spad" 719937 719947 721571 721576) (-413 "GALPOLYU.spad" 718383 718396 719927 719932) (-412 "GALFACTU.spad" 716548 716567 718373 718378) (-411 "GALFACT.spad" 706681 706692 716538 716543) (-410 "FVFUN.spad" 703694 703702 706661 706676) (-409 "FVC.spad" 702736 702744 703674 703689) (-408 "FUNCTION.spad" 702585 702597 702726 702731) (-407 "FT.spad" 700797 700805 702575 702580) (-406 "FTEM.spad" 699960 699968 700787 700792) (-405 "FSUPFACT.spad" 698861 698880 699897 699902) (-404 "FST.spad" 696947 696955 698851 698856) (-403 "FSRED.spad" 696425 696441 696937 696942) (-402 "FSPRMELT.spad" 695249 695265 696382 696387) (-401 "FSPECF.spad" 693326 693342 695239 695244) (-400 "FS.spad" 687377 687387 693090 693321) (-399 "FS.spad" 681219 681231 686934 686939) (-398 "FSINT.spad" 680877 680893 681209 681214) (-397 "FSERIES.spad" 680064 680076 680697 680796) (-396 "FSCINT.spad" 679377 679393 680054 680059) (-395 "FSAGG.spad" 678482 678492 679321 679372) (-394 "FSAGG.spad" 677561 677573 678402 678407) (-393 "FSAGG2.spad" 676260 676276 677551 677556) (-392 "FS2UPS.spad" 670649 670683 676250 676255) (-391 "FS2.spad" 670294 670310 670639 670644) (-390 "FS2EXPXP.spad" 669417 669440 670284 670289) (-389 "FRUTIL.spad" 668359 668369 669407 669412) (-388 "FR.spad" 662056 662066 667386 667455) (-387 "FRNAALG.spad" 657143 657153 661998 662051) (-386 "FRNAALG.spad" 652242 652254 657099 657104) (-385 "FRNAAF2.spad" 651696 651714 652232 652237) (-384 "FRMOD.spad" 651091 651121 651628 651633) (-383 "FRIDEAL.spad" 650286 650307 651071 651086) (-382 "FRIDEAL2.spad" 649888 649920 650276 650281) (-381 "FRETRCT.spad" 649399 649409 649878 649883) (-380 "FRETRCT.spad" 648778 648790 649259 649264) (-379 "FRAMALG.spad" 647106 647119 648734 648773) (-378 "FRAMALG.spad" 645466 645481 647096 647101) (-377 "FRAC.spad" 642569 642579 642972 643145) (-376 "FRAC2.spad" 642172 642184 642559 642564) (-375 "FR2.spad" 641506 641518 642162 642167) (-374 "FPS.spad" 638315 638323 641396 641501) (-373 "FPS.spad" 635152 635162 638235 638240) (-372 "FPC.spad" 634194 634202 635054 635147) (-371 "FPC.spad" 633322 633332 634184 634189) (-370 "FPATMAB.spad" 633074 633084 633302 633317) (-369 "FPARFRAC.spad" 631547 631564 633064 633069) (-368 "FORTRAN.spad" 630047 630096 631537 631542) (-367 "FORT.spad" 628976 628984 630037 630042) (-366 "FORTFN.spad" 626136 626144 628956 628971) (-365 "FORTCAT.spad" 625810 625818 626116 626131) (-364 "FORMULA.spad" 623148 623156 625800 625805) (-363 "FORMULA1.spad" 622627 622637 623138 623143) (-362 "FORDER.spad" 622318 622342 622617 622622) (-361 "FOP.spad" 621519 621527 622308 622313) (-360 "FNLA.spad" 620943 620965 621487 621514) (-359 "FNCAT.spad" 619271 619279 620933 620938) (-358 "FNAME.spad" 619163 619171 619261 619266) (-357 "FMTC.spad" 618961 618969 619089 619158) (-356 "FMONOID.spad" 616016 616026 618917 618922) (-355 "FM.spad" 615711 615723 615950 615977) (-354 "FMFUN.spad" 612731 612739 615691 615706) (-353 "FMC.spad" 611773 611781 612711 612726) (-352 "FMCAT.spad" 609427 609445 611741 611768) (-351 "FM1.spad" 608784 608796 609361 609388) (-350 "FLOATRP.spad" 606505 606519 608774 608779) (-349 "FLOAT.spad" 599669 599677 606371 606500) (-348 "FLOATCP.spad" 597086 597100 599659 599664) (-347 "FLINEXP.spad" 596798 596808 597066 597081) (-346 "FLINEXP.spad" 596464 596476 596734 596739) (-345 "FLASORT.spad" 595784 595796 596454 596459) (-344 "FLALG.spad" 593430 593449 595710 595779) (-343 "FLAGG.spad" 590436 590446 593398 593425) (-342 "FLAGG.spad" 587355 587367 590319 590324) (-341 "FLAGG2.spad" 586036 586052 587345 587350) (-340 "FINRALG.spad" 584065 584078 585992 586031) (-339 "FINRALG.spad" 582020 582035 583949 583954) (-338 "FINITE.spad" 581172 581180 582010 582015) (-337 "FINAALG.spad" 570153 570163 581114 581167) (-336 "FINAALG.spad" 559146 559158 570109 570114) (-335 "FILE.spad" 558729 558739 559136 559141) (-334 "FILECAT.spad" 557247 557264 558719 558724) (-333 "FIELD.spad" 556653 556661 557149 557242) (-332 "FIELD.spad" 556145 556155 556643 556648) (-331 "FGROUP.spad" 554754 554764 556125 556140) (-330 "FGLMICPK.spad" 553541 553556 554744 554749) (-329 "FFX.spad" 552916 552931 553257 553350) (-328 "FFSLPE.spad" 552405 552426 552906 552911) (-327 "FFPOLY.spad" 543657 543668 552395 552400) (-326 "FFPOLY2.spad" 542717 542734 543647 543652) (-325 "FFP.spad" 542114 542134 542433 542526) (-324 "FF.spad" 541562 541578 541795 541888) (-323 "FFNBX.spad" 540074 540094 541278 541371) (-322 "FFNBP.spad" 538587 538604 539790 539883) (-321 "FFNB.spad" 537052 537073 538268 538361) (-320 "FFINTBAS.spad" 534466 534485 537042 537047) (-319 "FFIELDC.spad" 532041 532049 534368 534461) (-318 "FFIELDC.spad" 529702 529712 532031 532036) (-317 "FFHOM.spad" 528450 528467 529692 529697) (-316 "FFF.spad" 525885 525896 528440 528445) (-315 "FFCGX.spad" 524732 524752 525601 525694) (-314 "FFCGP.spad" 523621 523641 524448 524541) (-313 "FFCG.spad" 522413 522434 523302 523395) (-312 "FFCAT.spad" 515314 515336 522252 522408) (-311 "FFCAT.spad" 508294 508318 515234 515239) (-310 "FFCAT2.spad" 508039 508079 508284 508289) (-309 "FEXPR.spad" 499752 499798 507799 507838) (-308 "FEVALAB.spad" 499458 499468 499742 499747) (-307 "FEVALAB.spad" 498949 498961 499235 499240) (-306 "FDIV.spad" 498391 498415 498939 498944) (-305 "FDIVCAT.spad" 496433 496457 498381 498386) (-304 "FDIVCAT.spad" 494473 494499 496423 496428) (-303 "FDIV2.spad" 494127 494167 494463 494468) (-302 "FCPAK1.spad" 492680 492688 494117 494122) (-301 "FCOMP.spad" 492059 492069 492670 492675) (-300 "FC.spad" 481884 481892 492049 492054) (-299 "FAXF.spad" 474819 474833 481786 481879) (-298 "FAXF.spad" 467806 467822 474775 474780) (-297 "FARRAY.spad" 466175 466185 467212 467239) (-296 "FAMR.spad" 464295 464307 466073 466170) (-295 "FAMR.spad" 462399 462413 464179 464184) (-294 "FAMONOID.spad" 462049 462059 462353 462358) (-293 "FAMONC.spad" 460271 460283 462039 462044) (-292 "FAGROUP.spad" 459877 459887 460167 460194) (-291 "FACUTIL.spad" 458073 458090 459867 459872) (-290 "FACTFUNC.spad" 457249 457259 458063 458068) (-289 "EXPUPXS.spad" 454082 454105 455381 455530) (-288 "EXPRTUBE.spad" 451310 451318 454072 454077) (-287 "EXPRODE.spad" 448182 448198 451300 451305) (-286 "EXPR.spad" 443484 443494 444198 444601) (-285 "EXPR2UPS.spad" 439576 439589 443474 443479) (-284 "EXPR2.spad" 439279 439291 439566 439571) (-283 "EXPEXPAN.spad" 436220 436245 436854 436947) (-282 "EXIT.spad" 435891 435899 436210 436215) (-281 "EVALCYC.spad" 435349 435363 435881 435886) (-280 "EVALAB.spad" 434913 434923 435339 435344) (-279 "EVALAB.spad" 434475 434487 434903 434908) (-278 "EUCDOM.spad" 432017 432025 434401 434470) (-277 "EUCDOM.spad" 429621 429631 432007 432012) (-276 "ESTOOLS.spad" 421461 421469 429611 429616) (-275 "ESTOOLS2.spad" 421062 421076 421451 421456) (-274 "ESTOOLS1.spad" 420747 420758 421052 421057) (-273 "ES.spad" 413294 413302 420737 420742) (-272 "ES.spad" 405749 405759 413194 413199) (-271 "ESCONT.spad" 402522 402530 405739 405744) (-270 "ESCONT1.spad" 402271 402283 402512 402517) (-269 "ES2.spad" 401766 401782 402261 402266) (-268 "ES1.spad" 401332 401348 401756 401761) (-267 "ERROR.spad" 398653 398661 401322 401327) (-266 "EQTBL.spad" 397687 397709 397896 397923) (-265 "EQ.spad" 392571 392581 395370 395479) (-264 "EQ2.spad" 392287 392299 392561 392566) (-263 "EP.spad" 388601 388611 392277 392282) (-262 "ENTIRER.spad" 388269 388277 388545 388596) (-261 "EMR.spad" 387470 387511 388195 388264) (-260 "ELTAGG.spad" 385710 385729 387460 387465) (-259 "ELTAGG.spad" 383914 383935 385666 385671) (-258 "ELTAB.spad" 383361 383379 383904 383909) (-257 "ELFUTS.spad" 382740 382759 383351 383356) (-256 "ELEMFUN.spad" 382429 382437 382730 382735) (-255 "ELEMFUN.spad" 382116 382126 382419 382424) (-254 "ELAGG.spad" 380047 380057 382084 382111) (-253 "ELAGG.spad" 377927 377939 379966 379971) (-252 "EFUPXS.spad" 374703 374733 377883 377888) (-251 "EFULS.spad" 371539 371562 374659 374664) (-250 "EFSTRUC.spad" 369494 369510 371529 371534) (-249 "EF.spad" 364260 364276 369484 369489) (-248 "EAB.spad" 362536 362544 364250 364255) (-247 "E04UCFA.spad" 362072 362080 362526 362531) (-246 "E04NAFA.spad" 361649 361657 362062 362067) (-245 "E04MBFA.spad" 361229 361237 361639 361644) (-244 "E04JAFA.spad" 360765 360773 361219 361224) (-243 "E04GCFA.spad" 360301 360309 360755 360760) (-242 "E04FDFA.spad" 359837 359845 360291 360296) (-241 "E04DGFA.spad" 359373 359381 359827 359832) (-240 "E04AGNT.spad" 355215 355223 359363 359368) (-239 "DVARCAT.spad" 351900 351910 355205 355210) (-238 "DVARCAT.spad" 348583 348595 351890 351895) (-237 "DSMP.spad" 346017 346031 346322 346449) (-236 "DROPT.spad" 339962 339970 346007 346012) (-235 "DROPT1.spad" 339625 339635 339952 339957) (-234 "DROPT0.spad" 334452 334460 339615 339620) (-233 "DRAWPT.spad" 332607 332615 334442 334447) (-232 "DRAW.spad" 325207 325220 332597 332602) (-231 "DRAWHACK.spad" 324515 324525 325197 325202) (-230 "DRAWCX.spad" 321957 321965 324505 324510) (-229 "DRAWCURV.spad" 321494 321509 321947 321952) (-228 "DRAWCFUN.spad" 310666 310674 321484 321489) (-227 "DQAGG.spad" 308822 308832 310622 310661) (-226 "DPOLCAT.spad" 304163 304179 308690 308817) (-225 "DPOLCAT.spad" 299590 299608 304119 304124) (-224 "DPMO.spad" 293633 293649 293771 294067) (-223 "DPMM.spad" 287689 287707 287814 288110) (-222 "domain.spad" 287458 287466 287679 287684) (-221 "DMP.spad" 284683 284698 285255 285382) (-220 "DLP.spad" 284031 284041 284673 284678) (-219 "DLIST.spad" 282666 282676 283437 283464) (-218 "DLAGG.spad" 281067 281077 282646 282661) (-217 "DIVRING.spad" 280514 280522 281011 281062) (-216 "DIVRING.spad" 280005 280015 280504 280509) (-215 "DISPLAY.spad" 278185 278193 279995 280000) (-214 "DIRPROD.spad" 270160 270176 270800 270929) (-213 "DIRPROD2.spad" 268968 268986 270150 270155) (-212 "DIRPCAT.spad" 267900 267916 268822 268963) (-211 "DIRPCAT.spad" 266572 266590 267496 267501) (-210 "DIOSP.spad" 265397 265405 266562 266567) (-209 "DIOPS.spad" 264369 264379 265365 265392) (-208 "DIOPS.spad" 263327 263339 264325 264330) (-207 "DIFRING.spad" 262619 262627 263307 263322) (-206 "DIFRING.spad" 261919 261929 262609 262614) (-205 "DIFEXT.spad" 261078 261088 261899 261914) (-204 "DIFEXT.spad" 260154 260166 260977 260982) (-203 "DIAGG.spad" 259772 259782 260122 260149) (-202 "DIAGG.spad" 259410 259422 259762 259767) (-201 "DHMATRIX.spad" 257937 257947 259090 259117) (-200 "DFSFUN.spad" 251345 251353 257927 257932) (-199 "DFLOAT.spad" 247868 247876 251235 251340) (-198 "DFINTTLS.spad" 246077 246093 247858 247863) (-197 "DERHAM.spad" 243987 244019 246057 246072) (-196 "DEQUEUE.spad" 243528 243538 243817 243844) (-195 "DEGRED.spad" 243143 243157 243518 243523) (-194 "DEFINTRF.spad" 240668 240678 243133 243138) (-193 "DEFINTEF.spad" 239164 239180 240658 240663) (-192 "DECIMAL.spad" 237048 237056 237634 237727) (-191 "DDFACT.spad" 234847 234864 237038 237043) (-190 "DBLRESP.spad" 234445 234469 234837 234842) (-189 "DBASE.spad" 233017 233027 234435 234440) (-188 "D03FAFA.spad" 232845 232853 233007 233012) (-187 "D03EEFA.spad" 232665 232673 232835 232840) (-186 "D03AGNT.spad" 231745 231753 232655 232660) (-185 "D02EJFA.spad" 231207 231215 231735 231740) (-184 "D02CJFA.spad" 230685 230693 231197 231202) (-183 "D02BHFA.spad" 230175 230183 230675 230680) (-182 "D02BBFA.spad" 229665 229673 230165 230170) (-181 "D02AGNT.spad" 224469 224477 229655 229660) (-180 "D01WGTS.spad" 222788 222796 224459 224464) (-179 "D01TRNS.spad" 222765 222773 222778 222783) (-178 "D01GBFA.spad" 222287 222295 222755 222760) (-177 "D01FCFA.spad" 221809 221817 222277 222282) (-176 "D01ASFA.spad" 221277 221285 221799 221804) (-175 "D01AQFA.spad" 220723 220731 221267 221272) (-174 "D01APFA.spad" 220147 220155 220713 220718) (-173 "D01ANFA.spad" 219641 219649 220137 220142) (-172 "D01AMFA.spad" 219151 219159 219631 219636) (-171 "D01ALFA.spad" 218691 218699 219141 219146) (-170 "D01AKFA.spad" 218217 218225 218681 218686) (-169 "D01AJFA.spad" 217740 217748 218207 218212) (-168 "D01AGNT.spad" 213799 213807 217730 217735) (-167 "CYCLOTOM.spad" 213305 213313 213789 213794) (-166 "CYCLES.spad" 210137 210145 213295 213300) (-165 "CVMP.spad" 209554 209564 210127 210132) (-164 "CTRIGMNP.spad" 208044 208060 209544 209549) (-163 "CSTTOOLS.spad" 207287 207300 208034 208039) (-162 "CRFP.spad" 200991 201004 207277 207282) (-161 "CRAPACK.spad" 200034 200044 200981 200986) (-160 "CPMATCH.spad" 199534 199549 199959 199964) (-159 "CPIMA.spad" 199239 199258 199524 199529) (-158 "COORDSYS.spad" 194132 194142 199229 199234) (-157 "CONTFRAC.spad" 189744 189754 194034 194127) (-156 "COMRING.spad" 189418 189426 189682 189739) (-155 "COMPPROP.spad" 188932 188940 189408 189413) (-154 "COMPLPAT.spad" 188699 188714 188922 188927) (-153 "COMPLEX.spad" 182732 182742 182976 183237) (-152 "COMPLEX2.spad" 182445 182457 182722 182727) (-151 "COMPFACT.spad" 182047 182061 182435 182440) (-150 "COMPCAT.spad" 180103 180113 181769 182042) (-149 "COMPCAT.spad" 177866 177878 179534 179539) (-148 "COMMUPC.spad" 177612 177630 177856 177861) (-147 "COMMONOP.spad" 177145 177153 177602 177607) (-146 "COMM.spad" 176954 176962 177135 177140) (-145 "COMBOPC.spad" 175859 175867 176944 176949) (-144 "COMBINAT.spad" 174604 174614 175849 175854) (-143 "COMBF.spad" 171972 171988 174594 174599) (-142 "COLOR.spad" 170809 170817 171962 171967) (-141 "CMPLXRT.spad" 170518 170535 170799 170804) (-140 "CLIP.spad" 166610 166618 170508 170513) (-139 "CLIF.spad" 165249 165265 166566 166605) (-138 "CLAGG.spad" 161724 161734 165229 165244) (-137 "CLAGG.spad" 158080 158092 161587 161592) (-136 "CINTSLPE.spad" 157405 157418 158070 158075) (-135 "CHVAR.spad" 155483 155505 157395 157400) (-134 "CHARZ.spad" 155398 155406 155463 155478) (-133 "CHARPOL.spad" 154906 154916 155388 155393) (-132 "CHARNZ.spad" 154659 154667 154886 154901) (-131 "CHAR.spad" 152549 152557 154649 154654) (-130 "CFCAT.spad" 151865 151873 152539 152544) (-129 "CDEN.spad" 151023 151037 151855 151860) (-128 "CCLASS.spad" 149230 149238 150492 150531) (-127 "CARTEN.spad" 144333 144357 149220 149225) (-126 "CARTEN2.spad" 143719 143746 144323 144328) (-125 "CARD.spad" 141008 141016 143693 143714) (-124 "CACHSET.spad" 140630 140638 140998 141003) (-123 "CABMON.spad" 140183 140191 140620 140625) (-122 "BTREE.spad" 139475 139485 140013 140040) (-121 "BTOURN.spad" 138701 138711 139305 139332) (-120 "BTCAT.spad" 138077 138087 138657 138696) (-119 "BTCAT.spad" 137485 137497 138067 138072) (-118 "BTAGG.spad" 136501 136509 137441 137480) (-117 "BTAGG.spad" 135549 135559 136491 136496) (-116 "BSTREE.spad" 134507 134517 135379 135406) (-115 "BRILL.spad" 132702 132713 134497 134502) (-114 "BRAGG.spad" 131616 131626 132682 132697) (-113 "BRAGG.spad" 130504 130516 131572 131577) (-112 "BPADICRT.spad" 128488 128500 128743 128836) (-111 "BPADIC.spad" 128152 128164 128414 128483) (-110 "BOUNDZRO.spad" 127808 127825 128142 128147) (-109 "BOP.spad" 123272 123280 127798 127803) (-108 "BOP1.spad" 120658 120668 123228 123233) (-107 "BOOLEAN.spad" 119516 119524 120648 120653) (-106 "BMODULE.spad" 119228 119240 119484 119511) (-105 "BITS.spad" 118705 118713 118922 118949) (-104 "BINFILE.spad" 118048 118056 118695 118700) (-103 "BINARY.spad" 115941 115949 116518 116611) (-102 "BGAGG.spad" 115126 115136 115909 115936) (-101 "BGAGG.spad" 114331 114343 115116 115121) (-100 "BFUNCT.spad" 113895 113903 114311 114326) (-99 "BEZOUT.spad" 113030 113056 113845 113850) (-98 "BBTREE.spad" 110073 110082 112860 112887) (-97 "BASTYPE.spad" 109746 109753 110063 110068) (-96 "BASTYPE.spad" 109417 109426 109736 109741) (-95 "BALFACT.spad" 108857 108869 109407 109412) (-94 "AUTOMOR.spad" 108304 108313 108837 108852) (-93 "ATTREG.spad" 105023 105030 108056 108299) (-92 "ATTRBUT.spad" 101046 101053 105003 105018) (-91 "ATRIG.spad" 100516 100523 101036 101041) (-90 "ATRIG.spad" 99984 99993 100506 100511) (-89 "ASTACK.spad" 99540 99549 99814 99841) (-88 "ASSOCEQ.spad" 98340 98351 99496 99501) (-87 "ASP9.spad" 97421 97434 98330 98335) (-86 "ASP8.spad" 96464 96477 97411 97416) (-85 "ASP80.spad" 95786 95799 96454 96459) (-84 "ASP7.spad" 94946 94959 95776 95781) (-83 "ASP78.spad" 94397 94410 94936 94941) (-82 "ASP77.spad" 93766 93779 94387 94392) (-81 "ASP74.spad" 92858 92871 93756 93761) (-80 "ASP73.spad" 92129 92142 92848 92853) (-79 "ASP6.spad" 90761 90774 92119 92124) (-78 "ASP55.spad" 89270 89283 90751 90756) (-77 "ASP50.spad" 87087 87100 89260 89265) (-76 "ASP4.spad" 86382 86395 87077 87082) (-75 "ASP49.spad" 85381 85394 86372 86377) (-74 "ASP42.spad" 83788 83827 85371 85376) (-73 "ASP41.spad" 82367 82406 83778 83783) (-72 "ASP35.spad" 81355 81368 82357 82362) (-71 "ASP34.spad" 80656 80669 81345 81350) (-70 "ASP33.spad" 80216 80229 80646 80651) (-69 "ASP31.spad" 79356 79369 80206 80211) (-68 "ASP30.spad" 78248 78261 79346 79351) (-67 "ASP29.spad" 77714 77727 78238 78243) (-66 "ASP28.spad" 68987 69000 77704 77709) (-65 "ASP27.spad" 67884 67897 68977 68982) (-64 "ASP24.spad" 66971 66984 67874 67879) (-63 "ASP20.spad" 66187 66200 66961 66966) (-62 "ASP1.spad" 65568 65581 66177 66182) (-61 "ASP19.spad" 60254 60267 65558 65563) (-60 "ASP12.spad" 59668 59681 60244 60249) (-59 "ASP10.spad" 58939 58952 59658 59663) (-58 "ARRAY2.spad" 58522 58531 58769 58796) (-57 "ARRAY1.spad" 57580 57589 57928 57955) (-56 "ARRAY12.spad" 56249 56260 57570 57575) (-55 "ARR2CAT.spad" 51899 51920 56205 56244) (-54 "ARR2CAT.spad" 47581 47604 51889 51894) (-53 "APPRULE.spad" 46825 46847 47571 47576) (-52 "APPLYORE.spad" 46440 46453 46815 46820) (-51 "ANY.spad" 44782 44789 46430 46435) (-50 "ANY1.spad" 43853 43862 44772 44777) (-49 "ANTISYM.spad" 42292 42308 43833 43848) (-48 "ANON.spad" 42205 42212 42282 42287) (-47 "AN.spad" 40508 40515 42023 42116) (-46 "AMR.spad" 38687 38698 40406 40503) (-45 "AMR.spad" 36703 36716 38424 38429) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
+((-1185 NIL 2205518 2205523 2205528 2205533) (-3 NIL 2205498 2205503 2205508 2205513) (-2 NIL 2205478 2205483 2205488 2205493) (-1 NIL 2205458 2205463 2205468 2205473) (0 NIL 2205438 2205443 2205448 2205453) (-1180 "ZMOD.spad" 2205247 2205260 2205376 2205433) (-1179 "ZLINDEP.spad" 2204291 2204302 2205237 2205242) (-1178 "ZDSOLVE.spad" 2194140 2194162 2204281 2204286) (-1177 "YSTREAM.spad" 2193633 2193644 2194130 2194135) (-1176 "XRPOLY.spad" 2192853 2192873 2193489 2193558) (-1175 "XPR.spad" 2190582 2190595 2192571 2192670) (-1174 "XPOLY.spad" 2190137 2190148 2190438 2190507) (-1173 "XPOLYC.spad" 2189454 2189470 2190063 2190132) (-1172 "XPBWPOLY.spad" 2187891 2187911 2189234 2189303) (-1171 "XF.spad" 2186352 2186367 2187793 2187886) (-1170 "XF.spad" 2184793 2184810 2186236 2186241) (-1169 "XFALG.spad" 2181817 2181833 2184719 2184788) (-1168 "XEXPPKG.spad" 2181068 2181094 2181807 2181812) (-1167 "XDPOLY.spad" 2180682 2180698 2180924 2180993) (-1166 "XALG.spad" 2180280 2180291 2180638 2180677) (-1165 "WUTSET.spad" 2176175 2176192 2179982 2180009) (-1164 "WP.spad" 2175189 2175233 2176033 2176100) (-1163 "WFFINTBS.spad" 2172752 2172774 2175179 2175184) (-1162 "WEIER.spad" 2170966 2170977 2172742 2172747) (-1161 "VSPACE.spad" 2170639 2170650 2170934 2170961) (-1160 "VSPACE.spad" 2170332 2170345 2170629 2170634) (-1159 "VOID.spad" 2169922 2169931 2170322 2170327) (-1158 "VIEW.spad" 2167544 2167553 2169912 2169917) (-1157 "VIEWDEF.spad" 2162741 2162750 2167534 2167539) (-1156 "VIEW3D.spad" 2146576 2146585 2162731 2162736) (-1155 "VIEW2D.spad" 2134313 2134322 2146566 2146571) (-1154 "VECTOR.spad" 2132990 2133001 2133241 2133268) (-1153 "VECTOR2.spad" 2131617 2131630 2132980 2132985) (-1152 "VECTCAT.spad" 2129505 2129516 2131573 2131612) (-1151 "VECTCAT.spad" 2127214 2127227 2129284 2129289) (-1150 "VARIABLE.spad" 2126994 2127009 2127204 2127209) (-1149 "UTSODETL.spad" 2126287 2126311 2126950 2126955) (-1148 "UTSODE.spad" 2124475 2124495 2126277 2126282) (-1147 "UTS.spad" 2119264 2119292 2122942 2123039) (-1146 "UTSCAT.spad" 2116715 2116731 2119162 2119259) (-1145 "UTSCAT.spad" 2113810 2113828 2116259 2116264) (-1144 "UTS2.spad" 2113403 2113438 2113800 2113805) (-1143 "URAGG.spad" 2108025 2108036 2113383 2113398) (-1142 "URAGG.spad" 2102621 2102634 2107981 2107986) (-1141 "UPXSSING.spad" 2100267 2100293 2101705 2101838) (-1140 "UPXS.spad" 2097294 2097322 2098399 2098548) (-1139 "UPXSCONS.spad" 2095051 2095071 2095426 2095575) (-1138 "UPXSCCA.spad" 2093509 2093529 2094897 2095046) (-1137 "UPXSCCA.spad" 2092109 2092131 2093499 2093504) (-1136 "UPXSCAT.spad" 2090690 2090706 2091955 2092104) (-1135 "UPXS2.spad" 2090231 2090284 2090680 2090685) (-1134 "UPSQFREE.spad" 2088643 2088657 2090221 2090226) (-1133 "UPSCAT.spad" 2086236 2086260 2088541 2088638) (-1132 "UPSCAT.spad" 2083535 2083561 2085842 2085847) (-1131 "UPOLYC.spad" 2078513 2078524 2083377 2083530) (-1130 "UPOLYC.spad" 2073383 2073396 2078249 2078254) (-1129 "UPOLYC2.spad" 2072852 2072871 2073373 2073378) (-1128 "UP.spad" 2069902 2069917 2070410 2070563) (-1127 "UPMP.spad" 2068792 2068805 2069892 2069897) (-1126 "UPDIVP.spad" 2068355 2068369 2068782 2068787) (-1125 "UPDECOMP.spad" 2066592 2066606 2068345 2068350) (-1124 "UPCDEN.spad" 2065799 2065815 2066582 2066587) (-1123 "UP2.spad" 2065161 2065182 2065789 2065794) (-1122 "UNISEG.spad" 2064514 2064525 2065080 2065085) (-1121 "UNISEG2.spad" 2064007 2064020 2064470 2064475) (-1120 "UNIFACT.spad" 2063108 2063120 2063997 2064002) (-1119 "ULS.spad" 2053667 2053695 2054760 2055189) (-1118 "ULSCONS.spad" 2047710 2047730 2048082 2048231) (-1117 "ULSCCAT.spad" 2045307 2045327 2047530 2047705) (-1116 "ULSCCAT.spad" 2043038 2043060 2045263 2045268) (-1115 "ULSCAT.spad" 2041254 2041270 2042884 2043033) (-1114 "ULS2.spad" 2040766 2040819 2041244 2041249) (-1113 "UFD.spad" 2039831 2039840 2040692 2040761) (-1112 "UFD.spad" 2038958 2038969 2039821 2039826) (-1111 "UDVO.spad" 2037805 2037814 2038948 2038953) (-1110 "UDPO.spad" 2035232 2035243 2037761 2037766) (-1109 "TYPE.spad" 2035154 2035163 2035212 2035227) (-1108 "TWOFACT.spad" 2033804 2033819 2035144 2035149) (-1107 "TUPLE.spad" 2033190 2033201 2033703 2033708) (-1106 "TUBETOOL.spad" 2030027 2030036 2033180 2033185) (-1105 "TUBE.spad" 2028668 2028685 2030017 2030022) (-1104 "TS.spad" 2027257 2027273 2028233 2028330) (-1103 "TSETCAT.spad" 2014372 2014389 2027213 2027252) (-1102 "TSETCAT.spad" 2001485 2001504 2014328 2014333) (-1101 "TRMANIP.spad" 1995851 1995868 2001191 2001196) (-1100 "TRIMAT.spad" 1994810 1994835 1995841 1995846) (-1099 "TRIGMNIP.spad" 1993327 1993344 1994800 1994805) (-1098 "TRIGCAT.spad" 1992839 1992848 1993317 1993322) (-1097 "TRIGCAT.spad" 1992349 1992360 1992829 1992834) (-1096 "TREE.spad" 1991143 1991154 1992179 1992206) (-1095 "TRANFUN.spad" 1990974 1990983 1991133 1991138) (-1094 "TRANFUN.spad" 1990803 1990814 1990964 1990969) (-1093 "TOPSP.spad" 1990477 1990486 1990793 1990798) (-1092 "TOOLSIGN.spad" 1990140 1990151 1990467 1990472) (-1091 "TEXTFILE.spad" 1988697 1988706 1990130 1990135) (-1090 "TEX.spad" 1985714 1985723 1988687 1988692) (-1089 "TEX1.spad" 1985270 1985281 1985704 1985709) (-1088 "TEMUTL.spad" 1984825 1984834 1985260 1985265) (-1087 "TBCMPPK.spad" 1982918 1982941 1984815 1984820) (-1086 "TBAGG.spad" 1981942 1981965 1982886 1982913) (-1085 "TBAGG.spad" 1980986 1981011 1981932 1981937) (-1084 "TANEXP.spad" 1980362 1980373 1980976 1980981) (-1083 "TABLE.spad" 1979335 1979358 1979605 1979632) (-1082 "TABLEAU.spad" 1978816 1978827 1979325 1979330) (-1081 "TABLBUMP.spad" 1975599 1975610 1978806 1978811) (-1080 "SYSSOLP.spad" 1973072 1973083 1975589 1975594) (-1079 "syntax.spad" 1971412 1971421 1973062 1973067) (-1078 "SYMTAB.spad" 1969468 1969477 1971402 1971407) (-1077 "SYMS.spad" 1965453 1965462 1969458 1969463) (-1076 "SYMPOLY.spad" 1964463 1964474 1964545 1964672) (-1075 "SYMFUNC.spad" 1963938 1963949 1964453 1964458) (-1074 "SYMBOL.spad" 1961274 1961283 1963928 1963933) (-1073 "SWITCH.spad" 1958031 1958040 1961264 1961269) (-1072 "SUTS.spad" 1954930 1954958 1956498 1956595) (-1071 "SUPXS.spad" 1951944 1951972 1953062 1953211) (-1070 "SUP.spad" 1948721 1948732 1949502 1949655) (-1069 "SUPFRACF.spad" 1947826 1947844 1948711 1948716) (-1068 "SUP2.spad" 1947216 1947229 1947816 1947821) (-1067 "SUMRF.spad" 1946182 1946193 1947206 1947211) (-1066 "SUMFS.spad" 1945815 1945832 1946172 1946177) (-1065 "SULS.spad" 1936361 1936389 1937467 1937896) (-1064 "SUCH.spad" 1936041 1936056 1936351 1936356) (-1063 "SUBSPACE.spad" 1928048 1928063 1936031 1936036) (-1062 "SUBRESP.spad" 1927208 1927222 1928004 1928009) (-1061 "STTF.spad" 1923307 1923323 1927198 1927203) (-1060 "STTFNC.spad" 1919775 1919791 1923297 1923302) (-1059 "STTAYLOR.spad" 1912173 1912184 1919656 1919661) (-1058 "STRTBL.spad" 1911252 1911269 1911401 1911428) (-1057 "STRING.spad" 1910719 1910728 1910733 1910760) (-1056 "STRICAT.spad" 1910495 1910504 1910675 1910714) (-1055 "STREAM.spad" 1907486 1907497 1910243 1910258) (-1054 "STREAM3.spad" 1907031 1907046 1907476 1907481) (-1053 "STREAM2.spad" 1906099 1906112 1907021 1907026) (-1052 "STREAM1.spad" 1905803 1905814 1906089 1906094) (-1051 "STINPROD.spad" 1904709 1904725 1905793 1905798) (-1050 "STEP.spad" 1903910 1903919 1904699 1904704) (-1049 "STBL.spad" 1902998 1903026 1903165 1903180) (-1048 "STAGG.spad" 1902063 1902074 1902978 1902993) (-1047 "STAGG.spad" 1901136 1901149 1902053 1902058) (-1046 "STACK.spad" 1900710 1900721 1900966 1900993) (-1045 "SREGSET.spad" 1898470 1898487 1900412 1900439) (-1044 "SRDCMPK.spad" 1897015 1897035 1898460 1898465) (-1043 "SRAGG.spad" 1892100 1892109 1896971 1897010) (-1042 "SRAGG.spad" 1887217 1887228 1892090 1892095) (-1041 "SQMATRIX.spad" 1884899 1884917 1885807 1885894) (-1040 "SPLTREE.spad" 1879766 1879779 1884650 1884677) (-1039 "SPLNODE.spad" 1876354 1876367 1879756 1879761) (-1038 "SPFCAT.spad" 1875131 1875140 1876344 1876349) (-1037 "SPECOUT.spad" 1873681 1873690 1875121 1875126) (-1036 "spad-parser.spad" 1873146 1873155 1873671 1873676) (-1035 "SPACEC.spad" 1857159 1857170 1873136 1873141) (-1034 "SPACE3.spad" 1856935 1856946 1857149 1857154) (-1033 "SORTPAK.spad" 1856480 1856493 1856891 1856896) (-1032 "SOLVETRA.spad" 1854237 1854248 1856470 1856475) (-1031 "SOLVESER.spad" 1852757 1852768 1854227 1854232) (-1030 "SOLVERAD.spad" 1848767 1848778 1852747 1852752) (-1029 "SOLVEFOR.spad" 1847187 1847205 1848757 1848762) (-1028 "SNTSCAT.spad" 1846775 1846792 1847143 1847182) (-1027 "SMTS.spad" 1845035 1845061 1846340 1846437) (-1026 "SMP.spad" 1842477 1842497 1842867 1842994) (-1025 "SMITH.spad" 1841320 1841345 1842467 1842472) (-1024 "SMATCAT.spad" 1839418 1839448 1841252 1841315) (-1023 "SMATCAT.spad" 1837460 1837492 1839296 1839301) (-1022 "SKAGG.spad" 1836409 1836420 1837416 1837455) (-1021 "SINT.spad" 1834717 1834726 1836275 1836404) (-1020 "SIMPAN.spad" 1834445 1834454 1834707 1834712) (-1019 "SIGNRF.spad" 1833553 1833564 1834435 1834440) (-1018 "SIGNEF.spad" 1832822 1832839 1833543 1833548) (-1017 "SHP.spad" 1830740 1830755 1832778 1832783) (-1016 "SHDP.spad" 1822846 1822873 1823355 1823484) (-1015 "SGROUP.spad" 1822312 1822321 1822836 1822841) (-1014 "SGROUP.spad" 1821776 1821787 1822302 1822307) (-1013 "SGCF.spad" 1814657 1814666 1821766 1821771) (-1012 "SFRTCAT.spad" 1813573 1813590 1814613 1814652) (-1011 "SFRGCD.spad" 1812636 1812656 1813563 1813568) (-1010 "SFQCMPK.spad" 1807273 1807293 1812626 1812631) (-1009 "SFORT.spad" 1806708 1806722 1807263 1807268) (-1008 "SEXOF.spad" 1806551 1806591 1806698 1806703) (-1007 "SEX.spad" 1806443 1806452 1806541 1806546) (-1006 "SEXCAT.spad" 1803547 1803587 1806433 1806438) (-1005 "SET.spad" 1801903 1801914 1803024 1803063) (-1004 "SETMN.spad" 1800337 1800354 1801893 1801898) (-1003 "SETCAT.spad" 1799822 1799831 1800327 1800332) (-1002 "SETCAT.spad" 1799305 1799316 1799812 1799817) (-1001 "SETAGG.spad" 1795828 1795839 1799273 1799300) (-1000 "SETAGG.spad" 1792371 1792384 1795818 1795823) (-999 "SEGXCAT.spad" 1791484 1791496 1792351 1792366) (-998 "SEG.spad" 1791298 1791308 1791403 1791408) (-997 "SEGCAT.spad" 1790118 1790128 1791278 1791293) (-996 "SEGBIND.spad" 1789191 1789201 1790073 1790078) (-995 "SEGBIND2.spad" 1788888 1788900 1789181 1789186) (-994 "SEG2.spad" 1788314 1788326 1788844 1788849) (-993 "SDVAR.spad" 1787591 1787601 1788304 1788309) (-992 "SDPOL.spad" 1784990 1785000 1785280 1785407) (-991 "SCPKG.spad" 1783070 1783080 1784980 1784985) (-990 "SCACHE.spad" 1781753 1781763 1783060 1783065) (-989 "SAOS.spad" 1781626 1781634 1781743 1781748) (-988 "SAERFFC.spad" 1781340 1781359 1781616 1781621) (-987 "SAE.spad" 1779519 1779534 1780129 1780264) (-986 "SAEFACT.spad" 1779221 1779240 1779509 1779514) (-985 "RURPK.spad" 1776863 1776878 1779211 1779216) (-984 "RULESET.spad" 1776305 1776328 1776853 1776858) (-983 "RULE.spad" 1774510 1774533 1776295 1776300) (-982 "RULECOLD.spad" 1774363 1774375 1774500 1774505) (-981 "RSETGCD.spad" 1770742 1770761 1774353 1774358) (-980 "RSETCAT.spad" 1760515 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(-678 "NAGC02.spad" 1118423 1118431 1119158 1119163) (-677 "NAALG.spad" 1117958 1117968 1118391 1118418) (-676 "NAALG.spad" 1117513 1117525 1117948 1117953) (-675 "MULTSQFR.spad" 1114471 1114488 1117503 1117508) (-674 "MULTFACT.spad" 1113854 1113871 1114461 1114466) (-673 "MTSCAT.spad" 1111888 1111909 1113752 1113849) (-672 "MTHING.spad" 1111545 1111555 1111878 1111883) (-671 "MSYSCMD.spad" 1110979 1110987 1111535 1111540) (-670 "MSET.spad" 1108977 1108987 1110741 1110780) (-669 "MSETAGG.spad" 1108810 1108820 1108933 1108972) (-668 "MRING.spad" 1105781 1105793 1108518 1108585) (-667 "MRF2.spad" 1105349 1105363 1105771 1105776) (-666 "MRATFAC.spad" 1104895 1104912 1105339 1105344) (-665 "MPRFF.spad" 1102925 1102944 1104885 1104890) (-664 "MPOLY.spad" 1100363 1100378 1100722 1100849) (-663 "MPCPF.spad" 1099627 1099646 1100353 1100358) (-662 "MPC3.spad" 1099442 1099482 1099617 1099622) (-661 "MPC2.spad" 1099084 1099117 1099432 1099437) (-660 "MONOTOOL.spad" 1097419 1097436 1099074 1099079) (-659 "MONOID.spad" 1096593 1096601 1097409 1097414) (-658 "MONOID.spad" 1095765 1095775 1096583 1096588) (-657 "MONOGEN.spad" 1094511 1094524 1095625 1095760) (-656 "MONOGEN.spad" 1093279 1093294 1094395 1094400) (-655 "MONADWU.spad" 1091293 1091301 1093269 1093274) (-654 "MONADWU.spad" 1089305 1089315 1091283 1091288) (-653 "MONAD.spad" 1088449 1088457 1089295 1089300) (-652 "MONAD.spad" 1087591 1087601 1088439 1088444) (-651 "MOEBIUS.spad" 1086277 1086291 1087571 1087586) (-650 "MODULE.spad" 1086147 1086157 1086245 1086272) (-649 "MODULE.spad" 1086037 1086049 1086137 1086142) (-648 "MODRING.spad" 1085368 1085407 1086017 1086032) (-647 "MODOP.spad" 1084027 1084039 1085190 1085257) (-646 "MODMONOM.spad" 1083559 1083577 1084017 1084022) (-645 "MODMON.spad" 1080269 1080285 1081045 1081198) (-644 "MODFIELD.spad" 1079627 1079666 1080171 1080264) (-643 "MMAP.spad" 1079367 1079401 1079617 1079622) (-642 "MLO.spad" 1077794 1077804 1079323 1079362) (-641 "MLIFT.spad" 1076366 1076383 1077784 1077789) (-640 "MKUCFUNC.spad" 1075899 1075917 1076356 1076361) (-639 "MKRECORD.spad" 1075501 1075514 1075889 1075894) (-638 "MKFUNC.spad" 1074882 1074892 1075491 1075496) (-637 "MKFLCFN.spad" 1073838 1073848 1074872 1074877) (-636 "MKCHSET.spad" 1073614 1073624 1073828 1073833) (-635 "MKBCFUNC.spad" 1073099 1073117 1073604 1073609) (-634 "MINT.spad" 1072538 1072546 1073001 1073094) (-633 "MHROWRED.spad" 1071039 1071049 1072528 1072533) (-632 "MFLOAT.spad" 1069484 1069492 1070929 1071034) (-631 "MFINFACT.spad" 1068884 1068906 1069474 1069479) (-630 "MESH.spad" 1066616 1066624 1068874 1068879) (-629 "MDDFACT.spad" 1064809 1064819 1066606 1066611) (-628 "MDAGG.spad" 1064084 1064094 1064777 1064804) (-627 "MCMPLX.spad" 1060064 1060072 1060678 1060879) (-626 "MCDEN.spad" 1059272 1059284 1060054 1060059) (-625 "MCALCFN.spad" 1056374 1056400 1059262 1059267) (-624 "MATSTOR.spad" 1053650 1053660 1056364 1056369) (-623 "MATRIX.spad" 1052577 1052587 1053061 1053088) (-622 "MATLIN.spad" 1049903 1049927 1052461 1052466) (-621 "MATCAT.spad" 1041476 1041498 1049859 1049898) (-620 "MATCAT.spad" 1032933 1032957 1041318 1041323) (-619 "MATCAT2.spad" 1032201 1032249 1032923 1032928) (-618 "MAPPKG3.spad" 1031100 1031114 1032191 1032196) (-617 "MAPPKG2.spad" 1030434 1030446 1031090 1031095) (-616 "MAPPKG1.spad" 1029252 1029262 1030424 1030429) (-615 "MAPHACK3.spad" 1029060 1029074 1029242 1029247) (-614 "MAPHACK2.spad" 1028825 1028837 1029050 1029055) (-613 "MAPHACK1.spad" 1028455 1028465 1028815 1028820) (-612 "MAGMA.spad" 1026245 1026262 1028445 1028450) (-611 "M3D.spad" 1024166 1024176 1025848 1025853) (-610 "LZSTAGG.spad" 1021384 1021394 1024146 1024161) (-609 "LZSTAGG.spad" 1018610 1018622 1021374 1021379) (-608 "LWORD.spad" 1015315 1015332 1018600 1018605) (-607 "LSQM.spad" 1013599 1013613 1013997 1014048) (-606 "LSPP.spad" 1013132 1013149 1013589 1013594) (-605 "LSMP.spad" 1011972 1012000 1013122 1013127) (-604 "LSMP1.spad" 1009776 1009790 1011962 1011967) (-603 "LSAGG.spad" 1009433 1009443 1009732 1009771) (-602 "LSAGG.spad" 1009122 1009134 1009423 1009428) (-601 "LPOLY.spad" 1008076 1008095 1008978 1009047) (-600 "LPEFRAC.spad" 1007333 1007343 1008066 1008071) (-599 "LO.spad" 1006734 1006748 1007267 1007294) (-598 "LOGIC.spad" 1006336 1006344 1006724 1006729) (-597 "LOGIC.spad" 1005936 1005946 1006326 1006331) (-596 "LODOOPS.spad" 1004854 1004866 1005926 1005931) (-595 "LODO.spad" 1004240 1004256 1004536 1004575) (-594 "LODOF.spad" 1003284 1003301 1004197 1004202) (-593 "LODOCAT.spad" 1001942 1001952 1003240 1003279) (-592 "LODOCAT.spad" 1000598 1000610 1001898 1001903) (-591 "LODO2.spad" 999873 999885 1000280 1000319) (-590 "LODO1.spad" 999275 999285 999555 999594) (-589 "LODEEF.spad" 998047 998065 999265 999270) (-588 "LNAGG.spad" 993839 993849 998027 998042) (-587 "LNAGG.spad" 989605 989617 993795 993800) (-586 "LMOPS.spad" 986341 986358 989595 989600) (-585 "LMODULE.spad" 985983 985993 986331 986336) (-584 "LMDICT.spad" 985489 985499 985757 985784) (-583 "LIST.spad" 983207 983217 984636 984663) (-582 "LIST3.spad" 982498 982512 983197 983202) (-581 "LIST2.spad" 981138 981150 982488 982493) (-580 "LIST2MAP.spad" 978015 978027 981128 981133) (-579 "LINEXP.spad" 977447 977457 977995 978010) (-578 "LINDEP.spad" 976224 976236 977359 977364) (-577 "LIMITRF.spad" 974138 974148 976214 976219) (-576 "LIMITPS.spad" 973021 973034 974128 974133) (-575 "LIE.spad" 971035 971047 972311 972456) (-574 "LIECAT.spad" 970511 970521 970961 971030) (-573 "LIECAT.spad" 970015 970027 970467 970472) (-572 "LIB.spad" 968645 968653 969256 969271) (-571 "LGROBP.spad" 965998 966017 968635 968640) (-570 "LF.spad" 964917 964933 965988 965993) (-569 "LFCAT.spad" 963936 963944 964907 964912) (-568 "LEXTRIPK.spad" 959439 959454 963926 963931) (-567 "LEXP.spad" 957442 957469 959419 959434) (-566 "LEADCDET.spad" 955826 955843 957432 957437) (-565 "LAZM3PK.spad" 954530 954552 955816 955821) (-564 "LAUPOL.spad" 953221 953234 954125 954194) (-563 "LAPLACE.spad" 952794 952810 953211 953216) (-562 "LA.spad" 952234 952248 952716 952755) (-561 "LALG.spad" 952010 952020 952214 952229) (-560 "LALG.spad" 951794 951806 952000 952005) (-559 "KOVACIC.spad" 950507 950524 951784 951789) (-558 "KONVERT.spad" 950229 950239 950497 950502) (-557 "KOERCE.spad" 949966 949976 950219 950224) (-556 "KERNEL.spad" 948501 948511 949750 949755) (-555 "KERNEL2.spad" 948204 948216 948491 948496) (-554 "KDAGG.spad" 947295 947317 948172 948199) (-553 "KDAGG.spad" 946406 946430 947285 947290) (-552 "KAFILE.spad" 945518 945534 945753 945780) (-551 "JORDAN.spad" 943345 943357 944808 944953) (-550 "IXAGG.spad" 941458 941482 943325 943340) (-549 "IXAGG.spad" 939436 939462 941305 941310) (-548 "IVECTOR.spad" 938432 938447 938587 938614) (-547 "ITUPLE.spad" 937577 937587 938422 938427) (-546 "ITRIGMNP.spad" 936388 936407 937567 937572) (-545 "ITFUN3.spad" 935882 935896 936378 936383) (-544 "ITFUN2.spad" 935612 935624 935872 935877) (-543 "ITAYLOR.spad" 933404 933419 935448 935573) (-542 "ISUPS.spad" 925815 925830 932378 932475) (-541 "ISUMP.spad" 925312 925328 925805 925810) (-540 "ISTRING.spad" 924315 924328 924481 924508) (-539 "IRURPK.spad" 923028 923047 924305 924310) (-538 "IRSN.spad" 920988 920996 923018 923023) (-537 "IRRF2F.spad" 919463 919473 920944 920949) (-536 "IRREDFFX.spad" 919064 919075 919453 919458) (-535 "IROOT.spad" 917395 917405 919054 919059) (-534 "IR.spad" 915185 915199 917251 917278) (-533 "IR2.spad" 914205 914221 915175 915180) (-532 "IR2F.spad" 913405 913421 914195 914200) (-531 "IPRNTPK.spad" 913165 913173 913395 913400) (-530 "IPF.spad" 912730 912742 912970 913063) (-529 "IPADIC.spad" 912491 912517 912656 912725) (-528 "INVLAPLA.spad" 912136 912152 912481 912486) (-527 "INTTR.spad" 905382 905399 912126 912131) (-526 "INTTOOLS.spad" 903094 903110 904957 904962) (-525 "INTSLPE.spad" 902400 902408 903084 903089) (-524 "INTRVL.spad" 901966 901976 902314 902395) (-523 "INTRF.spad" 900330 900344 901956 901961) (-522 "INTRET.spad" 899762 899772 900320 900325) (-521 "INTRAT.spad" 898437 898454 899752 899757) (-520 "INTPM.spad" 896800 896816 898080 898085) (-519 "INTPAF.spad" 894568 894586 896732 896737) (-518 "INTPACK.spad" 884878 884886 894558 894563) (-517 "INT.spad" 884239 884247 884732 884873) (-516 "INTHERTR.spad" 883505 883522 884229 884234) (-515 "INTHERAL.spad" 883171 883195 883495 883500) (-514 "INTHEORY.spad" 879584 879592 883161 883166) (-513 "INTG0.spad" 873047 873065 879516 879521) (-512 "INTFTBL.spad" 867076 867084 873037 873042) (-511 "INTFACT.spad" 866135 866145 867066 867071) (-510 "INTEF.spad" 864450 864466 866125 866130) (-509 "INTDOM.spad" 863065 863073 864376 864445) (-508 "INTDOM.spad" 861742 861752 863055 863060) (-507 "INTCAT.spad" 859995 860005 861656 861737) (-506 "INTBIT.spad" 859498 859506 859985 859990) (-505 "INTALG.spad" 858680 858707 859488 859493) (-504 "INTAF.spad" 858172 858188 858670 858675) (-503 "INTABL.spad" 857252 857283 857415 857442) (-502 "INS.spad" 854648 854656 857154 857247) (-501 "INS.spad" 852130 852140 854638 854643) (-500 "INPSIGN.spad" 851564 851577 852120 852125) (-499 "INPRODPF.spad" 850630 850649 851554 851559) (-498 "INPRODFF.spad" 849688 849712 850620 850625) (-497 "INNMFACT.spad" 848659 848676 849678 849683) (-496 "INMODGCD.spad" 848143 848173 848649 848654) (-495 "INFSP.spad" 846428 846450 848133 848138) (-494 "INFPROD0.spad" 845478 845497 846418 846423) (-493 "INFORM.spad" 842746 842754 845468 845473) (-492 "INFORM1.spad" 842371 842381 842736 842741) (-491 "INFINITY.spad" 841923 841931 842361 842366) (-490 "INEP.spad" 840455 840477 841913 841918) (-489 "INDE.spad" 840361 840378 840445 840450) (-488 "INCRMAPS.spad" 839782 839792 840351 840356) (-487 "INBFF.spad" 835552 835563 839772 839777) (-486 "IMATRIX.spad" 834720 834746 835232 835259) (-485 "IMATQF.spad" 833814 833858 834676 834681) (-484 "IMATLIN.spad" 832419 832443 833770 833775) (-483 "ILIST.spad" 831075 831090 831602 831629) (-482 "IIARRAY2.spad" 830686 830724 830905 830932) (-481 "IFF.spad" 830096 830112 830367 830460) (-480 "IFARRAY.spad" 827806 827821 829502 829529) (-479 "IFAMON.spad" 827668 827685 827762 827767) (-478 "IEVALAB.spad" 827057 827069 827658 827663) (-477 "IEVALAB.spad" 826444 826458 827047 827052) (-476 "IDPO.spad" 826242 826254 826434 826439) (-475 "IDPOAMS.spad" 825998 826010 826232 826237) (-474 "IDPOAM.spad" 825718 825730 825988 825993) (-473 "IDPC.spad" 824652 824664 825708 825713) (-472 "IDPAM.spad" 824397 824409 824642 824647) (-471 "IDPAG.spad" 824144 824156 824387 824392) (-470 "IDECOMP.spad" 821381 821399 824134 824139) (-469 "IDEAL.spad" 816304 816343 821316 821321) (-468 "ICDEN.spad" 815455 815471 816294 816299) (-467 "ICARD.spad" 814644 814652 815445 815450) (-466 "IBPTOOLS.spad" 813237 813254 814634 814639) (-465 "IBITS.spad" 812494 812507 812931 812958) (-464 "IBATOOL.spad" 809369 809388 812484 812489) (-463 "IBACHIN.spad" 807856 807871 809359 809364) (-462 "IARRAY2.spad" 807067 807093 807686 807713) (-461 "IARRAY1.spad" 806335 806350 806473 806500) (-460 "IAN.spad" 804550 804558 806153 806246) (-459 "IALGFACT.spad" 804151 804184 804540 804545) (-458 "HYPCAT.spad" 803575 803583 804141 804146) (-457 "HYPCAT.spad" 802997 803007 803565 803570) (-456 "HOAGG.spad" 800255 800265 802977 802992) (-455 "HOAGG.spad" 797298 797310 800022 800027) (-454 "HEXADEC.spad" 795170 795178 795768 795861) (-453 "HEUGCD.spad" 794185 794196 795160 795165) (-452 "HELLFDIV.spad" 793775 793799 794175 794180) (-451 "HEAP.spad" 793390 793400 793605 793632) (-450 "HDP.spad" 785628 785644 786005 786134) (-449 "HDMP.spad" 782807 782822 783425 783552) (-448 "HB.spad" 781044 781052 782797 782802) (-447 "HASHTBL.spad" 780076 780107 780287 780314) (-446 "HACKPI.spad" 779559 779567 779978 780071) (-445 "GTSET.spad" 778554 778570 779261 779288) (-444 "GSTBL.spad" 777635 777670 777809 777824) (-443 "GSERIES.spad" 774802 774829 775767 775916) (-442 "GROUP.spad" 773976 773984 774782 774797) (-441 "GROUP.spad" 773158 773168 773966 773971) (-440 "GROEBSOL.spad" 771646 771667 773148 773153) (-439 "GRMOD.spad" 770217 770229 771636 771641) (-438 "GRMOD.spad" 768786 768800 770207 770212) (-437 "GRIMAGE.spad" 761391 761399 768776 768781) (-436 "GRDEF.spad" 759770 759778 761381 761386) (-435 "GRAY.spad" 758229 758237 759760 759765) (-434 "GRALG.spad" 757276 757288 758219 758224) (-433 "GRALG.spad" 756321 756335 757266 757271) (-432 "GPOLSET.spad" 755831 755854 756059 756086) (-431 "GOSPER.spad" 755096 755114 755821 755826) (-430 "GMODPOL.spad" 754234 754261 755064 755091) (-429 "GHENSEL.spad" 753303 753317 754224 754229) (-428 "GENUPS.spad" 749404 749417 753293 753298) (-427 "GENUFACT.spad" 748981 748991 749394 749399) (-426 "GENPGCD.spad" 748565 748582 748971 748976) (-425 "GENMFACT.spad" 748017 748036 748555 748560) (-424 "GENEEZ.spad" 745956 745969 748007 748012) (-423 "GDMP.spad" 742977 742994 743753 743880) (-422 "GCNAALG.spad" 736872 736899 742771 742838) (-421 "GCDDOM.spad" 736044 736052 736798 736867) (-420 "GCDDOM.spad" 735278 735288 736034 736039) (-419 "GB.spad" 732796 732834 735234 735239) (-418 "GBINTERN.spad" 728816 728854 732786 732791) (-417 "GBF.spad" 724573 724611 728806 728811) (-416 "GBEUCLID.spad" 722447 722485 724563 724568) (-415 "GAUSSFAC.spad" 721744 721752 722437 722442) (-414 "GALUTIL.spad" 720066 720076 721700 721705) (-413 "GALPOLYU.spad" 718512 718525 720056 720061) (-412 "GALFACTU.spad" 716677 716696 718502 718507) (-411 "GALFACT.spad" 706810 706821 716667 716672) (-410 "FVFUN.spad" 703823 703831 706790 706805) (-409 "FVC.spad" 702865 702873 703803 703818) (-408 "FUNCTION.spad" 702714 702726 702855 702860) (-407 "FT.spad" 700926 700934 702704 702709) (-406 "FTEM.spad" 700089 700097 700916 700921) (-405 "FSUPFACT.spad" 698990 699009 700026 700031) (-404 "FST.spad" 697076 697084 698980 698985) (-403 "FSRED.spad" 696554 696570 697066 697071) (-402 "FSPRMELT.spad" 695378 695394 696511 696516) (-401 "FSPECF.spad" 693455 693471 695368 695373) (-400 "FS.spad" 687506 687516 693219 693450) (-399 "FS.spad" 681348 681360 687063 687068) (-398 "FSINT.spad" 681006 681022 681338 681343) (-397 "FSERIES.spad" 680193 680205 680826 680925) (-396 "FSCINT.spad" 679506 679522 680183 680188) (-395 "FSAGG.spad" 678611 678621 679450 679501) (-394 "FSAGG.spad" 677690 677702 678531 678536) (-393 "FSAGG2.spad" 676389 676405 677680 677685) (-392 "FS2UPS.spad" 670778 670812 676379 676384) (-391 "FS2.spad" 670423 670439 670768 670773) (-390 "FS2EXPXP.spad" 669546 669569 670413 670418) (-389 "FRUTIL.spad" 668488 668498 669536 669541) (-388 "FR.spad" 662185 662195 667515 667584) (-387 "FRNAALG.spad" 657272 657282 662127 662180) (-386 "FRNAALG.spad" 652371 652383 657228 657233) (-385 "FRNAAF2.spad" 651825 651843 652361 652366) (-384 "FRMOD.spad" 651220 651250 651757 651762) (-383 "FRIDEAL.spad" 650415 650436 651200 651215) (-382 "FRIDEAL2.spad" 650017 650049 650405 650410) (-381 "FRETRCT.spad" 649528 649538 650007 650012) (-380 "FRETRCT.spad" 648907 648919 649388 649393) (-379 "FRAMALG.spad" 647235 647248 648863 648902) (-378 "FRAMALG.spad" 645595 645610 647225 647230) (-377 "FRAC.spad" 642698 642708 643101 643274) (-376 "FRAC2.spad" 642301 642313 642688 642693) (-375 "FR2.spad" 641635 641647 642291 642296) (-374 "FPS.spad" 638444 638452 641525 641630) (-373 "FPS.spad" 635281 635291 638364 638369) (-372 "FPC.spad" 634323 634331 635183 635276) (-371 "FPC.spad" 633451 633461 634313 634318) (-370 "FPATMAB.spad" 633203 633213 633431 633446) (-369 "FPARFRAC.spad" 631676 631693 633193 633198) (-368 "FORTRAN.spad" 630176 630225 631666 631671) (-367 "FORT.spad" 629105 629113 630166 630171) (-366 "FORTFN.spad" 626265 626273 629085 629100) (-365 "FORTCAT.spad" 625939 625947 626245 626260) (-364 "FORMULA.spad" 623277 623285 625929 625934) (-363 "FORMULA1.spad" 622756 622766 623267 623272) (-362 "FORDER.spad" 622447 622471 622746 622751) (-361 "FOP.spad" 621648 621656 622437 622442) (-360 "FNLA.spad" 621072 621094 621616 621643) (-359 "FNCAT.spad" 619400 619408 621062 621067) (-358 "FNAME.spad" 619292 619300 619390 619395) (-357 "FMTC.spad" 619090 619098 619218 619287) (-356 "FMONOID.spad" 616145 616155 619046 619051) (-355 "FM.spad" 615840 615852 616079 616106) (-354 "FMFUN.spad" 612860 612868 615820 615835) (-353 "FMC.spad" 611902 611910 612840 612855) (-352 "FMCAT.spad" 609556 609574 611870 611897) (-351 "FM1.spad" 608913 608925 609490 609517) (-350 "FLOATRP.spad" 606634 606648 608903 608908) (-349 "FLOAT.spad" 599798 599806 606500 606629) (-348 "FLOATCP.spad" 597215 597229 599788 599793) (-347 "FLINEXP.spad" 596927 596937 597195 597210) (-346 "FLINEXP.spad" 596593 596605 596863 596868) (-345 "FLASORT.spad" 595913 595925 596583 596588) (-344 "FLALG.spad" 593559 593578 595839 595908) (-343 "FLAGG.spad" 590565 590575 593527 593554) (-342 "FLAGG.spad" 587484 587496 590448 590453) (-341 "FLAGG2.spad" 586165 586181 587474 587479) (-340 "FINRALG.spad" 584194 584207 586121 586160) (-339 "FINRALG.spad" 582149 582164 584078 584083) (-338 "FINITE.spad" 581301 581309 582139 582144) (-337 "FINAALG.spad" 570282 570292 581243 581296) (-336 "FINAALG.spad" 559275 559287 570238 570243) (-335 "FILE.spad" 558858 558868 559265 559270) (-334 "FILECAT.spad" 557376 557393 558848 558853) (-333 "FIELD.spad" 556782 556790 557278 557371) (-332 "FIELD.spad" 556274 556284 556772 556777) (-331 "FGROUP.spad" 554883 554893 556254 556269) (-330 "FGLMICPK.spad" 553670 553685 554873 554878) (-329 "FFX.spad" 553045 553060 553386 553479) (-328 "FFSLPE.spad" 552534 552555 553035 553040) (-327 "FFPOLY.spad" 543786 543797 552524 552529) (-326 "FFPOLY2.spad" 542846 542863 543776 543781) (-325 "FFP.spad" 542243 542263 542562 542655) (-324 "FF.spad" 541691 541707 541924 542017) (-323 "FFNBX.spad" 540203 540223 541407 541500) (-322 "FFNBP.spad" 538716 538733 539919 540012) (-321 "FFNB.spad" 537181 537202 538397 538490) (-320 "FFINTBAS.spad" 534595 534614 537171 537176) (-319 "FFIELDC.spad" 532170 532178 534497 534590) (-318 "FFIELDC.spad" 529831 529841 532160 532165) (-317 "FFHOM.spad" 528579 528596 529821 529826) (-316 "FFF.spad" 526014 526025 528569 528574) (-315 "FFCGX.spad" 524861 524881 525730 525823) (-314 "FFCGP.spad" 523750 523770 524577 524670) (-313 "FFCG.spad" 522542 522563 523431 523524) (-312 "FFCAT.spad" 515443 515465 522381 522537) (-311 "FFCAT.spad" 508423 508447 515363 515368) (-310 "FFCAT2.spad" 508168 508208 508413 508418) (-309 "FEXPR.spad" 499881 499927 507928 507967) (-308 "FEVALAB.spad" 499587 499597 499871 499876) (-307 "FEVALAB.spad" 499078 499090 499364 499369) (-306 "FDIV.spad" 498520 498544 499068 499073) (-305 "FDIVCAT.spad" 496562 496586 498510 498515) (-304 "FDIVCAT.spad" 494602 494628 496552 496557) (-303 "FDIV2.spad" 494256 494296 494592 494597) (-302 "FCPAK1.spad" 492809 492817 494246 494251) (-301 "FCOMP.spad" 492188 492198 492799 492804) (-300 "FC.spad" 482013 482021 492178 492183) (-299 "FAXF.spad" 474948 474962 481915 482008) (-298 "FAXF.spad" 467935 467951 474904 474909) (-297 "FARRAY.spad" 466304 466314 467341 467368) (-296 "FAMR.spad" 464424 464436 466202 466299) (-295 "FAMR.spad" 462528 462542 464308 464313) (-294 "FAMONOID.spad" 462178 462188 462482 462487) (-293 "FAMONC.spad" 460400 460412 462168 462173) (-292 "FAGROUP.spad" 460006 460016 460296 460323) (-291 "FACUTIL.spad" 458202 458219 459996 460001) (-290 "FACTFUNC.spad" 457378 457388 458192 458197) (-289 "EXPUPXS.spad" 454211 454234 455510 455659) (-288 "EXPRTUBE.spad" 451439 451447 454201 454206) (-287 "EXPRODE.spad" 448311 448327 451429 451434) (-286 "EXPR.spad" 443613 443623 444327 444730) (-285 "EXPR2UPS.spad" 439705 439718 443603 443608) (-284 "EXPR2.spad" 439408 439420 439695 439700) (-283 "EXPEXPAN.spad" 436349 436374 436983 437076) (-282 "EXIT.spad" 436020 436028 436339 436344) (-281 "EVALCYC.spad" 435478 435492 436010 436015) (-280 "EVALAB.spad" 435042 435052 435468 435473) (-279 "EVALAB.spad" 434604 434616 435032 435037) (-278 "EUCDOM.spad" 432146 432154 434530 434599) (-277 "EUCDOM.spad" 429750 429760 432136 432141) (-276 "ESTOOLS.spad" 421590 421598 429740 429745) (-275 "ESTOOLS2.spad" 421191 421205 421580 421585) (-274 "ESTOOLS1.spad" 420876 420887 421181 421186) (-273 "ES.spad" 413423 413431 420866 420871) (-272 "ES.spad" 405878 405888 413323 413328) (-271 "ESCONT.spad" 402651 402659 405868 405873) (-270 "ESCONT1.spad" 402400 402412 402641 402646) (-269 "ES2.spad" 401895 401911 402390 402395) (-268 "ES1.spad" 401461 401477 401885 401890) (-267 "ERROR.spad" 398782 398790 401451 401456) (-266 "EQTBL.spad" 397816 397838 398025 398052) (-265 "EQ.spad" 392700 392710 395499 395608) (-264 "EQ2.spad" 392416 392428 392690 392695) (-263 "EP.spad" 388730 388740 392406 392411) (-262 "ENTIRER.spad" 388398 388406 388674 388725) (-261 "EMR.spad" 387599 387640 388324 388393) (-260 "ELTAGG.spad" 385839 385858 387589 387594) (-259 "ELTAGG.spad" 384043 384064 385795 385800) (-258 "ELTAB.spad" 383490 383508 384033 384038) (-257 "ELFUTS.spad" 382869 382888 383480 383485) (-256 "ELEMFUN.spad" 382558 382566 382859 382864) (-255 "ELEMFUN.spad" 382245 382255 382548 382553) (-254 "ELAGG.spad" 380176 380186 382213 382240) (-253 "ELAGG.spad" 378056 378068 380095 380100) (-252 "EFUPXS.spad" 374832 374862 378012 378017) (-251 "EFULS.spad" 371668 371691 374788 374793) (-250 "EFSTRUC.spad" 369623 369639 371658 371663) (-249 "EF.spad" 364389 364405 369613 369618) (-248 "EAB.spad" 362665 362673 364379 364384) (-247 "E04UCFA.spad" 362201 362209 362655 362660) (-246 "E04NAFA.spad" 361778 361786 362191 362196) (-245 "E04MBFA.spad" 361358 361366 361768 361773) (-244 "E04JAFA.spad" 360894 360902 361348 361353) (-243 "E04GCFA.spad" 360430 360438 360884 360889) (-242 "E04FDFA.spad" 359966 359974 360420 360425) (-241 "E04DGFA.spad" 359502 359510 359956 359961) (-240 "E04AGNT.spad" 355344 355352 359492 359497) (-239 "DVARCAT.spad" 352029 352039 355334 355339) (-238 "DVARCAT.spad" 348712 348724 352019 352024) (-237 "DSMP.spad" 346146 346160 346451 346578) (-236 "DROPT.spad" 340091 340099 346136 346141) (-235 "DROPT1.spad" 339754 339764 340081 340086) (-234 "DROPT0.spad" 334581 334589 339744 339749) (-233 "DRAWPT.spad" 332736 332744 334571 334576) (-232 "DRAW.spad" 325336 325349 332726 332731) (-231 "DRAWHACK.spad" 324644 324654 325326 325331) (-230 "DRAWCX.spad" 322086 322094 324634 324639) (-229 "DRAWCURV.spad" 321623 321638 322076 322081) (-228 "DRAWCFUN.spad" 310795 310803 321613 321618) (-227 "DQAGG.spad" 308951 308961 310751 310790) (-226 "DPOLCAT.spad" 304292 304308 308819 308946) (-225 "DPOLCAT.spad" 299719 299737 304248 304253) (-224 "DPMO.spad" 293762 293778 293900 294196) (-223 "DPMM.spad" 287818 287836 287943 288239) (-222 "domain.spad" 287458 287466 287808 287813) (-221 "DMP.spad" 284683 284698 285255 285382) (-220 "DLP.spad" 284031 284041 284673 284678) (-219 "DLIST.spad" 282666 282676 283437 283464) (-218 "DLAGG.spad" 281067 281077 282646 282661) (-217 "DIVRING.spad" 280514 280522 281011 281062) (-216 "DIVRING.spad" 280005 280015 280504 280509) (-215 "DISPLAY.spad" 278185 278193 279995 280000) (-214 "DIRPROD.spad" 270160 270176 270800 270929) (-213 "DIRPROD2.spad" 268968 268986 270150 270155) (-212 "DIRPCAT.spad" 267900 267916 268822 268963) (-211 "DIRPCAT.spad" 266572 266590 267496 267501) (-210 "DIOSP.spad" 265397 265405 266562 266567) (-209 "DIOPS.spad" 264369 264379 265365 265392) (-208 "DIOPS.spad" 263327 263339 264325 264330) (-207 "DIFRING.spad" 262619 262627 263307 263322) (-206 "DIFRING.spad" 261919 261929 262609 262614) (-205 "DIFEXT.spad" 261078 261088 261899 261914) (-204 "DIFEXT.spad" 260154 260166 260977 260982) (-203 "DIAGG.spad" 259772 259782 260122 260149) (-202 "DIAGG.spad" 259410 259422 259762 259767) (-201 "DHMATRIX.spad" 257937 257947 259090 259117) (-200 "DFSFUN.spad" 251345 251353 257927 257932) (-199 "DFLOAT.spad" 247868 247876 251235 251340) (-198 "DFINTTLS.spad" 246077 246093 247858 247863) (-197 "DERHAM.spad" 243987 244019 246057 246072) (-196 "DEQUEUE.spad" 243528 243538 243817 243844) (-195 "DEGRED.spad" 243143 243157 243518 243523) (-194 "DEFINTRF.spad" 240668 240678 243133 243138) (-193 "DEFINTEF.spad" 239164 239180 240658 240663) (-192 "DECIMAL.spad" 237048 237056 237634 237727) (-191 "DDFACT.spad" 234847 234864 237038 237043) (-190 "DBLRESP.spad" 234445 234469 234837 234842) (-189 "DBASE.spad" 233017 233027 234435 234440) (-188 "D03FAFA.spad" 232845 232853 233007 233012) (-187 "D03EEFA.spad" 232665 232673 232835 232840) (-186 "D03AGNT.spad" 231745 231753 232655 232660) (-185 "D02EJFA.spad" 231207 231215 231735 231740) (-184 "D02CJFA.spad" 230685 230693 231197 231202) (-183 "D02BHFA.spad" 230175 230183 230675 230680) (-182 "D02BBFA.spad" 229665 229673 230165 230170) (-181 "D02AGNT.spad" 224469 224477 229655 229660) (-180 "D01WGTS.spad" 222788 222796 224459 224464) (-179 "D01TRNS.spad" 222765 222773 222778 222783) (-178 "D01GBFA.spad" 222287 222295 222755 222760) (-177 "D01FCFA.spad" 221809 221817 222277 222282) (-176 "D01ASFA.spad" 221277 221285 221799 221804) (-175 "D01AQFA.spad" 220723 220731 221267 221272) (-174 "D01APFA.spad" 220147 220155 220713 220718) (-173 "D01ANFA.spad" 219641 219649 220137 220142) (-172 "D01AMFA.spad" 219151 219159 219631 219636) (-171 "D01ALFA.spad" 218691 218699 219141 219146) (-170 "D01AKFA.spad" 218217 218225 218681 218686) (-169 "D01AJFA.spad" 217740 217748 218207 218212) (-168 "D01AGNT.spad" 213799 213807 217730 217735) (-167 "CYCLOTOM.spad" 213305 213313 213789 213794) (-166 "CYCLES.spad" 210137 210145 213295 213300) (-165 "CVMP.spad" 209554 209564 210127 210132) (-164 "CTRIGMNP.spad" 208044 208060 209544 209549) (-163 "CSTTOOLS.spad" 207287 207300 208034 208039) (-162 "CRFP.spad" 200991 201004 207277 207282) (-161 "CRAPACK.spad" 200034 200044 200981 200986) (-160 "CPMATCH.spad" 199534 199549 199959 199964) (-159 "CPIMA.spad" 199239 199258 199524 199529) (-158 "COORDSYS.spad" 194132 194142 199229 199234) (-157 "CONTFRAC.spad" 189744 189754 194034 194127) (-156 "COMRING.spad" 189418 189426 189682 189739) (-155 "COMPPROP.spad" 188932 188940 189408 189413) (-154 "COMPLPAT.spad" 188699 188714 188922 188927) (-153 "COMPLEX.spad" 182732 182742 182976 183237) (-152 "COMPLEX2.spad" 182445 182457 182722 182727) (-151 "COMPFACT.spad" 182047 182061 182435 182440) (-150 "COMPCAT.spad" 180103 180113 181769 182042) (-149 "COMPCAT.spad" 177866 177878 179534 179539) (-148 "COMMUPC.spad" 177612 177630 177856 177861) (-147 "COMMONOP.spad" 177145 177153 177602 177607) (-146 "COMM.spad" 176954 176962 177135 177140) (-145 "COMBOPC.spad" 175859 175867 176944 176949) (-144 "COMBINAT.spad" 174604 174614 175849 175854) (-143 "COMBF.spad" 171972 171988 174594 174599) (-142 "COLOR.spad" 170809 170817 171962 171967) (-141 "CMPLXRT.spad" 170518 170535 170799 170804) (-140 "CLIP.spad" 166610 166618 170508 170513) (-139 "CLIF.spad" 165249 165265 166566 166605) (-138 "CLAGG.spad" 161724 161734 165229 165244) (-137 "CLAGG.spad" 158080 158092 161587 161592) (-136 "CINTSLPE.spad" 157405 157418 158070 158075) (-135 "CHVAR.spad" 155483 155505 157395 157400) (-134 "CHARZ.spad" 155398 155406 155463 155478) (-133 "CHARPOL.spad" 154906 154916 155388 155393) (-132 "CHARNZ.spad" 154659 154667 154886 154901) (-131 "CHAR.spad" 152549 152557 154649 154654) (-130 "CFCAT.spad" 151865 151873 152539 152544) (-129 "CDEN.spad" 151023 151037 151855 151860) (-128 "CCLASS.spad" 149230 149238 150492 150531) (-127 "CARTEN.spad" 144333 144357 149220 149225) (-126 "CARTEN2.spad" 143719 143746 144323 144328) (-125 "CARD.spad" 141008 141016 143693 143714) (-124 "CACHSET.spad" 140630 140638 140998 141003) (-123 "CABMON.spad" 140183 140191 140620 140625) (-122 "BTREE.spad" 139475 139485 140013 140040) (-121 "BTOURN.spad" 138701 138711 139305 139332) (-120 "BTCAT.spad" 138077 138087 138657 138696) (-119 "BTCAT.spad" 137485 137497 138067 138072) (-118 "BTAGG.spad" 136501 136509 137441 137480) (-117 "BTAGG.spad" 135549 135559 136491 136496) (-116 "BSTREE.spad" 134507 134517 135379 135406) (-115 "BRILL.spad" 132702 132713 134497 134502) (-114 "BRAGG.spad" 131616 131626 132682 132697) (-113 "BRAGG.spad" 130504 130516 131572 131577) (-112 "BPADICRT.spad" 128488 128500 128743 128836) (-111 "BPADIC.spad" 128152 128164 128414 128483) (-110 "BOUNDZRO.spad" 127808 127825 128142 128147) (-109 "BOP.spad" 123272 123280 127798 127803) (-108 "BOP1.spad" 120658 120668 123228 123233) (-107 "BOOLEAN.spad" 119516 119524 120648 120653) (-106 "BMODULE.spad" 119228 119240 119484 119511) (-105 "BITS.spad" 118705 118713 118922 118949) (-104 "BINFILE.spad" 118048 118056 118695 118700) (-103 "BINARY.spad" 115941 115949 116518 116611) (-102 "BGAGG.spad" 115126 115136 115909 115936) (-101 "BGAGG.spad" 114331 114343 115116 115121) (-100 "BFUNCT.spad" 113895 113903 114311 114326) (-99 "BEZOUT.spad" 113030 113056 113845 113850) (-98 "BBTREE.spad" 110073 110082 112860 112887) (-97 "BASTYPE.spad" 109746 109753 110063 110068) (-96 "BASTYPE.spad" 109417 109426 109736 109741) (-95 "BALFACT.spad" 108857 108869 109407 109412) (-94 "AUTOMOR.spad" 108304 108313 108837 108852) (-93 "ATTREG.spad" 105023 105030 108056 108299) (-92 "ATTRBUT.spad" 101046 101053 105003 105018) (-91 "ATRIG.spad" 100516 100523 101036 101041) (-90 "ATRIG.spad" 99984 99993 100506 100511) (-89 "ASTACK.spad" 99540 99549 99814 99841) (-88 "ASSOCEQ.spad" 98340 98351 99496 99501) (-87 "ASP9.spad" 97421 97434 98330 98335) (-86 "ASP8.spad" 96464 96477 97411 97416) (-85 "ASP80.spad" 95786 95799 96454 96459) (-84 "ASP7.spad" 94946 94959 95776 95781) (-83 "ASP78.spad" 94397 94410 94936 94941) (-82 "ASP77.spad" 93766 93779 94387 94392) (-81 "ASP74.spad" 92858 92871 93756 93761) (-80 "ASP73.spad" 92129 92142 92848 92853) (-79 "ASP6.spad" 90761 90774 92119 92124) (-78 "ASP55.spad" 89270 89283 90751 90756) (-77 "ASP50.spad" 87087 87100 89260 89265) (-76 "ASP4.spad" 86382 86395 87077 87082) (-75 "ASP49.spad" 85381 85394 86372 86377) (-74 "ASP42.spad" 83788 83827 85371 85376) (-73 "ASP41.spad" 82367 82406 83778 83783) (-72 "ASP35.spad" 81355 81368 82357 82362) (-71 "ASP34.spad" 80656 80669 81345 81350) (-70 "ASP33.spad" 80216 80229 80646 80651) (-69 "ASP31.spad" 79356 79369 80206 80211) (-68 "ASP30.spad" 78248 78261 79346 79351) (-67 "ASP29.spad" 77714 77727 78238 78243) (-66 "ASP28.spad" 68987 69000 77704 77709) (-65 "ASP27.spad" 67884 67897 68977 68982) (-64 "ASP24.spad" 66971 66984 67874 67879) (-63 "ASP20.spad" 66187 66200 66961 66966) (-62 "ASP1.spad" 65568 65581 66177 66182) (-61 "ASP19.spad" 60254 60267 65558 65563) (-60 "ASP12.spad" 59668 59681 60244 60249) (-59 "ASP10.spad" 58939 58952 59658 59663) (-58 "ARRAY2.spad" 58522 58531 58769 58796) (-57 "ARRAY1.spad" 57580 57589 57928 57955) (-56 "ARRAY12.spad" 56249 56260 57570 57575) (-55 "ARR2CAT.spad" 51899 51920 56205 56244) (-54 "ARR2CAT.spad" 47581 47604 51889 51894) (-53 "APPRULE.spad" 46825 46847 47571 47576) (-52 "APPLYORE.spad" 46440 46453 46815 46820) (-51 "ANY.spad" 44782 44789 46430 46435) (-50 "ANY1.spad" 43853 43862 44772 44777) (-49 "ANTISYM.spad" 42292 42308 43833 43848) (-48 "ANON.spad" 42205 42212 42282 42287) (-47 "AN.spad" 40508 40515 42023 42116) (-46 "AMR.spad" 38687 38698 40406 40503) (-45 "AMR.spad" 36703 36716 38424 38429) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-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 8812be8f..d73ba07d 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,14 +1,14 @@
 
-(143833 . 3403927931)        
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+(143833 . 3404130415)        
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@@ -18,33 +18,33 @@
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@@ -54,10 +54,10 @@
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 ((($) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T)) 
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@@ -66,64 +66,64 @@
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@@ -132,32 +132,32 @@
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 (((|#1| (-703)) . T)) 
 (|has| |#2| (-725)) 
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@@ -168,17 +168,17 @@
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-((((-1056) |#1|) . T)) 
+((((-1057) |#1|) . T)) 
 (((|#3| |#3|) . T)) 
 ((((-787)) . T)) 
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-((($ $) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+((((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1| |#1|) . T) (($ $) -3763 (|has| |#1| (-156)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831)))) 
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@@ -186,42 +186,42 @@
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@@ -255,31 +255,31 @@
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 (|has| |#1| (-1003)) 
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@@ -378,49 +378,49 @@
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 ((((-377 (-517))) . T) (((-517)) . T)) 
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 ((($) . T)) 
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@@ -496,28 +496,28 @@
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 ((($) . T)) 
 (((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) (($) . T)) 
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@@ -572,99 +572,99 @@
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@@ -704,17 +704,17 @@
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 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 ((((-107)) . T)) 
@@ -749,38 +749,38 @@
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 (|has| |#1| (-509)) 
 (|has| |#1| (-831)) 
 (((|#1|) . T)) 
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 ((((-787)) . T)) 
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 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
-(((|#1| (-1153 |#1|) (-1153 |#1|)) . T)) 
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 ((((-517) (-131)) . T)) 
 ((($) . T)) 
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 ((((-787)) . T)) 
 (|has| |#1| (-1003)) 
 (((|#1| (-888)) . T)) 
 (((|#1| |#1|) . T)) 
 ((($) . T)) 
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 (((|#1|) . T)) 
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 (((|#1| |#2|) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (|has| |#2| (-777)) 
@@ -795,7 +795,7 @@
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
-((($) . T) (((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) . T)) 
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 (|has| |#1| (-760)) 
 ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) 
 (|has| |#1| (-1003)) 
@@ -806,8 +806,8 @@
 (((|#3|) |has| |#3| (-1003))) 
 (|has| |#3| (-338)) 
 (((|#1|) . T) (((-787)) . T)) 
-((((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1146 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) 
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 ((((-787)) . T)) 
 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#2|) . T)) 
@@ -817,30 +817,30 @@
 (((|#1|) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 ((((-377 (-517))) . T) (((-517)) . T)) 
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-((($) -3807 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
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+((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-509))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 ((((-131)) . T)) 
 (((|#1|) . T)) 
 ((((-131)) . T)) 
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 ((((-131)) . T)) 
 (((|#1| |#2| |#3|) . T)) 
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 (|has| $ (-134)) 
 (|has| $ (-134)) 
 (|has| |#1| (-1003)) 
 ((((-787)) . T)) 
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 ((($ $) |has| |#1| (-258 $ $)) ((|#1| $) |has| |#1| (-258 |#1| |#1|))) 
 (((|#1| (-377 (-517))) . T)) 
 (((|#1|) . T)) 
-((((-1073)) . T)) 
+((((-1074)) . T)) 
 (|has| |#1| (-509)) 
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 (|has| |#1| (-509)) 
 (|has| |#1| (-37 (-377 (-517)))) 
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@@ -851,7 +851,7 @@
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 (|has| |#1| (-132)) 
 (|has| |#4| (-777)) 
-(((|#2| (-214 (-2296 |#1|) (-703)) (-789 |#1|)) . T)) 
+(((|#2| (-214 (-2210 |#1|) (-703)) (-789 |#1|)) . T)) 
 (|has| |#3| (-777)) 
 (((|#1| (-489 |#3|) |#3|) . T)) 
 (|has| |#1| (-134)) 
@@ -865,21 +865,21 @@
 (|has| |#1| (-132)) 
 ((((-377 (-517))) |has| |#2| (-333)) (($) . T)) 
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-((((-1040 |#2| |#1|)) . T) ((|#1|) . T)) 
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 (|has| |#2| (-156)) 
 (((|#1| |#2|) . T)) 
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+(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
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 ((((-787)) . T)) 
 (((|#1|) . T)) 
 (((|#2|) . T) (($) . T)) 
 (((|#1|) . T) (($) . T)) 
 ((((-632)) . T)) 
-(-3807 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
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 (|has| |#1| (-509)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
@@ -887,7 +887,7 @@
 (((|#1|) . T)) 
 (((|#1|) . T)) 
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 ((((-787)) . T)) 
 ((((-493)) . T) (((-814 (-517))) . T) (((-349)) . T) (((-199)) . T)) 
 (((|#1|) . T)) 
@@ -901,33 +901,33 @@
 (((|#1| (-377 (-517))) . T)) 
 (((|#3|) . T) (((-556 $)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1|) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((($ $) . T) ((|#2| $) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
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 ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) 
 ((((-787)) . T)) 
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 (((|#1|) . T)) 
 ((($) . T) ((|#2|) . T)) 
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 (((|#3|) . T)) 
 ((($ $) . T) (((-789 |#1|) $) . T) (((-789 |#1|) |#2|) . T)) 
 (|has| |#1| (-760)) 
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-((((-517) (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T) ((|#1| |#2|) . T)) 
-(((|#2|) -3807 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-961))) (($) |has| |#2| (-156))) 
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+((((-517) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T) ((|#1| |#2|) . T)) 
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 ((((-703)) . T)) 
 ((((-517)) . T)) 
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@@ -940,100 +940,100 @@
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 ((((-787)) . T)) 
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 ((($) . T)) 
 ((((-787)) . T)) 
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 ((((-517) |#2|) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#1| |#2|) . T)) 
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 (-12 (|has| |#1| (-338)) (|has| |#2| (-338))) 
 ((((-787)) . T)) 
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-((((-1073)) |has| |#2| (-822 (-1073)))) 
+((((-1074)) |has| |#2| (-822 (-1074)))) 
 ((((-517) (-107)) . T)) 
 (|has| |#1| (-509)) 
 (((|#2|) . T)) 
@@ -1231,23 +1231,23 @@
 ((((-915 |#1|)) . T) ((|#1|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((((-377 (-517))) . T) (((-377 |#1|)) . T) ((|#1|) . T) (($) . T)) 
-(((|#1| (-1069 |#1|)) . T)) 
+(((|#1| (-1070 |#1|)) . T)) 
 ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) 
 (((|#3|) . T) (($) . T)) 
 (|has| |#1| (-779)) 
 (((|#2|) . T)) 
 ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) . T)) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) 
 ((((-517) |#2|) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 (((|#2|) . T)) 
 ((((-517) |#3|) . T)) 
 (((|#2|) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
-((((-1146 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 ((((-787)) . T)) 
@@ -1256,12 +1256,12 @@
 (((|#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) 
 (((|#2|) . T)) 
 (((|#1|) . T)) 
-(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))))) 
+(((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) 
 (((|#2| |#2|) . T)) 
 (|has| |#2| (-333)) 
 (((|#2|) . T) (((-517)) |has| |#2| (-952 (-517))) (((-377 (-517))) |has| |#2| (-952 (-377 (-517))))) 
 (((|#2|) . T)) 
-((((-1056) (-51)) . T)) 
+((((-1057) (-51)) . T)) 
 (((|#2|) |has| |#2| (-156))) 
 ((((-517) |#3|) . T)) 
 ((((-517) (-131)) . T)) 
@@ -1281,27 +1281,27 @@
 ((((-517)) |has| |#1| (-579 (-517))) ((|#1|) . T)) 
 ((((-517)) |has| |#1| (-579 (-517))) ((|#1|) . T)) 
 ((((-517)) |has| |#1| (-579 (-517))) ((|#1|) . T)) 
-((((-1056) (-51)) . T)) 
+((((-1057) (-51)) . T)) 
 (((|#1|) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#1| |#2|) . T)) 
 ((((-517) (-131)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
-((($) -3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
+((($) -3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (|has| |#1| (-779)) 
 (((|#2| (-703) (-989)) . T)) 
 (((|#1| |#2|) . T)) 
-(-3807 (|has| |#1| (-156)) (|has| |#1| (-509))) 
+(-3763 (|has| |#1| (-156)) (|has| |#1| (-509))) 
 (|has| |#1| (-723)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#4|) . T)) 
 (((|#4|) . T)) 
 (((|#1| |#2|) . T)) 
-(-3807 (|has| |#1| (-134)) (-12 (|has| |#1| (-333)) (|has| |#2| (-134)))) 
-(-3807 (|has| |#1| (-132)) (-12 (|has| |#1| (-333)) (|has| |#2| (-132)))) 
+(-3763 (|has| |#1| (-134)) (-12 (|has| |#1| (-333)) (|has| |#2| (-134)))) 
+(-3763 (|has| |#1| (-132)) (-12 (|has| |#1| (-333)) (|has| |#2| (-132)))) 
 (((|#4|) . T)) 
 (|has| |#1| (-132)) 
-((((-1056) |#1|) . T)) 
+((((-1057) |#1|) . T)) 
 (|has| |#1| (-134)) 
 (((|#1|) . T)) 
 ((((-517)) . T)) 
@@ -1310,25 +1310,25 @@
 ((((-787)) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#3|) . T)) 
-((((-1146 |#1| |#2| |#3|)) |has| |#1| (-333))) 
-(-3807 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
+((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
 (((|#1|) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003))) (((-879 |#1|)) . T)) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003))) (((-879 |#1|)) . T)) 
 (|has| |#1| (-777)) 
 (|has| |#1| (-777)) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (|has| |#2| (-333)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#2|) |has| |#2| (-961))) 
-((((-1056) |#1|) . T)) 
+((((-1057) |#1|) . T)) 
 (((|#3| |#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) 
 (((|#2| (-815 |#1|)) . T)) 
 ((($) . T)) 
-((((-358) (-1056)) . T)) 
+((((-358) (-1057)) . T)) 
 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
-((((-787)) -3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-557 (-787))) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((-1153 |#2|)) . T)) 
-((((-51)) . T) (((-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))) . T)) 
+((((-787)) -3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-557 (-787))) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) (((-1154 |#2|)) . T)) 
+((((-51)) . T) (((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
 (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
@@ -1336,7 +1336,7 @@
 (|has| |#2| (-132)) 
 (|has| |#2| (-134)) 
 (|has| |#1| (-442)) 
-(-3807 (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1073))) (|has| |#1| (-961))) 
+(-3763 (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) 
 (|has| |#1| (-333)) 
 ((((-787)) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
@@ -1345,18 +1345,18 @@
 (|has| |#1| (-777)) 
 (|has| |#1| (-777)) 
 ((((-787)) . T)) 
-((((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1146 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) 
-(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509)))) 
+((((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1147 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) 
+(((|#1|) |has| |#1| (-156)) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509)))) 
 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#1| |#2|) . T)) 
-((((-1073)) |has| |#1| (-822 (-1073)))) 
+((((-1074)) |has| |#1| (-822 (-1074)))) 
 ((((-832 |#1|)) . T) (((-377 (-517))) . T) (($) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (|has| |#1| (-1003)) 
-(((|#2| (-450 (-2296 |#1|) (-703)) (-789 |#1|)) . T)) 
+(((|#2| (-450 (-2210 |#1|) (-703)) (-789 |#1|)) . T)) 
 ((((-377 (-517))) |has| |#2| (-333)) (($) |has| |#2| (-333))) 
-(((|#1| (-489 (-1073)) (-1073)) . T)) 
+(((|#1| (-489 (-1074)) (-1074)) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
@@ -1374,22 +1374,22 @@
 (|has| |#1| (-134)) 
 (((|#1|) . T)) 
 (((|#2|) . T)) 
-(((|#1|) . T) (((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
-((((-1071 |#1| |#2| |#3|)) |has| |#1| (-333))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-1073) (-51)) . T)) 
+(((|#1|) . T) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-1074) (-51)) . T)) 
 ((($ $) . T)) 
 (((|#1| (-517)) . T)) 
 ((((-832 |#1|)) . T)) 
-(((|#1|) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961))) (($) -3807 (|has| |#1| (-822 (-1073))) (|has| |#1| (-961)))) 
+(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961))) (($) -3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)))) 
 (((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) 
 (|has| |#1| (-779)) 
 (|has| |#1| (-779)) 
 ((((-517) |#2|) . T)) 
 ((((-517)) . T)) 
-((((-1146 |#1| |#2| |#3|)) -12 (|has| (-1146 |#1| |#2| |#3|) (-280 (-1146 |#1| |#2| |#3|))) (|has| |#1| (-333)))) 
+((((-1147 |#1| |#2| |#3|)) -12 (|has| (-1147 |#1| |#2| |#3|) (-280 (-1147 |#1| |#2| |#3|))) (|has| |#1| (-333)))) 
 (|has| |#1| (-779)) 
 ((((-623 |#2|)) . T) (((-787)) . T)) 
 (((|#1| |#2|) . T)) 
@@ -1398,13 +1398,13 @@
 (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) 
-(((|#3|) -3807 (|has| |#3| (-156)) (|has| |#3| (-333)))) 
+(((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)))) 
 (|has| |#2| (-779)) 
 (|has| |#1| (-779)) 
-(-3807 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-831))) 
+(-3763 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-831))) 
 ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) 
 ((((-517) |#2|) . T)) 
-(((|#2|) -3807 (|has| |#2| (-156)) (|has| |#2| (-333)))) 
+(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)))) 
 (|has| |#1| (-319)) 
 (((|#3| |#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) 
 ((($) . T) (((-377 (-517))) . T)) 
@@ -1412,7 +1412,7 @@
 (|has| |#1| (-752)) 
 (|has| |#1| (-752)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) 
+(-3763 (|has| |#1| (-278)) (|has| |#1| (-333)) (|has| |#1| (-319))) 
 (|has| |#1| (-777)) 
 (|has| |#1| (-777)) 
 (|has| |#1| (-777)) 
@@ -1421,13 +1421,13 @@
 ((((-517)) . T) (($) . T) (((-377 (-517))) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-319))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) 
 (|has| |#1| (-37 (-377 (-517)))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-1073)) |has| |#1| (-822 (-1073))) (((-989)) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-1074)) |has| |#1| (-822 (-1074))) (((-989)) . T)) 
 (((|#1|) . T)) 
 (|has| |#1| (-777)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))) |has| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (-280 (-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))))) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))))) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (|has| |#1| (-1003)) 
 (((|#1|) . T)) 
@@ -1445,7 +1445,7 @@
 (((|#1|) . T)) 
 ((((-131)) . T)) 
 (((|#2|) |has| |#2| (-156))) 
-(-3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
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 (((|#1|) . T)) 
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
@@ -1455,43 +1455,43 @@
 (((|#1|) . T)) 
 (((|#2|) |has| |#1| (-333))) 
 (((|#2|) . T)) 
-(((|#1| (-1069 |#1|)) . T)) 
+(((|#1| (-1070 |#1|)) . T)) 
 ((((-989)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) 
 ((($) . T) ((|#1|) . T) (((-377 (-517))) . T)) 
 (((|#2|) . T)) 
-((((-1071 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 ((($) |has| |#1| (-777))) 
 (|has| |#1| (-831)) 
 ((((-787)) . T)) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#1|) . T)) 
 (((|#1| |#2|) . T)) 
-(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) |has| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (-280 (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))))) 
-(-3807 (|has| |#2| (-421)) (|has| |#2| (-831))) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-831))) 
+(((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))))) 
+(-3763 (|has| |#2| (-421)) (|has| |#2| (-831))) 
+(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) 
 (((|#1|) . T) (($) . T)) 
 (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (((|#1| |#2|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
-(((|#3|) -3807 (|has| |#3| (-156)) (|has| |#3| (-333)))) 
+(((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)))) 
 (|has| |#1| (-779)) 
 (|has| |#1| (-509)) 
 ((((-530 |#1|)) . T)) 
 ((($) . T)) 
 (((|#2|) . T)) 
-(-3807 (-12 (|has| |#1| (-333)) (|has| |#2| (-752))) (-12 (|has| |#1| (-333)) (|has| |#2| (-779)))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3763 (-12 (|has| |#1| (-333)) (|has| |#2| (-752))) (-12 (|has| |#1| (-333)) (|has| |#2| (-779)))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) 
 ((((-832 |#1|)) . T)) 
 (((|#1| (-461 |#1| |#3|) (-461 |#1| |#2|)) . T)) 
 (((|#1| |#4| |#5|) . T)) 
 (((|#1| (-703)) . T)) 
 ((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) |has| |#1| (-156)) (($) |has| |#1| (-509))) 
-((((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) (($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-1071 |#1| |#2| |#3|)) |has| |#1| (-333)) ((|#1|) |has| |#1| (-156))) 
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 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
 ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) 
 ((((-608 |#1|)) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
@@ -1499,19 +1499,19 @@
 ((((-787)) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 ((((-787)) . T)) 
-((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3807 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) 
+((((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) |has| |#2| (-156)) (($) -3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831)))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#2|) . T)) 
-(-3807 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) 
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 ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) 
-(|has| |#1| (-1094)) 
-(|has| |#1| (-1094)) 
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-(|has| |#1| (-1094)) 
-(|has| |#1| (-1094)) 
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+(|has| |#1| (-1095)) 
+(|has| |#1| (-1095)) 
 (((|#3| |#3|) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T) (((-377 |#1|) (-377 |#1|)) . T) ((|#1| |#1|) . T)) 
@@ -1520,45 +1520,45 @@
 ((($) . T) (((-377 (-517))) . T) (((-377 |#1|)) . T) ((|#1|) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
-((((-1056) (-51)) . T)) 
+((((-1057) (-51)) . T)) 
 (|has| |#1| (-1003)) 
-(-3807 (|has| |#2| (-752)) (|has| |#2| (-779))) 
+(-3763 (|has| |#2| (-752)) (|has| |#2| (-779))) 
 (((|#1|) . T)) 
-((($) -3807 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3807 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
+((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
 (((|#1|) |has| |#1| (-156)) (($) . T)) 
 ((($) . T)) 
-((((-1071 |#1| |#2| |#3|)) -12 (|has| (-1071 |#1| |#2| |#3|) (-280 (-1071 |#1| |#2| |#3|))) (|has| |#1| (-333)))) 
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 ((((-787)) . T)) 
-(-3807 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
+(-3763 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
 ((($) . T)) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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+(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 ((((-787)) . T)) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-831))) 
+(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) 
 (|has| |#2| (-831)) 
 (|has| |#1| (-333)) 
 (((|#2|) |has| |#2| (-1003))) 
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+(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 ((($) . T) ((|#2|) . T)) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-831))) 
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 (|has| |#1| (-831)) 
 (|has| |#1| (-831)) 
-((((-493)) . T) (((-377 (-1069 (-517)))) . T) (((-199)) . T) (((-349)) . T)) 
+((((-493)) . T) (((-377 (-1070 (-517)))) . T) (((-199)) . T) (((-349)) . T)) 
 ((((-349)) . T) (((-199)) . T) (((-787)) . T)) 
 (|has| |#1| (-831)) 
-(-3807 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
+(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
 (((|#1|) . T)) 
 (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 ((($ $) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((($ $) . T)) 
 ((((-517) (-107)) . T)) 
 ((($) . T)) 
 (((|#1|) . T)) 
 ((((-517)) . T)) 
 ((((-107)) . T)) 
-(-3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-509))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (((|#1| (-517)) . T)) 
 ((($) . T)) 
@@ -1567,29 +1567,29 @@
 (((|#1|) . T)) 
 ((((-517)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-1073)) |has| |#1| (-961))) 
+((((-1074)) |has| |#1| (-961))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
 (((|#1| (-517)) . T)) 
-(((|#1| (-1146 |#1| |#2| |#3|)) . T)) 
+(((|#1| (-1147 |#1| |#2| |#3|)) . T)) 
 (((|#1|) . T)) 
 (((|#1| (-377 (-517))) . T)) 
-(((|#1| (-1118 |#1| |#2| |#3|)) . T)) 
+(((|#1| (-1119 |#1| |#2| |#3|)) . T)) 
 (((|#1| (-703)) . T)) 
 (((|#1|) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((((-787)) . T)) 
 (|has| |#1| (-1003)) 
-((((-1056) |#1|) . T)) 
+((((-1057) |#1|) . T)) 
 ((($) . T)) 
 (|has| |#2| (-134)) 
 (|has| |#2| (-132)) 
-(((|#1| (-489 (-750 (-1073))) (-750 (-1073))) . T)) 
-((((-1140 |#1| |#2| |#3| |#4|)) . T)) 
-((((-1140 |#1| |#2| |#3| |#4|)) . T)) 
+(((|#1| (-489 (-750 (-1074))) (-750 (-1074))) . T)) 
+((((-1141 |#1| |#2| |#3| |#4|)) . T)) 
+((((-1141 |#1| |#2| |#3| |#4|)) . T)) 
 (((|#1|) |has| |#1| (-961))) 
 ((((-517) (-107)) . T)) 
 ((((-787)) |has| |#1| (-1003))) 
@@ -1599,34 +1599,34 @@
 (((|#1|) . T)) 
 ((((-517)) . T)) 
 ((((-787)) . T)) 
-(-3807 (|has| |#1| (-132)) (|has| |#1| (-319))) 
+(-3763 (|has| |#1| (-132)) (|has| |#1| (-319))) 
 ((((-787)) . T)) 
 (|has| |#1| (-134)) 
 (((|#3|) . T)) 
-(-3807 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) 
+(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) 
 ((((-787)) . T)) 
-((((-1139 |#2| |#3| |#4|)) . T) (((-1140 |#1| |#2| |#3| |#4|)) . T)) 
+((((-1140 |#2| |#3| |#4|)) . T) (((-1141 |#1| |#2| |#3| |#4|)) . T)) 
 ((((-787)) . T)) 
-((((-47)) -12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (((-556 $)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) -3807 (-12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (|has| |#1| (-952 (-377 (-517))))) (((-377 (-874 |#1|))) |has| |#1| (-509)) (((-874 |#1|)) |has| |#1| (-961)) (((-1073)) . T)) 
+((((-47)) -12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (((-556 $)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) -3763 (-12 (|has| |#1| (-509)) (|has| |#1| (-952 (-517)))) (|has| |#1| (-952 (-377 (-517))))) (((-377 (-874 |#1|))) |has| |#1| (-509)) (((-874 |#1|)) |has| |#1| (-961)) (((-1074)) . T)) 
 (((|#1|) . T) (($) . T)) 
 (((|#1| (-703)) . T)) 
-((($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
+((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
 (((|#1|) |has| |#1| (-280 |#1|))) 
-((((-1140 |#1| |#2| |#3| |#4|)) . T)) 
+((((-1141 |#1| |#2| |#3| |#4|)) . T)) 
 ((((-517)) |has| |#1| (-808 (-517))) (((-349)) |has| |#1| (-808 (-349)))) 
 (((|#1|) . T)) 
 (|has| |#1| (-509)) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
-(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))))) 
+(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) 
 (((|#1|) |has| |#1| (-156))) 
 ((($) |has| |#1| (-509)) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (((|#1|) . T)) 
 (((|#3|) |has| |#3| (-1003))) 
-(((|#2|) -3807 (|has| |#2| (-156)) (|has| |#2| (-333)))) 
-((((-1139 |#2| |#3| |#4|)) . T)) 
+(((|#2|) -3763 (|has| |#2| (-156)) (|has| |#2| (-333)))) 
+((((-1140 |#2| |#3| |#4|)) . T)) 
 ((((-107)) . T)) 
 (|has| |#1| (-752)) 
 (|has| |#1| (-752)) 
@@ -1635,8 +1635,8 @@
 (|has| |#1| (-777)) 
 (|has| |#1| (-777)) 
 (((|#1| (-517) (-989)) . T)) 
-(-3807 (|has| |#1| (-822 (-1073))) (|has| |#1| (-961))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+(-3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1| (-377 (-517)) (-989)) . T)) 
 (((|#1| (-703) (-989)) . T)) 
 (|has| |#1| (-779)) 
@@ -1652,28 +1652,28 @@
 (((|#1|) . T)) 
 (|has| |#1| (-1003)) 
 ((((-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-579 (-517)))) ((|#2|) |has| |#1| (-333))) 
-(-3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
+(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
 (((|#2|) |has| |#2| (-156))) 
 (((|#1|) |has| |#1| (-156))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) 
 ((((-787)) . T)) 
 (|has| |#3| (-777)) 
 ((((-787)) . T)) 
-((((-1139 |#2| |#3| |#4|) (-289 |#2| |#3| |#4|)) . T)) 
+((((-1140 |#2| |#3| |#4|) (-289 |#2| |#3| |#4|)) . T)) 
 ((((-787)) . T)) 
-(((|#1| |#1|) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) 
+(((|#1| |#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) 
 (((|#1|) . T)) 
 ((((-517)) . T)) 
 ((((-517)) . T)) 
-(((|#1|) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) 
+(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-961)))) 
 (((|#2|) |has| |#2| (-333))) 
 ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-333))) 
 (|has| |#1| (-779)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#2|) . T)) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) |has| (-2 (|:| -3435 (-1073)) (|:| -1257 (-51))) (-280 (-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))))) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-831))) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1074)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))))) 
+(-3763 (|has| |#1| (-421)) (|has| |#1| (-831))) 
 (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
@@ -1686,13 +1686,13 @@
 (((|#1|) . T)) 
 (((|#1| (-517)) . T)) 
 (|has| |#1| (-777)) 
-(((|#1| (-1071 |#1| |#2| |#3|)) . T)) 
+(((|#1| (-1072 |#1| |#2| |#3|)) . T)) 
 (((|#1| |#1|) . T)) 
 (((|#1| |#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1| (-377 (-517))) . T)) 
-(((|#1| (-1064 |#1| |#2| |#3|)) . T)) 
+(((|#1| (-1065 |#1| |#2| |#3|)) . T)) 
 (((|#1| (-703)) . T)) 
 (((|#1|) . T)) 
 (((|#1| |#1| |#2| (-214 |#1| |#2|) (-214 |#1| |#2|)) . T)) 
@@ -1707,18 +1707,18 @@
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (((|#1|) . T)) 
-(-3807 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
+(-3763 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
 (((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) 
 ((((-787)) . T)) 
 (((|#1|) . T) (((-377 (-517))) . T) (($) . T)) 
 ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-333)) 
 (|has| (-377 |#2|) (-207)) 
 (|has| |#1| (-831)) 
 (((|#2|) |has| |#2| (-961))) 
-(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))))) 
+(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) 
 (|has| |#1| (-333)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#1| |#1|) . T)) 
@@ -1743,7 +1743,7 @@
 (((|#1| (-377 (-517)) (-989)) . T)) 
 (((|#1| (-703) (-989)) . T)) 
 ((((-377 |#2|) (-377 |#2|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) 
-(((|#1|) . T) (((-517)) -3807 (|has| (-377 (-517)) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) . T)) 
+(((|#1|) . T) (((-517)) -3763 (|has| (-377 (-517)) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) . T)) 
 (((|#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#1|) . T)) 
@@ -1762,24 +1762,24 @@
 ((((-632)) . T)) 
 (((|#2|) |has| |#2| (-156))) 
 (|has| |#2| (-777)) 
-((((-107)) |has| |#1| (-1003)) (((-787)) -3807 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1073))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003)))) 
+((((-107)) |has| |#1| (-1003)) (((-787)) -3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1074))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003)))) 
 (((|#1|) . T) (($) . T)) 
 (((|#1| |#2|) . T)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))) . T)) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) 
 ((((-787)) . T)) 
 ((((-517) |#1|) . T)) 
 ((((-632)) . T) (((-377 (-517))) . T) (((-517)) . T)) 
 (((|#1| |#1|) |has| |#1| (-156))) 
 (((|#2|) . T)) 
-(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|))))) 
+(((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003))) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|))))) 
 ((((-349)) . T)) 
 ((((-632)) . T)) 
 ((((-377 (-517))) |has| |#2| (-333)) (($) |has| |#2| (-333))) 
 (((|#1|) |has| |#1| (-156))) 
 ((((-377 (-874 |#1|))) . T)) 
 (((|#2| |#2|) . T)) 
-(-3807 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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+(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 (((|#2|) . T)) 
 (|has| |#2| (-779)) 
 (((|#3|) |has| |#3| (-961))) 
@@ -1787,16 +1787,16 @@
 (|has| |#1| (-831)) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-779)) 
-((((-1073)) |has| |#2| (-822 (-1073)))) 
+((((-1074)) |has| |#2| (-822 (-1074)))) 
 ((((-787)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
 (|has| |#1| (-442)) 
 (|has| |#1| (-338)) 
 (|has| |#1| (-338)) 
 (|has| |#1| (-338)) 
 (|has| |#1| (-333)) 
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+(-3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-442)) (|has| |#1| (-509)) (|has| |#1| (-961)) (|has| |#1| (-1015))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 ((((-111 |#1|)) . T)) 
 ((((-111 |#1|)) . T)) 
@@ -1817,11 +1817,11 @@
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-779)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) . T)) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) 
 (((|#1| |#2|) . T)) 
 (|has| |#1| (-134)) 
 (|has| |#1| (-132)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) |has| (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)) (-280 (-2 (|:| -3435 |#1|) (|:| -1257 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) |has| (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)) (-280 (-2 (|:| -3342 |#1|) (|:| -1266 |#2|)))) ((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (((|#2|) . T)) 
 (((|#3|) . T)) 
 ((((-111 |#1|)) . T)) 
@@ -1839,11 +1839,11 @@
 ((((-493)) |has| |#1| (-558 (-493))) (((-814 (-517))) |has| |#1| (-558 (-814 (-517)))) (((-814 (-349))) |has| |#1| (-558 (-814 (-349)))) (((-349)) |has| |#1| (-937)) (((-199)) |has| |#1| (-937))) 
 (((|#1|) |has| |#1| (-333))) 
 ((((-787)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((($ $) . T) (((-556 $) $) . T)) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-509))) 
-((($) . T) (((-1140 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . T)) 
-((($) -3807 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-509))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+((($) . T) (((-1141 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . T)) 
+((($) -3763 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-509))) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-333)) 
@@ -1854,11 +1854,11 @@
 ((((-349)) . T)) 
 (((|#3|) -12 (|has| |#3| (-280 |#3|)) (|has| |#3| (-1003)))) 
 ((((-787)) . T)) 
-(-3807 (|has| |#2| (-421)) (|has| |#2| (-831))) 
+(-3763 (|has| |#2| (-421)) (|has| |#2| (-831))) 
 (((|#1|) . T)) 
 (|has| |#1| (-779)) 
 (|has| |#1| (-779)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 ((((-493)) |has| |#1| (-558 (-493)))) 
 (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (|has| |#1| (-1003)) 
@@ -1867,13 +1867,13 @@
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
 ((((-517)) . T)) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-509))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-509))) 
-((((-1139 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1139 |#2| |#3| |#4|) (-37 (-377 (-517)))) (($) . T)) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-509))) 
+((((-1140 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517)))) (($) . T)) 
 ((((-517)) . T)) 
 (|has| |#1| (-333)) 
-(-3807 (-12 (|has| (-1146 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) 
-(-3807 (-12 (|has| (-1146 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) 
+(-3763 (-12 (|has| (-1147 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) 
+(-3763 (-12 (|has| (-1147 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
@@ -1890,18 +1890,18 @@
 (((|#1| |#2|) . T)) 
 (((|#1|) . T) (((-517)) |has| |#1| (-579 (-517)))) 
 (((|#3|) |has| |#3| (-156))) 
-(-3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
+(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
 ((((-517)) . T)) 
 (((|#1| $) |has| |#1| (-258 |#1| |#1|))) 
 ((((-377 (-517))) . T) (($) . T) (((-377 |#1|)) . T) ((|#1|) . T)) 
 ((((-787)) . T)) 
 (((|#3|) . T)) 
-(((|#1| |#1|) . T) (($ $) -3807 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517)) (-377 (-517))) |has| |#1| (-333))) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
+(((|#1| |#1|) . T) (($ $) -3763 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517)) (-377 (-517))) |has| |#1| (-333))) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
 ((($) . T)) 
 ((((-517) |#1|) . T)) 
-((((-1073)) |has| (-377 |#2|) (-822 (-1073)))) 
-(((|#1|) . T) (($) -3807 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517))) |has| |#1| (-333))) 
+((((-1074)) |has| (-377 |#2|) (-822 (-1074)))) 
+(((|#1|) . T) (($) -3763 (|has| |#1| (-262)) (|has| |#1| (-333))) (((-377 (-517))) |has| |#1| (-333))) 
 ((((-493)) |has| |#2| (-558 (-493)))) 
 ((((-623 |#2|)) . T) (((-787)) . T)) 
 (((|#1|) . T)) 
@@ -1909,8 +1909,8 @@
 (((|#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) 
 ((((-794 |#1|)) . T)) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
-(-3807 (|has| |#4| (-725)) (|has| |#4| (-777))) 
-(-3807 (|has| |#3| (-725)) (|has| |#3| (-777))) 
+(-3763 (|has| |#4| (-725)) (|has| |#4| (-777))) 
+(-3763 (|has| |#3| (-725)) (|has| |#3| (-777))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) 
@@ -1926,17 +1926,17 @@
 ((((-377 (-517))) . T) (($) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-1112))) 
+(-3763 (|has| |#1| (-421)) (|has| |#1| (-1113))) 
 ((($) . T)) 
 ((((-377 (-517))) |has| (-377 |#2|) (-952 (-377 (-517)))) (((-517)) |has| (-377 |#2|) (-952 (-517))) (((-377 |#2|)) . T)) 
 (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) 
 (((|#1| (-703)) . T)) 
 (|has| |#1| (-779)) 
 (((|#1|) . T) (((-517)) |has| |#1| (-579 (-517)))) 
-((($) -3807 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3807 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
+((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) (((-377 (-517))) -3763 (|has| |#1| (-333)) (|has| |#1| (-319))) ((|#1|) . T)) 
 ((((-517)) . T)) 
 (|has| |#1| (-37 (-377 (-517)))) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))) |has| (-2 (|:| -3435 (-1056)) (|:| -1257 (-51))) (-280 (-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))))) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 (-51))) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))))) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (|has| |#1| (-777)) 
 (|has| |#1| (-37 (-377 (-517)))) 
@@ -1961,24 +1961,24 @@
 (((|#1| |#2|) . T)) 
 ((((-131)) . T)) 
 ((((-712 |#1| (-789 |#2|))) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
-(|has| |#1| (-1094)) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+(|has| |#1| (-1095)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) 
-((((-1073) |#1|) |has| |#1| (-478 (-1073) |#1|))) 
+(-3763 (|has| |#3| (-25)) (|has| |#3| (-123)) (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-338)) (|has| |#3| (-725)) (|has| |#3| (-777)) (|has| |#3| (-961)) (|has| |#3| (-1003))) 
+((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|))) 
 (((|#2|) . T)) 
-((($ $) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
-((($) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+((($ $) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+((($) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 ((((-832 |#1|)) . T)) 
 ((($) . T)) 
 ((((-377 (-874 |#1|))) . T)) 
 (((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 ((((-493)) |has| |#4| (-558 (-493)))) 
 ((((-787)) . T) (((-583 |#4|)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1|) . T)) 
 (|has| |#1| (-777)) 
-(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) |has| (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|)) (-280 (-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))))) 
+(((|#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) (((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) |has| (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|)) (-280 (-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))))) 
 (|has| |#1| (-1003)) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-779)) 
@@ -1986,17 +1986,17 @@
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 ((($) . T) (((-377 (-517))) . T)) 
-((($) -3807 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3807 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
+((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-509))) (((-377 (-517))) -3763 (|has| |#1| (-37 (-377 (-517)))) (|has| |#1| (-333))) ((|#1|) |has| |#1| (-156))) 
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
-(-3807 (-12 (|has| (-1071 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) 
-(-3807 (-12 (|has| (-1071 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) 
+(-3763 (-12 (|has| (-1072 |#1| |#2| |#3|) (-134)) (|has| |#1| (-333))) (|has| |#1| (-134))) 
+(-3763 (-12 (|has| (-1072 |#1| |#2| |#3|) (-132)) (|has| |#1| (-333))) (|has| |#1| (-132))) 
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
 (|has| |#1| (-134)) 
 (|has| |#1| (-132)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
-((((-1146 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 (|has| |#1| (-777)) 
 (((|#1| |#2|) . T)) 
 (((|#1|) . T) (((-517)) |has| |#1| (-579 (-517)))) 
@@ -2018,9 +2018,9 @@
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-493)) |has| |#1| (-558 (-493)))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-1073) |#1|) |has| |#1| (-478 (-1073) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) 
-(((|#1|) -3807 (|has| |#1| (-156)) (|has| |#1| (-333)))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) 
+(((|#1|) -3763 (|has| |#1| (-156)) (|has| |#1| (-333)))) 
 ((((-286 |#1|)) . T)) 
 (((|#2|) |has| |#2| (-333))) 
 (((|#2|) . T)) 
@@ -2031,8 +2031,8 @@
 (((|#2|) |has| |#2| (-156))) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#2|) . T)) 
-((((-1073)) |has| |#1| (-822 (-1073))) (((-989)) . T)) 
-((((-1073)) |has| |#1| (-822 (-1073))) (((-993 (-1073))) . T)) 
+((((-1074)) |has| |#1| (-822 (-1074))) (((-989)) . T)) 
+((((-1074)) |has| |#1| (-822 (-1074))) (((-993 (-1074))) . T)) 
 (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
@@ -2041,14 +2041,14 @@
 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
 ((($ $) . T)) 
-(-3807 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-442)) (|has| |#1| (-659)) (|has| |#1| (-822 (-1073))) (|has| |#1| (-961)) (|has| |#1| (-1015)) (|has| |#1| (-1003))) 
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 (|has| |#1| (-509)) 
 (((|#2|) . T)) 
 ((((-517)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#1| (-132)) (|has| |#1| (-134)) (|has| |#1| (-156)) (|has| |#1| (-509)) (|has| |#1| (-961))) 
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 ((((-530 |#1|)) . T)) 
 ((($) . T)) 
 (((|#1| (-57 |#1|) (-57 |#1|)) . T)) 
@@ -2056,7 +2056,7 @@
 ((($) . T)) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
-(((|#2|) |has| |#2| (-6 (-4182 "*")))) 
+(((|#2|) |has| |#2| (-6 (-4185 "*")))) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
@@ -2064,26 +2064,26 @@
 ((((-377 (-517))) |has| |#2| (-952 (-377 (-517)))) (((-517)) |has| |#2| (-952 (-517))) ((|#2|) . T) (((-789 |#1|)) . T)) 
 ((($) . T) (((-111 |#1|)) . T) (((-377 (-517))) . T)) 
 ((((-1026 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) 
-((((-1069 |#1|)) . T) (((-989)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) 
-((((-1026 |#1| (-1073))) . T) (((-993 (-1073))) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-1073)) . T)) 
+((((-1070 |#1|)) . T) (((-989)) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517))))) 
+((((-1026 |#1| (-1074))) . T) (((-993 (-1074))) . T) ((|#1|) . T) (((-517)) |has| |#1| (-952 (-517))) (((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-1074)) . T)) 
 (|has| |#1| (-1003)) 
 ((($) . T)) 
 (|has| |#1| (-1003)) 
 ((((-517)) -12 (|has| |#1| (-808 (-517))) (|has| |#2| (-808 (-517)))) (((-349)) -12 (|has| |#1| (-808 (-349))) (|has| |#2| (-808 (-349))))) 
 (((|#1| |#2|) . T)) 
-((((-1073) |#1|) . T)) 
+((((-1074) |#1|) . T)) 
 (((|#4|) . T)) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-319))) 
-((((-1073) (-51)) . T)) 
-((((-1139 |#2| |#3| |#4|) (-289 |#2| |#3| |#4|)) . T)) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) 
+((((-1074) (-51)) . T)) 
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 ((((-377 (-517))) |has| |#1| (-952 (-377 (-517)))) (((-517)) |has| |#1| (-952 (-517))) ((|#1|) . T)) 
 ((((-787)) . T)) 
-(-3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
-((((-1140 |#1| |#2| |#3| |#4|) (-1140 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) 
+(-3763 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-338)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961)) (|has| |#2| (-1003))) 
+((((-1141 |#1| |#2| |#3| |#4|) (-1141 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) . T) (($ $) . T)) 
 (((|#1| |#1|) |has| |#1| (-156)) (((-377 (-517)) (-377 (-517))) |has| |#1| (-509)) (($ $) |has| |#1| (-509))) 
 (((|#1|) . T) (($) . T) (((-377 (-517))) . T)) 
 (((|#1| $) |has| |#1| (-258 |#1| |#1|))) 
-((((-1140 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . T) (($) . T)) 
+((((-1141 |#1| |#2| |#3| |#4|)) . T) (((-377 (-517))) . T) (($) . T)) 
 (((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-509)) (($) |has| |#1| (-509))) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-132)) 
@@ -2093,33 +2093,33 @@
 ((((-377 (-517))) . T) (($) . T)) 
 (((|#3|) |has| |#3| (-333))) 
 (((|#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
-((((-1073)) . T)) 
+((((-1074)) . T)) 
 (((|#1|) . T)) 
 (((|#2| |#2|) -12 (|has| |#2| (-280 |#2|)) (|has| |#2| (-1003)))) 
 (((|#2| |#3|) . T)) 
-(-3807 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
+(-3763 (|has| |#2| (-333)) (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
 (((|#1| (-489 |#2|)) . T)) 
 (((|#1| (-703)) . T)) 
-(((|#1| (-489 (-993 (-1073)))) . T)) 
+(((|#1| (-489 (-993 (-1074)))) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#1|) . T)) 
 (|has| |#2| (-831)) 
-(-3807 (|has| |#2| (-725)) (|has| |#2| (-777))) 
+(-3763 (|has| |#2| (-725)) (|has| |#2| (-777))) 
 ((((-787)) . T)) 
-((($ $) . T) (((-1139 |#2| |#3| |#4|) (-1139 |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) |has| (-1139 |#2| |#3| |#4|) (-37 (-377 (-517))))) 
+((($ $) . T) (((-1140 |#2| |#3| |#4|) (-1140 |#2| |#3| |#4|)) . T) (((-377 (-517)) (-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517))))) 
 ((((-832 |#1|)) . T)) 
 (-12 (|has| |#1| (-333)) (|has| |#2| (-752))) 
 ((($) . T) (((-377 (-517))) . T)) 
 ((($) . T)) 
 ((($) . T)) 
 (|has| |#1| (-333)) 
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 (|has| |#1| (-333)) 
-((($) . T) (((-1139 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1139 |#2| |#3| |#4|) (-37 (-377 (-517))))) 
+((($) . T) (((-1140 |#2| |#3| |#4|)) . T) (((-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517))))) 
 (((|#1| |#2|) . T)) 
-((((-1071 |#1| |#2| |#3|)) |has| |#1| (-333))) 
-(-3807 (-12 (|has| |#1| (-278)) (|has| |#1| (-831))) (|has| |#1| (-333)) (|has| |#1| (-319))) 
-(-3807 (|has| |#1| (-822 (-1073))) (|has| |#1| (-961))) 
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+(-3763 (|has| |#1| (-822 (-1074))) (|has| |#1| (-961))) 
 ((((-517)) |has| |#1| (-579 (-517))) ((|#1|) . T)) 
 (((|#1| |#2|) . T)) 
 ((((-787)) . T)) 
@@ -2147,31 +2147,31 @@
 ((($ $) . T)) 
 ((($) . T)) 
 ((((-787)) . T)) 
-(((|#1| (-489 (-1073))) . T)) 
+(((|#1| (-489 (-1074))) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 ((((-787)) . T)) 
 (((|#4| |#4|) -12 (|has| |#4| (-280 |#4|)) (|has| |#4| (-1003)))) 
-(((|#2|) -3807 (|has| |#2| (-6 (-4182 "*"))) (|has| |#2| (-156)))) 
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-(-3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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 (|has| |#2| (-779)) 
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 (|has| |#1| (-831)) 
 (((|#2|) |has| |#2| (-156))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-1146 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-1147 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-493)) . T) (((-517)) . T) (((-814 (-517))) . T) (((-349)) . T) (((-199)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 (-51)))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 (-51)))) . T)) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#1| (-377 (-517))) . T)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#1| (-262)) (|has| |#1| (-333))) 
+(-3763 (|has| |#1| (-262)) (|has| |#1| (-333))) 
 ((((-131)) . T)) 
 ((((-377 |#2|)) . T) (((-377 (-517))) . T) (($) . T)) 
 (|has| |#1| (-777)) 
@@ -2186,19 +2186,19 @@
 ((((-377 (-517))) . T) (($) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#2| |#2|) . T) ((|#1| |#1|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-493)) |has| |#1| (-558 (-493))) (((-814 (-517))) |has| |#1| (-558 (-814 (-517)))) (((-814 (-349))) |has| |#1| (-558 (-814 (-349))))) 
-((((-1073) (-51)) . T)) 
+((((-1074) (-51)) . T)) 
 (((|#2|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
-((((-583 (-131))) . T) (((-1056)) . T)) 
+((((-583 (-131))) . T) (((-1057)) . T)) 
 ((((-787)) . T)) 
-((((-2 (|:| -3435 (-1056)) (|:| -1257 |#1|))) . T)) 
-((((-1073) |#1|) |has| |#1| (-478 (-1073) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) 
+((((-2 (|:| -3342 (-1057)) (|:| -1266 |#1|))) . T)) 
+((((-1074) |#1|) |has| |#1| (-478 (-1074) |#1|)) ((|#1| |#1|) |has| |#1| (-280 |#1|))) 
 (|has| |#1| (-779)) 
 ((((-787)) . T)) 
 ((((-493)) |has| |#1| (-558 (-493)))) 
@@ -2209,16 +2209,16 @@
 ((((-787)) . T) (((-583 |#4|)) . T)) 
 (((|#2|) . T)) 
 ((((-832 |#1|)) . T) (((-377 (-517))) . T) (($) . T)) 
-(-3807 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) 
-(-3807 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) 
-((((-1073) (-51)) . T)) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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+(-3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) 
+((((-1074) (-51)) . T)) 
+(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#2| (-25)) (|has| |#2| (-123)) (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-725)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
-(-3807 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
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+(-3763 (|has| |#2| (-156)) (|has| |#2| (-333)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
 (|has| |#1| (-831)) 
 (|has| |#1| (-831)) 
 (((|#2|) . T)) 
@@ -2233,12 +2233,12 @@
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
 (|has| |#1| (-37 (-377 (-517)))) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 (|has| |#1| (-752)) 
 ((((-832 |#1|) (-832 |#1|)) . T) (($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) 
 ((((-377 |#2|)) . T)) 
 (|has| |#1| (-777)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 (((|#1| |#1|) . T) (((-377 (-517)) (-377 (-517))) . T) (((-517) (-517)) . T) (($ $) . T)) 
 ((((-832 |#1|)) . T) (($) . T) (((-377 (-517))) . T)) 
 (((|#2|) |has| |#2| (-961)) (((-517)) -12 (|has| |#2| (-579 (-517))) (|has| |#2| (-961)))) 
@@ -2247,33 +2247,33 @@
 (|has| |#1| (-134)) 
 (|has| |#1| (-132)) 
 (((|#2|) . T)) 
-(-3807 (|has| |#1| (-132)) (|has| |#1| (-338))) 
-(-3807 (|has| |#1| (-132)) (|has| |#1| (-338))) 
-(-3807 (|has| |#1| (-132)) (|has| |#1| (-338))) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
-((((-51)) . T) (((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
+(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) 
+(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) 
+(-3763 (|has| |#1| (-132)) (|has| |#1| (-338))) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
+((((-51)) . T) (((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
 (|has| |#1| (-319)) 
 ((((-517)) . T)) 
 ((((-787)) . T)) 
-((((-1140 |#1| |#2| |#3| |#4|) $) |has| (-1140 |#1| |#2| |#3| |#4|) (-258 (-1140 |#1| |#2| |#3| |#4|) (-1140 |#1| |#2| |#3| |#4|)))) 
+((((-1141 |#1| |#2| |#3| |#4|) $) |has| (-1141 |#1| |#2| |#3| |#4|) (-258 (-1141 |#1| |#2| |#3| |#4|) (-1141 |#1| |#2| |#3| |#4|)))) 
 (|has| |#1| (-333)) 
 ((((-989) |#1|) . T) (((-989) $) . T) (($ $) . T)) 
-(-3807 (|has| |#1| (-333)) (|has| |#1| (-319))) 
+(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) 
 ((((-377 (-517)) (-377 (-517))) . T) (((-632) (-632)) . T) (($ $) . T)) 
 ((((-286 |#1|)) . T) (($) . T)) 
 (((|#1|) . T) (((-377 (-517))) |has| |#1| (-333))) 
 (|has| |#1| (-1003)) 
 (((|#1|) . T)) 
-(((|#1|) -3807 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) 
-(((|#1|) -3807 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) 
+(((|#1|) -3763 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) 
+(((|#1|) -3763 (|has| |#2| (-337 |#1|)) (|has| |#2| (-387 |#1|)))) 
 (((|#2|) . T)) 
 ((((-377 (-517))) . T) (((-632)) . T) (($) . T)) 
 (((|#3| |#3|) . T)) 
 (|has| |#2| (-207)) 
 ((((-789 |#1|)) . T)) 
-((((-1073)) |has| |#1| (-822 (-1073))) ((|#3|) . T)) 
+((((-1074)) |has| |#1| (-822 (-1074))) ((|#3|) . T)) 
 (-12 (|has| |#1| (-333)) (|has| |#2| (-937))) 
-((((-1071 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 ((((-787)) . T)) 
 (|has| |#1| (-333)) 
 (|has| |#1| (-333)) 
@@ -2284,7 +2284,7 @@
 (((|#2|) . T)) 
 (((|#1|) . T)) 
 ((((-517)) . T)) 
-(-3807 (|has| |#1| (-156)) (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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 (((|#2|) . T) (((-517)) |has| |#2| (-579 (-517)))) 
 (((|#1| |#2|) . T)) 
 ((($) . T)) 
@@ -2292,7 +2292,7 @@
 ((($) . T) (((-377 (-517))) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 (((|#1|) . T) (($) . T)) 
-(((|#1| (-1153 |#1|) (-1153 |#1|)) . T)) 
+(((|#1| (-1154 |#1|) (-1154 |#1|)) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
@@ -2321,7 +2321,7 @@
 (|has| |#2| (-937)) 
 ((($) . T)) 
 (|has| |#1| (-831)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((($) . T)) 
 (((|#2|) . T)) 
 (((|#1|) . T)) 
@@ -2329,24 +2329,24 @@
 ((($) . T)) 
 (|has| |#1| (-333)) 
 ((((-832 |#1|)) . T)) 
-((($) -3807 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
+((($) -3763 (|has| |#1| (-333)) (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) ((|#1|) |has| |#1| (-156)) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 ((($ $) . T) (((-377 (-517)) (-377 (-517))) . T)) 
-(-3807 (|has| |#1| (-338)) (|has| |#1| (-779))) 
+(-3763 (|has| |#1| (-338)) (|has| |#1| (-779))) 
 (((|#1|) . T)) 
 ((((-787)) . T)) 
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 ((((-377 |#2|) |#3|) . T)) 
 ((($) . T) (((-377 (-517))) . T)) 
 ((((-703) |#1|) . T)) 
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 (((|#1| (-489 |#3|)) . T)) 
 ((((-377 (-517))) . T)) 
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 ((((-787)) . T)) 
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 ((((-153 (-349))) . T) (((-199)) . T) (((-349)) . T)) 
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 (((|#1|) . T)) 
@@ -2363,13 +2363,13 @@
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 (-12 (|has| |#1| (-502)) (|has| |#1| (-760))) 
 ((((-787)) . T)) 
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 (|has| |#1| (-333)) 
 ((((-377 (-517))) . T) (($) . T)) 
 ((($) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) . T)) 
@@ -2377,22 +2377,22 @@
 (((|#1|) . T)) 
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 (((|#2|) |has| |#1| (-333))) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1|) . T)) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#1|) . T)) 
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+(((|#2|) . T) (((-1074)) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-1074)))) (((-517)) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-517)))) (((-377 (-517))) -12 (|has| |#1| (-333)) (|has| |#2| (-952 (-517))))) 
 (((|#2|) . T)) 
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 ((($ $) . T)) 
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 ((($) . T)) 
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@@ -2400,31 +2400,31 @@
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 (((|#3|) . T)) 
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 (((|#2|) . T)) 
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 (((|#1| |#2|) . T)) 
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+((((-1057) |#1|) . T)) 
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 ((($) . T)) 
@@ -2432,13 +2432,13 @@
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-((((-1038 |#1| |#2|)) . T)) 
+((((-1039 |#1| |#2|)) . T)) 
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@@ -2449,7 +2449,7 @@
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-((((-1073) (-51)) . T)) 
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@@ -2457,13 +2457,13 @@
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@@ -2476,22 +2476,22 @@
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 ((((-787)) . T)) 
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+((((-1057)) . T) (((-493)) . T) (((-517)) . T) (((-814 (-517))) . T) (((-349)) . T) (((-199)) . T)) 
 ((((-787)) . T)) 
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+((($) . T) (((-1140 |#2| |#3| |#4|)) |has| (-1140 |#2| |#3| |#4|) (-156)) (((-377 (-517))) |has| (-1140 |#2| |#3| |#4|) (-37 (-377 (-517))))) 
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@@ -2500,7 +2500,7 @@
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+((((-1074) |#1|) . T)) 
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@@ -2508,8 +2508,8 @@
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@@ -2518,7 +2518,7 @@
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@@ -2526,14 +2526,14 @@
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@@ -2542,41 +2542,41 @@
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-(((|#2|) |has| |#2| (-6 (-4182 "*")))) 
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 (((|#2| |#2|) . T) ((|#6| |#6|) . T)) 
 ((($) . T) (((-377 (-517))) |has| |#2| (-37 (-377 (-517)))) ((|#2|) . T)) 
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 (((|#2|) . T)) 
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 ((((-787)) . T)) 
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@@ -2656,14 +2656,14 @@
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@@ -2746,7 +2746,7 @@
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@@ -2754,7 +2754,7 @@
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@@ -2771,33 +2771,33 @@
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@@ -2810,21 +2810,21 @@
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 (((|#1|) . T) (($) . T) (((-377 (-517))) . T)) 
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 ((((-517)) . T)) 
 ((((-517)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (((|#1| |#2|) . T)) 
 (((|#1|) . T)) 
-(-3807 (|has| |#2| (-156)) (|has| |#2| (-777)) (|has| |#2| (-961))) 
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-(-3807 (-12 (|has| |#1| (-442)) (|has| |#2| (-442))) (-12 (|has| |#1| (-659)) (|has| |#2| (-659)))) 
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 (|has| |#1| (-132)) 
 (|has| |#1| (-134)) 
 (|has| |#1| (-333)) 
@@ -3036,10 +3036,10 @@
 ((((-377 (-517))) |has| |#1| (-37 (-377 (-517)))) ((|#1|) |has| |#1| (-156)) (($) |has| |#1| (-509))) 
 ((((-517)) . T)) 
 ((((-517)) . T)) 
-((((-1056) (-1073) (-517) (-199) (-787)) . T)) 
+((((-1057) (-1074) (-517) (-199) (-787)) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 (((|#1| |#2|) . T)) 
-(-3807 (|has| |#1| (-319)) (|has| |#1| (-338))) 
+(-3763 (|has| |#1| (-319)) (|has| |#1| (-338))) 
 (((|#1| |#2|) . T)) 
 ((($) . T) ((|#1|) . T)) 
 ((((-787)) . T)) 
@@ -3047,7 +3047,7 @@
 ((($) . T) ((|#1|) . T) (((-377 (-517))) |has| |#1| (-37 (-377 (-517))))) 
 (((|#2|) |has| |#2| (-1003)) (((-517)) -12 (|has| |#2| (-952 (-517))) (|has| |#2| (-1003))) (((-377 (-517))) -12 (|has| |#2| (-952 (-377 (-517)))) (|has| |#2| (-1003)))) 
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+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-779)) (|has| |#1| (-1003)))) 
 ((($) . T) (((-377 (-517))) . T)) 
 (|has| |#1| (-831)) 
 (|has| |#1| (-831)) 
@@ -3056,10 +3056,10 @@
 ((((-787)) . T)) 
 (((|#2| |#2|) . T)) 
 (((|#1| |#1|) |has| |#1| (-156))) 
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-(-3807 (|has| |#1| (-21)) (|has| |#1| (-777))) 
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 (((|#2|) . T)) 
-(-3807 (|has| |#1| (-21)) (|has| |#1| (-777))) 
+(-3763 (|has| |#1| (-21)) (|has| |#1| (-777))) 
 (((|#1|) |has| |#1| (-156))) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
@@ -3074,19 +3074,19 @@
 (((|#1|) . T) (((-377 (-517))) . T) (((-517)) . T) (($) . T)) 
 ((((-517) (-517)) . T)) 
 ((($) . T) (((-377 (-517))) . T)) 
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 ((((-517)) . T)) 
 (((|#2|) . T)) 
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-((((-1073)) -12 (|has| |#1| (-15 * (|#1| (-703) |#1|))) (|has| |#1| (-822 (-1073))))) 
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 (((|#1| |#1|) . T) (($ $) . T)) 
 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#1|) . T)) 
@@ -3096,34 +3096,34 @@
 (((|#1|) . T) (($) . T)) 
 (((|#1|) . T)) 
 ((((-789 |#1|)) . T)) 
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-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1039 |#1| |#2|)) . T)) 
+(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
 ((($) . T)) 
 (|has| |#1| (-937)) 
-(((|#2|) . T) (((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+(((|#2|) . T) (((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 ((((-787)) . T)) 
 ((((-493)) |has| |#2| (-558 (-493))) (((-814 (-517))) |has| |#2| (-558 (-814 (-517)))) (((-814 (-349))) |has| |#2| (-558 (-814 (-349)))) (((-349)) |has| |#2| (-937)) (((-199)) |has| |#2| (-937))) 
-((((-1073) (-51)) . T)) 
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 (|has| |#1| (-37 (-377 (-517)))) 
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 (((|#2|) . T)) 
 ((($ $) . T)) 
 ((((-377 (-517))) . T) (((-632)) . T) (($) . T)) 
-((((-1071 |#1| |#2| |#3|)) . T)) 
-((((-1071 |#1| |#2| |#3|)) . T) (((-1064 |#1| |#2| |#3|)) . T)) 
+((((-1072 |#1| |#2| |#3|)) . T)) 
+((((-1072 |#1| |#2| |#3|)) . T) (((-1065 |#1| |#2| |#3|)) . T)) 
 ((((-787)) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 ((((-517) |#1|) . T)) 
-((((-1071 |#1| |#2| |#3|)) |has| |#1| (-333))) 
+((((-1072 |#1| |#2| |#3|)) |has| |#1| (-333))) 
 (((|#1| |#2| |#3| |#4|) . T)) 
 (((|#1|) . T)) 
 (((|#2|) . T)) 
 (|has| |#2| (-333)) 
-(((|#3|) . T) ((|#2|) . T) (($) -3807 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) ((|#4|) -3807 (|has| |#4| (-156)) (|has| |#4| (-333)) (|has| |#4| (-961)))) 
-(((|#2|) . T) (($) -3807 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((|#3|) -3807 (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-961)))) 
+(((|#3|) . T) ((|#2|) . T) (($) -3763 (|has| |#4| (-156)) (|has| |#4| (-777)) (|has| |#4| (-961))) ((|#4|) -3763 (|has| |#4| (-156)) (|has| |#4| (-333)) (|has| |#4| (-961)))) 
+(((|#2|) . T) (($) -3763 (|has| |#3| (-156)) (|has| |#3| (-777)) (|has| |#3| (-961))) ((|#3|) -3763 (|has| |#3| (-156)) (|has| |#3| (-333)) (|has| |#3| (-961)))) 
 (((|#1|) . T)) 
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@@ -3135,37 +3135,37 @@
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#1|) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 ((((-517) |#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#1|) . T)) 
 (((|#2| $) -12 (|has| |#1| (-333)) (|has| |#2| (-258 |#2| |#2|))) (($ $) . T)) 
 ((($ $) . T)) 
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-(-3807 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
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+(-3763 (|has| |#1| (-779)) (|has| |#1| (-1003))) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 ((((-787)) . T)) 
 (((|#1| (-489 |#2|)) . T)) 
-((((-2 (|:| -3435 (-1073)) (|:| -1257 (-51)))) . T)) 
+((((-2 (|:| -3342 (-1074)) (|:| -1266 (-51)))) . T)) 
 (((|#1| (-517)) . T)) 
 (((|#1| (-377 (-517))) . T)) 
 (((|#1| (-703)) . T)) 
 ((((-111 |#1|)) . T) (($) . T) (((-377 (-517))) . T)) 
-(-3807 (|has| |#2| (-421)) (|has| |#2| (-509)) (|has| |#2| (-831))) 
-(-3807 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
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+(-3763 (|has| |#1| (-421)) (|has| |#1| (-509)) (|has| |#1| (-831))) 
 ((($) . T)) 
 (((|#2| (-489 (-789 |#1|))) . T)) 
 ((((-517) |#1|) . T)) 
 (((|#2|) . T)) 
 (((|#2| (-703)) . T)) 
-((((-787)) -3807 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
+((((-787)) -3763 (|has| |#1| (-557 (-787))) (|has| |#1| (-1003)))) 
 (((|#1|) . T)) 
 (((|#1| |#2|) . T)) 
-((((-1056) |#1|) . T)) 
+((((-1057) |#1|) . T)) 
 ((((-377 |#2|)) . T)) 
-((((-2 (|:| -3435 |#1|) (|:| -1257 |#2|))) . T)) 
+((((-2 (|:| -3342 |#1|) (|:| -1266 |#2|))) . T)) 
 (|has| |#1| (-509)) 
 (|has| |#1| (-509)) 
 ((($) . T) ((|#2|) . T)) 
@@ -3173,26 +3173,26 @@
 (((|#1| |#2|) . T)) 
 (((|#2| $) |has| |#2| (-258 |#2| |#2|))) 
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+(-3763 (|has| |#1| (-333)) (|has| |#1| (-319))) 
 (|has| |#1| (-1003)) 
 (((|#1|) . T)) 
 ((((-377 (-517))) . T) (($) . T)) 
-((((-915 |#1|)) . T) ((|#1|) . T) (((-517)) -3807 (|has| (-915 |#1|) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) -3807 (|has| (-915 |#1|) (-952 (-377 (-517)))) (|has| |#1| (-952 (-377 (-517)))))) 
+((((-915 |#1|)) . T) ((|#1|) . T) (((-517)) -3763 (|has| (-915 |#1|) (-952 (-517))) (|has| |#1| (-952 (-517)))) (((-377 (-517))) -3763 (|has| (-915 |#1|) (-952 (-377 (-517)))) (|has| |#1| (-952 (-377 (-517)))))) 
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-((((-1073)) |has| |#1| (-822 (-1073)))) 
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 (((|#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003)))) 
 (((|#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) . T)) 
 (((|#1|) . T)) 
 (((|#1| |#2| |#3| |#4|) . T)) 
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 ((($ $) . T)) 
 ((($ $) . T) (((-789 |#1|) $) . T) (((-789 |#1|) |#2|) . T)) 
 ((($ $) . T) ((|#2| $) |has| |#1| (-207)) ((|#2| |#1|) |has| |#1| (-207)) ((|#3| |#1|) . T) ((|#3| $) . T)) 
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. -134) 89892) ((-1027 . -132) 89871) ((-289 . -37) 89712) ((-153 . -123) T) ((-283 . -727) NIL) ((-283 . -724) NIL) ((-591 . -961) T) ((-47 . -585) 89677) ((-910 . -21) T) ((-122 . -926) 89661) ((-116 . -926) 89645) ((-910 . -25) T) ((-823 . -114) 89629) ((-1056 . -97) T) ((-748 . -779) 89608) ((-1127 . -123) T) ((-1069 . -25) T) ((-1069 . -21) T) ((-784 . -123) T) ((-1026 . -25) T) ((-1026 . -21) T) ((-783 . -25) T) ((-783 . -21) T) ((-714 . -278) 89587) ((-584 . -97) 89565) ((-572 . -97) T) ((-1057 . -280) 89360) ((-524 . -123) T) ((-562 . -777) 89339) ((-1054 . -456) 89323) ((-1048 . -138) 89273) ((-1044 . -557) 89235) ((-1044 . -558) 89196) ((-939 . -723) T) ((-939 . -726) T) ((-939 . -659) T) ((-451 . -280) 89134) ((-422 . -387) 89104) ((-321 . -156) T) ((-261 . -37) 89091) ((-247 . -97) T) ((-246 . -97) T) ((-245 . -97) T) ((-244 . -97) T) ((-243 . -97) T) ((-242 . -97) T) ((-241 . -97) T) ((-313 . -952) 89068) ((-188 . -97) T) ((-187 . -97) T) ((-185 . -97) T) ((-184 . -97) T) 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. -1015) T) ((-706 . -1003) T) ((-111 . -650) 86745) ((-608 . -952) 86729) ((-556 . -97) T) ((-766 . -23) T) ((-759 . -23) T) ((-1054 . -258) 86706) ((-1016 . -280) 86644) ((-1005 . -209) 86628) ((-62 . -366) T) ((-62 . -365) T) ((-105 . -97) T) ((-39 . -347) 86605) ((-590 . -781) 86589) ((-972 . -21) T) ((-972 . -25) T) ((-747 . -205) 86559) ((-874 . -25) T) ((-874 . -21) T) ((-562 . -968) T) ((-449 . -25) T) ((-449 . -21) T) ((-942 . -280) 86497) ((-811 . -557) 86479) ((-807 . -557) 86461) ((-224 . -779) 86412) ((-223 . -779) 86363) ((-486 . -478) 86296) ((-795 . -579) 86273) ((-445 . -280) 86211) ((-432 . -280) 86149) ((-321 . -262) T) ((-1054 . -1142) 86133) ((-1040 . -557) 86095) ((-1040 . -558) 86056) ((-1038 . -97) T) ((-915 . -967) 85952) ((-39 . -822) 85904) ((-1054 . -550) 85881) ((-1179 . -585) 85868) ((-973 . -138) 85814) ((-796 . -1112) T) ((-915 . -106) 85689) ((-309 . -650) 85673) ((-790 . -557) 85655) ((-157 . -650) 85587) ((-377 . -258) 85545) ((-796 . -509) T) ((-103 . -370) 85527) ((-82 . -354) T) ((-82 . -365) T) ((-634 . -156) T) ((-94 . -659) T) ((-450 . -97) 85338) ((-94 . -442) T) ((-111 . -156) T) ((-1016 . -37) 85308) ((-153 . -579) 85256) ((-965 . -97) T) ((-795 . -25) T) ((-747 . -212) 85235) ((-795 . -21) T) ((-750 . -97) T) ((-384 . -97) T) ((-355 . -97) T) ((-105 . -280) NIL) ((-201 . -97) 85213) ((-122 . -1108) T) ((-116 . -1108) T) ((-949 . -123) T) ((-607 . -337) 85197) ((-915 . -961) T) ((-1127 . -579) 85145) ((-1007 . -557) 85127) ((-919 . -557) 85109) ((-479 . -23) T) ((-474 . -23) T) ((-313 . -278) T) ((-472 . -23) T) ((-292 . -123) T) ((-3 . -1003) T) ((-919 . -558) 85093) ((-915 . -217) 85072) ((-915 . -207) 85051) ((-1179 . -659) T) ((-1146 . -132) 85030) ((-765 . -1003) T) ((-1146 . -134) 85009) ((-1139 . -134) 84988) ((-1139 . -132) 84967) ((-1138 . -1112) 84946) ((-1118 . -132) 84853) ((-1118 . -134) 84760) ((-1117 . -1112) 84739) ((-349 . -123) T) ((-517 . -808) 84721) ((0 . -1003) T) ((-157 . -156) T) ((-153 . -21) T) 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. -1003) T) ((-80 . -1108) T) ((-972 . -779) T) ((-874 . -779) 81361) ((-112 . -822) NIL) ((-714 . -842) 81340) ((-646 . -779) T) ((-489 . -1003) T) ((-465 . -1003) T) ((-325 . -1112) T) ((-322 . -1112) T) ((-314 . -1112) T) ((-237 . -1112) 81319) ((-221 . -1112) 81298) ((-1016 . -205) 81268) ((-449 . -779) 81247) ((-1040 . -967) 81231) ((-360 . -694) T) ((-1056 . -760) T) ((-627 . -1108) T) ((-325 . -509) T) ((-322 . -509) T) ((-314 . -509) T) ((-237 . -509) 81162) ((-221 . -509) 81093) ((-1040 . -106) 81072) ((-422 . -677) 81042) ((-790 . -967) 81012) ((-749 . -37) 80949) ((-627 . -806) 80931) ((-627 . -808) 80913) ((-266 . -280) 80717) ((-832 . -1112) T) ((-607 . -381) 80701) ((-790 . -106) 80666) ((-627 . -952) 80611) ((-920 . -421) T) ((-832 . -509) T) ((-530 . -842) T) ((-443 . -1015) T) ((-481 . -842) T) ((-1054 . -260) 80588) ((-836 . -421) T) ((-63 . -557) 80570) ((-572 . -203) 80516) ((-443 . -23) T) ((-1021 . -726) T) ((-796 . -123) T) ((-1021 . -723) T) ((-1166 . -1168) 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. -557) 14936) ((-865 . -260) 14913) ((-552 . -478) 14661) ((-750 . -952) 14645) ((-444 . -478) 14405) ((-884 . -659) T) ((-668 . -659) T) ((-648 . -659) T) ((-321 . -1015) T) ((-1076 . -557) 14387) ((-197 . -97) T) ((-450 . -347) 14357) ((-479 . -1003) T) ((-474 . -1003) T) ((-472 . -1003) T) ((-731 . -585) 14331) ((-939 . -421) T) ((-879 . -478) 14264) ((-321 . -23) T) ((-575 . -123) T) ((-551 . -123) T) ((-324 . -421) T) ((-214 . -338) 14243) ((-349 . -156) T) ((-1138 . -968) T) ((-1117 . -968) T) ((-199 . -918) T) ((-632 . -357) T) ((-388 . -659) T) ((-634 . -1112) T) ((-1040 . -579) 14191) ((-529 . -793) 14175) ((-1057 . -1085) 14151) ((-634 . -509) T) ((-121 . -1003) 14129) ((-1166 . -967) 14113) ((-647 . -1003) T) ((-450 . -822) 14046) ((-595 . -37) 14016) ((-324 . -372) T) ((-286 . -134) 13995) ((-286 . -132) 13974) ((-111 . -509) T) ((-283 . -134) 13930) ((-283 . -132) 13886) ((-47 . -421) T) ((-146 . -1003) T) ((-142 . -1003) T) ((-1057 . -102) 13833) ((-714 . -1049) 13811) 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\ No newline at end of file
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((-283 . -97) T) ((-261 . -23) T) ((-139 . -123) T) ((-356 . -659) T) ((-796 . -967) 132576) ((-832 . -557) 132558) ((-832 . -558) 132540) ((-796 . -106) 132471) ((-127 . -97) T) ((-109 . -97) T) ((-645 . -1131) 132455) ((-647 . -961) T) ((-627 . -319) NIL) ((-482 . -557) 132387) ((-349 . -727) T) ((-197 . -1003) T) ((-349 . -724) T) ((-199 . -726) T) ((-199 . -723) T) ((-57 . -558) 132348) ((-57 . -557) 132260) ((-199 . -659) T) ((-480 . -558) 132221) ((-480 . -557) 132133) ((-462 . -557) 132065) ((-461 . -558) 132026) ((-461 . -557) 131938) ((-987 . -333) 131889) ((-39 . -381) 131866) ((-75 . -1109) T) ((-795 . -831) NIL) ((-329 . -299) 131850) ((-329 . -333) T) ((-323 . -299) 131834) ((-323 . -333) T) ((-315 . -299) 131818) ((-315 . -333) T) ((-286 . -256) 131797) ((-103 . -333) T) ((-68 . -1109) T) ((-1119 . -308) 131749) ((-795 . -585) 131694) ((-1119 . -347) 131646) ((-885 . -123) 131501) ((-747 . -123) 131372) ((-879 . -588) 131356) ((-992 . -156) 131267) ((-879 . -343) 131251) 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-1003) 121209) ((-529 . -650) 121196) ((-517 . -650) 121183) ((-460 . -650) 121148) ((-286 . -569) 121127) ((-766 . -659) T) ((-759 . -659) T) ((-583 . -1109) T) ((-987 . -579) 121075) ((-1070 . -822) 121019) ((-1026 . -822) 121003) ((-599 . -967) 120987) ((-103 . -579) 120969) ((-450 . -123) 120840) ((-1076 . -1015) T) ((-874 . -46) 120809) ((-564 . -1003) T) ((-599 . -106) 120788) ((-297 . -260) 120765) ((-449 . -46) 120722) ((-1076 . -23) T) ((-112 . -1003) T) ((-98 . -97) 120700) ((-1164 . -1015) T) ((-965 . -123) T) ((-939 . -968) T) ((-751 . -952) 120684) ((-919 . -657) 120656) ((-1164 . -23) T) ((-632 . -650) 120621) ((-534 . -557) 120603) ((-356 . -952) 120587) ((-324 . -968) T) ((-355 . -123) T) ((-294 . -952) 120571) ((-199 . -808) 120553) ((-920 . -842) T) ((-89 . -33) T) ((-920 . -752) T) ((-836 . -842) T) ((-454 . -1113) T) ((-1090 . -557) 120535) ((-1008 . -1003) T) ((-192 . -1113) T) ((-915 . -280) 120500) ((-199 . -952) 120460) ((-39 . -262) T) ((-987 . -21) T) ((-987 . -25) T) ((-1021 . -760) T) ((-454 . -509) T) ((-329 . -25) T) ((-192 . -509) T) ((-329 . -21) T) ((-323 . -25) T) ((-323 . -21) T) ((-647 . -585) 120420) ((-315 . -25) T) ((-315 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -968) T) ((-529 . -156) T) ((-517 . -156) T) ((-460 . -156) T) ((-595 . -557) 120402) ((-670 . -669) 120386) ((-306 . -557) 120368) ((-66 . -353) T) ((-66 . -365) T) ((-1005 . -102) 120352) ((-972 . -808) 120334) ((-874 . -808) 120259) ((-590 . -1015) T) ((-564 . -650) 120246) ((-449 . -808) NIL) ((-1045 . -97) T) ((-972 . -952) 120228) ((-92 . -557) 120210) ((-446 . -134) T) ((-874 . -952) 120092) ((-112 . -650) 120037) ((-590 . -23) T) ((-449 . -952) 119915) ((-992 . -558) NIL) ((-992 . -557) 119897) ((-714 . -558) NIL) ((-714 . -557) 119858) ((-712 . -558) 119493) ((-712 . -557) 119407) ((-1016 . -579) 119315) ((-430 . -557) 119297) ((-423 . -557) 119279) ((-423 . -558) 119140) ((-950 . -203) 119086) ((-121 . -33) T) ((-749 . -123) T) ((-796 . -831) 119065) 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117966) ((-874 . -822) 117947) ((-1128 . -46) 117924) ((-832 . -338) T) ((-57 . -588) 117908) ((-480 . -588) 117892) ((-449 . -822) 117869) ((-69 . -410) T) ((-69 . -365) T) ((-461 . -588) 117853) ((-57 . -343) 117837) ((-564 . -156) T) ((-480 . -343) 117821) ((-461 . -343) 117805) ((-759 . -642) 117789) ((-1070 . -278) 117768) ((-1076 . -123) T) ((-112 . -156) T) ((-1045 . -280) 117706) ((-153 . -1109) T) ((-575 . -677) 117690) ((-551 . -677) 117674) ((-1164 . -123) T) ((-1140 . -842) 117653) ((-1119 . -842) 117632) ((-1119 . -752) NIL) ((-627 . -650) 117582) ((-1118 . -831) 117535) ((-939 . -1003) T) ((-795 . -347) 117512) ((-795 . -308) 117489) ((-827 . -1015) T) ((-153 . -806) 117473) ((-153 . -808) 117398) ((-454 . -1015) T) ((-324 . -1003) T) ((-192 . -1015) T) ((-74 . -410) T) ((-74 . -365) T) ((-153 . -952) 117296) ((-289 . -779) T) ((-1154 . -478) 117229) ((-1139 . -585) 117126) ((-1118 . -585) 116996) ((-796 . -726) 116975) ((-796 . -723) 116954) ((-796 . -659) T) ((-454 . -23) T) ((-197 . -557) 116936) ((-157 . -421) T) ((-196 . -280) 116874) ((-84 . -410) T) ((-84 . -365) T) ((-192 . -23) T) ((-1176 . -1169) 116853) ((-529 . -262) T) ((-517 . -262) T) ((-612 . -952) 116837) ((-460 . -262) T) ((-127 . -439) 116792) ((-47 . -1003) T) ((-645 . -205) 116776) ((-795 . -822) NIL) ((-1128 . -808) NIL) ((-811 . -97) T) ((-807 . -97) T) ((-358 . -1003) T) ((-153 . -347) 116760) ((-153 . -308) 116744) ((-1128 . -952) 116627) ((-784 . -952) 116525) ((-1041 . -97) T) ((-590 . -123) T) ((-112 . -478) 116388) ((-599 . -724) 116367) ((-599 . -727) 116346) ((-524 . -952) 116328) ((-265 . -1161) 116298) ((-790 . -97) T) ((-884 . -509) 116277) ((-1104 . -967) 116160) ((-450 . -579) 116068) ((-826 . -1003) T) ((-939 . -650) 116005) ((-644 . -967) 115970) ((-548 . -33) T) ((-1046 . -1109) T) ((-1104 . -106) 115832) ((-443 . -585) 115729) ((-324 . -650) 115674) ((-153 . -822) 115633) ((-632 . -262) T) ((-627 . -156) T) ((-644 . -106) 115582) ((-1180 . -968) T) ((-1128 . -347) 115566) ((-388 . -1113) 115544) ((-283 . -777) NIL) ((-388 . -509) T) ((-199 . -278) T) ((-1118 . -723) 115497) ((-1118 . -726) 115450) ((-1139 . -659) T) ((-1118 . -659) T) ((-47 . -650) 115415) ((-199 . -937) T) ((-321 . -1161) 115392) ((-1141 . -381) 115358) ((-651 . -659) T) ((-1128 . -822) 115302) ((-107 . -557) 115284) ((-107 . -558) 115266) ((-651 . -442) T) ((-450 . -21) 115177) ((-122 . -456) 115161) ((-116 . -456) 115145) ((-450 . -25) 114997) ((-564 . -262) T) ((-534 . -967) 114972) ((-407 . -1003) T) ((-972 . -278) T) ((-112 . -262) T) ((-1007 . -97) T) ((-919 . -97) T) ((-534 . -106) 114933) ((-1041 . -280) 114871) ((-1104 . -961) T) ((-972 . -937) T) ((-64 . -1109) T) ((-965 . -25) T) ((-965 . -21) T) ((-644 . -961) T) ((-355 . -21) T) ((-355 . -25) T) ((-627 . -478) NIL) ((-939 . -156) T) ((-644 . -217) T) ((-972 . -502) T) ((-467 . -97) T) ((-324 . -156) T) ((-313 . -557) 114853) ((-364 . -557) 114835) ((-443 . -659) T) ((-1021 . -777) T) ((-814 . -952) 114803) 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. -23) T) ((-714 . -952) 93071) ((-712 . -952) 92930) ((-112 . -585) 92875) ((-423 . -952) 92753) ((-586 . -952) 92737) ((-567 . -97) T) ((-196 . -456) 92721) ((-1154 . -33) T) ((-575 . -650) 92705) ((-551 . -650) 92689) ((-607 . -37) 92649) ((-289 . -97) T) ((-83 . -557) 92631) ((-49 . -952) 92615) ((-1021 . -967) 92602) ((-992 . -347) 92586) ((-58 . -55) 92548) ((-632 . -726) T) ((-632 . -723) T) ((-530 . -952) 92535) ((-481 . -952) 92512) ((-632 . -659) T) ((-286 . -961) 92403) ((-294 . -123) T) ((-283 . -961) T) ((-153 . -1015) T) ((-714 . -347) 92387) ((-712 . -347) 92371) ((-44 . -138) 92321) ((-920 . -909) 92303) ((-423 . -347) 92287) ((-377 . -156) T) ((-286 . -217) 92266) ((-283 . -217) T) ((-283 . -207) NIL) ((-265 . -1003) 92049) ((-199 . -123) T) ((-1021 . -106) 92034) ((-153 . -23) T) ((-731 . -134) 92013) ((-731 . -132) 91992) ((-224 . -579) 91900) ((-223 . -579) 91808) ((-289 . -256) 91774) ((-1055 . -478) 91707) ((-1034 . -1003) T) ((-199 . -970) T) ((-747 . -280) 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. -134) 89892) ((-1027 . -132) 89871) ((-289 . -37) 89712) ((-153 . -123) T) ((-283 . -727) NIL) ((-283 . -724) NIL) ((-591 . -961) T) ((-47 . -585) 89677) ((-910 . -21) T) ((-122 . -926) 89661) ((-116 . -926) 89645) ((-910 . -25) T) ((-823 . -114) 89629) ((-1057 . -97) T) ((-748 . -779) 89608) ((-1128 . -123) T) ((-1070 . -25) T) ((-1070 . -21) T) ((-784 . -123) T) ((-1026 . -25) T) ((-1026 . -21) T) ((-783 . -25) T) ((-783 . -21) T) ((-714 . -278) 89587) ((-584 . -97) 89565) ((-572 . -97) T) ((-1058 . -280) 89360) ((-524 . -123) T) ((-562 . -777) 89339) ((-1055 . -456) 89323) ((-1049 . -138) 89273) ((-1045 . -557) 89235) ((-1045 . -558) 89196) ((-939 . -723) T) ((-939 . -726) T) ((-939 . -659) T) ((-451 . -280) 89134) ((-422 . -387) 89104) ((-321 . -156) T) ((-261 . -37) 89091) ((-247 . -97) T) ((-246 . -97) T) ((-245 . -97) T) ((-244 . -97) T) ((-243 . -97) T) ((-242 . -97) T) ((-241 . -97) T) ((-313 . -952) 89068) ((-188 . -97) T) ((-187 . -97) T) ((-185 . -97) T) ((-184 . -97) T) 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. -1015) T) ((-706 . -1003) T) ((-111 . -650) 86745) ((-608 . -952) 86729) ((-556 . -97) T) ((-766 . -23) T) ((-759 . -23) T) ((-1055 . -258) 86706) ((-1016 . -280) 86644) ((-1005 . -209) 86628) ((-62 . -366) T) ((-62 . -365) T) ((-105 . -97) T) ((-39 . -347) 86605) ((-590 . -781) 86589) ((-972 . -21) T) ((-972 . -25) T) ((-747 . -205) 86559) ((-874 . -25) T) ((-874 . -21) T) ((-562 . -968) T) ((-449 . -25) T) ((-449 . -21) T) ((-942 . -280) 86497) ((-811 . -557) 86479) ((-807 . -557) 86461) ((-224 . -779) 86412) ((-223 . -779) 86363) ((-486 . -478) 86296) ((-795 . -579) 86273) ((-445 . -280) 86211) ((-432 . -280) 86149) ((-321 . -262) T) ((-1055 . -1143) 86133) ((-1041 . -557) 86095) ((-1041 . -558) 86056) ((-1039 . -97) T) ((-915 . -967) 85952) ((-39 . -822) 85904) ((-1055 . -550) 85881) ((-1180 . -585) 85868) ((-973 . -138) 85814) ((-796 . -1113) T) ((-915 . -106) 85689) ((-309 . -650) 85673) ((-790 . -557) 85655) ((-157 . -650) 85587) ((-377 . -258) 85545) ((-796 . -509) T) ((-103 . -370) 85527) ((-82 . -354) T) ((-82 . -365) T) ((-634 . -156) T) ((-94 . -659) T) ((-450 . -97) 85338) ((-94 . -442) T) ((-111 . -156) T) ((-1016 . -37) 85308) ((-153 . -579) 85256) ((-965 . -97) T) ((-795 . -25) T) ((-747 . -212) 85235) ((-795 . -21) T) ((-750 . -97) T) ((-384 . -97) T) ((-355 . -97) T) ((-105 . -280) NIL) ((-201 . -97) 85213) ((-122 . -1109) T) ((-116 . -1109) T) ((-949 . -123) T) ((-607 . -337) 85197) ((-915 . -961) T) ((-1128 . -579) 85145) ((-1007 . -557) 85127) ((-919 . -557) 85109) ((-479 . -23) T) ((-474 . -23) T) ((-313 . -278) T) ((-472 . -23) T) ((-292 . -123) T) ((-3 . -1003) T) ((-919 . -558) 85093) ((-915 . -217) 85072) ((-915 . -207) 85051) ((-1180 . -659) T) ((-1147 . -132) 85030) ((-765 . -1003) T) ((-1147 . -134) 85009) ((-1140 . -134) 84988) ((-1140 . -132) 84967) ((-1139 . -1113) 84946) ((-1119 . -132) 84853) ((-1119 . -134) 84760) ((-1118 . -1113) 84739) ((-349 . -123) T) ((-517 . -808) 84721) ((0 . -1003) T) ((-157 . -156) T) ((-153 . -21) T) 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. -1003) T) ((-80 . -1109) T) ((-972 . -779) T) ((-874 . -779) 81361) ((-112 . -822) NIL) ((-714 . -842) 81340) ((-646 . -779) T) ((-489 . -1003) T) ((-465 . -1003) T) ((-325 . -1113) T) ((-322 . -1113) T) ((-314 . -1113) T) ((-237 . -1113) 81319) ((-221 . -1113) 81298) ((-1016 . -205) 81268) ((-449 . -779) 81247) ((-1041 . -967) 81231) ((-360 . -694) T) ((-1057 . -760) T) ((-627 . -1109) T) ((-325 . -509) T) ((-322 . -509) T) ((-314 . -509) T) ((-237 . -509) 81162) ((-221 . -509) 81093) ((-1041 . -106) 81072) ((-422 . -677) 81042) ((-790 . -967) 81012) ((-749 . -37) 80949) ((-627 . -806) 80931) ((-627 . -808) 80913) ((-266 . -280) 80717) ((-832 . -1113) T) ((-607 . -381) 80701) ((-790 . -106) 80666) ((-627 . -952) 80611) ((-920 . -421) T) ((-832 . -509) T) ((-530 . -842) T) ((-443 . -1015) T) ((-481 . -842) T) ((-1055 . -260) 80588) ((-836 . -421) T) ((-63 . -557) 80570) ((-572 . -203) 80516) ((-443 . -23) T) ((-1021 . -726) T) ((-796 . -123) T) ((-1021 . -723) T) ((-1167 . -1169) 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. -1003) T) ((-920 . -97) T) ((-888 . -97) T) ((-836 . -97) T) ((-815 . -952) 69673) ((-1041 . -659) T) ((-919 . -585) 69618) ((-445 . -1003) T) ((-432 . -1003) T) ((-534 . -23) T) ((-524 . -34) T) ((-524 . -91) T) ((-397 . -97) T) ((-973 . -203) 69564) ((-1072 . -37) 69461) ((-790 . -659) T) ((-627 . -842) T) ((-475 . -25) T) ((-471 . -21) T) ((-471 . -25) T) ((-1071 . -37) 69302) ((-309 . -961) T) ((-1065 . -37) 69098) ((-987 . -156) T) ((-157 . -961) T) ((-1027 . -37) 68995) ((-645 . -46) 68972) ((-329 . -156) T) ((-323 . -156) T) ((-482 . -55) 68946) ((-462 . -55) 68896) ((-321 . -1171) 68873) ((-199 . -421) T) ((-289 . -262) 68824) ((-315 . -156) T) ((-157 . -217) T) ((-1118 . -779) 68723) ((-103 . -156) T) ((-796 . -909) 68707) ((-595 . -1015) T) ((-530 . -333) T) ((-530 . -299) 68694) ((-481 . -299) 68671) ((-481 . -333) T) ((-286 . -278) 68650) ((-283 . -278) T) ((-548 . -779) 68629) ((-1016 . -650) 68571) ((-483 . -254) 68555) ((-595 . -23) T) ((-388 . -205) 68539) ((-283 . 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. -557) 14936) ((-865 . -260) 14913) ((-552 . -478) 14661) ((-750 . -952) 14645) ((-444 . -478) 14405) ((-884 . -659) T) ((-668 . -659) T) ((-648 . -659) T) ((-321 . -1015) T) ((-1077 . -557) 14387) ((-197 . -97) T) ((-450 . -347) 14357) ((-479 . -1003) T) ((-474 . -1003) T) ((-472 . -1003) T) ((-731 . -585) 14331) ((-939 . -421) T) ((-879 . -478) 14264) ((-321 . -23) T) ((-575 . -123) T) ((-551 . -123) T) ((-324 . -421) T) ((-214 . -338) 14243) ((-349 . -156) T) ((-1139 . -968) T) ((-1118 . -968) T) ((-199 . -918) T) ((-632 . -357) T) ((-388 . -659) T) ((-634 . -1113) T) ((-1041 . -579) 14191) ((-529 . -793) 14175) ((-1058 . -1086) 14151) ((-634 . -509) T) ((-121 . -1003) 14129) ((-1167 . -967) 14113) ((-647 . -1003) T) ((-450 . -822) 14046) ((-595 . -37) 14016) ((-324 . -372) T) ((-286 . -134) 13995) ((-286 . -132) 13974) ((-111 . -509) T) ((-283 . -134) 13930) ((-283 . -132) 13886) ((-47 . -421) T) ((-146 . -1003) T) ((-142 . -1003) T) ((-1058 . -102) 13833) ((-714 . -1050) 13811) 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T) ((-530 . -319) T) ((-481 . -319) T) ((-1118 . -478) 5286) ((-286 . -421) 5265) ((-283 . -421) T) ((-766 . -258) 5244) ((-309 . -123) T) ((-157 . -123) T) ((-265 . -25) 5109) ((-265 . -21) 4993) ((-44 . -1086) 4972) ((-64 . -557) 4954) ((-814 . -557) 4936) ((-548 . -478) 4869) ((-44 . -102) 4819) ((-1005 . -395) 4803) ((-1005 . -338) 4782) ((-973 . -1109) T) ((-972 . -967) 4769) ((-874 . -967) 4612) ((-449 . -967) 4455) ((-601 . -650) 4439) ((-972 . -106) 4424) ((-874 . -106) 4246) ((-446 . -333) T) ((-325 . -650) 4198) ((-322 . -650) 4150) ((-314 . -650) 4102) ((-237 . -650) 3951) ((-221 . -650) 3800) ((-865 . -588) 3784) ((-449 . -106) 3606) ((-1155 . -97) T) ((-865 . -343) 3590) ((-1119 . -831) NIL) ((-72 . -557) 3572) ((-884 . -46) 3551) ((-562 . -1015) T) ((-1 . -1003) T) ((-632 . -97) T) ((-1154 . -97) 3501) ((-1147 . -585) 3426) ((-1140 . -585) 3323) ((-121 . -456) 3307) ((-1091 . -557) 3289) ((-993 . -557) 3271) ((-360 . -23) T) ((-983 . -557) 3253) ((-85 . -1109) T) ((-1119 . -585) 3105) ((-832 . -650) 3070) ((-562 . -23) T) ((-552 . -557) 3052) ((-552 . -558) NIL) ((-444 . -558) NIL) ((-444 . -557) 3034) ((-475 . -1003) T) ((-471 . -1003) T) ((-321 . -25) T) ((-321 . -21) T) ((-122 . -280) 2972) ((-116 . -280) 2910) ((-543 . -585) 2897) ((-199 . -961) T) ((-542 . -585) 2822) ((-349 . -918) T) ((-199 . -217) T) ((-199 . -207) T) ((-879 . -558) 2783) ((-879 . -557) 2695) ((-794 . -37) 2682) ((-1139 . -262) 2633) ((-1118 . -262) 2584) ((-1021 . -421) T) ((-467 . -779) T) ((-286 . -1038) 2563) ((-915 . -134) 2542) ((-915 . -132) 2521) ((-460 . -280) 2508) ((-266 . -1086) 2487) ((-446 . -1015) T) ((-795 . -967) 2432) ((-564 . -97) T) ((-1096 . -456) 2416) ((-224 . -338) 2395) ((-223 . -338) 2374) ((-266 . -102) 2324) ((-972 . -961) T) ((-112 . -97) T) ((-874 . -961) T) ((-795 . -106) 2241) ((-446 . -23) T) ((-449 . -961) T) ((-972 . -207) T) ((-874 . -296) 2210) ((-449 . -296) 2167) ((-325 . -156) T) ((-322 . -156) T) ((-314 . -156) T) ((-237 . -156) 2078) 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((-795 . -207) NIL) ((-623 . -1109) T) ((-1176 . -23) T) ((-748 . -585) 536) ((-503 . -1109) T) ((-388 . -308) 520) ((-524 . -967) 507) ((-1128 . -106) 309) ((-634 . -579) 291) ((-784 . -106) 270) ((-351 . -23) T) ((-1083 . -478) 30)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index e4492c87..7224bcf6 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,3 +1,3 @@
 
-(30 . 3403927921)            
-(4183 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| |AlgebraicallyClosedField&| |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AlgebraicFunction| |Aggregate&| |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate| |Algebra&| |Algebra| |AlgFactor| |AlgebraicFunctionField| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraPackage| |AlgebraGivenByStructuralConstants| |AssociationList| |AbelianMonoidRing&| |AbelianMonoidRing| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |AnyFunctions1| |Any| |ApplyUnivariateSkewPolynomial| |ApplyRules| |TwoDimensionalArrayCategory&| |TwoDimensionalArrayCategory| |OneDimensionalArrayFunctions2| |OneDimensionalArray| |TwoDimensionalArray| |Asp10| |Asp12| |Asp19| |Asp1| |Asp20| |Asp24| |Asp27| |Asp28| |Asp29| |Asp30| |Asp31| |Asp33| |Asp34| |Asp35| |Asp41| |Asp42| |Asp49| |Asp4| |Asp50| |Asp55| |Asp6| |Asp73| |Asp74| |Asp77| |Asp78| |Asp7| |Asp80| |Asp8| |Asp9| |AssociatedEquations| |ArrayStack| |ArcTrigonometricFunctionCategory&| |ArcTrigonometricFunctionCategory| |AttributeButtons| |AttributeRegistry| |Automorphism| |BalancedFactorisation| |BasicType&| |BasicType| |BalancedBinaryTree| |BezoutMatrix| |BasicFunctions| |BagAggregate&| |BagAggregate| |BinaryExpansion| |BinaryFile| |Bits| |BiModule| |Boolean| |BasicOperatorFunctions1| |BasicOperator| |BoundIntegerRoots| |BalancedPAdicInteger| |BalancedPAdicRational| |BinaryRecursiveAggregate&| |BinaryRecursiveAggregate| |BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate| |BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament| |BinaryTree| |CancellationAbelianMonoid| |CachableSet| |CardinalNumber| |CartesianTensorFunctions2| |CartesianTensor| |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory| |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage| |CharacteristicZero| |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation| |Collection&| |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping| |ComplexRootPackage| |Color| |CombinatorialFunction| |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |Commutator| |CommonOperators| |CommuteUnivariatePolynomialCategory| |ComplexCategory&| |ComplexCategory| |ComplexFactorization| |ComplexFunctions2| |Complex| |ComplexPattern| |SubSpaceComponentProperty| |CommutativeRing| |ContinuedFraction| |CoordinateSystems| |CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch| |CRApackage| |ComplexRootFindingPackage| |CyclicStreamTools| |ComplexTrigonometricManipulations| |CoerceVectorMatrixPackage| |CycleIndicators| |CyclotomicPolynomialPackage| 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|DivisionRing| |DoublyLinkedAggregate| |DataList| |DiscreteLogarithmPackage| |DistributedMultivariatePolynomial| |Domain| |DirectProductMatrixModule| |DirectProductModule| |DifferentialPolynomialCategory&| |DifferentialPolynomialCategory| |DequeueAggregate| |TopLevelDrawFunctionsForCompiledFunctions| |TopLevelDrawFunctionsForAlgebraicCurves| |DrawComplex| |DrawNumericHack| |TopLevelDrawFunctions| |TopLevelDrawFunctionsForPoints| |DrawOptionFunctions0| |DrawOptionFunctions1| |DrawOption| |DifferentialSparseMultivariatePolynomial| |DifferentialVariableCategory&| |DifferentialVariableCategory| |e04AgentsPackage| |e04dgfAnnaType| |e04fdfAnnaType| |e04gcfAnnaType| |e04jafAnnaType| |e04mbfAnnaType| |e04nafAnnaType| |e04ucfAnnaType| |ExtAlgBasis| |ElementaryFunction| |ElementaryFunctionStructurePackage| |ElementaryFunctionsUnivariateLaurentSeries| |ElementaryFunctionsUnivariatePuiseuxSeries| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate| |ElementaryFunctionCategory&| |ElementaryFunctionCategory| |EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&| |EltableAggregate| |EuclideanModularRing| |EntireRing| |EigenPackage| |EquationFunctions2| |Equation| |EqTable| |ErrorFunctions| |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |ExpertSystemContinuityPackage1| |ExpertSystemContinuityPackage| |ExpressionSpace&| |ExpressionSpace| |ExpertSystemToolsPackage1| |ExpertSystemToolsPackage2| |ExpertSystemToolsPackage| |EuclideanDomain&| |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit| |ExponentialExpansion| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries| |Expression| |ExpressionSpaceODESolver| |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&| |FiniteAlgebraicExtensionField| |FortranCode| |FourierComponent| |FortranCodePackage1| |FiniteDivisorFunctions2| |FiniteDivisorCategory&| |FiniteDivisorCategory| |FiniteDivisor| |FullyEvalableOver&| |FullyEvalableOver| |FortranExpression| |FunctionFieldCategoryFunctions2| |FunctionFieldCategory&| |FunctionFieldCategory| |FiniteFieldCyclicGroup| |FiniteFieldCyclicGroupExtensionByPolynomial| |FiniteFieldCyclicGroupExtension| |FiniteFieldFunctions| |FiniteFieldHomomorphisms| |FiniteFieldCategory&| |FiniteFieldCategory| |FunctionFieldIntegralBasis| |FiniteFieldNormalBasis| |FiniteFieldNormalBasisExtensionByPolynomial| |FiniteFieldNormalBasisExtension| |FiniteField| |FiniteFieldExtensionByPolynomial| |FiniteFieldPolynomialPackage2| |FiniteFieldPolynomialPackage| |FiniteFieldSolveLinearPolynomialEquation| |FiniteFieldExtension| |FGLMIfCanPackage| |FreeGroup| |Field&| |Field| |FileCategory| |File| |FiniteRankNonAssociativeAlgebra&| |FiniteRankNonAssociativeAlgebra| |Finite| |FiniteRankAlgebra&| |FiniteRankAlgebra| |FiniteLinearAggregateFunctions2| |FiniteLinearAggregate&| |FiniteLinearAggregate| |FreeLieAlgebra| |FiniteLinearAggregateSort| |FullyLinearlyExplicitRingOver&| |FullyLinearlyExplicitRingOver| |FloatingComplexPackage| |Float| |FloatingRealPackage| |FreeModule1| |FreeModuleCat| |FortranMatrixCategory| |FortranMatrixFunctionCategory| |FreeModule| |FreeMonoid| |FortranMachineTypeCategory| |FileName| |FileNameCategory| |FreeNilpotentLie| |FortranOutputStackPackage| |FindOrderFinite| |ScriptFormulaFormat1| |ScriptFormulaFormat| |FortranProgramCategory| |FortranFunctionCategory| |FortranPackage| |FortranProgram| |FullPartialFractionExpansion| |FullyPatternMatchable| |FieldOfPrimeCharacteristic&| |FieldOfPrimeCharacteristic| |FloatingPointSystem&| |FloatingPointSystem| |FactoredFunctions2| |FractionFunctions2| |Fraction| |FramedAlgebra&| |FramedAlgebra| |FullyRetractableTo&| |FullyRetractableTo| |FractionalIdealFunctions2| |FractionalIdeal| |FramedModule| |FramedNonAssociativeAlgebraFunctions2| |FramedNonAssociativeAlgebra&| |FramedNonAssociativeAlgebra| |Factored| |FactoredFunctionUtilities| |FunctionSpaceToExponentialExpansion| |FunctionSpaceFunctions2| |FunctionSpaceToUnivariatePowerSeries| |FiniteSetAggregateFunctions2| |FiniteSetAggregate&| |FiniteSetAggregate| |FunctionSpaceComplexIntegration| |FourierSeries| |FunctionSpaceIntegration| |FunctionSpace&| |FunctionSpace| |FunctionalSpecialFunction| |FunctionSpacePrimitiveElement| |FunctionSpaceReduce| |FortranScalarType| |FunctionSpaceUnivariatePolynomialFactor| |FortranTemplate| |FortranType| |FunctionCalled| |FortranVectorCategory| |FortranVectorFunctionCategory| |GaloisGroupFactorizer| |GaloisGroupFactorizationUtilities| |GaloisGroupPolynomialUtilities| |GaloisGroupUtilities| |GaussianFactorizationPackage| |EuclideanGroebnerBasisPackage| |GroebnerFactorizationPackage| |GroebnerInternalPackage| |GroebnerPackage| |GcdDomain&| |GcdDomain| |GenericNonAssociativeAlgebra| |GeneralDistributedMultivariatePolynomial| |GenExEuclid| |GeneralizedMultivariateFactorize| |GeneralPolynomialGcdPackage| |GenUFactorize| |GenerateUnivariatePowerSeries| |GeneralHenselPackage| |GeneralModulePolynomial| |GosperSummationMethod| |GeneralPolynomialSet| |GradedAlgebra&| |GradedAlgebra| |GrayCode| |GraphicsDefaults| |GraphImage| |GradedModule&| |GradedModule| |GroebnerSolve| |Group&| |Group| |GeneralUnivariatePowerSeries| |GeneralSparseTable| |GeneralTriangularSet| |Pi| |HashTable| |HallBasis| |HomogeneousDistributedMultivariatePolynomial| |HomogeneousDirectProduct| |Heap| |HyperellipticFiniteDivisor| |HeuGcd| |HexadecimalExpansion| |HomogeneousAggregate&| |HomogeneousAggregate| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |IndexedTwoDimensionalArray| |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits| |IntegralBasisPolynomialTools| |IndexCard| |InnerCommonDenominator| |PolynomialIdeals| |IdealDecompositionPackage| |IndexedDirectProductAbelianGroup| |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory| |IndexedDirectProductOrderedAbelianMonoid| |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedDirectProductObject| |InnerEvalable&| |InnerEvalable| |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |InnerFiniteField| |InnerIndexedTwoDimensionalArray| |IndexedList| |InnerMatrixLinearAlgebraFunctions| |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |InnerNormalBasisFieldFunctions| |IncrementingMaps| |IndexedExponents| |InnerNumericEigenPackage| |Infinity| |InputFormFunctions1| |InputForm| |InfiniteProductCharacteristicZero| |InnerNumericFloatSolvePackage| |InnerModularGcd| |InnerMultFact| |InfiniteProductFiniteField| |InfiniteProductPrimeField| |InnerPolySign| |IntegerNumberSystem&| |IntegerNumberSystem| |InnerTable| |AlgebraicIntegration| |AlgebraicIntegrate| |IntegerBits| |IntervalCategory| |IntegralDomain&| |IntegralDomain| |ElementaryIntegration| |IntegerFactorizationPackage| |IntegrationFunctionsTable| |GenusZeroIntegration| |IntegerNumberTheoryFunctions| |AlgebraicHermiteIntegration| |TranscendentalHermiteIntegration| |Integer| |AnnaNumericalIntegrationPackage| |PureAlgebraicIntegration| |PatternMatchIntegration| |RationalIntegration| |IntegerRetractions| |RationalFunctionIntegration| |Interval| |IntegerSolveLinearPolynomialEquation| |IntegrationTools| |TranscendentalIntegration| |InverseLaplaceTransform| |InnerPAdicInteger| |InnerPrimeField| |InternalPrintPackage| |IntegrationResultToFunction| |IntegrationResultFunctions2| |IntegrationResult| |IntegerRoots| |IrredPolyOverFiniteField| |IntegrationResultRFToFunction| |IrrRepSymNatPackage| |InternalRationalUnivariateRepresentationPackage| |IndexedString| |InnerPolySum| |InnerSparseUnivariatePowerSeries| |InnerTaylorSeries| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| |AssociatedJordanAlgebra| |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| |CoercibleTo| |ConvertibleTo| |Kovacic| |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| |LazardSetSolvingPackage| |LeadingCoefDetermination| |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearDependence| |LinearlyExplicitRingOver| |ListToMap| |ListFunctions2| |ListFunctions3| |List| |ListMultiDictionary| |LeftModule| |ListMonoidOps| |LinearAggregate&| |LinearAggregate| |ElementaryFunctionLODESolver| |LinearOrdinaryDifferentialOperator1| |LinearOrdinaryDifferentialOperator2| |LinearOrdinaryDifferentialOperatorCategory&| |LinearOrdinaryDifferentialOperatorCategory| |LinearOrdinaryDifferentialOperatorFactorizer| |LinearOrdinaryDifferentialOperator| |LinearOrdinaryDifferentialOperatorsOps| |Logic&| |Logic| |Localize| |LinearPolynomialEquationByFractions| |LiePolynomial| |ListAggregate&| |ListAggregate| |LinearSystemMatrixPackage1| |LinearSystemMatrixPackage| |LinearSystemPolynomialPackage| |LieSquareMatrix| |LyndonWord| |LazyStreamAggregate&| |LazyStreamAggregate| |ThreeDimensionalMatrix| |Magma| |MappingPackageInternalHacks1| |MappingPackageInternalHacks2| |MappingPackageInternalHacks3| |MappingPackage1| |MappingPackage2| |MappingPackage3| |MatrixCategoryFunctions2| |MatrixCategory&| |MatrixCategory| |MatrixLinearAlgebraFunctions| |Matrix| |StorageEfficientMatrixOperations| |MultiVariableCalculusFunctions| |MatrixCommonDenominator| |MachineComplex| |MultiDictionary| |ModularDistinctDegreeFactorizer| |MeshCreationRoutinesForThreeDimensions| |MultFiniteFactorize| |MachineFloat| |ModularHermitianRowReduction| |MachineInteger| |MakeBinaryCompiledFunction| |MakeCachableSet| |MakeFloatCompiledFunction| |MakeFunction| |MakeRecord| |MakeUnaryCompiledFunction| |MultivariateLifting| |MonogenicLinearOperator| |MultipleMap| |ModularField| |ModMonic| |ModuleMonomial| |ModuleOperator| |ModularRing| |Module&| |Module| |MoebiusTransform| |Monad&| |Monad| |MonadWithUnit&| |MonadWithUnit| |MonogenicAlgebra&| |MonogenicAlgebra| |Monoid&| |Monoid| |MonomialExtensionTools| |MPolyCatFunctions2| |MPolyCatFunctions3| |MPolyCatPolyFactorizer| |MultivariatePolynomial| |MPolyCatRationalFunctionFactorizer| |MRationalFactorize| |MonoidRingFunctions2| |MonoidRing| |MultisetAggregate| |Multiset| |MoreSystemCommands| |MergeThing| |MultivariateTaylorSeriesCategory| |MultivariateFactorize| |MultivariateSquareFree| |NonAssociativeAlgebra&| |NonAssociativeAlgebra| |NagPolynomialRootsPackage| |NagRootFindingPackage| |NagSeriesSummationPackage| |NagIntegrationPackage| |NagOrdinaryDifferentialEquationsPackage| |NagPartialDifferentialEquationsPackage| |NagInterpolationPackage| |NagFittingPackage| |NagOptimisationPackage| |NagMatrixOperationsPackage| |NagEigenPackage| |NagLinearEquationSolvingPackage| |NagLapack| |NagSpecialFunctionsPackage| |NAGLinkSupportPackage| |NonAssociativeRng&| |NonAssociativeRng| |NonAssociativeRing&| |NonAssociativeRing| |NumericComplexEigenPackage| |NumericContinuedFraction| |NonCommutativeOperatorDivision| |NumberFieldIntegralBasis| |NumericalIntegrationProblem| |NonLinearSolvePackage| |NonNegativeInteger| |NonLinearFirstOrderODESolver| |NoneFunctions1| |None| |NormInMonogenicAlgebra| |NormalizationPackage| |NormRetractPackage| |NPCoef| |NumericRealEigenPackage| |NewSparseMultivariatePolynomial| |NewSparseUnivariatePolynomialFunctions2| |NewSparseUnivariatePolynomial| |NumberTheoreticPolynomialFunctions| |NormalizedTriangularSetCategory| |Numeric| |NumberFormats| |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OrderedCancellationAbelianMonoid| |OctonionCategory&| |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| |ElementaryFunctionODESolver| |ODEIntensityFunctionsTable| |ODEIntegration| |AnnaOrdinaryDifferentialEquationPackage| |PureAlgebraicLODE| |PrimitiveRatDE| |NumericalODEProblem| |PrimitiveRatRicDE| |RationalLODE| |ReduceLODE| |RationalRicDE| |SystemODESolver| |ODETools| |OrderedDirectProduct| |OrderlyDifferentialPolynomial| |OrdinaryDifferentialRing| |OrderlyDifferentialVariable| |OrderedFreeMonoid| |OrderedIntegralDomain| |OpenMathConnection| |OpenMathDevice| |OpenMathEncoding| |OpenMathErrorKind| |OpenMathError| |ExpressionToOpenMath| |OppositeMonogenicLinearOperator| |OpenMath| |OpenMathPackage| |OrderedMultisetAggregate| |OpenMathServerPackage| |OnePointCompletionFunctions2| |OnePointCompletion| |Operator| |OperationsQuery| |NumericalOptimizationCategory| |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| |OrderedSet&| |OrderedSet| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| |OrdSetInts| |OutputForm| |OutputPackage| |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| |ParametricSpaceCurve| |ParametricSurfaceFunctions2| |ParametricSurface| |PartitionsAndPermutations| |Patternable| |PatternMatchListResult| |PatternMatchable| |PatternMatch| |PatternMatchResultFunctions2| |PatternMatchResult| |PatternFunctions1| |PatternFunctions2| |Pattern| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| |PlotTools| |FunctionSpaceAssertions| |PatternMatchAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |FunctionSpaceAttachPredicates| |AttachPredicates| |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| |PriorityQueueAggregate| |PseudoRemainderSequence| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| |PseudoLinearNormalForm| |PolynomialSquareFree| |PointCategory| |PointFunctions2| |PointPackage| |PartialTranscendentalFunctions| |PushVariables| |PAdicWildFunctionFieldIntegralBasis| |QuasiAlgebraicSet2| |QuasiAlgebraicSet| |QuasiComponentPackage| |QueryEquation| |QuotientFieldCategoryFunctions2| |QuotientFieldCategory&| |QuotientFieldCategory| |QuadraticForm| |QueueAggregate| |QuaternionCategory&| |QuaternionCategory| |QuaternionCategoryFunctions2| |Quaternion| |Queue| |RadicalCategory&| |RadicalCategory| |RadicalFunctionField| |RadixExpansion| |RadixUtilities| |RandomNumberSource| |RationalFactorize| |RationalRetractions| |RecursiveAggregate&| |RecursiveAggregate| |RealClosedField&| |RealClosedField| |ElementaryRischDE| |ElementaryRischDESystem| |TranscendentalRischDE| |TranscendentalRischDESystem| |RandomDistributions| |ReducedDivisor| |RealZeroPackage| |RealZeroPackageQ| |RealConstant| |RealSolvePackage| |RealClosure| |ReductionOfOrder| |Reference| |RegularTriangularSet| |RepresentationPackage1| |RepresentationPackage2| |RepeatedDoubling| |RadicalEigenPackage| |RepeatedSquaring| |ResolveLatticeCompletion| |ResidueRing| |Result| |RetractableTo&| |RetractableTo| |RetractSolvePackage| |RandomFloatDistributions| |RationalFunctionFactor| |RationalFunctionFactorizer| |RationalFunction| |RegularChain| |RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation| |RectangularMatrixCategory&| |RectangularMatrixCategory| |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng| |RealNumberSystem&| |RealNumberSystem| |RightOpenIntervalRootCharacterization| |RomanNumeral| |RoutinesTable| |RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RealRootCharacterizationCategory&| |RealRootCharacterizationCategory| |RegularSetDecompositionPackage| |RegularTriangularSetCategory&| |RegularTriangularSetCategory| |RegularTriangularSetGcdPackage| |RuleCalled| |RewriteRule| |Ruleset| |RationalUnivariateRepresentationPackage| 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+(30 . 3404130409)            
+(4186 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&| |AbelianSemiGroup| |AlgebraicallyClosedField&| |AlgebraicallyClosedField| |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace| |PlaneAlgebraicCurvePlot| |AlgebraicFunction| |Aggregate&| |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate| |Algebra&| |Algebra| |AlgFactor| |AlgebraicFunctionField| |AlgebraicManipulations| |AlgebraicMultFact| |AlgebraPackage| |AlgebraGivenByStructuralConstants| |AssociationList| |AbelianMonoidRing&| |AbelianMonoidRing| |AlgebraicNumber| |AnonymousFunction| |AntiSymm| |AnyFunctions1| |Any| |ApplyUnivariateSkewPolynomial| |ApplyRules| |TwoDimensionalArrayCategory&| |TwoDimensionalArrayCategory| 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|PatternFunctions1| |PatternFunctions2| |Pattern| |PoincareBirkhoffWittLyndonBasis| |PolynomialComposition| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| |PrimeField| |PointsOfFiniteOrder| |PointsOfFiniteOrderRational| |PointsOfFiniteOrderTools| |PartialFraction| |PartialFractionPackage| |PolynomialGcdPackage| |PermutationGroupExamples| |PolyGroebner| |PiCoercions| |PrincipalIdealDomain| |PositiveInteger| |PolynomialInterpolationAlgorithms| |PolynomialInterpolation| |ParametricLinearEquations| |PlotFunctions1| |Plot3D| |Plot| |PlotTools| |FunctionSpaceAssertions| |PatternMatchAssertions| |PatternMatchPushDown| |PatternMatchFunctionSpace| |PatternMatchIntegerNumberSystem| |PatternMatchKernel| |PatternMatchListAggregate| |PatternMatchPolynomialCategory| |FunctionSpaceAttachPredicates| |AttachPredicates| |PatternMatchQuotientFieldCategory| |PatternMatchSymbol| |PatternMatchTools| |PolynomialNumberTheoryFunctions| |Point| |PolToPol| |RealPolynomialUtilitiesPackage| |PolynomialFunctions2| |PolynomialToUnivariatePolynomial| |PolynomialCategory&| |PolynomialCategory| |PolynomialCategoryQuotientFunctions| |PolynomialCategoryLifting| |Polynomial| |PolynomialRoots| |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| |PriorityQueueAggregate| |PseudoRemainderSequence| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| |PolynomialSetUtilitiesPackage| 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|linearAssociatedOrder| |read!| |numberOfComputedEntries| |zCoord| |nextItem| |ScanFloatIgnoreSpacesIfCan| |rightExactQuotient| RF2UTS |OMunhandledSymbol| NOT |complement| |mapExponents| |An| |relerror| |plus!| |exptMod| |radicalSimplify| |squareFreeLexTriangular| |swapRows!| |imagK| |twoFactor| |dihedralGroup| |leaf?| OR |nor| |sizeLess?| |credPol| |associates?| |repeating?| |extension| |matrixGcd| |leftRemainder| |ricDsolve| |horizConcat| |romberg| |destruct| |linearDependenceOverZ| |lineColorDefault| |coshIfCan| AND |OMconnInDevice| |suchThat| |binaryTree| |toseLastSubResultant| |rootPoly| |safeCeiling| |df2mf| |symFunc| |createPrimitiveElement| |numberOfNormalPoly| |genericLeftNorm| |primextendedint| |coefChoose| |mix| |setTopPredicate| |rank| |iiacos| |whileLoop| |nthFlag| |keys| |explicitlyEmpty?| |presub| |denominators| |differentialVariables| |characteristicPolynomial| |xor| |seed| |coth2tanh| |over| |basis| |cAtanh| |stoseInvertibleSetsqfreg| |op| |removeSuperfluousCases| |quadratic| |stFunc1| |insert!| |intcompBasis| |drawComplex| |degreePartition| |idealSimplify| |fixedPoint| |simplify| |leftTrace| |supersub| |reducedQPowers| |generateIrredPoly| |cSech| |plot| |ScanArabic| |imagI| |isobaric?| |antiAssociative?| |showClipRegion| |subMatrix| |jacobian| |heap| |positiveRemainder| |doubleFloatFormat| |polyRicDE| |poisson| |lieAlgebra?| |semiIndiceSubResultantEuclidean| |forLoop| |iisech| |zeroVector| |nodeOf?| |trim| |removeSinSq| |cubic| |edf2fi| |setProperty| |blue| |primaryDecomp| |withPredicates| |goodPoint| |iiperm| |modularFactor| |LyndonBasis| |lllip| |totalDegree| |permutationGroup| |purelyAlgebraicLeadingMonomial?| |cardinality| |e01sff| |latex| |principal?| |rotatey| |OMputAttr| |leftQuotient| |complexRoots| |pointColorDefault| |diophantineSystem| |symbol| |expintegrate| |getlo| |lazy?| |getCode| |lazyGintegrate| |implies| |sncndn| |sizeMultiplication| |clearDenominator| |any?| |constantLeft| |lists| |extendIfCan| |string| |powern| |mergeFactors| |moduloP| |createLowComplexityNormalBasis| |sin?| |iitan| |integerIfCan| |cycleRagits| |round| |linears| * |checkForZero| |setright!| |getOperator| |separateFactors| |hermiteH| |obj| |moebius| |extractIndex| |removeSinhSq| |unmakeSUP| |untab| |integer| |firstDenom| |dioSolve| |lquo| |semicolonSeparate| |cyclicEntries| |branchPoint?| |factorSFBRlcUnit| |rightExtendedGcd| |lagrange| |cCsch| |selectODEIVPRoutines| |rightRegularRepresentation| |factorPolynomial| |stoseSquareFreePart| |extendedSubResultantGcd| |drawComplexVectorField| |factor1| |bfEntry| |maxrank| |cycle| |f2df| |makeEq| |prefixRagits| |rischDE| |children| |tubePlot| |messagePrint| |squareFreePart| |qqq| |divisorCascade| |subCase?| |palgLODE0| |modifyPointData| |binaryTournament| |pointColor| |palgextint| |rombergo| |complexSolve| |complexEigenvectors| |totolex| |hasHi| |isAbsolutelyIrreducible?| |closeComponent| |solveLinearPolynomialEquationByRecursion| |expandLog| |totalDifferential| |OMputEndAtp| |nextNormalPrimitivePoly| |hermite| |neglist| |minimize| |modulus| |scripted?| |allRootsOf| |contractSolve| |copyInto!| |imagJ| |identitySquareMatrix| |fibonacci| |partialDenominators| |replaceKthElement| |duplicates| |isPower| |viewSizeDefault| FG2F |solid| |real?| |numberOfPrimitivePoly| |HenselLift| |rootBound| |pascalTriangle| |fprindINFO| |adaptive3D?| |octon| |datalist| |constantToUnaryFunction| |inverseIntegralMatrixAtInfinity| |intChoose| |orthonormalBasis| |cSec| |expressIdealMember| |fintegrate| |integralBasis| |even?| |perfectNthRoot| |minimumExponent| |createPrimitiveNormalPoly| |OMgetEndObject| |tryFunctionalDecomposition| |iExquo| |getOperands| |cot2trig| |OMencodingXML| |fracPart| |numberOfFractionalTerms| |lowerCase!| |degree| |double| |float| |bipolarCylindrical| |collect| |reducedSystem| |leftLcm| |typeLists| |predicate| |edf2efi| |monicRightFactorIfCan| |factorByRecursion| |generalSqFr| |qelt| |printStatement| |jacobiIdentity?| |OMgetInteger| |rewriteIdealWithHeadRemainder| |operators| |pol| |meshFun2Var| |parabolic| |mergeDifference| |rootSplit| |bracket| |legendre| |sturmSequence| |insertMatch| |subset?| |lazyPrem| |axes| |eigenvectors| |slex| |terms| |createZechTable| |discriminant| |solveLinearlyOverQ| |quadraticNorm| |youngGroup| |identification| |returns| |element?| |extract!| |exprToXXP| |OMopenFile| |inRadical?| |removeSuperfluousQuasiComponents| |computeCycleEntry| |Si| |OMread| |reducedForm| |formula| |zeroDimPrime?| |numeric| |addmod| |pointData| |complementaryBasis| |more?| |lastSubResultant| |firstNumer| |acscIfCan| |squareTop| |radical| |addMatch| |bfKeys| |setvalue!| |alphanumeric?| |fortranComplex| |dom| |bumprow| |imaginary| |rational| |normDeriv2| |enterInCache| |repeatUntilLoop| |zag| |consnewpol| |cycleTail| GE |indices| |anfactor| |buildSyntax| |standardBasisOfCyclicSubmodule| |doubleResultant| |cyclotomicFactorization| |integralDerivationMatrix| |numerators| |selectIntegrationRoutines| GT |crest| |appendPoint| |OMconnectTCP| |roman| |gbasis| |quasiMonicPolynomials| |generalTwoFactor| |base| |quoted?| |removeRoughlyRedundantFactorsInPol| LE |surface| |rootPower| |makingStats?| |showFortranOutputStack| |node| |stripCommentsAndBlanks| |genericRightDiscriminant| |OMclose| |conical| |midpoint| LT |fortranDouble| |selectfirst| |createGenericMatrix| |indicialEquations| |nrows| |inv| |coHeight| |mainPrimitivePart| |limitPlus| |compdegd| |isTimes| |gcdPolynomial| |associatedEquations| |mainCoefficients| |ideal| |minPoly| |ground?| |integralBasisAtInfinity| |cAcoth| |halfExtendedSubResultantGcd2| |primPartElseUnitCanonical!| |algint| |compiledFunction| |movedPoints| |interval| |top| |ground| |lifting1| |getGoodPrime| |mathieu11| |pointColorPalette| |thetaCoord| |graeffe| |topFortranOutputStack| |PDESolve| |title| |xRange| |maxrow| |char| |continue| |is?| |leadingMonomial| |tableForDiscreteLogarithm| |OMputObject| |radicalEigenvalues| |nullSpace| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|) 
\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 5bef96d4..354d41d2 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4838 +1,4842 @@
 
-(3124874 . 3403927952)       
-((-2044 (((-107) (-1 (-107) |#2| |#2|) $) 62) (((-107) $) NIL)) (-2034 (($ (-1 (-107) |#2| |#2|) $) 17) (($ $) NIL)) (-2411 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-1121 (-517)) |#2|) 34)) (-4020 (($ $) 58)) (-3225 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-2607 (((-517) (-1 (-107) |#2|) $) 22) (((-517) |#2| $) NIL) (((-517) |#2| $ (-517)) 70)) (-1536 (((-583 |#2|) $) 13)) (-3237 (($ (-1 (-107) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (-1433 (($ (-1 |#2| |#2|) $) 29)) (-1893 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-2620 (($ |#2| $ (-517)) NIL) (($ $ $ (-517)) 49)) (-2887 (((-3 |#2| "failed") (-1 (-107) |#2|) $) 24)) (-2048 (((-107) (-1 (-107) |#2|) $) 21)) (-1449 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-517)) NIL) (($ $ (-1121 (-517))) 48)) (-3750 (($ $ (-517)) 55) (($ $ (-1121 (-517))) 54)) (-3217 (((-703) (-1 (-107) |#2|) $) 26) (((-703) |#2| $) NIL)) (-1906 (($ $ $ (-517)) 51)) (-2433 (($ $) 50)) (-2276 (($ (-583 |#2|)) 52)) (-2452 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 63) (($ (-583 $)) 61)) (-2256 (((-787) $) 68)) (-3675 (((-107) (-1 (-107) |#2|) $) 20)) (-1547 (((-107) $ $) 69)) (-1572 (((-107) $ $) 72))) 
-(((-18 |#1| |#2|) (-10 -8 (-15 -1547 ((-107) |#1| |#1|)) (-15 -2256 ((-787) |#1|)) (-15 -1572 ((-107) |#1| |#1|)) (-15 -2034 (|#1| |#1|)) (-15 -2034 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -4020 (|#1| |#1|)) (-15 -1906 (|#1| |#1| |#1| (-517))) (-15 -2044 ((-107) |#1|)) (-15 -3237 (|#1| |#1| |#1|)) (-15 -2607 ((-517) |#2| |#1| (-517))) (-15 -2607 ((-517) |#2| |#1|)) (-15 -2607 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -2044 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -3237 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2411 (|#2| |#1| (-1121 (-517)) |#2|)) (-15 -2620 (|#1| |#1| |#1| (-517))) (-15 -2620 (|#1| |#2| |#1| (-517))) (-15 -3750 (|#1| |#1| (-1121 (-517)))) (-15 -3750 (|#1| |#1| (-517))) (-15 -1449 (|#1| |#1| (-1121 (-517)))) (-15 -1893 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -2452 (|#1| (-583 |#1|))) (-15 -2452 (|#1| |#1| |#1|)) (-15 -2452 (|#1| |#2| |#1|)) (-15 -2452 (|#1| |#1| |#2|)) (-15 -2276 (|#1| (-583 |#2|))) (-15 -2887 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -1449 (|#2| |#1| (-517))) (-15 -1449 (|#2| |#1| (-517) |#2|)) (-15 -2411 (|#2| |#1| (-517) |#2|)) (-15 -3217 ((-703) |#2| |#1|)) (-15 -1536 ((-583 |#2|) |#1|)) (-15 -3217 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -2048 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3675 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -1433 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1893 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2433 (|#1| |#1|))) (-19 |#2|) (-1108)) (T -18)) 
-NIL 
-(-10 -8 (-15 -1547 ((-107) |#1| |#1|)) (-15 -2256 ((-787) |#1|)) (-15 -1572 ((-107) |#1| |#1|)) (-15 -2034 (|#1| |#1|)) (-15 -2034 (|#1| (-1 (-107) |#2| |#2|) |#1|)) (-15 -4020 (|#1| |#1|)) (-15 -1906 (|#1| |#1| |#1| (-517))) (-15 -2044 ((-107) |#1|)) (-15 -3237 (|#1| |#1| |#1|)) (-15 -2607 ((-517) |#2| |#1| (-517))) (-15 -2607 ((-517) |#2| |#1|)) (-15 -2607 ((-517) (-1 (-107) |#2|) |#1|)) (-15 -2044 ((-107) (-1 (-107) |#2| |#2|) |#1|)) (-15 -3237 (|#1| (-1 (-107) |#2| |#2|) |#1| |#1|)) (-15 -2411 (|#2| |#1| (-1121 (-517)) |#2|)) (-15 -2620 (|#1| |#1| |#1| (-517))) (-15 -2620 (|#1| |#2| |#1| (-517))) (-15 -3750 (|#1| |#1| (-1121 (-517)))) (-15 -3750 (|#1| |#1| (-517))) (-15 -1449 (|#1| |#1| (-1121 (-517)))) (-15 -1893 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -2452 (|#1| (-583 |#1|))) (-15 -2452 (|#1| |#1| |#1|)) (-15 -2452 (|#1| |#2| |#1|)) (-15 -2452 (|#1| |#1| |#2|)) (-15 -2276 (|#1| (-583 |#2|))) (-15 -2887 ((-3 |#2| "failed") (-1 (-107) |#2|) |#1|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3225 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -1449 (|#2| |#1| (-517))) (-15 -1449 (|#2| |#1| (-517) |#2|)) (-15 -2411 (|#2| |#1| (-517) |#2|)) (-15 -3217 ((-703) |#2| |#1|)) (-15 -1536 ((-583 |#2|) |#1|)) (-15 -3217 ((-703) (-1 (-107) |#2|) |#1|)) (-15 -2048 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -3675 ((-107) (-1 (-107) |#2|) |#1|)) (-15 -1433 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1893 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2433 (|#1| |#1|))) 
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-(((-19 |#1|) (-1184) (-1108)) (T -19)) 
-NIL 
-(-13 (-343 |t#1|) (-10 -7 (-6 -4181))) 
-(((-33) . T) ((-97) -3807 (|has| |#1| (-1003)) (|has| |#1| (-779))) ((-557 (-787)) -3807 (|has| |#1| (-1003)) (|has| |#1| (-779)) (|has| |#1| (-557 (-787)))) ((-138 |#1|) . T) ((-558 (-493)) |has| |#1| (-558 (-493))) ((-258 (-517) |#1|) . T) ((-260 (-517) |#1|) . T) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-343 |#1|) . T) ((-456 |#1|) . T) ((-550 (-517) |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-588 |#1|) . T) ((-779) |has| |#1| (-779)) ((-1003) -3807 (|has| |#1| (-1003)) (|has| |#1| (-779))) ((-1108) . T)) 
-((-4038 (((-3 $ "failed") $ $) 12)) (-1654 (($ $) NIL) (($ $ $) 9)) (* (($ (-843) $) NIL) (($ (-703) $) 16) (($ (-517) $) 21))) 
-(((-20 |#1|) (-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1654 (|#1| |#1| |#1|)) (-15 -1654 (|#1| |#1|)) (-15 -4038 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-843) |#1|))) (-21)) (T -20)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1654 (|#1| |#1| |#1|)) (-15 -1654 (|#1| |#1|)) (-15 -4038 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-843) |#1|))) 
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-(((-21) (-1184)) (T -21)) 
-((-1654 (*1 *1 *1) (-4 *1 (-21))) (-1654 (*1 *1 *1 *1) (-4 *1 (-21))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-517))))) 
-(-13 (-123) (-10 -8 (-15 -1654 ($ $)) (-15 -1654 ($ $ $)) (-15 * ($ (-517) $)))) 
+(3125242 . 3404130428)       
+((-2866 (((-107) (-1 (-107) |#2| |#2|) $) 62) (((-107) $) NIL)) (-2740 (($ (-1 (-107) |#2| |#2|) $) 17) (($ $) NIL)) (-2307 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-1122 (-517)) |#2|) 34)) (-1227 (($ $) 58)) (-2521 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-2446 (((-517) (-1 (-107) |#2|) $) 22) (((-517) |#2| $) NIL) (((-517) |#2| $ (-517)) 70)) (-3037 (((-583 |#2|) $) 13)) (-2262 (($ (-1 (-107) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (-1213 (($ (-1 |#2| |#2|) $) 29)) (-1857 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-2454 (($ |#2| $ (-517)) NIL) (($ $ $ (-517)) 49)) (-2293 (((-3 |#2| "failed") (-1 (-107) |#2|) $) 24)) (-2925 (((-107) (-1 (-107) |#2|) $) 21)) (-1986 ((|#2| $ (-517) |#2|) NIL) ((|#2| $ (-517)) NIL) (($ $ (-1122 (-517))) 48)) (-3685 (($ $ (-517)) 55) (($ $ (-1122 (-517))) 54)) (-3105 (((-703) (-1 (-107) |#2|) $) 26) (((-703) |#2| $) NIL)) (-3966 (($ $ $ (-517)) 51)) (-2322 (($ $) 50)) (-2197 (($ (-583 |#2|)) 52)) (-2337 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 63) (($ (-583 $)) 61)) (-2182 (((-787) $) 68)) (-3883 (((-107) (-1 (-107) |#2|) $) 20)) (-1539 (((-107) $ $) 69)) (-1560 (((-107) $ $) 72))) 
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+NIL 
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+(((-19 |#1|) (-1185) (-1109)) (T -19)) 
+NIL 
+(-13 (-343 |t#1|) (-10 -7 (-6 -4184))) 
+(((-33) . T) ((-97) -3763 (|has| |#1| (-1003)) (|has| |#1| (-779))) ((-557 (-787)) -3763 (|has| |#1| (-1003)) (|has| |#1| (-779)) (|has| |#1| (-557 (-787)))) ((-138 |#1|) . T) ((-558 (-493)) |has| |#1| (-558 (-493))) ((-258 (-517) |#1|) . T) ((-260 (-517) |#1|) . T) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-343 |#1|) . T) ((-456 |#1|) . T) ((-550 (-517) |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-588 |#1|) . T) ((-779) |has| |#1| (-779)) ((-1003) -3763 (|has| |#1| (-1003)) (|has| |#1| (-779))) ((-1109) . T)) 
+((-1387 (((-3 $ "failed") $ $) 12)) (-1637 (($ $) NIL) (($ $ $) 9)) (* (($ (-843) $) NIL) (($ (-703) $) 16) (($ (-517) $) 21))) 
+(((-20 |#1|) (-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1637 (|#1| |#1| |#1|)) (-15 -1637 (|#1| |#1|)) (-15 -1387 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-843) |#1|))) (-21)) (T -20)) 
+NIL 
+(-10 -8 (-15 * (|#1| (-517) |#1|)) (-15 -1637 (|#1| |#1| |#1|)) (-15 -1637 (|#1| |#1|)) (-15 -1387 ((-3 |#1| "failed") |#1| |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-843) |#1|))) 
+((-2571 (((-107) $ $) 7)) (-2745 (((-107) $) 16)) (-1387 (((-3 $ "failed") $ $) 19)) (-3473 (($) 17 T CONST)) (-3865 (((-1057) $) 9)) (-3094 (((-1021) $) 10)) (-2182 (((-787) $) 11)) (-2297 (($) 18 T CONST)) (-1539 (((-107) $ $) 6)) (-1637 (($ $) 22) (($ $ $) 21)) (-1626 (($ $ $) 14)) (* (($ (-843) $) 13) (($ (-703) $) 15) (($ (-517) $) 20))) 
+(((-21) (-1185)) (T -21)) 
+((-1637 (*1 *1 *1) (-4 *1 (-21))) (-1637 (*1 *1 *1 *1) (-4 *1 (-21))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-517))))) 
+(-13 (-123) (-10 -8 (-15 -1637 ($ $)) (-15 -1637 ($ $ $)) (-15 * ($ (-517) $)))) 
 (((-23) . T) ((-25) . T) ((-97) . T) ((-123) . T) ((-557 (-787)) . T) ((-1003) . T)) 
-((-2814 (((-107) $) 10)) (-3092 (($) 15)) (* (($ (-843) $) 14) (($ (-703) $) 18))) 
-(((-22 |#1|) (-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2814 ((-107) |#1|)) (-15 -3092 (|#1|)) (-15 * (|#1| (-843) |#1|))) (-23)) (T -22)) 
-NIL 
-(-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2814 ((-107) |#1|)) (-15 -3092 (|#1|)) (-15 * (|#1| (-843) |#1|))) 
-((-2750 (((-107) $ $) 7)) (-2814 (((-107) $) 16)) (-3092 (($) 17 T CONST)) (-3985 (((-1056) $) 9)) (-3206 (((-1021) $) 10)) (-2256 (((-787) $) 11)) (-2396 (($) 18 T CONST)) (-1547 (((-107) $ $) 6)) (-1642 (($ $ $) 14)) (* (($ (-843) $) 13) (($ (-703) $) 15))) 
-(((-23) (-1184)) (T -23)) 
-((-2396 (*1 *1) (-4 *1 (-23))) (-3092 (*1 *1) (-4 *1 (-23))) (-2814 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-107)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-703))))) 
-(-13 (-25) (-10 -8 (-15 (-2396) ($) -1619) (-15 -3092 ($) -1619) (-15 -2814 ((-107) $)) (-15 * ($ (-703) $)))) 
+((-2745 (((-107) $) 10)) (-3473 (($) 15)) (* (($ (-843) $) 14) (($ (-703) $) 18))) 
+(((-22 |#1|) (-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2745 ((-107) |#1|)) (-15 -3473 (|#1|)) (-15 * (|#1| (-843) |#1|))) (-23)) (T -22)) 
+NIL 
+(-10 -8 (-15 * (|#1| (-703) |#1|)) (-15 -2745 ((-107) |#1|)) (-15 -3473 (|#1|)) (-15 * (|#1| (-843) |#1|))) 
+((-2571 (((-107) $ $) 7)) (-2745 (((-107) $) 16)) (-3473 (($) 17 T CONST)) (-3865 (((-1057) $) 9)) (-3094 (((-1021) $) 10)) (-2182 (((-787) $) 11)) (-2297 (($) 18 T CONST)) (-1539 (((-107) $ $) 6)) (-1626 (($ $ $) 14)) (* (($ (-843) $) 13) (($ (-703) $) 15))) 
+(((-23) (-1185)) (T -23)) 
+((-2297 (*1 *1) (-4 *1 (-23))) (-3473 (*1 *1) (-4 *1 (-23))) (-2745 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-107)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-703))))) 
+(-13 (-25) (-10 -8 (-15 (-2297) ($) -1605) (-15 -3473 ($) -1605) (-15 -2745 ((-107) $)) (-15 * ($ (-703) $)))) 
 (((-25) . T) ((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
 ((* (($ (-843) $) 10))) 
 (((-24 |#1|) (-10 -8 (-15 * (|#1| (-843) |#1|))) (-25)) (T -24)) 
 NIL 
 (-10 -8 (-15 * (|#1| (-843) |#1|))) 
-((-2750 (((-107) $ $) 7)) (-3985 (((-1056) $) 9)) (-3206 (((-1021) $) 10)) (-2256 (((-787) $) 11)) (-1547 (((-107) $ $) 6)) (-1642 (($ $ $) 14)) (* (($ (-843) $) 13))) 
-(((-25) (-1184)) (T -25)) 
-((-1642 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-843))))) 
-(-13 (-1003) (-10 -8 (-15 -1642 ($ $ $)) (-15 * ($ (-843) $)))) 
+((-2571 (((-107) $ $) 7)) (-3865 (((-1057) $) 9)) (-3094 (((-1021) $) 10)) (-2182 (((-787) $) 11)) (-1539 (((-107) $ $) 6)) (-1626 (($ $ $) 14)) (* (($ (-843) $) 13))) 
+(((-25) (-1185)) (T -25)) 
+((-1626 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-843))))) 
+(-13 (-1003) (-10 -8 (-15 -1626 ($ $ $)) (-15 * ($ (-843) $)))) 
 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
-((-2888 (((-583 $) (-874 $)) 29) (((-583 $) (-1069 $)) 16) (((-583 $) (-1069 $) (-1073)) 20)) (-3869 (($ (-874 $)) 27) (($ (-1069 $)) 11) (($ (-1069 $) (-1073)) 54)) (-1649 (((-583 $) (-874 $)) 30) (((-583 $) (-1069 $)) 18) (((-583 $) (-1069 $) (-1073)) 19)) (-3267 (($ (-874 $)) 28) (($ (-1069 $)) 13) (($ (-1069 $) (-1073)) NIL))) 
-(((-26 |#1|) (-10 -8 (-15 -2888 ((-583 |#1|) (-1069 |#1|) (-1073))) (-15 -2888 ((-583 |#1|) (-1069 |#1|))) (-15 -2888 ((-583 |#1|) (-874 |#1|))) (-15 -3869 (|#1| (-1069 |#1|) (-1073))) (-15 -3869 (|#1| (-1069 |#1|))) (-15 -3869 (|#1| (-874 |#1|))) (-15 -1649 ((-583 |#1|) (-1069 |#1|) (-1073))) (-15 -1649 ((-583 |#1|) (-1069 |#1|))) (-15 -1649 ((-583 |#1|) (-874 |#1|))) (-15 -3267 (|#1| (-1069 |#1|) (-1073))) (-15 -3267 (|#1| (-1069 |#1|))) (-15 -3267 (|#1| (-874 |#1|)))) (-27)) (T -26)) 
-NIL 
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-NIL 
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 (((-48) (-1003)) (T -48)) 
 NIL 
 (-1003) 
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+(((-85 |#1|) (-13 (-354) (-10 -8 (-15 -2182 ($ (-623 (-309 (-2197 (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (-2197) (-632))))))) (-1074)) (T -85)) 
+((-2182 (*1 *1 *2) (-12 (-5 *2 (-623 (-309 (-2197 (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (-2197) (-632)))) (-5 *1 (-85 *3)) (-14 *3 (-1074))))) 
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+(((-86 |#1|) (-409) (-1074)) (T -86)) 
 NIL 
 (-409) 
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-NIL 
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-NIL 
-(((-93) (-1184)) (T -93)) 
-NIL 
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-NIL 
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-((-2750 (((-107) $ $) 7)) (-1547 (((-107) $ $) 6))) 
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 NIL 
 (-13 (-961)) 
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-NIL 
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 (((-169) (-719)) (T -169)) 
 NIL 
 (-719) 
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 (((-170) (-719)) (T -170)) 
 NIL 
 (-719) 
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 (((-171) (-719)) (T -171)) 
 NIL 
 (-719) 
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 (((-172) (-719)) (T -172)) 
 NIL 
 (-719) 
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 (((-173) (-719)) (T -173)) 
 NIL 
 (-719) 
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 (((-174) (-719)) (T -174)) 
 NIL 
 (-719) 
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 (((-175) (-719)) (T -175)) 
 NIL 
 (-719) 
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 (((-176) (-719)) (T -176)) 
 NIL 
 (-719) 
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 (((-177) (-719)) (T -177)) 
 NIL 
 (-719) 
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 (((-178) (-719)) (T -178)) 
 NIL 
 (-719) 
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 (((-179) (-719)) (T -179)) 
 NIL 
 (-719) 
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 (((-182) (-732)) (T -182)) 
 NIL 
 (-732) 
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 (((-183) (-732)) (T -183)) 
 NIL 
 (-732) 
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 (((-184) (-732)) (T -184)) 
 NIL 
 (-732) 
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 (((-185) (-732)) (T -185)) 
 NIL 
 (-732) 
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 (((-187) (-817)) (T -187)) 
 NIL 
 (-817) 
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 (((-188) (-817)) (T -188)) 
 NIL 
 (-817) 
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-NIL 
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 NIL 
 (-212 |#1| |#2|) 
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-NIL 
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+NIL 
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+(((-217) (-1185)) (T -217)) 
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+(-13 (-262) (-37 (-377 (-517))) (-10 -8 (-15 ** ($ $ (-517))) (-15 -2146 ($ $ (-517))) (-15 -4123 ($ $)))) 
 (((-21) . T) ((-23) . T) ((-25) . T) ((-37 (-377 (-517))) . T) ((-97) . T) ((-106 (-377 (-517)) (-377 (-517))) . T) ((-106 $ $) . T) ((-123) . T) ((-557 (-787)) . T) ((-262) . T) ((-585 (-377 (-517))) . T) ((-585 $) . T) ((-650 (-377 (-517))) . T) ((-659) . T) ((-967 (-377 (-517))) . T) ((-967 $) . T) ((-961) . T) ((-968) . T) ((-1015) . T) ((-1003) . T)) 
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 NIL 
 (-13 (-226 |#1| |#2| |#3| (-489 |#3|)) (-952 (-1026 |#1| |#2|))) 
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-NIL 
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+NIL 
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+(((-239 |#1|) (-1185) (-779)) (T -239)) 
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 (((-97) . T) ((-557 (-787)) . T) ((-779) . T) ((-952 |#1|) . T) ((-1003) . T)) 
-((-1364 (((-583 (-1073)) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2836 (-583 (-199))))) 40)) (-3463 (((-583 (-1073)) (-286 (-199)) (-703)) 79)) (-2438 (((-3 (-286 (-199)) "failed") (-286 (-199))) 50)) (-2172 (((-286 (-199)) (-286 (-199))) 65)) (-4062 (((-2 (|:| |fn| (-286 (-199))) (|:| -2836 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199))))) (-2 (|:| |fn| (-286 (-199))) (|:| -2836 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) 26)) (-3648 (((-107) (-583 (-286 (-199)))) 83)) (-2792 (((-107) (-286 (-199))) 24)) (-1815 (((-583 (-1056)) (-3 (|:| |noa| (-2 (|:| |fn| (-286 (-199))) (|:| -2836 (-583 (-199))) (|:| |lb| (-583 (-772 (-199)))) (|:| |cf| (-583 (-286 (-199)))) (|:| |ub| (-583 (-772 (-199)))))) (|:| |lsa| (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2836 (-583 (-199))))))) 104)) (-3162 (((-583 (-286 (-199))) (-583 (-286 (-199)))) 86)) (-3919 (((-583 (-286 (-199))) (-583 (-286 (-199)))) 85)) (-3564 (((-623 (-199)) (-583 (-286 (-199))) (-703)) 93)) (-2035 (((-107) (-286 (-199))) 20) (((-107) (-583 (-286 (-199)))) 84)) (-3795 (((-583 (-199)) (-583 (-772 (-199))) (-199)) 14)) (-2455 (((-349) (-2 (|:| |lfn| (-583 (-286 (-199)))) (|:| -2836 (-583 (-199))))) 99)) (-3878 (((-950) (-1073) (-950)) 33))) 
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 (((-241) (-768)) (T -241)) 
 NIL 
 (-768) 
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 (((-242) (-768)) (T -242)) 
 NIL 
 (-768) 
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 (((-243) (-768)) (T -243)) 
 NIL 
 (-768) 
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 (((-244) (-768)) (T -244)) 
 NIL 
 (-768) 
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 (((-245) (-768)) (T -245)) 
 NIL 
 (-768) 
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 (((-246) (-768)) (T -246)) 
 NIL 
 (-768) 
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 (((-247) (-768)) (T -247)) 
 NIL 
 (-768) 
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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) ((-97) . T) ((-106 |#1| |#1|) . T) ((-123) . T) ((-557 (-787)) . T) ((-585 |#1|) . T) ((-650 |#1|) . T) ((-653) . T) ((-677 |#1|) . T) ((-694) . T) ((-967 |#1|) . T) ((-1003) . T)) 
-((-2750 (((-107) $ $) 7)) (-1611 (((-703)) 16)) (-3209 (($) 13)) (-1549 (((-843) $) 14)) (-3985 (((-1056) $) 9)) (-3448 (($ (-843)) 15)) (-3206 (((-1021) $) 10)) (-2256 (((-787) $) 11)) (-1547 (((-107) $ $) 6))) 
-(((-338) (-1184)) (T -338)) 
-((-1611 (*1 *2) (-12 (-4 *1 (-338)) (-5 *2 (-703)))) (-3448 (*1 *1 *2) (-12 (-5 *2 (-843)) (-4 *1 (-338)))) (-1549 (*1 *2 *1) (-12 (-4 *1 (-338)) (-5 *2 (-843)))) (-3209 (*1 *1) (-4 *1 (-338)))) 
-(-13 (-1003) (-10 -8 (-15 -1611 ((-703))) (-15 -3448 ($ (-843))) (-15 -1549 ((-843) $)) (-15 -3209 ($)))) 
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+(((-338) (-1185)) (T -338)) 
+((-1598 (*1 *2) (-12 (-4 *1 (-338)) (-5 *2 (-703)))) (-3353 (*1 *1 *2) (-12 (-5 *2 (-843)) (-4 *1 (-338)))) (-2903 (*1 *2 *1) (-12 (-4 *1 (-338)) (-5 *2 (-843)))) (-3098 (*1 *1) (-4 *1 (-338)))) 
+(-13 (-1003) (-10 -8 (-15 -1598 ((-703))) (-15 -3353 ($ (-843))) (-15 -2903 ((-843) $)) (-15 -3098 ($)))) 
 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
-((-3055 (((-623 |#2|) (-1153 $)) 40)) (-1967 (($ (-1153 |#2|) (-1153 $)) 35)) (-2410 (((-623 |#2|) $ (-1153 $)) 43)) (-3010 ((|#2| (-1153 $)) 13)) (-4114 (((-1153 |#2|) $ (-1153 $)) NIL) (((-623 |#2|) (-1153 $) (-1153 $)) 25))) 
-(((-339 |#1| |#2| |#3|) (-10 -8 (-15 -3055 ((-623 |#2|) (-1153 |#1|))) (-15 -3010 (|#2| (-1153 |#1|))) (-15 -1967 (|#1| (-1153 |#2|) (-1153 |#1|))) (-15 -4114 ((-623 |#2|) (-1153 |#1|) (-1153 |#1|))) (-15 -4114 ((-1153 |#2|) |#1| (-1153 |#1|))) (-15 -2410 ((-623 |#2|) |#1| (-1153 |#1|)))) (-340 |#2| |#3|) (-156) (-1130 |#2|)) (T -339)) 
-NIL 
-(-10 -8 (-15 -3055 ((-623 |#2|) (-1153 |#1|))) (-15 -3010 (|#2| (-1153 |#1|))) (-15 -1967 (|#1| (-1153 |#2|) (-1153 |#1|))) (-15 -4114 ((-623 |#2|) (-1153 |#1|) (-1153 |#1|))) (-15 -4114 ((-1153 |#2|) |#1| (-1153 |#1|))) (-15 -2410 ((-623 |#2|) |#1| (-1153 |#1|)))) 
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-(((-340 |#1| |#2|) (-1184) (-156) (-1130 |t#1|)) (T -340)) 
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+((-3129 (((-623 |#2|) (-1154 $)) 40)) (-3291 (($ (-1154 |#2|) (-1154 $)) 35)) (-2148 (((-623 |#2|) $ (-1154 $)) 43)) (-4042 ((|#2| (-1154 $)) 13)) (-2575 (((-1154 |#2|) $ (-1154 $)) NIL) (((-623 |#2|) (-1154 $) (-1154 $)) 25))) 
+(((-339 |#1| |#2| |#3|) (-10 -8 (-15 -3129 ((-623 |#2|) (-1154 |#1|))) (-15 -4042 (|#2| (-1154 |#1|))) (-15 -3291 (|#1| (-1154 |#2|) (-1154 |#1|))) (-15 -2575 ((-623 |#2|) (-1154 |#1|) (-1154 |#1|))) (-15 -2575 ((-1154 |#2|) |#1| (-1154 |#1|))) (-15 -2148 ((-623 |#2|) |#1| (-1154 |#1|)))) (-340 |#2| |#3|) (-156) (-1131 |#2|)) (T -339)) 
+NIL 
+(-10 -8 (-15 -3129 ((-623 |#2|) (-1154 |#1|))) (-15 -4042 (|#2| (-1154 |#1|))) (-15 -3291 (|#1| (-1154 |#2|) (-1154 |#1|))) (-15 -2575 ((-623 |#2|) (-1154 |#1|) (-1154 |#1|))) (-15 -2575 ((-1154 |#2|) |#1| (-1154 |#1|))) (-15 -2148 ((-623 |#2|) |#1| (-1154 |#1|)))) 
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+(((-340 |#1| |#2|) (-1185) (-156) (-1131 |t#1|)) (T -340)) 
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 (((-21) . T) ((-23) . T) ((-25) . T) ((-37 |#1|) . T) ((-97) . T) ((-106 |#1| |#1|) . T) ((-123) . T) ((-132) |has| |#1| (-132)) ((-134) |has| |#1| (-134)) ((-557 (-787)) . T) ((-585 |#1|) . T) ((-585 $) . T) ((-650 |#1|) . T) ((-659) . T) ((-967 |#1|) . T) ((-961) . T) ((-968) . T) ((-1015) . T) ((-1003) . T)) 
-((-3905 ((|#4| (-1 |#3| |#1| |#3|) |#2| |#3|) 23)) (-3225 ((|#3| (-1 |#3| |#1| |#3|) |#2| |#3|) 15)) (-1893 ((|#4| (-1 |#3| |#1|) |#2|) 21))) 
-(((-341 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -1893 (|#4| (-1 |#3| |#1|) |#2|)) (-15 -3225 (|#3| (-1 |#3| |#1| |#3|) |#2| |#3|)) (-15 -3905 (|#4| (-1 |#3| |#1| |#3|) |#2| |#3|))) (-1108) (-343 |#1|) (-1108) (-343 |#3|)) (T -341)) 
-((-3905 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *6 *5)) (-4 *6 (-1108)) (-4 *5 (-1108)) (-4 *2 (-343 *5)) (-5 *1 (-341 *6 *4 *5 *2)) (-4 *4 (-343 *6)))) (-3225 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1108)) (-4 *2 (-1108)) (-5 *1 (-341 *5 *4 *2 *6)) (-4 *4 (-343 *5)) (-4 *6 (-343 *2)))) (-1893 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1108)) (-4 *6 (-1108)) (-4 *2 (-343 *6)) (-5 *1 (-341 *5 *4 *6 *2)) (-4 *4 (-343 *5))))) 
-(-10 -7 (-15 -1893 (|#4| (-1 |#3| |#1|) |#2|)) (-15 -3225 (|#3| (-1 |#3| |#1| |#3|) |#2| |#3|)) (-15 -3905 (|#4| (-1 |#3| |#1| |#3|) |#2| |#3|))) 
-((-2044 (((-107) (-1 (-107) |#2| |#2|) $) NIL) (((-107) $) 18)) (-2034 (($ (-1 (-107) |#2| |#2|) $) NIL) (($ $) 28)) (-3166 (($ (-1 (-107) |#2| |#2|) $) 27) (($ $) 22)) (-3093 (($ $) 25)) (-2607 (((-517) (-1 (-107) |#2|) $) NIL) (((-517) |#2| $) 11) (((-517) |#2| $ (-517)) NIL)) (-3237 (($ (-1 (-107) |#2| |#2|) $ $) NIL) (($ $ $) 20))) 
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-NIL 
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+((-2325 ((|#4| (-1 |#3| |#1| |#3|) |#2| |#3|) 23)) (-2521 ((|#3| (-1 |#3| |#1| |#3|) |#2| |#3|) 15)) (-1857 ((|#4| (-1 |#3| |#1|) |#2|) 21))) 
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+((-2325 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *6 *5)) (-4 *6 (-1109)) (-4 *5 (-1109)) (-4 *2 (-343 *5)) (-5 *1 (-341 *6 *4 *5 *2)) (-4 *4 (-343 *6)))) (-2521 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *5 *2)) (-4 *5 (-1109)) (-4 *2 (-1109)) (-5 *1 (-341 *5 *4 *2 *6)) (-4 *4 (-343 *5)) (-4 *6 (-343 *2)))) (-1857 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1109)) (-4 *6 (-1109)) (-4 *2 (-343 *6)) (-5 *1 (-341 *5 *4 *6 *2)) (-4 *4 (-343 *5))))) 
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+NIL 
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 (((-21) . T) ((-23) . T) ((-25) . T) ((-97) . T) ((-106 |#2| |#2|) . T) ((-123) . T) ((-557 (-787)) . T) ((-585 |#2|) . T) ((-574 |#2|) . T) ((-650 |#2|) . T) ((-967 |#2|) . T) ((-1003) . T)) 
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 NIL 
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 NIL 
 (-13 (-579 |t#1|) (-10 -7 (IF (|has| |t#1| (-579 (-517))) (-6 (-579 (-517))) |noBranch|))) 
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+(((-357) (-1185)) (T -357)) 
 NIL 
 (-13 (-509) (-779) (-952 (-517))) 
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 (((-358) (-359)) (T -358)) 
 NIL 
 (-359) 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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+(((-379 |#1| |#2|) (-1185) (-156) (-1131 |t#1|)) (T -379)) 
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 (((-21) . T) ((-23) . T) ((-25) . T) ((-37 |#1|) . T) ((-97) . T) ((-106 |#1| |#1|) . T) ((-123) . T) ((-132) |has| |#1| (-132)) ((-134) |has| |#1| (-134)) ((-557 (-787)) . T) ((-340 |#1| |#2|) . T) ((-585 |#1|) . T) ((-585 $) . T) ((-650 |#1|) . T) ((-659) . T) ((-967 |#1|) . T) ((-961) . T) ((-968) . T) ((-1015) . T) ((-1003) . T)) 
-((-1772 (((-3 |#2| "failed") $) NIL) (((-3 (-377 (-517)) "failed") $) 27) (((-3 (-517) "failed") $) 19)) (-3189 ((|#2| $) NIL) (((-377 (-517)) $) 24) (((-517) $) 14)) (-2256 (($ |#2|) NIL) (($ (-377 (-517))) 22) (($ (-517)) 11))) 
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+((-1759 (((-3 |#2| "failed") $) NIL) (((-3 (-377 (-517)) "failed") $) 27) (((-3 (-517) "failed") $) 19)) (-3076 ((|#2| $) NIL) (((-377 (-517)) $) 24) (((-517) $) 14)) (-2182 (($ |#2|) NIL) (($ (-377 (-517))) 22) (($ (-517)) 11))) 
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 NIL 
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-(((-381 |#1|) (-1184) (-1108)) (T -381)) 
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+((-1759 (((-3 |#1| "failed") $) 7) (((-3 (-377 (-517)) "failed") $) 16 (|has| |#1| (-952 (-377 (-517))))) (((-3 (-517) "failed") $) 13 (|has| |#1| (-952 (-517))))) (-3076 ((|#1| $) 8) (((-377 (-517)) $) 15 (|has| |#1| (-952 (-377 (-517))))) (((-517) $) 12 (|has| |#1| (-952 (-517))))) (-2182 (($ |#1|) 6) (($ (-377 (-517))) 17 (|has| |#1| (-952 (-377 (-517))))) (($ (-517)) 14 (|has| |#1| (-952 (-517)))))) 
+(((-381 |#1|) (-1185) (-1109)) (T -381)) 
 NIL 
 (-13 (-952 |t#1|) (-10 -7 (IF (|has| |t#1| (-952 (-517))) (-6 (-952 (-517))) |noBranch|) (IF (|has| |t#1| (-952 (-377 (-517)))) (-6 (-952 (-377 (-517)))) |noBranch|))) 
 (((-952 (-377 (-517))) |has| |#1| (-952 (-377 (-517)))) ((-952 (-517)) |has| |#1| (-952 (-517))) ((-952 |#1|) . T)) 
-((-1893 (((-383 |#5| |#6| |#7| |#8|) (-1 |#5| |#1|) (-383 |#1| |#2| |#3| |#4|)) 33))) 
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-(-10 -7 (-15 -1893 ((-383 |#5| |#6| |#7| |#8|) (-1 |#5| |#1|) (-383 |#1| |#2| |#3| |#4|)))) 
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-((-1893 ((|#3| (-1 |#4| |#2|) |#1|) 26))) 
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-((-1893 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-156)) (-4 *6 (-156)) (-4 *2 (-387 *6)) (-5 *1 (-385 *4 *5 *2 *6)) (-4 *4 (-387 *5))))) 
-(-10 -7 (-15 -1893 (|#3| (-1 |#4| |#2|) |#1|))) 
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-NIL 
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-NIL 
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+NIL 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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-NIL 
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-NIL 
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-((-2645 (*1 *1) (-5 *1 (-446)))) 
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 NIL 
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 NIL 
 (-55 |#1| (-461 |#1| |#3|) (-461 |#1| |#2|)) 
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 (((-471 |#1| |#2|) (-13 (-21) (-473 |#1| |#2|)) (-21) (-779)) (T -471)) 
 NIL 
 (-13 (-21) (-473 |#1| |#2|)) 
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 (((-472 |#1| |#2|) (-13 (-23) (-473 |#1| |#2|)) (-23) (-779)) (T -472)) 
 NIL 
 (-13 (-23) (-473 |#1| |#2|)) 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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 NIL 
 (-13 (-724) (-473 |#1| |#2|)) 
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 (((-475 |#1| |#2|) (-13 (-725) (-473 |#1| |#2|)) (-725) (-779)) (T -475)) 
 NIL 
 (-13 (-725) (-473 |#1| |#2|)) 
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 (((-476 |#1| |#2|) (-473 |#1| |#2|) (-1003) (-779)) (T -476)) 
 NIL 
 (-473 |#1| |#2|) 
-((-2051 (($ $ (-583 |#2|) (-583 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
-(((-477 |#1| |#2| |#3|) (-10 -8 (-15 -2051 (|#1| |#1| |#2| |#3|)) (-15 -2051 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) (-478 |#2| |#3|) (-1003) (-1108)) (T -477)) 
-NIL 
-(-10 -8 (-15 -2051 (|#1| |#1| |#2| |#3|)) (-15 -2051 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) 
-((-2051 (($ $ (-583 |#1|) (-583 |#2|)) 7) (($ $ |#1| |#2|) 6))) 
-(((-478 |#1| |#2|) (-1184) (-1003) (-1108)) (T -478)) 
-((-2051 (*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *5)) (-4 *1 (-478 *4 *5)) (-4 *4 (-1003)) (-4 *5 (-1108)))) (-2051 (*1 *1 *1 *2 *3) (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1003)) (-4 *3 (-1108))))) 
-(-13 (-10 -8 (-15 -2051 ($ $ |t#1| |t#2|)) (-15 -2051 ($ $ (-583 |t#1|) (-583 |t#2|))))) 
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+((-1979 (($ $ (-583 |#2|) (-583 |#3|)) NIL) (($ $ |#2| |#3|) 12))) 
+(((-477 |#1| |#2| |#3|) (-10 -8 (-15 -1979 (|#1| |#1| |#2| |#3|)) (-15 -1979 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) (-478 |#2| |#3|) (-1003) (-1109)) (T -477)) 
+NIL 
+(-10 -8 (-15 -1979 (|#1| |#1| |#2| |#3|)) (-15 -1979 (|#1| |#1| (-583 |#2|) (-583 |#3|)))) 
+((-1979 (($ $ (-583 |#1|) (-583 |#2|)) 7) (($ $ |#1| |#2|) 6))) 
+(((-478 |#1| |#2|) (-1185) (-1003) (-1109)) (T -478)) 
+((-1979 (*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 *4)) (-5 *3 (-583 *5)) (-4 *1 (-478 *4 *5)) (-4 *4 (-1003)) (-4 *5 (-1109)))) (-1979 (*1 *1 *1 *2 *3) (-12 (-4 *1 (-478 *2 *3)) (-4 *2 (-1003)) (-4 *3 (-1109))))) 
+(-13 (-10 -8 (-15 -1979 ($ $ |t#1| |t#2|)) (-15 -1979 ($ $ (-583 |t#1|) (-583 |t#2|))))) 
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 (((-479 |#1| |#2| |#3|) (-293 |#1| |#2|) (-1003) (-123) |#2|) (T -479)) 
 NIL 
 (-293 |#1| |#2|) 
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-(((-480 |#1| |#2|) (-13 (-19 |#1|) (-254 |#1|) (-10 -8 (-15 -1977 ($ (-583 |#1|))) (-15 -4019 ((-703) $)) (-15 -3809 ($ $ (-517))) (-15 -2484 ((-107) (-107))))) (-1108) (-517)) (T -480)) 
-((-1977 (*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1108)) (-5 *1 (-480 *3 *4)) (-14 *4 (-517)))) (-4019 (*1 *2 *1) (-12 (-5 *2 (-703)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1108)) (-14 *4 (-517)))) (-3809 (*1 *1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1108)) (-14 *4 *2))) (-2484 (*1 *2 *2) (-12 (-5 *2 (-107)) (-5 *1 (-480 *3 *4)) (-4 *3 (-1108)) (-14 *4 (-517))))) 
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 NIL 
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 NIL 
 (-55 |#1| |#4| |#5|) 
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NIL (|has| $ (-6 -4180)))) (-1606 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1583 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1547 (((-107) $ $) 47 (|has| |#1| (-1003)))) (-1595 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1572 (((-107) $ $) NIL (|has| |#1| (-779)))) (-2296 (((-703) $) 9 (|has| $ (-6 -4180))))) 
-(((-483 |#1| |#2|) (-603 |#1|) (-1108) (-517)) (T -483)) 
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NIL (|has| $ (-6 -4183)))) (-1593 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1570 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1539 (((-107) $ $) 47 (|has| |#1| (-1003)))) (-1582 (((-107) $ $) NIL (|has| |#1| (-779)))) (-1560 (((-107) $ $) NIL (|has| |#1| (-779)))) (-2210 (((-703) $) 9 (|has| $ (-6 -4183))))) 
+(((-483 |#1| |#2|) (-603 |#1|) (-1109) (-517)) (T -483)) 
 NIL 
 (-603 |#1|) 
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 NIL 
 (-621 |#1| (-548 |#1| |#3|) (-548 |#1| |#2|)) 
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 (((-489 |#1|) (-13 (-725) (-473 (-703) |#1|)) (-779)) (T -489)) 
 NIL 
 (-13 (-725) (-473 (-703) |#1|)) 
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 (((-530 |#1|) (-13 (-319) (-299 $) (-558 (-517))) (-843)) (T -530)) 
 NIL 
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-(((-33) . T) ((-97) |has| |#1| (-1003)) ((-557 (-787)) -3807 (|has| |#1| (-1003)) (|has| |#1| (-557 (-787)))) ((-138 |#1|) . T) ((-558 (-493)) |has| |#1| (-558 (-493))) ((-258 (-517) |#1|) . T) ((-260 (-517) |#1|) . T) ((-280 |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-456 |#1|) . T) ((-550 (-517) |#1|) . T) ((-478 |#1| |#1|) -12 (|has| |#1| (-280 |#1|)) (|has| |#1| (-1003))) ((-1003) |has| |#1| (-1003)) ((-1108) . T)) 
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 NIL 
 (-593 |#1|) 
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 NIL 
 (-13 (-593 |#1|) (-258 |#2| |#2|)) 
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-NIL 
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 NIL 
 (-13 (-1024 |#1| |#2| (-214 |#1| |#2|) (-214 |#1| |#2|)) (-557 (-623 |#2|)) (-387 |#2|)) 
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-NIL 
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 NIL 
 (-10 -8 (-15 * (|#1| |#1| |#2|)) (-15 * (|#1| |#2| |#1|)) (-15 * (|#1| (-517) |#1|)) (-15 * (|#1| (-703) |#1|)) (-15 * (|#1| (-843) |#1|))) 
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+(((-650 |#1|) (-1185) (-156)) (T -650)) 
 NIL 
 (-13 (-106 |t#1| |t#1|)) 
 (((-21) . T) ((-23) . T) ((-25) . T) ((-97) . T) ((-106 |#1| |#1|) . T) ((-123) . T) ((-557 (-787)) . T) ((-585 |#1|) . T) ((-967 |#1|) . T) ((-1003) . T)) 
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-NIL 
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-(((-653) (-1184)) (T -653)) 
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+NIL 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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-NIL 
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+NIL 
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 (((-97) . T) ((-557 (-787)) . T) ((-653) . T) ((-1003) . T)) 
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-NIL 
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 NIL 
 (-13 (-727) (-21)) 
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 NIL 
 (-13 (-726) (-23)) 
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 NIL 
 (-13 (-779) (-23)) 
 (((-23) . T) ((-25) . T) ((-97) . T) ((-557 (-787)) . T) ((-779) . T) ((-1003) . T)) 
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 NIL 
 (-13 (-724) (-123)) 
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+NIL 
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 (((-750 |#1|) (-239 |#1|) (-779)) (T -750)) 
 NIL 
 (-239 |#1|) 
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-(((-752) (-1184)) (T -752)) 
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+(((-752) (-1185)) (T -752)) 
 NIL 
 (-13 (-509) (-777)) 
 (((-21) . T) ((-23) . T) ((-25) . T) ((-37 $) . T) ((-97) . T) ((-106 $ $) . T) ((-123) . T) ((-557 (-787)) . T) ((-156) . T) ((-262) . T) ((-509) . T) ((-585 $) . T) ((-650 $) . T) ((-659) . T) ((-723) . T) ((-724) . T) ((-726) . T) ((-727) . T) ((-777) . T) ((-779) . T) ((-967 $) . T) ((-961) . T) ((-968) . T) ((-1015) . T) ((-1003) . T)) 
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 NIL 
 (-13 (-779) (-338)) 
 (((-97) . T) ((-557 (-787)) . T) ((-338) . T) ((-779) . T) ((-1003) . T)) 
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 NIL 
 (-13 (-779) (-659)) 
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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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 (((-865 |#1|) (-897 |#1|) (-961)) (T -865)) 
 NIL 
 (-897 |#1|) 
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-NIL 
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+((-2571 (((-107) $ $) NIL)) (-2745 (((-107) $) NIL)) (-1387 (((-3 $ "failed") $ $) 26)) (-3473 (($) NIL T CONST)) (-2653 (((-583 (-583 (-517))) (-583 (-517))) 28)) (-3012 (((-517) $) 44)) (-3648 (($ (-583 (-517))) 17)) (-1575 (($ $ $) NIL)) (-2986 (($ $ $) NIL)) (-3865 (((-1057) $) NIL)) (-3094 (((-1021) $) NIL)) (-3582 (((-583 (-517)) $) 11)) (-2013 (($ $) 31)) (-2182 (((-787) $) 42) (((-583 (-517)) $) 9)) (-2297 (($) 7 T CONST)) (-1593 (((-107) $ $) NIL)) (-1570 (((-107) $ $) NIL)) (-1539 (((-107) $ $) 19)) (-1582 (((-107) $ $) NIL)) (-1560 (((-107) $ $) 18)) (-1626 (($ $ $) 20)) (* (($ (-703) $) 24) (($ (-843) $) NIL))) 
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+(-13 (-727) (-558 (-583 (-517))) (-10 -8 (-15 -3648 ($ (-583 (-517)))) (-15 -2653 ((-583 (-583 (-517))) (-583 (-517)))) (-15 -3012 ((-517) $)) (-15 -2013 ($ $)) (-15 -2182 ((-583 (-517)) $)))) 
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+NIL 
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 (((-557 (-787)) . T)) 
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-NIL 
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+NIL 
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 (((-993 |#1|) (-239 |#1|) (-779)) (T -993)) 
 NIL 
 (-239 |#1|) 
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-(((-1108) . T)) 
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 NIL 
 (-13 (-997 |#1|) (-10 -7 (IF (|has| |#1| (-1003)) (-6 (-1003)) |noBranch|) (IF (|has| |#1| (-777)) (-6 (-999 |#1| (-583 |#1|))) |noBranch|))) 
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-(((-997 |#1|) . T) ((-1108) . T)) 
-((-1413 (($ $ $) NIL) (($ $ |#2|) 13) (($ |#2| $) 14)) (-3245 (($ $ $) 10)) (-3170 (($ $ $) NIL) (($ $ |#2|) 15))) 
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-NIL 
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 (((-1005 |#1|) (-395 |#1|) (-1003)) (T -1005)) 
 NIL 
 (-395 |#1|) 
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+(((-1006 |#1| |#2| |#3| |#4| |#5|) (-1185) (-1003) (-1003) (-1003) (-1003) (-1003)) (T -1006)) 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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-(((-1007) (-1006 (-1056) (-1073) (-517) (-199) (-787))) (T -1007)) 
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 NIL 
-(-1006 (-1056) (-1073) (-517) (-199) (-787)) 
-((-2750 (((-107) $ $) NIL)) (-2710 (((-107) $) 37)) (-3881 ((|#2| $) 41)) (-2347 (((-107) $) 36)) (-3890 ((|#1| $) 40)) (-1533 (((-107) $) 34)) (-2636 (((-107) $) 14)) (-3567 (((-107) $) 35)) (-3985 (((-1056) $) NIL)) (-1973 (((-107) $) 38)) (-3912 ((|#3| $) 43)) (-3206 (((-1021) $) NIL)) (-2056 (((-107) $) 39)) (-4005 ((|#4| $) 42)) (-1556 ((|#5| $) 44)) (-2131 (((-107) $ $) 33)) (-1449 (($ $ (-517)) 55) (($ $ (-583 (-517))) 57)) (-3814 (((-583 $) $) 21)) (-3645 (($ (-583 $)) 45) (($ |#1|) 46) (($ |#2|) 47) (($ |#3|) 48) (($ |#4|) 49) (($ |#5|) 50)) (-2256 (((-787) $) 22)) (-2705 (($ $) 20)) (-2694 (($ $) 51)) (-1491 (((-107) $) 18)) (-1547 (((-107) $ $) 32)) (-2296 (((-517) $) 53))) 
+(-1006 (-1057) (-1074) (-517) (-199) (-787)) 
+((-2571 (((-107) $ $) NIL)) (-2999 (((-107) $) 37)) (-3873 ((|#2| $) 41)) (-2649 (((-107) $) 36)) (-3887 ((|#1| $) 40)) (-1394 (((-107) $) 34)) (-3649 (((-107) $) 14)) (-2179 (((-107) $) 35)) (-3865 (((-1057) $) NIL)) (-3337 (((-107) $) 38)) (-3910 ((|#3| $) 43)) (-3094 (((-1021) $) NIL)) (-2996 (((-107) $) 39)) (-4009 ((|#4| $) 42)) (-1549 ((|#5| $) 44)) (-2075 (((-107) $ $) 33)) (-1986 (($ $ (-517)) 55) (($ $ (-583 (-517))) 57)) (-3775 (((-583 $) $) 21)) (-3582 (($ (-583 $)) 45) (($ |#1|) 46) (($ |#2|) 47) (($ |#3|) 48) (($ |#4|) 49) (($ |#5|) 50)) (-2182 (((-787) $) 22)) (-2048 (($ $) 20)) (-2036 (($ $) 51)) (-2041 (((-107) $) 18)) (-1539 (((-107) $ $) 32)) (-2210 (((-517) $) 53))) 
 (((-1008 |#1| |#2| |#3| |#4| |#5|) (-1006 |#1| |#2| |#3| |#4| |#5|) (-1003) (-1003) (-1003) (-1003) (-1003)) (T -1008)) 
 NIL 
 (-1006 |#1| |#2| |#3| |#4| |#5|) 
-((-4155 (((-1158) $) 23)) (-2231 (($ (-1073) (-404) |#2|) 11)) (-2256 (((-787) $) 16))) 
-(((-1009 |#1| |#2|) (-13 (-365) (-10 -8 (-15 -2231 ($ (-1073) (-404) |#2|)))) (-779) (-400 |#1|)) (T -1009)) 
-((-2231 (*1 *1 *2 *3 *4) (-12 (-5 *2 (-1073)) (-5 *3 (-404)) (-4 *5 (-779)) (-5 *1 (-1009 *5 *4)) (-4 *4 (-400 *5))))) 
-(-13 (-365) (-10 -8 (-15 -2231 ($ (-1073) (-404) |#2|)))) 
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 NIL 
 (-13 (-980 |t#1| |t#2| |t#3| |t#4|)) 
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-NIL 
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+NIL 
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 (((-1026 |#1| |#2|) (-871 |#1| (-489 |#2|) |#2|) (-961) (-779)) (T -1026)) 
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 NIL 
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 NIL 
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 (((-97) . T) ((-557 (-787)) . T) ((-1003) . T)) 
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-NIL 
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-NIL 
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-NIL 
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(-777) (-278) (-134) (-937))) (-5 *2 (-583 (-2 (|:| -3870 (-1070 *5)) (|:| -2575 (-583 (-874 *5)))))) (-5 *1 (-1178 *5 *6 *7)) (-5 *3 (-583 (-874 *5))) (-14 *6 (-583 (-1074))) (-14 *7 (-583 (-1074))))) (-2308 (*1 *2 *3) (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-777) (-278) (-134) (-937))) (-14 *5 (-583 (-1074))) (-5 *2 (-583 (-2 (|:| -3870 (-1070 *4)) (|:| -2575 (-583 (-874 *4)))))) (-5 *1 (-1178 *4 *5 *6)) (-14 *6 (-583 (-1074))))) (-3075 (*1 *2 *3) (-12 (-5 *3 (-583 (-874 *4))) (-4 *4 (-13 (-777) (-278) (-134) (-937))) (-5 *2 (-583 (-958 *4 *5))) (-5 *1 (-1178 *4 *5 *6)) (-14 *5 (-583 (-1074))) (-14 *6 (-583 (-1074))))) (-3075 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-874 *5))) (-5 *4 (-107)) (-4 *5 (-13 (-777) (-278) (-134) (-937))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1178 *5 *6 *7)) (-14 *6 (-583 (-1074))) (-14 *7 (-583 (-1074))))) (-3075 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-583 (-874 *5))) (-5 *4 (-107)) (-4 *5 (-13 (-777) (-278) (-134) (-937))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1178 *5 *6 *7)) (-14 *6 (-583 (-1074))) (-14 *7 (-583 (-1074)))))) 
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+((-4043 (((-3 (-1154 (-377 (-517))) "failed") (-1154 |#1|) |#1|) 17)) (-2818 (((-107) (-1154 |#1|)) 11)) (-3776 (((-3 (-1154 (-517)) "failed") (-1154 |#1|)) 14))) 
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+((-4043 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1154 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-1154 (-377 (-517)))) (-5 *1 (-1179 *4)))) (-3776 (*1 *2 *3) (|partial| -12 (-5 *3 (-1154 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-1154 (-517))) (-5 *1 (-1179 *4)))) (-2818 (*1 *2 *3) (-12 (-5 *3 (-1154 *4)) (-4 *4 (-579 (-517))) (-5 *2 (-107)) (-5 *1 (-1179 *4))))) 
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+((-2571 (((-107) $ $) NIL)) (-2745 (((-107) $) 11)) (-1387 (((-3 $ "failed") $ $) NIL)) (-1598 (((-703)) 8)) (-3473 (($) NIL T CONST)) (-1568 (((-3 $ "failed") $) 43)) (-3098 (($) 36)) (-2955 (((-107) $) NIL)) (-3744 (((-3 $ "failed") $) 29)) (-2903 (((-843) $) 15)) (-3865 (((-1057) $) NIL)) (-2663 (($) 25 T CONST)) (-3353 (($ (-843)) 37)) (-3094 (((-1021) $) NIL)) (-3582 (((-517) $) 13)) (-2182 (((-787) $) 22) (($ (-517)) 19)) (-1865 (((-703)) 9)) (-2146 (($ $ (-843)) NIL) (($ $ (-703)) NIL)) (-2297 (($) 23 T CONST)) (-2306 (($) 24 T CONST)) (-1539 (((-107) $ $) 27)) (-1637 (($ $) 38) (($ $ $) 35)) (-1626 (($ $ $) 26)) (** (($ $ (-843)) NIL) (($ $ (-703)) 40)) (* (($ (-843) $) NIL) (($ (-703) $) NIL) (($ (-517) $) 32) (($ $ $) 31))) 
+(((-1180 |#1|) (-13 (-156) (-338) (-558 (-517)) (-1050)) (-843)) (T -1180)) 
 NIL 
-(-13 (-156) (-338) (-558 (-517)) (-1049)) 
+(-13 (-156) (-338) (-558 (-517)) (-1050)) 
 NIL 
 NIL 
 NIL 
@@ -4848,4 +4852,4 @@ NIL
 NIL 
 NIL 
 NIL 
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"XPBWPOLY" 3101114 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1170 3093712 3096025 3096068 "XF" 3096689 NIL XF (NIL T) -9 NIL 3097085) (-1169 3093333 3093421 3093590 "XF-" 3093595 NIL XF- (NIL T T) -8 NIL NIL) (-1168 3088714 3090013 3090068 "XFALG" 3092216 NIL XFALG (NIL T T) -9 NIL 3093001) (-1167 3087851 3087955 3088159 "XEXPPKG" 3088606 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1166 3085949 3087702 3087797 "XDPOLY" 3087802 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1165 3084828 3085438 3085481 "XALG" 3085543 NIL XALG (NIL T) -9 NIL 3085661) (-1164 3078304 3082812 3083305 "WUTSET" 3084420 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1163 3076120 3076927 3077276 "WP" 3078088 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1162 3075006 3075204 3075499 "WFFINTBS" 3075917 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1161 3072910 3073337 3073799 "WEIER" 3074578 NIL WEIER (NIL T) -7 NIL NIL) (-1160 3072058 3072482 3072525 "VSPACE" 3072661 NIL VSPACE (NIL T) -9 NIL 3072735) (-1159 3071896 3071923 3072014 "VSPACE-" 3072019 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1158 3071642 3071685 3071756 "VOID" 3071847 T VOID (NIL) -8 NIL NIL) (-1157 3069778 3070137 3070543 "VIEW" 3071258 T VIEW (NIL) -7 NIL NIL) (-1156 3066203 3066841 3067578 "VIEWDEF" 3069063 T VIEWDEF (NIL) -7 NIL NIL) (-1155 3055542 3057751 3059924 "VIEW3D" 3064052 T VIEW3D (NIL) -8 NIL NIL) (-1154 3047824 3049453 3051032 "VIEW2D" 3053985 T VIEW2D (NIL) -8 NIL NIL) (-1153 3043233 3047594 3047686 "VECTOR" 3047767 NIL VECTOR (NIL T) -8 NIL NIL) (-1152 3041810 3042069 3042387 "VECTOR2" 3042963 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1151 3035359 3039605 3039649 "VECTCAT" 3040637 NIL VECTCAT (NIL T) -9 NIL 3041214) (-1150 3034373 3034627 3035017 "VECTCAT-" 3035022 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1149 3033854 3034024 3034144 "VARIABLE" 3034288 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1148 3032691 3032845 3033105 "UTSODETL" 3033681 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1147 3030131 3030591 3031115 "UTSODE" 3032232 NIL UTSODE (NIL T T) -7 NIL NIL) (-1146 3021981 3027773 3028260 "UTS" 3029701 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1145 3013286 3018648 3018691 "UTSCAT" 3019792 NIL UTSCAT (NIL T) -9 NIL 3020542) (-1144 3010642 3011357 3012345 "UTSCAT-" 3012350 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1143 3010273 3010316 3010447 "UTS2" 3010593 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1142 3004549 3007114 3007158 "URAGG" 3009228 NIL URAGG (NIL T) -9 NIL 3009949) (-1141 3001488 3002351 3003474 "URAGG-" 3003479 NIL URAGG- (NIL T T) -8 NIL NIL) (-1140 2997174 3000105 3000576 "UPXSSING" 3001152 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1139 2989070 2996297 2996576 "UPXS" 2996952 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1138 2982102 2988975 2989046 "UPXSCONS" 2989051 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1137 2972330 2979157 2979219 "UPXSCCA" 2979868 NIL UPXSCCA (NIL T T) -9 NIL 2980109) (-1136 2971969 2972054 2972227 "UPXSCCA-" 2972232 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1135 2962126 2968726 2968769 "UPXSCAT" 2969412 NIL UPXSCAT (NIL T) -9 NIL 2970013) (-1134 2961560 2961639 2961816 "UPXS2" 2962041 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1133 2960214 2960467 2960818 "UPSQFREE" 2961303 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1132 2954068 2957120 2957175 "UPSCAT" 2958324 NIL UPSCAT (NIL T T) -9 NIL 2959091) (-1131 2953282 2953486 2953809 "UPSCAT-" 2953814 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1130 2939361 2947358 2947401 "UPOLYC" 2949479 NIL UPOLYC (NIL T) -9 NIL 2950693) (-1129 2930754 2933158 2936283 "UPOLYC-" 2936288 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1128 2930385 2930428 2930559 "UPOLYC2" 2930705 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1127 2921844 2929954 2930091 "UP" 2930295 NIL UP (NIL NIL T) -8 NIL NIL) (-1126 2921187 2921294 2921457 "UPMP" 2921733 NIL UPMP (NIL T T) -7 NIL NIL) (-1125 2920740 2920821 2920960 "UPDIVP" 2921100 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1124 2919308 2919557 2919873 "UPDECOMP" 2920489 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1123 2918543 2918655 2918840 "UPCDEN" 2919192 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1122 2918066 2918135 2918282 "UP2" 2918468 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1121 2916595 2917281 2917553 "UNISEG" 2917829 NIL UNISEG (NIL T) -8 NIL NIL) (-1120 2915812 2915939 2916143 "UNISEG2" 2916439 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1119 2914872 2915052 2915278 "UNIFACT" 2915628 NIL UNIFACT (NIL T) -7 NIL NIL) (-1118 2898773 2914055 2914304 "ULS" 2914680 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1117 2886741 2898678 2898749 "ULSCONS" 2898754 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1116 2869445 2881455 2881517 "ULSCCAT" 2882229 NIL ULSCCAT (NIL T T) -9 NIL 2882524) (-1115 2868496 2868741 2869128 "ULSCCAT-" 2869133 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1114 2858447 2864961 2865004 "ULSCAT" 2865860 NIL ULSCAT (NIL T) -9 NIL 2866582) (-1113 2857881 2857960 2858137 "ULS2" 2858362 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1112 2856278 2857245 2857276 "UFD" 2857488 T UFD (NIL) -9 NIL 2857602) (-1111 2856072 2856118 2856213 "UFD-" 2856218 NIL UFD- (NIL T) -8 NIL NIL) (-1110 2855154 2855337 2855553 "UDVO" 2855878 T UDVO (NIL) -7 NIL NIL) (-1109 2852972 2853381 2853851 "UDPO" 2854719 NIL UDPO (NIL T) -7 NIL NIL) (-1108 2852904 2852909 2852940 "TYPE" 2852945 T TYPE (NIL) -9 NIL NIL) (-1107 2851875 2852077 2852317 "TWOFACT" 2852698 NIL TWOFACT (NIL T) -7 NIL NIL) (-1106 2850817 2851154 2851415 "TUPLE" 2851649 NIL TUPLE (NIL T) -8 NIL NIL) (-1105 2848508 2849027 2849566 "TUBETOOL" 2850300 T TUBETOOL (NIL) -7 NIL NIL) (-1104 2847357 2847562 2847803 "TUBE" 2848301 NIL TUBE (NIL T) -8 NIL NIL) (-1103 2842083 2846337 2846618 "TS" 2847110 NIL TS (NIL T) -8 NIL NIL) (-1102 2830787 2834879 2834976 "TSETCAT" 2840210 NIL TSETCAT (NIL T T T T) -9 NIL 2841740) (-1101 2825523 2827120 2829010 "TSETCAT-" 2829015 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1100 2819794 2820640 2821578 "TRMANIP" 2824663 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1099 2819235 2819298 2819461 "TRIMAT" 2819726 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1098 2817041 2817278 2817641 "TRIGMNIP" 2818984 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1097 2816560 2816673 2816704 "TRIGCAT" 2816917 T TRIGCAT (NIL) -9 NIL NIL) (-1096 2816229 2816308 2816449 "TRIGCAT-" 2816454 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1095 2813134 2815089 2815369 "TREE" 2815984 NIL TREE (NIL T) -8 NIL NIL) (-1094 2812407 2812935 2812966 "TRANFUN" 2813001 T TRANFUN (NIL) -9 NIL 2813067) (-1093 2811686 2811877 2812157 "TRANFUN-" 2812162 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1092 2811490 2811522 2811583 "TOPSP" 2811647 T TOPSP (NIL) -7 NIL NIL) (-1091 2810842 2810957 2811110 "TOOLSIGN" 2811371 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1090 2809503 2810019 2810258 "TEXTFILE" 2810625 T TEXTFILE (NIL) -8 NIL NIL) (-1089 2807368 2807882 2808320 "TEX" 2809087 T TEX (NIL) -8 NIL NIL) (-1088 2807149 2807180 2807252 "TEX1" 2807331 NIL TEX1 (NIL T) -7 NIL NIL) (-1087 2806797 2806860 2806950 "TEMUTL" 2807081 T TEMUTL (NIL) -7 NIL NIL) (-1086 2804951 2805231 2805556 "TBCMPPK" 2806520 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1085 2796609 2802869 2802926 "TBAGG" 2803326 NIL TBAGG (NIL T T) -9 NIL 2803537) (-1084 2791679 2793167 2794921 "TBAGG-" 2794926 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1083 2791063 2791170 2791315 "TANEXP" 2791568 NIL TANEXP (NIL T) -7 NIL NIL) (-1082 2784576 2790920 2791013 "TABLE" 2791018 NIL TABLE (NIL T T) -8 NIL NIL) (-1081 2783989 2784087 2784225 "TABLEAU" 2784473 NIL TABLEAU (NIL T) -8 NIL NIL) (-1080 2778597 2779817 2781065 "TABLBUMP" 2782775 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1079 2775060 2775755 2776538 "SYSSOLP" 2777848 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1078 2773614 2773869 2774181 "SYNTAX" 2774770 T SYNTAX (NIL) -8 NIL NIL) (-1077 2770748 2771356 2771994 "SYMTAB" 2772998 T SYMTAB (NIL) -8 NIL NIL) (-1076 2765997 2766899 2767882 "SYMS" 2769787 T SYMS (NIL) -8 NIL NIL) (-1075 2763236 2765463 2765689 "SYMPOLY" 2765805 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1074 2762756 2762831 2762953 "SYMFUNC" 2763148 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1073 2758734 2759993 2760815 "SYMBOL" 2761956 T SYMBOL (NIL) -8 NIL NIL) (-1072 2752273 2753962 2755682 "SWITCH" 2757036 T SWITCH (NIL) -8 NIL NIL) (-1071 2745508 2751102 2751403 "SUTS" 2752029 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1070 2737403 2744631 2744910 "SUPXS" 2745286 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1069 2728936 2737024 2737149 "SUP" 2737312 NIL SUP (NIL T) -8 NIL NIL) (-1068 2728095 2728222 2728439 "SUPFRACF" 2728804 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1067 2727720 2727779 2727890 "SUP2" 2728030 NIL SUP2 (NIL T T) -7 NIL NIL) (-1066 2726146 2726418 2726778 "SUMRF" 2727421 NIL SUMRF (NIL T) -7 NIL NIL) (-1065 2725467 2725532 2725729 "SUMFS" 2726068 NIL SUMFS (NIL T T) -7 NIL NIL) (-1064 2709408 2724650 2724899 "SULS" 2725275 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1063 2708730 2708933 2709073 "SUCH" 2709316 NIL SUCH (NIL T T) -8 NIL NIL) (-1062 2702657 2703669 2704627 "SUBSPACE" 2707818 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1061 2702089 2702179 2702342 "SUBRESP" 2702546 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1060 2695458 2696754 2698065 "STTF" 2700825 NIL STTF (NIL T) -7 NIL NIL) (-1059 2689631 2690751 2691898 "STTFNC" 2694358 NIL STTFNC (NIL T) -7 NIL NIL) (-1058 2680986 2682853 2684644 "STTAYLOR" 2687874 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1057 2674242 2680850 2680933 "STRTBL" 2680938 NIL STRTBL (NIL T) -8 NIL NIL) (-1056 2669633 2674197 2674228 "STRING" 2674233 T STRING (NIL) -8 NIL NIL) (-1055 2664491 2668976 2669007 "STRICAT" 2669066 T STRICAT (NIL) -9 NIL 2669128) (-1054 2657216 2662018 2662636 "STREAM" 2663908 NIL STREAM (NIL T) -8 NIL NIL) (-1053 2656726 2656803 2656947 "STREAM3" 2657133 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1052 2655708 2655891 2656126 "STREAM2" 2656539 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1051 2655396 2655448 2655541 "STREAM1" 2655650 NIL STREAM1 (NIL T) -7 NIL NIL) (-1050 2654412 2654593 2654824 "STINPROD" 2655212 NIL STINPROD (NIL T) -7 NIL NIL) (-1049 2653990 2654174 2654205 "STEP" 2654285 T STEP (NIL) -9 NIL 2654363) (-1048 2647545 2653889 2653966 "STBL" 2653971 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1047 2642717 2646764 2646808 "STAGG" 2646961 NIL STAGG (NIL T) -9 NIL 2647050) (-1046 2640419 2641021 2641893 "STAGG-" 2641898 NIL STAGG- (NIL T T) -8 NIL NIL) (-1045 2638617 2640189 2640281 "STACK" 2640362 NIL STACK (NIL T) -8 NIL NIL) (-1044 2631348 2636764 2637219 "SREGSET" 2638247 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1043 2623788 2625156 2626668 "SRDCMPK" 2629954 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1042 2616731 2621198 2621229 "SRAGG" 2622532 T SRAGG (NIL) -9 NIL 2623140) (-1041 2615748 2616003 2616382 "SRAGG-" 2616387 NIL SRAGG- (NIL T) -8 NIL NIL) (-1040 2610205 2614675 2615098 "SQMATRIX" 2615371 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1039 2603963 2606925 2607651 "SPLTREE" 2609551 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1038 2599953 2600619 2601265 "SPLNODE" 2603389 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1037 2598999 2599232 2599263 "SPFCAT" 2599707 T SPFCAT (NIL) -9 NIL NIL) (-1036 2597736 2597946 2598210 "SPECOUT" 2598757 T SPECOUT (NIL) -7 NIL NIL) (-1035 2589758 2591505 2591548 "SPACEC" 2595871 NIL SPACEC (NIL T) -9 NIL 2597687) (-1034 2587930 2589691 2589739 "SPACE3" 2589744 NIL SPACE3 (NIL T) -8 NIL NIL) (-1033 2586684 2586855 2587145 "SORTPAK" 2587736 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1032 2584740 2585043 2585461 "SOLVETRA" 2586348 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1031 2583751 2583973 2584247 "SOLVESER" 2584513 NIL SOLVESER (NIL T) -7 NIL NIL) (-1030 2578971 2579852 2580854 "SOLVERAD" 2582803 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1029 2574786 2575395 2576124 "SOLVEFOR" 2578338 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1028 2569085 2574137 2574234 "SNTSCAT" 2574239 NIL SNTSCAT (NIL T T T T) -9 NIL 2574309) (-1027 2563192 2567418 2567807 "SMTS" 2568776 NIL SMTS (NIL T T T) -8 NIL NIL) (-1026 2557602 2563081 2563157 "SMP" 2563162 NIL SMP (NIL T T) -8 NIL NIL) (-1025 2555761 2556062 2556460 "SMITH" 2557299 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1024 2548728 2552924 2553027 "SMATCAT" 2554367 NIL SMATCAT (NIL NIL T T T) -9 NIL 2554913) (-1023 2545669 2546492 2547669 "SMATCAT-" 2547674 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1022 2543388 2544905 2544949 "SKAGG" 2545210 NIL SKAGG (NIL T) -9 NIL 2545345) (-1021 2539446 2542492 2542770 "SINT" 2543132 T SINT (NIL) -8 NIL NIL) (-1020 2539218 2539256 2539322 "SIMPAN" 2539402 T SIMPAN (NIL) -7 NIL NIL) (-1019 2538056 2538277 2538552 "SIGNRF" 2538977 NIL SIGNRF (NIL T) -7 NIL NIL) (-1018 2536865 2537016 2537306 "SIGNEF" 2537885 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1017 2534557 2535011 2535516 "SHP" 2536407 NIL SHP (NIL T NIL) -7 NIL NIL) (-1016 2528416 2534458 2534534 "SHDP" 2534539 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1015 2527905 2528097 2528128 "SGROUP" 2528280 T SGROUP (NIL) -9 NIL 2528367) (-1014 2527675 2527727 2527831 "SGROUP-" 2527836 NIL SGROUP- (NIL T) -8 NIL NIL) (-1013 2524511 2525208 2525931 "SGCF" 2526974 T SGCF (NIL) -7 NIL NIL) (-1012 2518909 2523961 2524058 "SFRTCAT" 2524063 NIL SFRTCAT (NIL T T T T) -9 NIL 2524101) (-1011 2512369 2513384 2514518 "SFRGCD" 2517892 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1010 2505535 2506606 2507790 "SFQCMPK" 2511302 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1009 2505157 2505246 2505356 "SFORT" 2505476 NIL SFORT (NIL T T) -8 NIL NIL) (-1008 2504302 2504997 2505118 "SEXOF" 2505123 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1007 2503436 2504183 2504251 "SEX" 2504256 T SEX (NIL) -8 NIL NIL) (-1006 2498212 2498901 2498997 "SEXCAT" 2502768 NIL SEXCAT (NIL T T T T T) -9 NIL 2503387) (-1005 2495392 2498146 2498194 "SET" 2498199 NIL SET (NIL T) -8 NIL NIL) (-1004 2493643 2494105 2494410 "SETMN" 2495133 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1003 2493250 2493376 2493407 "SETCAT" 2493524 T SETCAT (NIL) -9 NIL 2493608) (-1002 2493030 2493082 2493181 "SETCAT-" 2493186 NIL SETCAT- (NIL T) -8 NIL NIL) (-1001 2489417 2491491 2491535 "SETAGG" 2492405 NIL SETAGG (NIL T) -9 NIL 2492745) (-1000 2488875 2488991 2489228 "SETAGG-" 2489233 NIL SETAGG- (NIL T T) -8 NIL NIL) (-999 2488085 2488378 2488438 "SEGXCAT" 2488721 NIL SEGXCAT (NIL T T) -9 NIL 2488840) (-998 2487151 2487761 2487937 "SEG" 2487942 NIL SEG (NIL T) -8 NIL NIL) (-997 2486068 2486281 2486323 "SEGCAT" 2486896 NIL SEGCAT (NIL T) -9 NIL 2487134) (-996 2485132 2485460 2485655 "SEGBIND" 2485906 NIL SEGBIND (NIL T) -8 NIL NIL) (-995 2484764 2484821 2484930 "SEGBIND2" 2485069 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-994 2484001 2484124 2484322 "SEG2" 2484612 NIL SEG2 (NIL T T) -7 NIL NIL) (-993 2483440 2483938 2483983 "SDVAR" 2483988 NIL SDVAR (NIL T) -8 NIL NIL) (-992 2475746 2483219 2483343 "SDPOL" 2483348 NIL SDPOL (NIL T) -8 NIL NIL) (-991 2474345 2474611 2474928 "SCPKG" 2475461 NIL SCPKG (NIL T) -7 NIL NIL) (-990 2473572 2473705 2473882 "SCACHE" 2474200 NIL SCACHE (NIL T) -7 NIL NIL) (-989 2473015 2473336 2473419 "SAOS" 2473509 T SAOS (NIL) -8 NIL NIL) (-988 2472583 2472618 2472789 "SAERFFC" 2472974 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-987 2466479 2472482 2472560 "SAE" 2472565 NIL SAE (NIL T T NIL) -8 NIL NIL) (-986 2466075 2466110 2466267 "SAEFACT" 2466438 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-985 2464401 2464715 2465114 "RURPK" 2465741 NIL RURPK (NIL T NIL) -7 NIL NIL) (-984 2463054 2463331 2463638 "RULESET" 2464237 NIL RULESET (NIL T T T) -8 NIL NIL) (-983 2460262 2460765 2461226 "RULE" 2462736 NIL RULE (NIL T T T) -8 NIL NIL) (-982 2459904 2460059 2460140 "RULECOLD" 2460214 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-981 2454796 2455590 2456506 "RSETGCD" 2459103 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-980 2444110 2449162 2449257 "RSETCAT" 2453322 NIL RSETCAT (NIL T T T T) -9 NIL 2454419) (-979 2442041 2442580 2443400 "RSETCAT-" 2443405 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-978 2434471 2435846 2437362 "RSDCMPK" 2440640 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-977 2432488 2432929 2433002 "RRCC" 2434078 NIL RRCC (NIL T T) -9 NIL 2434422) (-976 2431842 2432016 2432292 "RRCC-" 2432297 NIL RRCC- (NIL T T T) -8 NIL NIL) (-975 2406172 2415797 2415862 "RPOLCAT" 2426364 NIL RPOLCAT (NIL T T T) -9 NIL 2429511) (-974 2397676 2400014 2403132 "RPOLCAT-" 2403137 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-973 2388754 2395906 2396386 "ROUTINE" 2397216 T ROUTINE (NIL) -8 NIL NIL) (-972 2385459 2388310 2388457 "ROMAN" 2388627 T ROMAN (NIL) -8 NIL NIL) (-971 2383745 2384330 2384587 "ROIRC" 2385265 NIL ROIRC (NIL T T) -8 NIL NIL) (-970 2380102 2382406 2382435 "RNS" 2382731 T RNS (NIL) -9 NIL 2383001) (-969 2378616 2378999 2379530 "RNS-" 2379603 NIL RNS- (NIL T) -8 NIL NIL) (-968 2378041 2378449 2378478 "RNG" 2378483 T RNG (NIL) -9 NIL 2378504) (-967 2377438 2377800 2377841 "RMODULE" 2377901 NIL RMODULE (NIL T) -9 NIL 2377943) (-966 2376290 2376384 2376714 "RMCAT2" 2377339 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-965 2373008 2375477 2375796 "RMATRIX" 2376027 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-964 2366009 2368243 2368356 "RMATCAT" 2371665 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2372642) (-963 2365388 2365535 2365838 "RMATCAT-" 2365843 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-962 2364958 2365033 2365159 "RINTERP" 2365307 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-961 2364008 2364572 2364601 "RING" 2364711 T RING (NIL) -9 NIL 2364805) (-960 2363803 2363847 2363941 "RING-" 2363946 NIL RING- (NIL T) -8 NIL NIL) (-959 2362655 2362891 2363146 "RIDIST" 2363568 T RIDIST (NIL) -7 NIL NIL) (-958 2353977 2362129 2362332 "RGCHAIN" 2362504 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-957 2350982 2351596 2352264 "RF" 2353341 NIL RF (NIL T) -7 NIL NIL) (-956 2350631 2350694 2350795 "RFFACTOR" 2350913 NIL RFFACTOR (NIL T) -7 NIL NIL) (-955 2350359 2350394 2350489 "RFFACT" 2350590 NIL RFFACT (NIL T) -7 NIL NIL) (-954 2348489 2348853 2349233 "RFDIST" 2349999 T RFDIST (NIL) -7 NIL NIL) (-953 2347947 2348039 2348199 "RETSOL" 2348391 NIL RETSOL (NIL T T) -7 NIL NIL) (-952 2347539 2347619 2347661 "RETRACT" 2347851 NIL RETRACT (NIL T) -9 NIL NIL) (-951 2347391 2347416 2347500 "RETRACT-" 2347505 NIL RETRACT- (NIL T T) -8 NIL NIL) (-950 2340261 2347048 2347173 "RESULT" 2347286 T RESULT (NIL) -8 NIL NIL) (-949 2338846 2339535 2339732 "RESRING" 2340164 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-948 2338486 2338535 2338631 "RESLATC" 2338783 NIL RESLATC (NIL T) -7 NIL NIL) (-947 2338195 2338229 2338334 "REPSQ" 2338445 NIL REPSQ (NIL T) -7 NIL NIL) (-946 2335626 2336206 2336806 "REP" 2337615 T REP (NIL) -7 NIL NIL) (-945 2335327 2335361 2335470 "REPDB" 2335585 NIL REPDB (NIL T) -7 NIL NIL) (-944 2329280 2330659 2331875 "REP2" 2334143 NIL REP2 (NIL T) -7 NIL NIL) (-943 2325690 2326371 2327174 "REP1" 2328509 NIL REP1 (NIL T) -7 NIL NIL) (-942 2318436 2323851 2324303 "REGSET" 2325321 NIL REGSET (NIL T T T T) -8 NIL NIL) (-941 2317259 2317594 2317841 "REF" 2318222 NIL REF (NIL T) -8 NIL NIL) (-940 2316640 2316743 2316908 "REDORDER" 2317143 NIL REDORDER (NIL T T) -7 NIL NIL) (-939 2312609 2315874 2316095 "RECLOS" 2316471 NIL RECLOS (NIL T) -8 NIL NIL) (-938 2311666 2311847 2312060 "REALSOLV" 2312416 T REALSOLV (NIL) -7 NIL NIL) (-937 2311513 2311554 2311583 "REAL" 2311588 T REAL (NIL) -9 NIL 2311623) (-936 2308004 2308806 2309688 "REAL0Q" 2310678 NIL REAL0Q (NIL T) -7 NIL NIL) (-935 2303615 2304603 2305662 "REAL0" 2306985 NIL REAL0 (NIL T) -7 NIL NIL) (-934 2303023 2303095 2303300 "RDIV" 2303537 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-933 2302096 2302270 2302481 "RDIST" 2302845 NIL RDIST (NIL T) -7 NIL NIL) (-932 2300700 2300987 2301356 "RDETRS" 2301804 NIL RDETRS (NIL T T) -7 NIL NIL) (-931 2298521 2298975 2299510 "RDETR" 2300242 NIL RDETR (NIL T T) -7 NIL NIL) (-930 2297137 2297415 2297816 "RDEEFS" 2298237 NIL RDEEFS (NIL T T) -7 NIL NIL) (-929 2295637 2295943 2296372 "RDEEF" 2296825 NIL RDEEF (NIL T T) -7 NIL NIL) (-928 2289862 2292794 2292823 "RCFIELD" 2294100 T RCFIELD (NIL) -9 NIL 2294830) (-927 2287931 2288435 2289128 "RCFIELD-" 2289201 NIL RCFIELD- (NIL T) -8 NIL NIL) (-926 2284264 2286049 2286091 "RCAGG" 2287162 NIL RCAGG (NIL T) -9 NIL 2287625) (-925 2283895 2283989 2284149 "RCAGG-" 2284154 NIL RCAGG- (NIL T T) -8 NIL NIL) (-924 2283240 2283351 2283513 "RATRET" 2283779 NIL RATRET (NIL T) -7 NIL NIL) (-923 2282797 2282864 2282983 "RATFACT" 2283168 NIL RATFACT (NIL T) -7 NIL NIL) (-922 2282112 2282232 2282382 "RANDSRC" 2282667 T RANDSRC (NIL) -7 NIL NIL) (-921 2281849 2281893 2281964 "RADUTIL" 2282061 T RADUTIL (NIL) -7 NIL NIL) (-920 2274856 2280592 2280909 "RADIX" 2281564 NIL RADIX (NIL NIL) -8 NIL NIL) (-919 2266426 2274700 2274828 "RADFF" 2274833 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-918 2266077 2266152 2266181 "RADCAT" 2266338 T RADCAT (NIL) -9 NIL NIL) (-917 2265862 2265910 2266007 "RADCAT-" 2266012 NIL RADCAT- (NIL T) -8 NIL NIL) (-916 2264019 2265637 2265726 "QUEUE" 2265806 NIL QUEUE (NIL T) -8 NIL NIL) (-915 2260516 2263956 2264001 "QUAT" 2264006 NIL QUAT (NIL T) -8 NIL NIL) (-914 2260154 2260197 2260324 "QUATCT2" 2260467 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-913 2253908 2257288 2257329 "QUATCAT" 2258108 NIL QUATCAT (NIL T) -9 NIL 2258865) (-912 2250052 2251089 2252476 "QUATCAT-" 2252570 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-911 2247578 2249136 2249178 "QUAGG" 2249553 NIL QUAGG (NIL T) -9 NIL 2249728) (-910 2246503 2246976 2247148 "QFORM" 2247450 NIL QFORM (NIL NIL T) -8 NIL NIL) (-909 2237764 2243022 2243063 "QFCAT" 2243721 NIL QFCAT (NIL T) -9 NIL 2244702) (-908 2233336 2234537 2236128 "QFCAT-" 2236222 NIL QFCAT- (NIL T T) -8 NIL NIL) (-907 2232974 2233017 2233144 "QFCAT2" 2233287 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-906 2232434 2232544 2232674 "QEQUAT" 2232864 T QEQUAT (NIL) -8 NIL NIL) (-905 2225620 2226691 2227873 "QCMPACK" 2231367 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-904 2223200 2223621 2224047 "QALGSET" 2225277 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-903 2222445 2222619 2222851 "QALGSET2" 2223020 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-902 2221136 2221359 2221676 "PWFFINTB" 2222218 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-901 2219324 2219492 2219845 "PUSHVAR" 2220950 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-900 2215241 2216295 2216337 "PTRANFN" 2218221 NIL PTRANFN (NIL T) -9 NIL NIL) (-899 2213653 2213944 2214265 "PTPACK" 2214952 NIL PTPACK (NIL T) -7 NIL NIL) (-898 2213289 2213346 2213453 "PTFUNC2" 2213590 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-897 2207768 2212103 2212144 "PTCAT" 2212512 NIL PTCAT (NIL T) -9 NIL 2212674) (-896 2207426 2207461 2207585 "PSQFR" 2207727 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-895 2206021 2206319 2206653 "PSEUDLIN" 2207124 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-894 2192835 2195199 2197519 "PSETPK" 2203784 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-893 2185922 2188636 2188731 "PSETCAT" 2191712 NIL PSETCAT (NIL T T T T) -9 NIL 2192525) (-892 2183760 2184394 2185213 "PSETCAT-" 2185218 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-891 2183117 2183279 2183308 "PSCURVE" 2183573 T PSCURVE (NIL) -9 NIL 2183737) (-890 2179521 2181047 2181112 "PSCAT" 2181948 NIL PSCAT (NIL T T T) -9 NIL 2182188) (-889 2178585 2178801 2179200 "PSCAT-" 2179205 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-888 2177238 2177870 2178084 "PRTITION" 2178391 T PRTITION (NIL) -8 NIL NIL) (-887 2166338 2168544 2170731 "PRS" 2175101 NIL PRS (NIL T T) -7 NIL NIL) (-886 2164202 2165688 2165729 "PRQAGG" 2165912 NIL PRQAGG (NIL T) -9 NIL 2166014) (-885 2158008 2162400 2163204 "PRODUCT" 2163444 NIL PRODUCT (NIL T T) -8 NIL NIL) (-884 2155290 2157474 2157704 "PR" 2157822 NIL PR (NIL T T) -8 NIL NIL) (-883 2155086 2155118 2155177 "PRINT" 2155251 T PRINT (NIL) -7 NIL NIL) (-882 2154426 2154543 2154695 "PRIMES" 2154966 NIL PRIMES (NIL T) -7 NIL NIL) (-881 2152491 2152892 2153358 "PRIMELT" 2154005 NIL PRIMELT (NIL T) -7 NIL NIL) (-880 2152222 2152270 2152299 "PRIMCAT" 2152422 T PRIMCAT (NIL) -9 NIL NIL) (-879 2148383 2152160 2152205 "PRIMARR" 2152210 NIL PRIMARR (NIL T) -8 NIL NIL) (-878 2147390 2147568 2147796 "PRIMARR2" 2148201 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-877 2147033 2147089 2147200 "PREASSOC" 2147328 NIL PREASSOC (NIL T T) -7 NIL NIL) (-876 2146513 2146644 2146673 "PPCURVE" 2146876 T PPCURVE (NIL) -9 NIL 2147010) (-875 2143874 2144273 2144864 "POLYROOT" 2146095 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-874 2137782 2143482 2143640 "POLY" 2143748 NIL POLY (NIL T) -8 NIL NIL) (-873 2137167 2137225 2137458 "POLYLIFT" 2137718 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-872 2133452 2133901 2134529 "POLYCATQ" 2136712 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-871 2120460 2125857 2125922 "POLYCAT" 2129407 NIL POLYCAT (NIL T T T) -9 NIL 2131319) (-870 2113911 2115772 2118155 "POLYCAT-" 2118160 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-869 2113500 2113568 2113687 "POLY2UP" 2113837 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-868 2113136 2113193 2113300 "POLY2" 2113437 NIL POLY2 (NIL T T) -7 NIL NIL) (-867 2111823 2112062 2112337 "POLUTIL" 2112911 NIL POLUTIL (NIL T T) -7 NIL NIL) (-866 2110185 2110462 2110792 "POLTOPOL" 2111545 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-865 2105714 2110122 2110167 "POINT" 2110172 NIL POINT (NIL T) -8 NIL NIL) (-864 2103901 2104258 2104633 "PNTHEORY" 2105359 T PNTHEORY (NIL) -7 NIL NIL) (-863 2102329 2102626 2103035 "PMTOOLS" 2103599 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-862 2101922 2102000 2102117 "PMSYM" 2102245 NIL PMSYM (NIL T) -7 NIL NIL) (-861 2101432 2101501 2101675 "PMQFCAT" 2101847 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-860 2100787 2100897 2101053 "PMPRED" 2101309 NIL PMPRED (NIL T) -7 NIL NIL) (-859 2100183 2100269 2100430 "PMPREDFS" 2100688 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-858 2098831 2099039 2099422 "PMPLCAT" 2099946 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-857 2098363 2098442 2098594 "PMLSAGG" 2098746 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-856 2097840 2097916 2098096 "PMKERNEL" 2098281 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-855 2097457 2097532 2097645 "PMINS" 2097759 NIL PMINS (NIL T) -7 NIL NIL) (-854 2096887 2096956 2097171 "PMFS" 2097382 NIL PMFS (NIL T T T) -7 NIL NIL) (-853 2096118 2096236 2096440 "PMDOWN" 2096764 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-852 2095281 2095440 2095622 "PMASS" 2095956 T PMASS (NIL) -7 NIL NIL) (-851 2094555 2094666 2094829 "PMASSFS" 2095167 NIL PMASSFS (NIL T T) -7 NIL NIL) (-850 2094214 2094281 2094374 "PLOTTOOL" 2094482 T PLOTTOOL (NIL) -7 NIL NIL) (-849 2088915 2090081 2091208 "PLOT" 2093107 T PLOT (NIL) -8 NIL NIL) (-848 2084788 2085803 2086708 "PLOT3D" 2088030 T PLOT3D (NIL) -8 NIL NIL) (-847 2083712 2083886 2084118 "PLOT1" 2084595 NIL PLOT1 (NIL T) -7 NIL NIL) (-846 2059107 2063778 2068629 "PLEQN" 2078978 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-845 2058425 2058547 2058727 "PINTERP" 2058972 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-844 2058118 2058165 2058268 "PINTERPA" 2058372 NIL PINTERPA (NIL T T) -7 NIL NIL) (-843 2057345 2057912 2058005 "PI" 2058045 T PI (NIL) -8 NIL NIL) (-842 2055736 2056721 2056750 "PID" 2056932 T PID (NIL) -9 NIL 2057066) (-841 2055461 2055498 2055586 "PICOERCE" 2055693 NIL PICOERCE (NIL T) -7 NIL NIL) (-840 2054782 2054920 2055096 "PGROEB" 2055317 NIL PGROEB (NIL T) -7 NIL NIL) (-839 2050369 2051183 2052088 "PGE" 2053897 T PGE (NIL) -7 NIL NIL) (-838 2048493 2048739 2049105 "PGCD" 2050086 NIL PGCD (NIL T T T T) -7 NIL NIL) (-837 2047831 2047934 2048095 "PFRPAC" 2048377 NIL PFRPAC (NIL T) -7 NIL NIL) (-836 2044446 2046379 2046732 "PFR" 2047510 NIL PFR (NIL T) -8 NIL NIL) (-835 2042835 2043079 2043404 "PFOTOOLS" 2044193 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-834 2041368 2041607 2041958 "PFOQ" 2042592 NIL PFOQ (NIL T T T) -7 NIL NIL) (-833 2039845 2040057 2040419 "PFO" 2041152 NIL PFO (NIL T T T T T) -7 NIL NIL) (-832 2036368 2039734 2039803 "PF" 2039808 NIL PF (NIL NIL) -8 NIL NIL) (-831 2033797 2035078 2035107 "PFECAT" 2035692 T PFECAT (NIL) -9 NIL 2036075) (-830 2033242 2033396 2033610 "PFECAT-" 2033615 NIL PFECAT- (NIL T) -8 NIL NIL) (-829 2031846 2032097 2032398 "PFBRU" 2032991 NIL PFBRU (NIL T T) -7 NIL NIL) (-828 2029713 2030064 2030496 "PFBR" 2031497 NIL PFBR (NIL T T T T) -7 NIL NIL) (-827 2025569 2027093 2027767 "PERM" 2029072 NIL PERM (NIL T) -8 NIL NIL) (-826 2020836 2021776 2022646 "PERMGRP" 2024732 NIL PERMGRP (NIL T) -8 NIL NIL) (-825 2018908 2019901 2019943 "PERMCAT" 2020389 NIL PERMCAT (NIL T) -9 NIL 2020692) (-824 2018563 2018604 2018727 "PERMAN" 2018861 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-823 2016009 2018132 2018263 "PENDTREE" 2018465 NIL PENDTREE (NIL T) -8 NIL NIL) (-822 2014081 2014859 2014901 "PDRING" 2015558 NIL PDRING (NIL T) -9 NIL 2015843) (-821 2013184 2013402 2013764 "PDRING-" 2013769 NIL PDRING- (NIL T T) -8 NIL NIL) (-820 2010326 2011076 2011767 "PDEPROB" 2012513 T PDEPROB (NIL) -8 NIL NIL) (-819 2007897 2008393 2008942 "PDEPACK" 2009797 T PDEPACK (NIL) -7 NIL NIL) (-818 2006809 2006999 2007250 "PDECOMP" 2007696 NIL PDECOMP (NIL T T) -7 NIL NIL) (-817 2004420 2005235 2005264 "PDECAT" 2006049 T PDECAT (NIL) -9 NIL 2006760) (-816 2004173 2004206 2004295 "PCOMP" 2004381 NIL PCOMP (NIL T T) -7 NIL NIL) (-815 2002380 2002976 2003272 "PBWLB" 2003903 NIL PBWLB (NIL T) -8 NIL NIL) (-814 1994889 1996457 1997793 "PATTERN" 2001065 NIL PATTERN (NIL T) -8 NIL NIL) (-813 1994521 1994578 1994687 "PATTERN2" 1994826 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-812 1992278 1992666 1993123 "PATTERN1" 1994110 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-811 1989673 1990227 1990708 "PATRES" 1991843 NIL PATRES (NIL T T) -8 NIL NIL) (-810 1989237 1989304 1989436 "PATRES2" 1989600 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-809 1987134 1987534 1987939 "PATMATCH" 1988906 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-808 1986670 1986853 1986895 "PATMAB" 1987002 NIL PATMAB (NIL T) -9 NIL 1987085) (-807 1985215 1985524 1985782 "PATLRES" 1986475 NIL PATLRES (NIL T T T) -8 NIL NIL) (-806 1984762 1984885 1984927 "PATAB" 1984932 NIL PATAB (NIL T) -9 NIL 1985102) (-805 1982243 1982775 1983348 "PARTPERM" 1984209 T PARTPERM (NIL) -7 NIL NIL) (-804 1981864 1981927 1982029 "PARSURF" 1982174 NIL PARSURF (NIL T) -8 NIL NIL) (-803 1981496 1981553 1981662 "PARSU2" 1981801 NIL PARSU2 (NIL T T) -7 NIL NIL) (-802 1981117 1981180 1981282 "PARSCURV" 1981427 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980749 1980806 1980915 "PARSC2" 1981054 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980388 1980446 1980543 "PARPCURV" 1980685 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1980020 1980077 1980186 "PARPC2" 1980325 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1979540 1979626 1979745 "PAN2EXPR" 1979921 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978346 1978661 1978889 "PALETTE" 1979332 T PALETTE (NIL) -8 NIL NIL) (-796 1972196 1977605 1977799 "PADICRC" 1978201 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965404 1971542 1971726 "PADICRAT" 1972044 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963708 1965341 1965386 "PADIC" 1965391 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1960912 1962486 1962527 "PADICCT" 1963108 NIL PADICCT (NIL NIL) -9 NIL 1963390) (-792 1959869 1960069 1960337 "PADEPAC" 1960699 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1959081 1959214 1959420 "PADE" 1959731 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1957096 1957928 1958241 "OWP" 1958851 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956205 1956701 1956873 "OVAR" 1956964 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1955469 1955590 1955751 "OUT" 1956064 T OUT (NIL) -7 NIL NIL) (-787 1944515 1946694 1948864 "OUTFORM" 1953319 T OUTFORM (NIL) -8 NIL NIL) (-786 1943923 1944244 1944333 "OSI" 1944446 T OSI (NIL) -8 NIL NIL) (-785 1942670 1942897 1943181 "ORTHPOL" 1943671 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1940041 1942331 1942469 "OREUP" 1942613 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937437 1939734 1939860 "ORESUP" 1939983 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1934976 1935476 1936034 "OREPCTO" 1936928 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1928889 1931095 1931136 "OREPCAT" 1933457 NIL OREPCAT (NIL T) -9 NIL 1934556) (-780 1926037 1926819 1927876 "OREPCAT-" 1927881 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925214 1925486 1925515 "ORDSET" 1925824 T ORDSET (NIL) -9 NIL 1925988) (-778 1924733 1924855 1925048 "ORDSET-" 1925053 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923346 1924147 1924176 "ORDRING" 1924378 T ORDRING (NIL) -9 NIL 1924502) (-776 1922991 1923085 1923229 "ORDRING-" 1923234 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922366 1922847 1922876 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T ODEPACK (NIL) -7 NIL NIL) (-736 1833561 1833668 1833896 "ODEINT" 1834413 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1827662 1829087 1830534 "ODEIFTBL" 1832134 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1823006 1823792 1824750 "ODEEF" 1826821 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822343 1822432 1822661 "ODECONST" 1822911 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1820500 1821133 1821162 "ODECAT" 1821765 T ODECAT (NIL) -9 NIL 1822294) (-731 1817372 1820212 1820331 "OCT" 1820413 NIL OCT (NIL T) -8 NIL NIL) (-730 1817010 1817053 1817180 "OCTCT2" 1817323 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1811851 1814289 1814330 "OC" 1815426 NIL OC (NIL T) -9 NIL 1816275) (-728 1809078 1809826 1810816 "OC-" 1810910 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808456 1808898 1808927 "OCAMON" 1808932 T OCAMON (NIL) -9 NIL 1808953) (-726 1807909 1808316 1808345 "OASGP" 1808350 T OASGP (NIL) -9 NIL 1808370) (-725 1807196 1807659 1807688 "OAMONS" 1807728 T OAMONS (NIL) -9 NIL 1807771) (-724 1806636 1807043 1807072 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(-685 1684207 1686310 1688422 "NAGE02" 1690874 T NAGE02 (NIL) -7 NIL NIL) (-684 1680200 1681137 1682091 "NAGE01" 1683273 T NAGE01 (NIL) -7 NIL NIL) (-683 1678007 1678538 1679093 "NAGD03" 1679665 T NAGD03 (NIL) -7 NIL NIL) (-682 1669793 1671712 1673657 "NAGD02" 1676082 T NAGD02 (NIL) -7 NIL NIL) (-681 1663652 1665065 1666493 "NAGD01" 1668385 T NAGD01 (NIL) -7 NIL NIL) (-680 1659909 1660719 1661544 "NAGC06" 1662847 T NAGC06 (NIL) -7 NIL NIL) (-679 1658386 1658715 1659068 "NAGC05" 1659576 T NAGC05 (NIL) -7 NIL NIL) (-678 1657770 1657887 1658029 "NAGC02" 1658264 T NAGC02 (NIL) -7 NIL NIL) (-677 1656831 1657388 1657429 "NAALG" 1657508 NIL NAALG (NIL T) -9 NIL 1657569) (-676 1656666 1656695 1656785 "NAALG-" 1656790 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650616 1651724 1652911 "MULTSQFR" 1655562 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1649935 1650010 1650194 "MULTFACT" 1650528 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1643077 1646988 1647041 "MTSCAT" 1648101 NIL MTSCAT (NIL T T) -9 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1619321 1619711 "MONOTOOL" 1620343 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1618108 1618443 1618472 "MONOID" 1618749 T MONOID (NIL) -9 NIL 1618921) (-658 1617486 1617649 1617892 "MONOID-" 1617897 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608422 1614408 1614468 "MONOGEN" 1615142 NIL MONOGEN (NIL T T) -9 NIL 1615595) (-656 1605640 1606375 1607375 "MONOGEN-" 1607494 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604499 1604919 1604948 "MONADWU" 1605340 T MONADWU (NIL) -9 NIL 1605578) (-654 1603871 1604030 1604278 "MONADWU-" 1604283 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603256 1603474 1603503 "MONAD" 1603710 T MONAD (NIL) -9 NIL 1603822) (-652 1602941 1603019 1603151 "MONAD-" 1603156 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601192 1601854 1602133 "MOEBIUS" 1602694 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600585 1600963 1601004 "MODULE" 1601009 NIL MODULE (NIL T) -9 NIL 1601035) (-649 1600153 1600249 1600439 "MODULE-" 1600444 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597824 1598519 1598845 "MODRING" 1599978 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594786 1595951 1596465 "MODOP" 1597359 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1592973 1593425 1593766 "MODMONOM" 1594585 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582695 1591181 1591601 "MODMON" 1592603 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579821 1581539 1581815 "MODFIELD" 1582570 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579347 1579390 1579569 "MMAP" 1579772 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577584 1578361 1578402 "MLO" 1578819 NIL MLO (NIL T) -9 NIL 1579059) (-641 1574951 1575466 1576068 "MLIFT" 1577065 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574342 1574426 1574580 "MKUCFUNC" 1574862 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1573941 1574011 1574134 "MKRECORD" 1574265 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1572989 1573150 1573378 "MKFUNC" 1573752 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572377 1572481 1572637 "MKFLCFN" 1572872 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571803 1572170 1572259 "MKCHSET" 1572321 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1571080 1571182 1571367 "MKBCFUNC" 1571696 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567764 1570634 1570770 "MINT" 1570964 T MINT (NIL) -8 NIL NIL) (-633 1566576 1566819 1567096 "MHROWRED" 1567519 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1561847 1565021 1565445 "MFLOAT" 1566172 T MFLOAT (NIL) -8 NIL NIL) (-631 1561204 1561280 1561451 "MFINFACT" 1561759 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557551 1558390 1559265 "MESH" 1560349 T MESH (NIL) -7 NIL NIL) (-629 1555941 1556253 1556606 "MDDFACT" 1557238 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552789 1555100 1555142 "MDAGG" 1555397 NIL MDAGG (NIL T) -9 NIL 1555540) (-627 1542487 1552082 1552289 "MCMPLX" 1552602 T MCMPLX (NIL) -8 NIL NIL) (-626 1541628 1541774 1541974 "MCDEN" 1542336 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539518 1539788 1540168 "MCALCFN" 1541358 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1537140 1537663 1538224 "MATSTOR" 1538989 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1533158 1536519 1536764 "MATRIX" 1536927 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1528933 1529637 1530370 "MATLIN" 1532518 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1519142 1522274 1522351 "MATCAT" 1527189 NIL MATCAT (NIL T T T) -9 NIL 1528600) (-620 1515507 1516520 1517875 "MATCAT-" 1517880 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1514109 1514262 1514593 "MATCAT2" 1515342 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1512221 1512545 1512929 "MAPPKG3" 1513784 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1511202 1511375 1511597 "MAPPKG2" 1512045 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509701 1509985 1510312 "MAPPKG1" 1510908 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509312 1509370 1509493 "MAPHACK3" 1509637 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1508904 1508965 1509079 "MAPHACK2" 1509244 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508342 1508445 1508587 "MAPHACK1" 1508795 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506450 1507044 1507347 "MAGMA" 1508071 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1502933 1504696 1505155 "M3D" 1506024 NIL M3D (NIL T) -8 NIL NIL) (-610 1497091 1501300 1501342 "LZSTAGG" 1502124 NIL LZSTAGG (NIL T) -9 NIL 1502419) (-609 1493065 1494222 1495679 "LZSTAGG-" 1495684 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1490181 1490958 1491444 "LWORD" 1492611 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483341 1489952 1490086 "LSQM" 1490091 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482565 1482704 1482932 "LSPP" 1483196 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480377 1480678 1481134 "LSMP" 1482254 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1477156 1477830 1478560 "LSMP1" 1479679 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1471079 1476321 1476363 "LSAGG" 1476425 NIL LSAGG (NIL T) -9 NIL 1476503) (-602 1467774 1468698 1469911 "LSAGG-" 1469916 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465400 1466918 1467167 "LPOLY" 1467569 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1464982 1465067 1465190 "LPEFRAC" 1465309 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463331 1464078 1464330 "LO" 1464815 NIL LO (NIL T T T) -8 NIL NIL) (-598 1462984 1463096 1463125 "LOGIC" 1463236 T LOGIC (NIL) -9 NIL 1463316) (-597 1462846 1462869 1462940 "LOGIC-" 1462945 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1462039 1462179 1462372 "LODOOPS" 1462702 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459457 1461956 1462021 "LODO" 1462026 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1458005 1458240 1458590 "LODOF" 1459205 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454425 1456861 1456902 "LODOCAT" 1457334 NIL LODOCAT (NIL T) -9 NIL 1457544) (-592 1454159 1454217 1454343 "LODOCAT-" 1454348 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451473 1454000 1454118 "LODO2" 1454123 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1448902 1451410 1451455 "LODO1" 1451460 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447765 1447930 1448241 "LODEEF" 1448725 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1443049 1445893 1445935 "LNAGG" 1446882 NIL LNAGG (NIL T) -9 NIL 1447325) (-587 1442196 1442410 1442752 "LNAGG-" 1442757 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438361 1439123 1439761 "LMOPS" 1441612 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437758 1438120 1438161 "LMODULE" 1438221 NIL LMODULE (NIL T) -9 NIL 1438263) (-584 1435010 1437403 1437526 "LMDICT" 1437668 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1428241 1433960 1434256 "LIST" 1434747 NIL LIST (NIL T) -8 NIL NIL) (-582 1427766 1427840 1427979 "LIST3" 1428161 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426773 1426951 1427179 "LIST2" 1427584 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1424907 1425219 1425618 "LIST2MAP" 1426420 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423619 1424299 1424340 "LINEXP" 1424593 NIL LINEXP (NIL T) -9 NIL 1424741) (-578 1422266 1422526 1422823 "LINDEP" 1423371 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1419033 1419752 1420529 "LIMITRF" 1421521 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417314 1417608 1418023 "LIMITPS" 1418728 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411773 1416829 1417055 "LIE" 1417137 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410824 1411267 1411308 "LIECAT" 1411448 NIL LIECAT (NIL T) -9 NIL 1411598) (-573 1410665 1410692 1410780 "LIECAT-" 1410785 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1403289 1410114 1410279 "LIB" 1410520 T LIB (NIL) -8 NIL NIL) (-571 1398926 1399807 1400742 "LGROBP" 1402406 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396796 1397069 1397430 "LF" 1398648 NIL LF (NIL T T) -7 NIL NIL) (-569 1395636 1396327 1396356 "LFCAT" 1396563 T LFCAT (NIL) -9 NIL 1396702) (-568 1392548 1393174 1393860 "LEXTRIPK" 1395002 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1389254 1390118 1390621 "LEXP" 1392128 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387652 1387965 1388366 "LEADCDET" 1388936 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1386848 1386922 1387149 "LAZM3PK" 1387573 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381771 1384933 1385467 "LAUPOL" 1386364 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381338 1381382 1381549 "LAPLACE" 1381721 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1379268 1380441 1380691 "LA" 1381172 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378330 1378924 1378965 "LALG" 1379026 NIL LALG (NIL T) -9 NIL 1379084) (-560 1378045 1378104 1378239 "LALG-" 1378244 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1376955 1377142 1377439 "KOVACIC" 1377845 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376789 1376813 1376855 "KONVERT" 1376917 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376623 1376647 1376689 "KOERCE" 1376751 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374359 1375119 1375511 "KERNEL" 1376263 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1373861 1373942 1374072 "KERNEL2" 1374273 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367476 1372158 1372213 "KDAGG" 1372590 NIL KDAGG (NIL T T) -9 NIL 1372796) (-553 1367005 1367129 1367334 "KDAGG-" 1367339 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360180 1366666 1366821 "KAFILE" 1366883 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354639 1359695 1359921 "JORDAN" 1360003 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1350948 1352848 1352903 "IXAGG" 1353832 NIL IXAGG (NIL T T) -9 NIL 1354287) (-549 1349867 1350173 1350592 "IXAGG-" 1350597 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345458 1349789 1349848 "IVECTOR" 1349853 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344224 1344461 1344727 "ITUPLE" 1345225 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342660 1342837 1343143 "ITRIGMNP" 1344046 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341405 1341609 1341892 "ITFUN3" 1342436 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1341037 1341094 1341203 "ITFUN2" 1341342 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338841 1339912 1340208 "ITAYLOR" 1340773 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327835 1333029 1334187 "ISUPS" 1337715 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1326943 1327082 1327317 "ISUMP" 1327683 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322207 1326744 1326823 "ISTRING" 1326896 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321420 1321501 1321716 "IRURPK" 1322121 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320356 1320557 1320797 "IRSN" 1321200 T IRSN (NIL) -7 NIL NIL) (-537 1318393 1318748 1319182 "IRRF2F" 1319995 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318140 1318178 1318254 "IRREDFFX" 1318349 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316755 1317014 1317313 "IROOT" 1317873 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313397 1314448 1315136 "IR" 1316099 NIL IR (NIL T) -8 NIL NIL) (-533 1311010 1311505 1312071 "IR2" 1312875 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1310086 1310199 1310419 "IR2F" 1310893 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1309877 1309911 1309971 "IPRNTPK" 1310046 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306431 1309766 1309835 "IPF" 1309840 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304748 1306356 1306413 "IPADIC" 1306418 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304247 1304305 1304494 "INVLAPLA" 1304684 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1293896 1296249 1298635 "INTTR" 1301911 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290258 1290999 1291855 "INTTOOLS" 1293089 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1289844 1289935 1290052 "INTSLPE" 1290161 T INTSLPE (NIL) -7 NIL NIL) (-524 1287794 1289767 1289826 "INTRVL" 1289831 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285401 1285913 1286487 "INTRF" 1287279 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284816 1284913 1285054 "INTRET" 1285299 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282818 1283207 1283676 "INTRAT" 1284424 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1280059 1280642 1281263 "INTPM" 1282307 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276770 1277369 1278112 "INTPAF" 1279446 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1272053 1272989 1274014 "INTPACK" 1275765 T INTPACK (NIL) -7 NIL NIL) (-517 1268907 1271782 1271909 "INT" 1271946 T INT (NIL) -8 NIL NIL) (-516 1268159 1268311 1268519 "INTHERTR" 1268749 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267598 1267678 1267866 "INTHERAL" 1268073 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265444 1265887 1266344 "INTHEORY" 1267161 T INTHEORY (NIL) -7 NIL NIL) (-513 1256769 1258389 1260166 "INTG0" 1263797 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237366 1242150 1246954 "INTFTBL" 1251985 T INTFTBL (NIL) -8 NIL NIL) (-511 1236615 1236753 1236926 "INTFACT" 1237225 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1234006 1234452 1235015 "INTEF" 1236169 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232467 1233216 1233245 "INTDOM" 1233546 T INTDOM (NIL) -9 NIL 1233753) (-508 1231836 1232010 1232252 "INTDOM-" 1232257 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228328 1230260 1230315 "INTCAT" 1231114 NIL INTCAT (NIL T) -9 NIL 1231433) (-506 1227801 1227903 1228031 "INTBIT" 1228220 T INTBIT (NIL) -7 NIL NIL) (-505 1226476 1226630 1226943 "INTALG" 1227646 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1225933 1226023 1226193 "INTAF" 1226380 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219399 1225743 1225883 "INTABL" 1225888 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214349 1217078 1217107 "INS" 1218075 T INS (NIL) -9 NIL 1218756) (-501 1211589 1212360 1213334 "INS-" 1213407 NIL INS- (NIL T) -8 NIL NIL) (-500 1210368 1210595 1210892 "INPSIGN" 1211342 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209486 1209603 1209800 "INPRODPF" 1210248 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208380 1208497 1208734 "INPRODFF" 1209366 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207380 1207532 1207792 "INNMFACT" 1208216 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206577 1206674 1206862 "INMODGCD" 1207279 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1205086 1205330 1205654 "INFSP" 1206322 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204270 1204387 1204570 "INFPROD0" 1204966 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201280 1202439 1202930 "INFORM" 1203787 T INFORM (NIL) -8 NIL NIL) (-492 1200890 1200950 1201048 "INFORM1" 1201215 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200413 1200502 1200616 "INFINITY" 1200796 T INFINITY (NIL) -7 NIL NIL) (-490 1199031 1199279 1199600 "INEP" 1200161 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198307 1198928 1198993 "INDE" 1198998 NIL INDE (NIL T) -8 NIL NIL) (-488 1197871 1197939 1198056 "INCRMAPS" 1198234 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1193182 1194107 1195051 "INBFF" 1196959 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189683 1193027 1193130 "IMATRIX" 1193135 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188397 1188520 1188834 "IMATQF" 1189540 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186619 1186846 1187182 "IMATLIN" 1188154 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181245 1186543 1186601 "ILIST" 1186606 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1179204 1181105 1181218 "IIARRAY2" 1181223 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174572 1179115 1179179 "IFF" 1179184 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169621 1173864 1174052 "IFARRAY" 1174429 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168828 1169525 1169598 "IFAMON" 1169603 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168411 1168476 1168531 "IEVALAB" 1168738 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1168086 1168154 1168314 "IEVALAB-" 1168319 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167744 1168000 1168063 "IDPO" 1168068 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1167021 1167633 1167708 "IDPOAMS" 1167713 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166355 1166910 1166985 "IDPOAM" 1166990 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165440 1165690 1165744 "IDPC" 1166157 NIL IDPC (NIL T T) -9 NIL 1166306) (-472 1164936 1165332 1165405 "IDPAM" 1165410 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164339 1164828 1164901 "IDPAG" 1164906 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160594 1161442 1162337 "IDECOMP" 1163496 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153470 1154519 1155565 "IDEAL" 1159631 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152634 1152746 1152945 "ICDEN" 1153354 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151733 1152114 1152261 "ICARD" 1152507 T ICARD (NIL) -8 NIL NIL) (-466 1149805 1150118 1150521 "IBPTOOLS" 1151410 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145419 1149425 1149538 "IBITS" 1149724 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1142142 1142718 1143413 "IBATOOL" 1144836 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1139922 1140383 1140916 "IBACHIN" 1141677 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137805 1139768 1139871 "IARRAY2" 1139876 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1133964 1137731 1137788 "IARRAY1" 1137793 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1127904 1132382 1132860 "IAN" 1133506 T IAN (NIL) -8 NIL NIL) (-459 1127415 1127472 1127645 "IALGFACT" 1127841 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1126942 1127055 1127084 "HYPCAT" 1127291 T HYPCAT (NIL) -9 NIL NIL) (-457 1126480 1126597 1126783 "HYPCAT-" 1126788 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1123166 1124497 1124539 "HOAGG" 1125520 NIL HOAGG (NIL T) -9 NIL 1126192) (-455 1121760 1122159 1122685 "HOAGG-" 1122690 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115591 1121201 1121367 "HEXADEC" 1121614 T HEXADEC (NIL) -8 NIL NIL) (-453 1114339 1114561 1114824 "HEUGCD" 1115368 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113442 1114176 1114306 "HELLFDIV" 1114311 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111676 1113219 1113307 "HEAP" 1113386 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105549 1111591 1111653 "HDP" 1111658 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099261 1105186 1105337 "HDMP" 1105450 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098586 1098725 1098889 "HB" 1099117 T HB (NIL) -7 NIL NIL) (-447 1092095 1098432 1098536 "HASHTBL" 1098541 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1089848 1091723 1091902 "HACKPI" 1091936 T HACKPI (NIL) -8 NIL NIL) (-445 1085544 1089702 1089814 "GTSET" 1089819 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1079082 1085422 1085520 "GSTBL" 1085525 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071320 1078120 1078383 "GSERIES" 1078874 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070342 1070795 1070824 "GROUP" 1071085 T GROUP (NIL) -9 NIL 1071244) (-441 1069458 1069681 1070025 "GROUP-" 1070030 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067827 1068146 1068533 "GROEBSOL" 1069135 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066767 1067029 1067081 "GRMOD" 1067610 NIL GRMOD (NIL T T) -9 NIL 1067778) (-438 1066535 1066571 1066699 "GRMOD-" 1066704 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1061875 1062897 1063894 "GRIMAGE" 1065558 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060342 1060602 1060926 "GRDEF" 1061571 T GRDEF (NIL) -7 NIL NIL) (-435 1059786 1059902 1060043 "GRAY" 1060221 T GRAY (NIL) -7 NIL NIL) (-434 1059019 1059399 1059451 "GRALG" 1059604 NIL GRALG (NIL T T) -9 NIL 1059696) (-433 1058680 1058753 1058916 "GRALG-" 1058921 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055488 1058269 1058445 "GPOLSET" 1058587 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1054844 1054901 1055158 "GOSPER" 1055425 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050603 1051282 1051808 "GMODPOL" 1054543 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049608 1049792 1050030 "GHENSEL" 1050415 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043674 1044517 1045543 "GENUPS" 1048692 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043371 1043422 1043511 "GENUFACT" 1043617 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042783 1042860 1043025 "GENPGCD" 1043289 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1042257 1042292 1042505 "GENMFACT" 1042742 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040825 1041080 1041387 "GENEEZ" 1042000 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034699 1040438 1040599 "GDMP" 1040748 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1024080 1028472 1029577 "GCNAALG" 1033683 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022501 1023373 1023402 "GCDDOM" 1023657 T GCDDOM (NIL) -9 NIL 1023814) (-420 1021971 1022098 1022313 "GCDDOM-" 1022318 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020645 1020830 1021133 "GB" 1021751 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1009265 1011591 1013983 "GBINTERN" 1018336 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1007102 1007394 1007815 "GBF" 1008940 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1005883 1006048 1006315 "GBEUCLID" 1006918 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1005232 1005357 1005506 "GAUSSFAC" 1005754 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003611 1003913 1004225 "GALUTIL" 1004952 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1001928 1002202 1002525 "GALPOLYU" 1003338 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999317 999607 1000012 "GALFACTU" 1001625 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 991123 992622 994230 "GALFACT" 997749 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988510 989168 989197 "FVFUN" 990353 T FVFUN (NIL) -9 NIL 991073) (-409 987775 987957 987986 "FVC" 988277 T FVC (NIL) -9 NIL 988460) (-408 987417 987572 987653 "FUNCTION" 987727 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 985087 985638 986127 "FT" 986948 T FT (NIL) -8 NIL NIL) (-406 983905 984388 984591 "FTEM" 984904 T FTEM (NIL) -8 NIL NIL) (-405 982172 982460 982861 "FSUPFACT" 983598 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980569 980858 981190 "FST" 981860 T FST (NIL) -8 NIL NIL) (-403 979744 979850 980044 "FSRED" 980451 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978425 978680 979033 "FSPRMELT" 979460 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975510 975948 976447 "FSPECF" 977988 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 957847 966404 966445 "FS" 970283 NIL FS (NIL T) -9 NIL 972554) (-399 946497 949487 953543 "FS-" 953840 NIL FS- (NIL T T) -8 NIL NIL) (-398 946013 946067 946243 "FSINT" 946438 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944298 945010 945311 "FSERIES" 945794 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943316 943432 943662 "FSCINT" 944178 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939552 942262 942304 "FSAGG" 942674 NIL FSAGG (NIL T) -9 NIL 942931) (-394 937314 937915 938711 "FSAGG-" 938806 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936356 936499 936726 "FSAGG2" 937167 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 934015 934294 934847 "FS2UPS" 936074 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933601 933644 933797 "FS2" 933966 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932461 932632 932940 "FS2EXPXP" 933426 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 931887 932002 932154 "FRUTIL" 932341 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923324 927402 928750 "FR" 930571 NIL FR (NIL T) -8 NIL NIL) (-387 918401 921044 921085 "FRNAALG" 922481 NIL FRNAALG (NIL T) -9 NIL 923087) (-386 914080 915150 916425 "FRNAALG-" 917175 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913718 913761 913888 "FRNAAF2" 914031 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 912085 912577 912870 "FRMOD" 913532 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909808 910476 910792 "FRIDEAL" 911876 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 909007 909094 909381 "FRIDEAL2" 909715 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 908266 908674 908716 "FRETRCT" 908721 NIL FRETRCT (NIL T) -9 NIL 908890) (-380 907378 907609 907960 "FRETRCT-" 907965 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904587 905807 905867 "FRAMALG" 906749 NIL FRAMALG (NIL T T) -9 NIL 907041) (-378 902720 903176 903806 "FRAMALG-" 904029 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896632 902205 902476 "FRAC" 902481 NIL FRAC (NIL T) -8 NIL NIL) (-376 896268 896325 896432 "FRAC2" 896569 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 895904 895961 896068 "FR2" 896205 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890533 893446 893475 "FPS" 894594 T FPS (NIL) -9 NIL 895147) (-373 889982 890091 890255 "FPS-" 890401 NIL FPS- (NIL T) -8 NIL NIL) (-372 887383 889080 889109 "FPC" 889334 T FPC (NIL) -9 NIL 889476) (-371 887176 887216 887313 "FPC-" 887318 NIL FPC- (NIL T) -8 NIL NIL) (-370 886056 886666 886708 "FPATMAB" 886713 NIL FPATMAB (NIL T) -9 NIL 886863) (-369 883756 884232 884658 "FPARFRAC" 885693 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 879151 879648 880330 "FORTRAN" 883188 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 876867 877367 877906 "FORT" 878632 T FORT (NIL) -7 NIL NIL) (-366 874542 875104 875133 "FORTFN" 876193 T FORTFN (NIL) -9 NIL 876817) (-365 874305 874355 874384 "FORTCAT" 874443 T FORTCAT (NIL) -9 NIL 874505) (-364 872365 872848 873247 "FORMULA" 873926 T FORMULA (NIL) -8 NIL NIL) (-363 872153 872183 872252 "FORMULA1" 872329 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871676 871728 871901 "FORDER" 872095 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870772 870936 871129 "FOP" 871503 T FOP (NIL) -7 NIL NIL) (-360 869380 870052 870226 "FNLA" 870654 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 868048 868437 868466 "FNCAT" 869038 T FNCAT (NIL) -9 NIL 869331) (-358 867614 868007 868035 "FNAME" 868040 T FNAME (NIL) -8 NIL NIL) (-357 866273 867246 867275 "FMTC" 867280 T FMTC (NIL) -9 NIL 867315) (-356 862593 863800 864427 "FMONOID" 865679 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861815 862338 862485 "FM" 862490 NIL FM (NIL T T) -8 NIL NIL) (-354 859238 859884 859913 "FMFUN" 861057 T FMFUN (NIL) -9 NIL 861765) (-353 858506 858687 858716 "FMC" 859006 T FMC (NIL) -9 NIL 859188) (-352 855736 856570 856624 "FMCAT" 857806 NIL FMCAT (NIL T T) -9 NIL 858299) (-351 854631 855504 855603 "FM1" 855681 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852405 852821 853315 "FLOATRP" 854182 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 845892 850061 850691 "FLOAT" 851795 T FLOAT (NIL) -8 NIL NIL) (-348 843330 843830 844408 "FLOATCP" 845359 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 842119 842967 843008 "FLINEXP" 843013 NIL FLINEXP (NIL T) -9 NIL 843105) (-346 841274 841509 841836 "FLINEXP-" 841841 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840350 840494 840718 "FLASORT" 841126 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837568 838410 838463 "FLALG" 839690 NIL FLALG (NIL T T) -9 NIL 840157) (-343 831359 835055 835097 "FLAGG" 836359 NIL FLAGG (NIL T) -9 NIL 837007) (-342 830085 830424 830914 "FLAGG-" 830919 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 829127 829270 829497 "FLAGG2" 829938 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 826102 827120 827180 "FINRALG" 828308 NIL FINRALG (NIL T T) -9 NIL 828813) (-339 825262 825491 825830 "FINRALG-" 825835 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824668 824881 824910 "FINITE" 825106 T FINITE (NIL) -9 NIL 825213) (-337 817128 819289 819330 "FINAALG" 822997 NIL FINAALG (NIL T) -9 NIL 824449) (-336 812469 813510 814654 "FINAALG-" 816033 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 811864 812224 812327 "FILE" 812399 NIL FILE (NIL T) -8 NIL NIL) (-334 810548 810860 810915 "FILECAT" 811599 NIL FILECAT (NIL T T) -9 NIL 811815) (-333 808363 809919 809948 "FIELD" 809988 T FIELD (NIL) -9 NIL 810068) (-332 806983 807368 807879 "FIELD-" 807884 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804798 805620 805966 "FGROUP" 806670 NIL FGROUP (NIL T) -8 NIL NIL) (-330 803888 804052 804272 "FGLMICPK" 804630 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799690 803813 803870 "FFX" 803875 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799291 799352 799487 "FFSLPE" 799623 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795287 796063 796859 "FFPOLY" 798527 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794791 794827 795036 "FFPOLY2" 795245 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790613 794710 794773 "FFP" 794778 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 785981 790524 790588 "FF" 790593 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 781077 785324 785514 "FFNBX" 785835 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 775987 780212 780470 "FFNBP" 780931 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770590 775271 775482 "FFNB" 775820 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769422 769620 769935 "FFINTBAS" 770387 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765598 767838 767867 "FFIELDC" 768487 T FFIELDC (NIL) -9 NIL 768863) (-318 764261 764631 765128 "FFIELDC-" 765133 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763831 763876 764000 "FFHOM" 764203 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761529 762013 762530 "FFF" 763346 NIL FFF (NIL T) -7 NIL NIL) (-315 757117 761271 761372 "FFCGX" 761472 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752719 756849 756956 "FFCGP" 757060 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 747872 752446 752554 "FFCG" 752655 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729671 738794 738881 "FFCAT" 744046 NIL FFCAT (NIL T T T) -9 NIL 745531) (-311 724869 725916 727230 "FFCAT-" 728460 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724280 724323 724558 "FFCAT2" 724820 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713484 717274 718489 "FEXPR" 723137 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712486 712921 712963 "FEVALAB" 713047 NIL FEVALAB (NIL T) -9 NIL 713305) (-307 711645 711855 712193 "FEVALAB-" 712198 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710238 711028 711231 "FDIV" 711544 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707304 708019 708135 "FDIVCAT" 709703 NIL FDIVCAT (NIL T T T T) -9 NIL 710140) (-304 707066 707093 707263 "FDIVCAT-" 707268 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706286 706373 706650 "FDIV2" 706973 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 704979 705236 705523 "FCPAK1" 706019 T FCPAK1 (NIL) -7 NIL NIL) (-301 704107 704479 704620 "FCOMP" 704870 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687747 691159 694719 "FC" 700567 T FC (NIL) -8 NIL NIL) (-299 680296 684342 684383 "FAXF" 686185 NIL FAXF (NIL T) -9 NIL 686875) (-298 677575 678230 679055 "FAXF-" 679520 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672681 676951 677127 "FARRAY" 677432 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668027 670098 670151 "FAMR" 671163 NIL FAMR (NIL T T) -9 NIL 671620) (-295 666918 667220 667654 "FAMR-" 667659 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666114 666840 666893 "FAMONOID" 666898 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 663947 664631 664685 "FAMONC" 665626 NIL FAMONC (NIL T T) -9 NIL 666010) (-292 662641 663703 663839 "FAGROUP" 663844 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660444 660763 661165 "FACUTIL" 662322 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659543 659728 659950 "FACTFUNC" 660254 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 651866 658794 659006 "EXPUPXS" 659399 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649365 649901 650483 "EXPRTUBE" 651304 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645559 646151 646888 "EXPRODE" 648704 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630727 644224 644647 "EXPR" 645168 NIL EXPR (NIL T) -8 NIL NIL) (-285 625155 625742 626554 "EXPR2UPS" 630025 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624791 624848 624955 "EXPR2" 625092 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616145 623928 624223 "EXPEXPAN" 624629 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 615972 616102 616131 "EXIT" 616136 T EXIT (NIL) -8 NIL NIL) (-281 615599 615661 615774 "EVALCYC" 615904 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615139 615257 615299 "EVALAB" 615469 NIL EVALAB (NIL T) -9 NIL 615573) (-279 614620 614742 614963 "EVALAB-" 614968 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612082 613394 613423 "EUCDOM" 613978 T EUCDOM (NIL) -9 NIL 614328) (-277 610487 610929 611519 "EUCDOM-" 611524 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598100 600839 603570 "ESTOOLS" 607776 T ESTOOLS (NIL) -7 NIL NIL) (-275 597736 597793 597900 "ESTOOLS2" 598037 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597487 597529 597609 "ESTOOLS1" 597688 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591426 593150 593179 "ES" 595943 T ES (NIL) -9 NIL 597347) (-272 586374 587660 589477 "ES-" 589641 NIL ES- (NIL T) -8 NIL NIL) (-271 582781 583533 584305 "ESCONT" 585622 T ESCONT (NIL) -7 NIL NIL) (-270 582526 582558 582640 "ESCONT1" 582743 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582201 582251 582351 "ES2" 582470 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581831 581889 581998 "ES1" 582137 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581047 581176 581352 "ERROR" 581675 T ERROR (NIL) -7 NIL NIL) (-266 574562 580906 580997 "EQTBL" 581002 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 567027 569908 571341 "EQ" 573162 NIL -3128 (NIL T) -8 NIL NIL) (-264 566659 566716 566825 "EQ2" 566964 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 561951 562997 564090 "EP" 565598 NIL EP (NIL T) -7 NIL NIL) (-262 561110 561674 561703 "ENTIRER" 561708 T ENTIRER (NIL) -9 NIL 561753) (-261 557566 559065 559435 "EMR" 560909 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556710 556895 556950 "ELTAGG" 557330 NIL ELTAGG (NIL T T) -9 NIL 557540) (-259 556429 556491 556632 "ELTAGG-" 556637 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556217 556246 556301 "ELTAB" 556385 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555343 555489 555688 "ELFUTS" 556068 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555084 555140 555169 "ELEMFUN" 555274 T ELEMFUN (NIL) -9 NIL NIL) (-255 554954 554975 555043 "ELEMFUN-" 555048 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 549850 553053 553095 "ELAGG" 554035 NIL ELAGG (NIL T) -9 NIL 554496) (-253 548135 548569 549232 "ELAGG-" 549237 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 541005 542804 543630 "EFUPXS" 547412 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534457 536258 537067 "EFULS" 540282 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 531888 532246 532724 "EFSTRUC" 534089 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 520960 522525 524085 "EF" 530403 NIL EF (NIL T T) -7 NIL NIL) (-248 520061 520445 520594 "EAB" 520831 T EAB (NIL) -8 NIL NIL) (-247 519274 520020 520048 "E04UCFA" 520053 T E04UCFA (NIL) -8 NIL NIL) (-246 518487 519233 519261 "E04NAFA" 519266 T E04NAFA (NIL) -8 NIL NIL) (-245 517700 518446 518474 "E04MBFA" 518479 T E04MBFA (NIL) -8 NIL NIL) (-244 516913 517659 517687 "E04JAFA" 517692 T E04JAFA (NIL) -8 NIL NIL) (-243 516128 516872 516900 "E04GCFA" 516905 T E04GCFA (NIL) -8 NIL NIL) (-242 515343 516087 516115 "E04FDFA" 516120 T E04FDFA (NIL) -8 NIL NIL) (-241 514556 515302 515330 "E04DGFA" 515335 T E04DGFA (NIL) -8 NIL NIL) (-240 508742 510086 511448 "E04AGNT" 513214 T E04AGNT (NIL) -7 NIL NIL) (-239 507468 507948 507989 "DVARCAT" 508464 NIL DVARCAT (NIL T) -9 NIL 508662) (-238 506672 506884 507198 "DVARCAT-" 507203 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499534 506474 506601 "DSMP" 506606 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494360 495491 496555 "DROPT" 498490 T DROPT (NIL) -8 NIL NIL) (-235 494025 494084 494182 "DROPT1" 494295 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489147 490271 491406 "DROPT0" 492910 T DROPT0 (NIL) -7 NIL NIL) (-233 487492 487817 488203 "DRAWPT" 488781 T DRAWPT (NIL) -7 NIL NIL) (-232 482167 483066 484121 "DRAW" 486490 NIL DRAW (NIL T) -7 NIL NIL) (-231 481808 481859 481975 "DRAWHACK" 482110 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480553 480818 481105 "DRAWCX" 481541 T DRAWCX (NIL) -7 NIL NIL) (-229 480071 480139 480289 "DRAWCURV" 480479 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470675 472597 474676 "DRAWCFUN" 478012 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467494 469370 469412 "DQAGG" 470041 NIL DQAGG (NIL T) -9 NIL 470314) (-226 455954 462692 462775 "DPOLCAT" 464613 NIL DPOLCAT (NIL T T T T) -9 NIL 465156) (-225 450794 452140 454097 "DPOLCAT-" 454102 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 444878 450656 450753 "DPMO" 450758 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 438865 444659 444825 "DPMM" 444830 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438784 438810 438845 "DOMAIN" 438850 T DOMAIN (NIL) -8 NIL NIL) (-221 432496 438421 438572 "DMP" 438685 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 432096 432152 432296 "DLP" 432434 NIL DLP (NIL T) -7 NIL NIL) (-219 425746 431197 431424 "DLIST" 431901 NIL DLIST (NIL T) -8 NIL NIL) (-218 422599 424602 424644 "DLAGG" 425194 NIL DLAGG (NIL T) -9 NIL 425422) (-217 421261 421953 421982 "DIVRING" 422132 T DIVRING (NIL) -9 NIL 422240) (-216 420249 420502 420895 "DIVRING-" 420900 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 418351 418708 419114 "DISPLAY" 419863 T DISPLAY (NIL) -7 NIL NIL) (-214 412246 418265 418328 "DIRPROD" 418333 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 411094 411297 411562 "DIRPROD2" 412039 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400738 406737 406791 "DIRPCAT" 407199 NIL DIRPCAT (NIL NIL T) -9 NIL 408015) (-211 398064 398706 399587 "DIRPCAT-" 399924 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 397351 397511 397697 "DIOSP" 397898 T DIOSP (NIL) -7 NIL NIL) (-209 394060 396264 396306 "DIOPS" 396740 NIL DIOPS (NIL T) -9 NIL 396968) (-208 393609 393723 393914 "DIOPS-" 393919 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392480 393118 393147 "DIFRING" 393334 T DIFRING (NIL) -9 NIL 393443) (-206 392126 392203 392355 "DIFRING-" 392360 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389917 391199 391240 "DIFEXT" 391599 NIL DIFEXT (NIL T) -9 NIL 391890) (-204 388203 388631 389296 "DIFEXT-" 389301 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385531 387735 387777 "DIAGG" 387782 NIL DIAGG (NIL T) -9 NIL 387802) (-202 384915 385072 385324 "DIAGG-" 385329 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 380386 383874 384151 "DHMATRIX" 384684 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375998 376907 377917 "DFSFUN" 379396 T DFSFUN (NIL) -7 NIL NIL) (-199 370784 374712 375077 "DFLOAT" 375653 T DFLOAT (NIL) -8 NIL NIL) (-198 369017 369298 369693 "DFINTTLS" 370492 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 366050 367052 367450 "DERHAM" 368684 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363905 365825 365914 "DEQUEUE" 365994 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 363123 363256 363451 "DEGRED" 363767 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359539 360280 361128 "DEFINTRF" 362355 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 357078 357545 358141 "DEFINTEF" 359060 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350909 356519 356685 "DECIMAL" 356932 T DECIMAL (NIL) -8 NIL NIL) (-191 348421 348879 349385 "DDFACT" 350453 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 348017 348060 348211 "DBLRESP" 348372 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345727 346061 346430 "DBASE" 347775 NIL DBASE (NIL T) -8 NIL NIL) (-188 344862 345686 345714 "D03FAFA" 345719 T D03FAFA (NIL) -8 NIL NIL) (-187 343998 344821 344849 "D03EEFA" 344854 T D03EEFA (NIL) -8 NIL NIL) (-186 341948 342414 342903 "D03AGNT" 343529 T D03AGNT (NIL) -7 NIL NIL) (-185 341266 341907 341935 "D02EJFA" 341940 T D02EJFA (NIL) -8 NIL NIL) (-184 340584 341225 341253 "D02CJFA" 341258 T D02CJFA (NIL) -8 NIL NIL) (-183 339902 340543 340571 "D02BHFA" 340576 T D02BHFA (NIL) -8 NIL NIL) (-182 339220 339861 339889 "D02BBFA" 339894 T D02BBFA (NIL) -8 NIL NIL) (-181 332419 334006 335612 "D02AGNT" 337634 T D02AGNT (NIL) -7 NIL NIL) (-180 330200 330719 331262 "D01WGTS" 331896 T D01WGTS (NIL) -7 NIL NIL) (-179 329307 330159 330187 "D01TRNS" 330192 T D01TRNS (NIL) -8 NIL NIL) (-178 328414 329266 329294 "D01GBFA" 329299 T D01GBFA (NIL) -8 NIL NIL) (-177 327521 328373 328401 "D01FCFA" 328406 T D01FCFA (NIL) -8 NIL NIL) (-176 326628 327480 327508 "D01ASFA" 327513 T D01ASFA (NIL) -8 NIL NIL) (-175 325735 326587 326615 "D01AQFA" 326620 T D01AQFA (NIL) -8 NIL NIL) (-174 324842 325694 325722 "D01APFA" 325727 T D01APFA (NIL) -8 NIL NIL) (-173 323949 324801 324829 "D01ANFA" 324834 T D01ANFA (NIL) -8 NIL NIL) (-172 323056 323908 323936 "D01AMFA" 323941 T D01AMFA (NIL) -8 NIL NIL) (-171 322163 323015 323043 "D01ALFA" 323048 T D01ALFA (NIL) -8 NIL NIL) (-170 321270 322122 322150 "D01AKFA" 322155 T D01AKFA (NIL) -8 NIL NIL) (-169 320377 321229 321257 "D01AJFA" 321262 T D01AJFA (NIL) -8 NIL NIL) (-168 313709 315251 316803 "D01AGNT" 318845 T D01AGNT (NIL) -7 NIL NIL) (-167 313046 313174 313326 "CYCLOTOM" 313577 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309781 310494 311221 "CYCLES" 312339 T CYCLES (NIL) -7 NIL NIL) (-165 309093 309227 309398 "CVMP" 309642 NIL CVMP (NIL T) -7 NIL NIL) (-164 306875 307132 307507 "CTRIGMNP" 308821 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 306249 306348 306501 "CSTTOOLS" 306772 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 302048 302705 303463 "CRFP" 305561 NIL CRFP (NIL T T) -7 NIL NIL) (-161 301095 301280 301508 "CRAPACK" 301852 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 300481 300582 300785 "CPMATCH" 300972 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 300206 300234 300340 "CPIMA" 300447 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 296570 297242 297960 "COORDSYS" 299541 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 292431 294573 295065 "CONTFRAC" 296110 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291584 292148 292177 "COMRING" 292182 T COMRING (NIL) -9 NIL 292233) (-155 290665 290942 291126 "COMPPROP" 291420 T COMPPROP (NIL) -8 NIL NIL) (-154 290326 290361 290489 "COMPLPAT" 290624 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 280309 290137 290245 "COMPLEX" 290250 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279945 280002 280109 "COMPLEX2" 280246 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279663 279698 279796 "COMPFACT" 279904 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263943 274237 274278 "COMPCAT" 275280 NIL COMPCAT (NIL T) -9 NIL 276656) (-149 253459 256382 260009 "COMPCAT-" 260365 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 253190 253218 253320 "COMMUPC" 253425 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252985 253018 253077 "COMMONOP" 253151 T COMMONOP (NIL) -7 NIL NIL) (-146 252568 252736 252823 "COMM" 252918 T COMM (NIL) -8 NIL NIL) (-145 251822 252014 252043 "COMBOPC" 252379 T COMBOPC (NIL) -9 NIL 252552) (-144 250718 250928 251170 "COMBINAT" 251612 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246924 247495 248133 "COMBF" 250142 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245710 246040 246275 "COLOR" 246709 T COLOR (NIL) -8 NIL NIL) (-141 245350 245397 245522 "CMPLXRT" 245657 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240908 241922 242988 "CLIP" 244304 T CLIP (NIL) -7 NIL NIL) (-139 239246 240016 240254 "CLIF" 240736 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 235477 237395 237437 "CLAGG" 238366 NIL CLAGG (NIL T) -9 NIL 238899) (-137 233899 234356 234939 "CLAGG-" 234944 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 233443 233528 233668 "CINTSLPE" 233808 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230944 231415 231963 "CHVAR" 232971 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 230166 230730 230759 "CHARZ" 230764 T CHARZ (NIL) -9 NIL 230778) (-133 229920 229960 230038 "CHARPOL" 230120 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 229026 229623 229652 "CHARNZ" 229699 T CHARNZ (NIL) -9 NIL 229754) (-131 227049 227716 228051 "CHAR" 228711 T CHAR (NIL) -8 NIL NIL) (-130 226774 226835 226864 "CFCAT" 226975 T CFCAT (NIL) -9 NIL NIL) (-129 226019 226130 226312 "CDEN" 226658 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 222011 225172 225452 "CCLASS" 225759 T CCLASS (NIL) -8 NIL NIL) (-127 217064 218040 218793 "CARTEN" 221314 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 216172 216320 216541 "CARTEN2" 216911 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 214469 215324 215580 "CARD" 215936 T CARD (NIL) -8 NIL NIL) (-124 213841 214169 214198 "CACHSET" 214330 T CACHSET (NIL) -9 NIL 214407) (-123 213337 213633 213662 "CABMON" 213712 T CABMON (NIL) -9 NIL 213768) (-122 210900 213029 213136 "BTREE" 213263 NIL BTREE (NIL T) -8 NIL NIL) (-121 208404 210548 210670 "BTOURN" 210810 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205828 207875 207917 "BTCAT" 207985 NIL BTCAT (NIL T) -9 NIL 208062) (-119 205495 205575 205724 "BTCAT-" 205729 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200685 204556 204585 "BTAGG" 204841 T BTAGG (NIL) -9 NIL 205020) (-117 200108 200252 200482 "BTAGG-" 200487 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 197158 199386 199601 "BSTREE" 199925 NIL BSTREE (NIL T) -8 NIL NIL) (-115 196296 196422 196606 "BRILL" 197014 NIL BRILL (NIL T) -7 NIL NIL) (-114 193004 195025 195067 "BRAGG" 195716 NIL BRAGG (NIL T) -9 NIL 195972) (-113 191533 191939 192494 "BRAGG-" 192499 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184741 190879 191063 "BPADICRT" 191381 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 183045 184678 184723 "BPADIC" 184728 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182745 182775 182888 "BOUNDZRO" 183009 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 178260 179351 180218 "BOP" 181898 T BOP (NIL) -8 NIL NIL) (-108 175883 176327 176846 "BOP1" 177774 NIL BOP1 (NIL T) -7 NIL NIL) (-107 174236 174926 175220 "BOOLEAN" 175609 T BOOLEAN (NIL) -8 NIL NIL) (-106 173602 173980 174033 "BMODULE" 174038 NIL BMODULE (NIL T T) -9 NIL 174102) (-105 169412 173400 173473 "BITS" 173549 T BITS (NIL) -8 NIL NIL) (-104 168509 168944 169096 "BINFILE" 169280 T BINFILE (NIL) -8 NIL NIL) (-103 162344 167953 168118 "BINARY" 168364 T BINARY (NIL) -8 NIL NIL) (-102 160177 161599 161641 "BGAGG" 161901 NIL BGAGG (NIL T) -9 NIL 162038) (-101 160008 160040 160131 "BGAGG-" 160136 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 159106 159392 159597 "BFUNCT" 159823 T BFUNCT (NIL) -8 NIL NIL) (-99 157809 157987 158271 "BEZOUT" 158931 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154340 156669 156997 "BBTREE" 157512 NIL BBTREE (NIL T) -8 NIL NIL) (-97 154077 154130 154157 "BASTYPE" 154274 T BASTYPE (NIL) -9 NIL NIL) (-96 153933 153961 154031 "BASTYPE-" 154036 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153371 153447 153597 "BALFACT" 153844 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 152193 152790 152975 "AUTOMOR" 153216 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151918 151923 151950 "ATTREG" 151955 T ATTREG (NIL) -9 NIL NIL) (-92 150197 150615 150967 "ATTRBUT" 151584 T ATTRBUT (NIL) -8 NIL NIL) (-91 149732 149845 149872 "ATRIG" 150073 T ATRIG (NIL) -9 NIL NIL) (-90 149541 149582 149669 "ATRIG-" 149674 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147744 149317 149405 "ASTACK" 149484 NIL ASTACK (NIL T) -8 NIL NIL) (-88 146251 146548 146912 "ASSOCEQ" 147427 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 145283 145910 146034 "ASP9" 146158 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 145047 145231 145270 "ASP8" 145275 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143917 144652 144794 "ASP80" 144936 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142816 143552 143684 "ASP7" 143816 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141772 142493 142611 "ASP78" 142729 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140743 141452 141569 "ASP77" 141686 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139658 140381 140512 "ASP74" 140643 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138559 139293 139425 "ASP73" 139557 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137514 138236 138354 "ASP6" 138472 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136463 137191 137309 "ASP55" 137427 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135413 136137 136256 "ASP50" 136375 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134501 135114 135224 "ASP4" 135334 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133589 134202 134312 "ASP49" 134422 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132374 133128 133296 "ASP42" 133478 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 131152 131907 132077 "ASP41" 132261 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 130104 130829 130947 "ASP35" 131065 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129869 130052 130091 "ASP34" 130096 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129606 129673 129749 "ASP33" 129824 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128502 129241 129373 "ASP31" 129505 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 128267 128450 128489 "ASP30" 128494 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 128002 128071 128147 "ASP29" 128222 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127767 127950 127989 "ASP28" 127994 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127532 127715 127754 "ASP27" 127759 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126616 127230 127341 "ASP24" 127452 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125533 126257 126387 "ASP20" 126517 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124621 125234 125344 "ASP1" 125454 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123565 124295 124414 "ASP19" 124533 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 123302 123369 123445 "ASP12" 123520 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 122155 122901 123045 "ASP10" 123189 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 120060 121999 122090 "ARRAY2" 122095 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115882 119708 119822 "ARRAY1" 119977 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114914 115087 115308 "ARRAY12" 115705 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 109279 111144 111220 "ARR2CAT" 113850 NIL ARR2CAT (NIL T T T) -9 NIL 114608) (-54 106713 107457 108411 "ARR2CAT-" 108416 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105473 105623 105926 "APPRULE" 106551 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 105126 105174 105292 "APPLYORE" 105419 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 104100 104391 104586 "ANY" 104949 T ANY (NIL) -8 NIL NIL) (-50 103378 103501 103658 "ANY1" 103974 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100910 101828 102153 "ANTISYM" 103103 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100737 100869 100896 "ANON" 100901 T ANON (NIL) -8 NIL NIL) (-47 94814 99282 99733 "AN" 100304 T AN (NIL) -8 NIL NIL) (-46 91126 92524 92575 "AMR" 93314 NIL AMR (NIL T T) -9 NIL 93907) (-45 90239 90460 90822 "AMR-" 90827 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74801 90156 90217 "ALIST" 90222 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71638 74395 74564 "ALGSC" 74719 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 68196 68750 69356 "ALGPKG" 71079 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 67473 67574 67758 "ALGMFACT" 68082 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 63230 63911 64561 "ALGMANIP" 67001 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 54549 62856 63006 "ALGFF" 63163 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53745 53876 54055 "ALGFACT" 54407 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52735 53345 53384 "ALGEBRA" 53444 NIL ALGEBRA (NIL T) -9 NIL 53502) (-36 52453 52512 52644 "ALGEBRA-" 52649 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34174 49899 49952 "ALAGG" 50088 NIL ALAGG (NIL T T) -9 NIL 50249) (-34 33709 33822 33849 "AHYP" 34050 T AHYP (NIL) -9 NIL NIL) (-33 32640 32888 32915 "AGG" 33414 T AGG (NIL) -9 NIL 33692) (-32 32074 32236 32450 "AGG-" 32455 NIL AGG- (NIL T) -8 NIL NIL) (-31 29763 30181 30597 "AF" 31718 NIL AF (NIL T T) -7 NIL NIL) (-30 29041 29295 29449 "ACPLOT" 29627 T ACPLOT (NIL) -8 NIL NIL) (-29 18460 26406 26458 "ACFS" 27169 NIL ACFS (NIL T) -9 NIL 27408) (-28 16474 16964 17739 "ACFS-" 17744 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12694 14650 14677 "ACF" 15556 T ACF (NIL) -9 NIL 15968) (-26 11398 11732 12225 "ACF-" 12230 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11192 "ABELSG" 11284 T ABELSG (NIL) -9 NIL 11349) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10232 10493 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9896 9980 10118 "ABELMON-" 10123 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9230 9576 9603 "ABELGRP" 9728 T ABELGRP (NIL) -9 NIL 9810) (-20 8693 8822 9038 "ABELGRP-" 9043 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8029 8069 "A1AGG" 8074 NIL A1AGG (NIL T) -9 NIL 8114) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) 
\ No newline at end of file
+((-1185 3125227 3125232 3125237 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3125212 3125217 3125222 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3125197 3125202 3125207 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3125182 3125187 3125192 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3125167 3125172 3125177 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1180 3124297 3125042 3125119 "ZMOD" 3125124 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1179 3123407 3123571 3123780 "ZLINDEP" 3124129 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1178 3112811 3114556 3116508 "ZDSOLVE" 3121556 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1177 3112057 3112198 3112387 "YSTREAM" 3112657 NIL YSTREAM (NIL T) -7 NIL NIL) (-1176 3109826 3111362 3111565 "XRPOLY" 3111900 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1175 3106296 3107625 3108203 "XPR" 3109294 NIL XPR (NIL T T) -8 NIL NIL) (-1174 3104010 3105631 3105834 "XPOLY" 3106127 NIL XPOLY (NIL T) -8 NIL NIL) (-1173 3101823 3103201 3103256 "XPOLYC" 3103541 NIL XPOLYC (NIL T T) -9 NIL 3103654) (-1172 3098197 3100342 3100729 "XPBWPOLY" 3101482 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1171 3094080 3096393 3096436 "XF" 3097057 NIL XF (NIL T) -9 NIL 3097453) (-1170 3093701 3093789 3093958 "XF-" 3093963 NIL XF- (NIL T T) -8 NIL NIL) (-1169 3089082 3090381 3090436 "XFALG" 3092584 NIL XFALG (NIL T T) -9 NIL 3093369) (-1168 3088219 3088323 3088527 "XEXPPKG" 3088974 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1167 3086317 3088070 3088165 "XDPOLY" 3088170 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1166 3085196 3085806 3085849 "XALG" 3085911 NIL XALG (NIL T) -9 NIL 3086029) (-1165 3078672 3083180 3083673 "WUTSET" 3084788 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1164 3076488 3077295 3077644 "WP" 3078456 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1163 3075374 3075572 3075867 "WFFINTBS" 3076285 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1162 3073278 3073705 3074167 "WEIER" 3074946 NIL WEIER (NIL T) -7 NIL NIL) (-1161 3072426 3072850 3072893 "VSPACE" 3073029 NIL VSPACE (NIL T) -9 NIL 3073103) (-1160 3072264 3072291 3072382 "VSPACE-" 3072387 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1159 3072010 3072053 3072124 "VOID" 3072215 T VOID (NIL) -8 NIL NIL) (-1158 3070146 3070505 3070911 "VIEW" 3071626 T VIEW (NIL) -7 NIL NIL) (-1157 3066571 3067209 3067946 "VIEWDEF" 3069431 T VIEWDEF (NIL) -7 NIL NIL) (-1156 3055910 3058119 3060292 "VIEW3D" 3064420 T VIEW3D (NIL) -8 NIL NIL) (-1155 3048192 3049821 3051400 "VIEW2D" 3054353 T VIEW2D (NIL) -8 NIL NIL) (-1154 3043601 3047962 3048054 "VECTOR" 3048135 NIL VECTOR (NIL T) -8 NIL NIL) (-1153 3042178 3042437 3042755 "VECTOR2" 3043331 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1152 3035727 3039973 3040017 "VECTCAT" 3041005 NIL VECTCAT (NIL T) -9 NIL 3041582) (-1151 3034741 3034995 3035385 "VECTCAT-" 3035390 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1150 3034222 3034392 3034512 "VARIABLE" 3034656 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1149 3033059 3033213 3033473 "UTSODETL" 3034049 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1148 3030499 3030959 3031483 "UTSODE" 3032600 NIL UTSODE (NIL T T) -7 NIL NIL) (-1147 3022349 3028141 3028628 "UTS" 3030069 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1146 3013654 3019016 3019059 "UTSCAT" 3020160 NIL UTSCAT (NIL T) -9 NIL 3020910) (-1145 3011010 3011725 3012713 "UTSCAT-" 3012718 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1144 3010641 3010684 3010815 "UTS2" 3010961 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1143 3004917 3007482 3007526 "URAGG" 3009596 NIL URAGG (NIL T) -9 NIL 3010317) (-1142 3001856 3002719 3003842 "URAGG-" 3003847 NIL URAGG- (NIL T T) -8 NIL NIL) (-1141 2997542 3000473 3000944 "UPXSSING" 3001520 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1140 2989438 2996665 2996944 "UPXS" 2997320 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1139 2982470 2989343 2989414 "UPXSCONS" 2989419 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1138 2972698 2979525 2979587 "UPXSCCA" 2980236 NIL UPXSCCA (NIL T T) -9 NIL 2980477) (-1137 2972337 2972422 2972595 "UPXSCCA-" 2972600 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1136 2962494 2969094 2969137 "UPXSCAT" 2969780 NIL UPXSCAT (NIL T) -9 NIL 2970381) (-1135 2961928 2962007 2962184 "UPXS2" 2962409 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1134 2960582 2960835 2961186 "UPSQFREE" 2961671 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1133 2954436 2957488 2957543 "UPSCAT" 2958692 NIL UPSCAT (NIL T T) -9 NIL 2959459) (-1132 2953650 2953854 2954177 "UPSCAT-" 2954182 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1131 2939729 2947726 2947769 "UPOLYC" 2949847 NIL UPOLYC (NIL T) -9 NIL 2951061) (-1130 2931122 2933526 2936651 "UPOLYC-" 2936656 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1129 2930753 2930796 2930927 "UPOLYC2" 2931073 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1128 2922212 2930322 2930459 "UP" 2930663 NIL UP (NIL NIL T) -8 NIL NIL) (-1127 2921555 2921662 2921825 "UPMP" 2922101 NIL UPMP (NIL T T) -7 NIL NIL) (-1126 2921108 2921189 2921328 "UPDIVP" 2921468 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1125 2919676 2919925 2920241 "UPDECOMP" 2920857 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1124 2918911 2919023 2919208 "UPCDEN" 2919560 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1123 2918434 2918503 2918650 "UP2" 2918836 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1122 2916963 2917649 2917921 "UNISEG" 2918197 NIL UNISEG (NIL T) -8 NIL NIL) (-1121 2916180 2916307 2916511 "UNISEG2" 2916807 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1120 2915240 2915420 2915646 "UNIFACT" 2915996 NIL UNIFACT (NIL T) -7 NIL NIL) (-1119 2899141 2914423 2914672 "ULS" 2915048 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1118 2887109 2899046 2899117 "ULSCONS" 2899122 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1117 2869813 2881823 2881885 "ULSCCAT" 2882597 NIL ULSCCAT (NIL T T) -9 NIL 2882892) (-1116 2868864 2869109 2869496 "ULSCCAT-" 2869501 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1115 2858815 2865329 2865372 "ULSCAT" 2866228 NIL ULSCAT (NIL T) -9 NIL 2866950) (-1114 2858249 2858328 2858505 "ULS2" 2858730 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1113 2856646 2857613 2857644 "UFD" 2857856 T UFD (NIL) -9 NIL 2857970) (-1112 2856440 2856486 2856581 "UFD-" 2856586 NIL UFD- (NIL T) -8 NIL NIL) (-1111 2855522 2855705 2855921 "UDVO" 2856246 T UDVO (NIL) -7 NIL NIL) (-1110 2853340 2853749 2854219 "UDPO" 2855087 NIL UDPO (NIL T) -7 NIL NIL) (-1109 2853272 2853277 2853308 "TYPE" 2853313 T TYPE (NIL) -9 NIL NIL) (-1108 2852243 2852445 2852685 "TWOFACT" 2853066 NIL TWOFACT (NIL T) -7 NIL NIL) (-1107 2851185 2851522 2851783 "TUPLE" 2852017 NIL TUPLE (NIL T) -8 NIL NIL) (-1106 2848876 2849395 2849934 "TUBETOOL" 2850668 T TUBETOOL (NIL) -7 NIL NIL) (-1105 2847725 2847930 2848171 "TUBE" 2848669 NIL TUBE (NIL T) -8 NIL NIL) (-1104 2842451 2846705 2846986 "TS" 2847478 NIL TS (NIL T) -8 NIL NIL) (-1103 2831155 2835247 2835344 "TSETCAT" 2840578 NIL TSETCAT (NIL T T T T) -9 NIL 2842108) (-1102 2825891 2827488 2829378 "TSETCAT-" 2829383 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1101 2820162 2821008 2821946 "TRMANIP" 2825031 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1100 2819603 2819666 2819829 "TRIMAT" 2820094 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1099 2817409 2817646 2818009 "TRIGMNIP" 2819352 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1098 2816928 2817041 2817072 "TRIGCAT" 2817285 T TRIGCAT (NIL) -9 NIL NIL) (-1097 2816597 2816676 2816817 "TRIGCAT-" 2816822 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1096 2813502 2815457 2815737 "TREE" 2816352 NIL TREE (NIL T) -8 NIL NIL) (-1095 2812775 2813303 2813334 "TRANFUN" 2813369 T TRANFUN (NIL) -9 NIL 2813435) (-1094 2812054 2812245 2812525 "TRANFUN-" 2812530 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1093 2811858 2811890 2811951 "TOPSP" 2812015 T TOPSP (NIL) -7 NIL NIL) (-1092 2811210 2811325 2811478 "TOOLSIGN" 2811739 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1091 2809871 2810387 2810626 "TEXTFILE" 2810993 T TEXTFILE (NIL) -8 NIL NIL) (-1090 2807736 2808250 2808688 "TEX" 2809455 T TEX (NIL) -8 NIL NIL) (-1089 2807517 2807548 2807620 "TEX1" 2807699 NIL TEX1 (NIL T) -7 NIL NIL) (-1088 2807165 2807228 2807318 "TEMUTL" 2807449 T TEMUTL (NIL) -7 NIL NIL) (-1087 2805319 2805599 2805924 "TBCMPPK" 2806888 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1086 2796977 2803237 2803294 "TBAGG" 2803694 NIL TBAGG (NIL T T) -9 NIL 2803905) (-1085 2792047 2793535 2795289 "TBAGG-" 2795294 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1084 2791431 2791538 2791683 "TANEXP" 2791936 NIL TANEXP (NIL T) -7 NIL NIL) (-1083 2784944 2791288 2791381 "TABLE" 2791386 NIL TABLE (NIL T T) -8 NIL NIL) (-1082 2784357 2784455 2784593 "TABLEAU" 2784841 NIL TABLEAU (NIL T) -8 NIL NIL) (-1081 2778965 2780185 2781433 "TABLBUMP" 2783143 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1080 2775428 2776123 2776906 "SYSSOLP" 2778216 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1079 2774010 2774258 2774563 "SYNTAX" 2775145 T SYNTAX (NIL) -8 NIL NIL) (-1078 2771144 2771752 2772390 "SYMTAB" 2773394 T SYMTAB (NIL) -8 NIL NIL) (-1077 2766393 2767295 2768278 "SYMS" 2770183 T SYMS (NIL) -8 NIL NIL) (-1076 2763632 2765859 2766085 "SYMPOLY" 2766201 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1075 2763152 2763227 2763349 "SYMFUNC" 2763544 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1074 2759130 2760389 2761211 "SYMBOL" 2762352 T SYMBOL (NIL) -8 NIL NIL) (-1073 2752669 2754358 2756078 "SWITCH" 2757432 T SWITCH (NIL) -8 NIL NIL) (-1072 2745904 2751498 2751799 "SUTS" 2752425 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1071 2737799 2745027 2745306 "SUPXS" 2745682 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1070 2729332 2737420 2737545 "SUP" 2737708 NIL SUP (NIL T) -8 NIL NIL) (-1069 2728491 2728618 2728835 "SUPFRACF" 2729200 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1068 2728116 2728175 2728286 "SUP2" 2728426 NIL SUP2 (NIL T T) -7 NIL NIL) (-1067 2726542 2726814 2727174 "SUMRF" 2727817 NIL SUMRF (NIL T) -7 NIL NIL) (-1066 2725863 2725928 2726125 "SUMFS" 2726464 NIL SUMFS (NIL T T) -7 NIL NIL) (-1065 2709804 2725046 2725295 "SULS" 2725671 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1064 2709126 2709329 2709469 "SUCH" 2709712 NIL SUCH (NIL T T) -8 NIL NIL) (-1063 2703053 2704065 2705023 "SUBSPACE" 2708214 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1062 2702485 2702575 2702738 "SUBRESP" 2702942 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1061 2695854 2697150 2698461 "STTF" 2701221 NIL STTF (NIL T) -7 NIL NIL) (-1060 2690027 2691147 2692294 "STTFNC" 2694754 NIL STTFNC (NIL T) -7 NIL NIL) (-1059 2681382 2683249 2685040 "STTAYLOR" 2688270 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1058 2674638 2681246 2681329 "STRTBL" 2681334 NIL STRTBL (NIL T) -8 NIL NIL) (-1057 2670029 2674593 2674624 "STRING" 2674629 T STRING (NIL) -8 NIL NIL) (-1056 2664887 2669372 2669403 "STRICAT" 2669462 T STRICAT (NIL) -9 NIL 2669524) (-1055 2657612 2662414 2663032 "STREAM" 2664304 NIL STREAM (NIL T) -8 NIL NIL) (-1054 2657122 2657199 2657343 "STREAM3" 2657529 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1053 2656104 2656287 2656522 "STREAM2" 2656935 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1052 2655792 2655844 2655937 "STREAM1" 2656046 NIL STREAM1 (NIL T) -7 NIL NIL) (-1051 2654808 2654989 2655220 "STINPROD" 2655608 NIL STINPROD (NIL T) -7 NIL NIL) (-1050 2654386 2654570 2654601 "STEP" 2654681 T STEP (NIL) -9 NIL 2654759) (-1049 2647941 2654285 2654362 "STBL" 2654367 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1048 2643113 2647160 2647204 "STAGG" 2647357 NIL STAGG (NIL T) -9 NIL 2647446) (-1047 2640815 2641417 2642289 "STAGG-" 2642294 NIL STAGG- (NIL T T) -8 NIL NIL) (-1046 2639013 2640585 2640677 "STACK" 2640758 NIL STACK (NIL T) -8 NIL NIL) (-1045 2631744 2637160 2637615 "SREGSET" 2638643 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1044 2624184 2625552 2627064 "SRDCMPK" 2630350 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1043 2617127 2621594 2621625 "SRAGG" 2622928 T SRAGG (NIL) -9 NIL 2623536) (-1042 2616144 2616399 2616778 "SRAGG-" 2616783 NIL SRAGG- (NIL T) -8 NIL NIL) (-1041 2610601 2615071 2615494 "SQMATRIX" 2615767 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1040 2604359 2607321 2608047 "SPLTREE" 2609947 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1039 2600349 2601015 2601661 "SPLNODE" 2603785 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1038 2599395 2599628 2599659 "SPFCAT" 2600103 T SPFCAT (NIL) -9 NIL NIL) (-1037 2598132 2598342 2598606 "SPECOUT" 2599153 T SPECOUT (NIL) -7 NIL NIL) (-1036 2597893 2597933 2598002 "SPADPRSR" 2598085 T SPADPRSR (NIL) -7 NIL NIL) (-1035 2589915 2591662 2591705 "SPACEC" 2596028 NIL SPACEC (NIL T) -9 NIL 2597844) (-1034 2588087 2589848 2589896 "SPACE3" 2589901 NIL SPACE3 (NIL T) -8 NIL NIL) (-1033 2586841 2587012 2587302 "SORTPAK" 2587893 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1032 2584897 2585200 2585618 "SOLVETRA" 2586505 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1031 2583908 2584130 2584404 "SOLVESER" 2584670 NIL SOLVESER (NIL T) -7 NIL NIL) (-1030 2579128 2580009 2581011 "SOLVERAD" 2582960 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1029 2574943 2575552 2576281 "SOLVEFOR" 2578495 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1028 2569242 2574294 2574391 "SNTSCAT" 2574396 NIL SNTSCAT (NIL T T T T) -9 NIL 2574466) (-1027 2563349 2567575 2567964 "SMTS" 2568933 NIL SMTS (NIL T T T) -8 NIL NIL) (-1026 2557759 2563238 2563314 "SMP" 2563319 NIL SMP (NIL T T) -8 NIL NIL) (-1025 2555918 2556219 2556617 "SMITH" 2557456 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1024 2548885 2553081 2553184 "SMATCAT" 2554524 NIL SMATCAT (NIL NIL T T T) -9 NIL 2555070) (-1023 2545826 2546649 2547826 "SMATCAT-" 2547831 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1022 2543545 2545062 2545106 "SKAGG" 2545367 NIL SKAGG (NIL T) -9 NIL 2545502) (-1021 2539603 2542649 2542927 "SINT" 2543289 T SINT (NIL) -8 NIL NIL) (-1020 2539375 2539413 2539479 "SIMPAN" 2539559 T SIMPAN (NIL) -7 NIL NIL) (-1019 2538213 2538434 2538709 "SIGNRF" 2539134 NIL SIGNRF (NIL T) -7 NIL NIL) (-1018 2537022 2537173 2537463 "SIGNEF" 2538042 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1017 2534714 2535168 2535673 "SHP" 2536564 NIL SHP (NIL T NIL) -7 NIL NIL) (-1016 2528573 2534615 2534691 "SHDP" 2534696 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1015 2528062 2528254 2528285 "SGROUP" 2528437 T SGROUP (NIL) -9 NIL 2528524) (-1014 2527832 2527884 2527988 "SGROUP-" 2527993 NIL SGROUP- (NIL T) -8 NIL NIL) (-1013 2524668 2525365 2526088 "SGCF" 2527131 T SGCF (NIL) -7 NIL NIL) (-1012 2519066 2524118 2524215 "SFRTCAT" 2524220 NIL SFRTCAT (NIL T T T T) -9 NIL 2524258) (-1011 2512526 2513541 2514675 "SFRGCD" 2518049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1010 2505692 2506763 2507947 "SFQCMPK" 2511459 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1009 2505314 2505403 2505513 "SFORT" 2505633 NIL SFORT (NIL T T) -8 NIL NIL) (-1008 2504459 2505154 2505275 "SEXOF" 2505280 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1007 2503593 2504340 2504408 "SEX" 2504413 T SEX (NIL) -8 NIL NIL) (-1006 2498369 2499058 2499154 "SEXCAT" 2502925 NIL SEXCAT (NIL T T T T T) -9 NIL 2503544) (-1005 2495549 2498303 2498351 "SET" 2498356 NIL SET (NIL T) -8 NIL NIL) (-1004 2493800 2494262 2494567 "SETMN" 2495290 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1003 2493407 2493533 2493564 "SETCAT" 2493681 T SETCAT (NIL) -9 NIL 2493765) (-1002 2493187 2493239 2493338 "SETCAT-" 2493343 NIL SETCAT- (NIL T) -8 NIL NIL) (-1001 2489574 2491648 2491692 "SETAGG" 2492562 NIL SETAGG (NIL T) -9 NIL 2492902) (-1000 2489032 2489148 2489385 "SETAGG-" 2489390 NIL SETAGG- (NIL T T) -8 NIL NIL) (-999 2488242 2488535 2488595 "SEGXCAT" 2488878 NIL SEGXCAT (NIL T T) -9 NIL 2488997) (-998 2487308 2487918 2488094 "SEG" 2488099 NIL SEG (NIL T) -8 NIL NIL) (-997 2486225 2486438 2486480 "SEGCAT" 2487053 NIL SEGCAT (NIL T) -9 NIL 2487291) (-996 2485289 2485617 2485812 "SEGBIND" 2486063 NIL SEGBIND (NIL T) -8 NIL NIL) (-995 2484921 2484978 2485087 "SEGBIND2" 2485226 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-994 2484158 2484281 2484479 "SEG2" 2484769 NIL SEG2 (NIL T T) -7 NIL NIL) (-993 2483597 2484095 2484140 "SDVAR" 2484145 NIL SDVAR (NIL T) -8 NIL NIL) (-992 2475903 2483376 2483500 "SDPOL" 2483505 NIL SDPOL (NIL T) -8 NIL NIL) (-991 2474502 2474768 2475085 "SCPKG" 2475618 NIL SCPKG (NIL T) -7 NIL NIL) (-990 2473729 2473862 2474039 "SCACHE" 2474357 NIL SCACHE (NIL T) -7 NIL NIL) (-989 2473172 2473493 2473576 "SAOS" 2473666 T SAOS (NIL) -8 NIL NIL) (-988 2472740 2472775 2472946 "SAERFFC" 2473131 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-987 2466636 2472639 2472717 "SAE" 2472722 NIL SAE (NIL T T NIL) -8 NIL NIL) (-986 2466232 2466267 2466424 "SAEFACT" 2466595 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-985 2464558 2464872 2465271 "RURPK" 2465898 NIL RURPK (NIL T NIL) -7 NIL NIL) (-984 2463211 2463488 2463795 "RULESET" 2464394 NIL RULESET (NIL T T T) -8 NIL NIL) (-983 2460419 2460922 2461383 "RULE" 2462893 NIL RULE (NIL T T T) -8 NIL NIL) (-982 2460061 2460216 2460297 "RULECOLD" 2460371 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-981 2454953 2455747 2456663 "RSETGCD" 2459260 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-980 2444267 2449319 2449414 "RSETCAT" 2453479 NIL RSETCAT (NIL T T T T) -9 NIL 2454576) (-979 2442198 2442737 2443557 "RSETCAT-" 2443562 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-978 2434628 2436003 2437519 "RSDCMPK" 2440797 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-977 2432645 2433086 2433159 "RRCC" 2434235 NIL RRCC (NIL T T) -9 NIL 2434579) (-976 2431999 2432173 2432449 "RRCC-" 2432454 NIL RRCC- (NIL T T T) -8 NIL NIL) (-975 2406329 2415954 2416019 "RPOLCAT" 2426521 NIL RPOLCAT (NIL T T T) -9 NIL 2429668) (-974 2397833 2400171 2403289 "RPOLCAT-" 2403294 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-973 2388911 2396063 2396543 "ROUTINE" 2397373 T ROUTINE (NIL) -8 NIL NIL) (-972 2385616 2388467 2388614 "ROMAN" 2388784 T ROMAN (NIL) -8 NIL NIL) (-971 2383902 2384487 2384744 "ROIRC" 2385422 NIL ROIRC (NIL T T) -8 NIL NIL) (-970 2380259 2382563 2382592 "RNS" 2382888 T RNS (NIL) -9 NIL 2383158) (-969 2378773 2379156 2379687 "RNS-" 2379760 NIL RNS- (NIL T) -8 NIL NIL) (-968 2378198 2378606 2378635 "RNG" 2378640 T RNG (NIL) -9 NIL 2378661) (-967 2377595 2377957 2377998 "RMODULE" 2378058 NIL RMODULE (NIL T) -9 NIL 2378100) (-966 2376447 2376541 2376871 "RMCAT2" 2377496 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-965 2373165 2375634 2375953 "RMATRIX" 2376184 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-964 2366166 2368400 2368513 "RMATCAT" 2371822 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2372799) (-963 2365545 2365692 2365995 "RMATCAT-" 2366000 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-962 2365115 2365190 2365316 "RINTERP" 2365464 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-961 2364165 2364729 2364758 "RING" 2364868 T RING (NIL) -9 NIL 2364962) (-960 2363960 2364004 2364098 "RING-" 2364103 NIL RING- (NIL T) -8 NIL NIL) (-959 2362812 2363048 2363303 "RIDIST" 2363725 T RIDIST (NIL) -7 NIL NIL) (-958 2354134 2362286 2362489 "RGCHAIN" 2362661 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-957 2351139 2351753 2352421 "RF" 2353498 NIL RF (NIL T) -7 NIL NIL) (-956 2350788 2350851 2350952 "RFFACTOR" 2351070 NIL RFFACTOR (NIL T) -7 NIL NIL) (-955 2350516 2350551 2350646 "RFFACT" 2350747 NIL RFFACT (NIL T) -7 NIL NIL) (-954 2348646 2349010 2349390 "RFDIST" 2350156 T RFDIST (NIL) -7 NIL NIL) (-953 2348104 2348196 2348356 "RETSOL" 2348548 NIL RETSOL (NIL T T) -7 NIL NIL) (-952 2347696 2347776 2347818 "RETRACT" 2348008 NIL RETRACT (NIL T) -9 NIL NIL) (-951 2347548 2347573 2347657 "RETRACT-" 2347662 NIL RETRACT- (NIL T T) -8 NIL NIL) (-950 2340418 2347205 2347330 "RESULT" 2347443 T RESULT (NIL) -8 NIL NIL) (-949 2339003 2339692 2339889 "RESRING" 2340321 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-948 2338643 2338692 2338788 "RESLATC" 2338940 NIL RESLATC (NIL T) -7 NIL NIL) (-947 2338352 2338386 2338491 "REPSQ" 2338602 NIL REPSQ (NIL T) -7 NIL NIL) (-946 2335783 2336363 2336963 "REP" 2337772 T REP (NIL) -7 NIL NIL) (-945 2335484 2335518 2335627 "REPDB" 2335742 NIL REPDB (NIL T) -7 NIL NIL) (-944 2329437 2330816 2332032 "REP2" 2334300 NIL REP2 (NIL T) -7 NIL NIL) (-943 2325847 2326528 2327331 "REP1" 2328666 NIL REP1 (NIL T) -7 NIL NIL) (-942 2318593 2324008 2324460 "REGSET" 2325478 NIL REGSET (NIL T T T T) -8 NIL NIL) (-941 2317416 2317751 2317998 "REF" 2318379 NIL REF (NIL T) -8 NIL NIL) (-940 2316797 2316900 2317065 "REDORDER" 2317300 NIL REDORDER (NIL T T) -7 NIL NIL) (-939 2312766 2316031 2316252 "RECLOS" 2316628 NIL RECLOS (NIL T) -8 NIL NIL) (-938 2311823 2312004 2312217 "REALSOLV" 2312573 T REALSOLV (NIL) -7 NIL NIL) (-937 2311670 2311711 2311740 "REAL" 2311745 T REAL (NIL) -9 NIL 2311780) (-936 2308161 2308963 2309845 "REAL0Q" 2310835 NIL REAL0Q (NIL T) -7 NIL NIL) (-935 2303772 2304760 2305819 "REAL0" 2307142 NIL REAL0 (NIL T) -7 NIL NIL) (-934 2303180 2303252 2303457 "RDIV" 2303694 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-933 2302253 2302427 2302638 "RDIST" 2303002 NIL RDIST (NIL T) -7 NIL NIL) (-932 2300857 2301144 2301513 "RDETRS" 2301961 NIL RDETRS (NIL T T) -7 NIL NIL) (-931 2298678 2299132 2299667 "RDETR" 2300399 NIL RDETR (NIL T T) -7 NIL NIL) (-930 2297294 2297572 2297973 "RDEEFS" 2298394 NIL RDEEFS (NIL T T) -7 NIL NIL) (-929 2295794 2296100 2296529 "RDEEF" 2296982 NIL RDEEF (NIL T T) -7 NIL NIL) (-928 2290019 2292951 2292980 "RCFIELD" 2294257 T RCFIELD (NIL) -9 NIL 2294987) (-927 2288088 2288592 2289285 "RCFIELD-" 2289358 NIL RCFIELD- (NIL T) -8 NIL NIL) (-926 2284421 2286206 2286248 "RCAGG" 2287319 NIL RCAGG (NIL T) -9 NIL 2287782) (-925 2284052 2284146 2284306 "RCAGG-" 2284311 NIL RCAGG- (NIL T T) -8 NIL NIL) (-924 2283397 2283508 2283670 "RATRET" 2283936 NIL RATRET (NIL T) -7 NIL NIL) (-923 2282954 2283021 2283140 "RATFACT" 2283325 NIL RATFACT (NIL T) -7 NIL NIL) (-922 2282269 2282389 2282539 "RANDSRC" 2282824 T RANDSRC (NIL) -7 NIL NIL) (-921 2282006 2282050 2282121 "RADUTIL" 2282218 T RADUTIL (NIL) -7 NIL NIL) (-920 2275013 2280749 2281066 "RADIX" 2281721 NIL RADIX (NIL NIL) -8 NIL NIL) (-919 2266583 2274857 2274985 "RADFF" 2274990 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-918 2266234 2266309 2266338 "RADCAT" 2266495 T RADCAT (NIL) -9 NIL NIL) (-917 2266019 2266067 2266164 "RADCAT-" 2266169 NIL RADCAT- (NIL T) -8 NIL NIL) (-916 2264176 2265794 2265883 "QUEUE" 2265963 NIL QUEUE (NIL T) -8 NIL NIL) (-915 2260673 2264113 2264158 "QUAT" 2264163 NIL QUAT (NIL T) -8 NIL NIL) (-914 2260311 2260354 2260481 "QUATCT2" 2260624 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-913 2254065 2257445 2257486 "QUATCAT" 2258265 NIL QUATCAT (NIL T) -9 NIL 2259022) (-912 2250209 2251246 2252633 "QUATCAT-" 2252727 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-911 2247735 2249293 2249335 "QUAGG" 2249710 NIL QUAGG (NIL T) -9 NIL 2249885) (-910 2246660 2247133 2247305 "QFORM" 2247607 NIL QFORM (NIL NIL T) -8 NIL NIL) (-909 2237921 2243179 2243220 "QFCAT" 2243878 NIL QFCAT (NIL T) -9 NIL 2244859) (-908 2233493 2234694 2236285 "QFCAT-" 2236379 NIL QFCAT- (NIL T T) -8 NIL NIL) (-907 2233131 2233174 2233301 "QFCAT2" 2233444 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-906 2232591 2232701 2232831 "QEQUAT" 2233021 T QEQUAT (NIL) -8 NIL NIL) (-905 2225777 2226848 2228030 "QCMPACK" 2231524 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-904 2223357 2223778 2224204 "QALGSET" 2225434 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-903 2222602 2222776 2223008 "QALGSET2" 2223177 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-902 2221293 2221516 2221833 "PWFFINTB" 2222375 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-901 2219481 2219649 2220002 "PUSHVAR" 2221107 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-900 2215398 2216452 2216494 "PTRANFN" 2218378 NIL PTRANFN (NIL T) -9 NIL NIL) (-899 2213810 2214101 2214422 "PTPACK" 2215109 NIL PTPACK (NIL T) -7 NIL NIL) (-898 2213446 2213503 2213610 "PTFUNC2" 2213747 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-897 2207925 2212260 2212301 "PTCAT" 2212669 NIL PTCAT (NIL T) -9 NIL 2212831) (-896 2207583 2207618 2207742 "PSQFR" 2207884 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-895 2206178 2206476 2206810 "PSEUDLIN" 2207281 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-894 2192992 2195356 2197676 "PSETPK" 2203941 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-893 2186079 2188793 2188888 "PSETCAT" 2191869 NIL PSETCAT (NIL T T T T) -9 NIL 2192682) (-892 2183917 2184551 2185370 "PSETCAT-" 2185375 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-891 2183274 2183436 2183465 "PSCURVE" 2183730 T PSCURVE (NIL) -9 NIL 2183894) (-890 2179678 2181204 2181269 "PSCAT" 2182105 NIL PSCAT (NIL T T T) -9 NIL 2182345) (-889 2178742 2178958 2179357 "PSCAT-" 2179362 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-888 2177395 2178027 2178241 "PRTITION" 2178548 T PRTITION (NIL) -8 NIL NIL) (-887 2166495 2168701 2170888 "PRS" 2175258 NIL PRS (NIL T T) -7 NIL NIL) (-886 2164359 2165845 2165886 "PRQAGG" 2166069 NIL PRQAGG (NIL T) -9 NIL 2166171) (-885 2158165 2162557 2163361 "PRODUCT" 2163601 NIL PRODUCT (NIL T T) -8 NIL NIL) (-884 2155447 2157631 2157861 "PR" 2157979 NIL PR (NIL T T) -8 NIL NIL) (-883 2155243 2155275 2155334 "PRINT" 2155408 T PRINT (NIL) -7 NIL NIL) (-882 2154583 2154700 2154852 "PRIMES" 2155123 NIL PRIMES (NIL T) -7 NIL NIL) (-881 2152648 2153049 2153515 "PRIMELT" 2154162 NIL PRIMELT (NIL T) -7 NIL NIL) (-880 2152379 2152427 2152456 "PRIMCAT" 2152579 T PRIMCAT (NIL) -9 NIL NIL) (-879 2148540 2152317 2152362 "PRIMARR" 2152367 NIL PRIMARR (NIL T) -8 NIL NIL) (-878 2147547 2147725 2147953 "PRIMARR2" 2148358 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-877 2147190 2147246 2147357 "PREASSOC" 2147485 NIL PREASSOC (NIL T T) -7 NIL NIL) (-876 2146670 2146801 2146830 "PPCURVE" 2147033 T PPCURVE (NIL) -9 NIL 2147167) (-875 2144031 2144430 2145021 "POLYROOT" 2146252 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-874 2137939 2143639 2143797 "POLY" 2143905 NIL POLY (NIL T) -8 NIL NIL) (-873 2137324 2137382 2137615 "POLYLIFT" 2137875 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-872 2133609 2134058 2134686 "POLYCATQ" 2136869 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-871 2120617 2126014 2126079 "POLYCAT" 2129564 NIL POLYCAT (NIL T T T) -9 NIL 2131476) (-870 2114068 2115929 2118312 "POLYCAT-" 2118317 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-869 2113657 2113725 2113844 "POLY2UP" 2113994 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-868 2113293 2113350 2113457 "POLY2" 2113594 NIL POLY2 (NIL T T) -7 NIL NIL) (-867 2111980 2112219 2112494 "POLUTIL" 2113068 NIL POLUTIL (NIL T T) -7 NIL NIL) (-866 2110342 2110619 2110949 "POLTOPOL" 2111702 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-865 2105871 2110279 2110324 "POINT" 2110329 NIL POINT (NIL T) -8 NIL NIL) (-864 2104058 2104415 2104790 "PNTHEORY" 2105516 T PNTHEORY (NIL) -7 NIL NIL) (-863 2102486 2102783 2103192 "PMTOOLS" 2103756 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-862 2102079 2102157 2102274 "PMSYM" 2102402 NIL PMSYM (NIL T) -7 NIL NIL) (-861 2101589 2101658 2101832 "PMQFCAT" 2102004 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-860 2100944 2101054 2101210 "PMPRED" 2101466 NIL PMPRED (NIL T) -7 NIL NIL) (-859 2100340 2100426 2100587 "PMPREDFS" 2100845 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-858 2098988 2099196 2099579 "PMPLCAT" 2100103 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-857 2098520 2098599 2098751 "PMLSAGG" 2098903 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-856 2097997 2098073 2098253 "PMKERNEL" 2098438 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-855 2097614 2097689 2097802 "PMINS" 2097916 NIL PMINS (NIL T) -7 NIL NIL) (-854 2097044 2097113 2097328 "PMFS" 2097539 NIL PMFS (NIL T T T) -7 NIL NIL) (-853 2096275 2096393 2096597 "PMDOWN" 2096921 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-852 2095438 2095597 2095779 "PMASS" 2096113 T PMASS (NIL) -7 NIL NIL) (-851 2094712 2094823 2094986 "PMASSFS" 2095324 NIL PMASSFS (NIL T T) -7 NIL NIL) (-850 2094371 2094438 2094531 "PLOTTOOL" 2094639 T PLOTTOOL (NIL) -7 NIL NIL) (-849 2089072 2090238 2091365 "PLOT" 2093264 T PLOT (NIL) -8 NIL NIL) (-848 2084945 2085960 2086865 "PLOT3D" 2088187 T PLOT3D (NIL) -8 NIL NIL) (-847 2083869 2084043 2084275 "PLOT1" 2084752 NIL PLOT1 (NIL T) -7 NIL NIL) (-846 2059264 2063935 2068786 "PLEQN" 2079135 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-845 2058582 2058704 2058884 "PINTERP" 2059129 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-844 2058275 2058322 2058425 "PINTERPA" 2058529 NIL PINTERPA (NIL T T) -7 NIL NIL) (-843 2057502 2058069 2058162 "PI" 2058202 T PI (NIL) -8 NIL NIL) (-842 2055893 2056878 2056907 "PID" 2057089 T PID (NIL) -9 NIL 2057223) (-841 2055618 2055655 2055743 "PICOERCE" 2055850 NIL PICOERCE (NIL T) -7 NIL NIL) (-840 2054939 2055077 2055253 "PGROEB" 2055474 NIL PGROEB (NIL T) -7 NIL NIL) (-839 2050526 2051340 2052245 "PGE" 2054054 T PGE (NIL) -7 NIL NIL) (-838 2048650 2048896 2049262 "PGCD" 2050243 NIL PGCD (NIL T T T T) -7 NIL NIL) (-837 2047988 2048091 2048252 "PFRPAC" 2048534 NIL PFRPAC (NIL T) -7 NIL NIL) (-836 2044603 2046536 2046889 "PFR" 2047667 NIL PFR (NIL T) -8 NIL NIL) (-835 2042992 2043236 2043561 "PFOTOOLS" 2044350 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-834 2041525 2041764 2042115 "PFOQ" 2042749 NIL PFOQ (NIL T T T) -7 NIL NIL) (-833 2040002 2040214 2040576 "PFO" 2041309 NIL PFO (NIL T T T T T) -7 NIL NIL) (-832 2036525 2039891 2039960 "PF" 2039965 NIL PF (NIL NIL) -8 NIL NIL) (-831 2033954 2035235 2035264 "PFECAT" 2035849 T PFECAT (NIL) -9 NIL 2036232) (-830 2033399 2033553 2033767 "PFECAT-" 2033772 NIL PFECAT- (NIL T) -8 NIL NIL) (-829 2032003 2032254 2032555 "PFBRU" 2033148 NIL PFBRU (NIL T T) -7 NIL NIL) (-828 2029870 2030221 2030653 "PFBR" 2031654 NIL PFBR (NIL T T T T) -7 NIL NIL) (-827 2025726 2027250 2027924 "PERM" 2029229 NIL PERM (NIL T) -8 NIL NIL) (-826 2020993 2021933 2022803 "PERMGRP" 2024889 NIL PERMGRP (NIL T) -8 NIL NIL) (-825 2019065 2020058 2020100 "PERMCAT" 2020546 NIL PERMCAT (NIL T) -9 NIL 2020849) (-824 2018720 2018761 2018884 "PERMAN" 2019018 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-823 2016166 2018289 2018420 "PENDTREE" 2018622 NIL PENDTREE (NIL T) -8 NIL NIL) (-822 2014238 2015016 2015058 "PDRING" 2015715 NIL PDRING (NIL T) -9 NIL 2016000) (-821 2013341 2013559 2013921 "PDRING-" 2013926 NIL PDRING- (NIL T T) -8 NIL NIL) (-820 2010483 2011233 2011924 "PDEPROB" 2012670 T PDEPROB (NIL) -8 NIL NIL) (-819 2008054 2008550 2009099 "PDEPACK" 2009954 T PDEPACK (NIL) -7 NIL NIL) (-818 2006966 2007156 2007407 "PDECOMP" 2007853 NIL PDECOMP (NIL T T) -7 NIL NIL) (-817 2004577 2005392 2005421 "PDECAT" 2006206 T PDECAT (NIL) -9 NIL 2006917) (-816 2004330 2004363 2004452 "PCOMP" 2004538 NIL PCOMP (NIL T T) -7 NIL NIL) (-815 2002537 2003133 2003429 "PBWLB" 2004060 NIL PBWLB (NIL T) -8 NIL NIL) (-814 1995046 1996614 1997950 "PATTERN" 2001222 NIL PATTERN (NIL T) -8 NIL NIL) (-813 1994678 1994735 1994844 "PATTERN2" 1994983 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-812 1992435 1992823 1993280 "PATTERN1" 1994267 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-811 1989830 1990384 1990865 "PATRES" 1992000 NIL PATRES (NIL T T) -8 NIL NIL) (-810 1989394 1989461 1989593 "PATRES2" 1989757 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-809 1987291 1987691 1988096 "PATMATCH" 1989063 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-808 1986827 1987010 1987052 "PATMAB" 1987159 NIL PATMAB (NIL T) -9 NIL 1987242) (-807 1985372 1985681 1985939 "PATLRES" 1986632 NIL PATLRES (NIL T T T) -8 NIL NIL) (-806 1984919 1985042 1985084 "PATAB" 1985089 NIL PATAB (NIL T) -9 NIL 1985259) (-805 1982400 1982932 1983505 "PARTPERM" 1984366 T PARTPERM (NIL) -7 NIL NIL) (-804 1982021 1982084 1982186 "PARSURF" 1982331 NIL PARSURF (NIL T) -8 NIL NIL) (-803 1981653 1981710 1981819 "PARSU2" 1981958 NIL PARSU2 (NIL T T) -7 NIL NIL) (-802 1981274 1981337 1981439 "PARSCURV" 1981584 NIL PARSCURV (NIL T) -8 NIL NIL) (-801 1980906 1980963 1981072 "PARSC2" 1981211 NIL PARSC2 (NIL T T) -7 NIL NIL) (-800 1980545 1980603 1980700 "PARPCURV" 1980842 NIL PARPCURV (NIL T) -8 NIL NIL) (-799 1980177 1980234 1980343 "PARPC2" 1980482 NIL PARPC2 (NIL T T) -7 NIL NIL) (-798 1979697 1979783 1979902 "PAN2EXPR" 1980078 T PAN2EXPR (NIL) -7 NIL NIL) (-797 1978503 1978818 1979046 "PALETTE" 1979489 T PALETTE (NIL) -8 NIL NIL) (-796 1972353 1977762 1977956 "PADICRC" 1978358 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-795 1965561 1971699 1971883 "PADICRAT" 1972201 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-794 1963865 1965498 1965543 "PADIC" 1965548 NIL PADIC (NIL NIL) -8 NIL NIL) (-793 1961069 1962643 1962684 "PADICCT" 1963265 NIL PADICCT (NIL NIL) -9 NIL 1963547) (-792 1960026 1960226 1960494 "PADEPAC" 1960856 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-791 1959238 1959371 1959577 "PADE" 1959888 NIL PADE (NIL T T T) -7 NIL NIL) (-790 1957253 1958085 1958398 "OWP" 1959008 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-789 1956362 1956858 1957030 "OVAR" 1957121 NIL OVAR (NIL NIL) -8 NIL NIL) (-788 1955626 1955747 1955908 "OUT" 1956221 T OUT (NIL) -7 NIL NIL) (-787 1944672 1946851 1949021 "OUTFORM" 1953476 T OUTFORM (NIL) -8 NIL NIL) (-786 1944080 1944401 1944490 "OSI" 1944603 T OSI (NIL) -8 NIL NIL) (-785 1942827 1943054 1943338 "ORTHPOL" 1943828 NIL ORTHPOL (NIL T) -7 NIL NIL) (-784 1940198 1942488 1942626 "OREUP" 1942770 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-783 1937594 1939891 1940017 "ORESUP" 1940140 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-782 1935133 1935633 1936191 "OREPCTO" 1937085 NIL OREPCTO (NIL T T) -7 NIL NIL) (-781 1929046 1931252 1931293 "OREPCAT" 1933614 NIL OREPCAT (NIL T) -9 NIL 1934713) (-780 1926194 1926976 1928033 "OREPCAT-" 1928038 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-779 1925371 1925643 1925672 "ORDSET" 1925981 T ORDSET (NIL) -9 NIL 1926145) (-778 1924890 1925012 1925205 "ORDSET-" 1925210 NIL ORDSET- (NIL T) -8 NIL NIL) (-777 1923503 1924304 1924333 "ORDRING" 1924535 T ORDRING (NIL) -9 NIL 1924659) (-776 1923148 1923242 1923386 "ORDRING-" 1923391 NIL ORDRING- (NIL T) -8 NIL NIL) (-775 1922523 1923004 1923033 "ORDMON" 1923038 T ORDMON (NIL) -9 NIL 1923059) (-774 1921685 1921832 1922027 "ORDFUNS" 1922372 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-773 1921196 1921555 1921584 "ORDFIN" 1921589 T ORDFIN (NIL) -9 NIL 1921610) (-772 1917714 1919788 1920194 "ORDCOMP" 1920823 NIL ORDCOMP (NIL T) -8 NIL NIL) (-771 1916980 1917107 1917293 "ORDCOMP2" 1917574 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-770 1913488 1914370 1915207 "OPTPROB" 1916163 T OPTPROB (NIL) -8 NIL NIL) (-769 1910330 1910959 1911653 "OPTPACK" 1912814 T OPTPACK (NIL) -7 NIL NIL) (-768 1908055 1908791 1908820 "OPTCAT" 1909635 T OPTCAT (NIL) -9 NIL 1910281) (-767 1907823 1907862 1907928 "OPQUERY" 1908009 T OPQUERY (NIL) -7 NIL NIL) (-766 1904965 1906156 1906653 "OP" 1907358 NIL OP (NIL T) -8 NIL NIL) (-765 1901736 1903768 1904134 "ONECOMP" 1904632 NIL ONECOMP (NIL T) -8 NIL NIL) (-764 1901041 1901156 1901330 "ONECOMP2" 1901608 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-763 1900460 1900566 1900696 "OMSERVER" 1900931 T OMSERVER (NIL) -7 NIL NIL) (-762 1897348 1899900 1899941 "OMSAGG" 1900002 NIL OMSAGG (NIL T) -9 NIL 1900066) (-761 1895971 1896234 1896516 "OMPKG" 1897086 T OMPKG (NIL) -7 NIL NIL) (-760 1895400 1895503 1895532 "OM" 1895831 T OM (NIL) -9 NIL NIL) (-759 1893941 1894954 1895121 "OMLO" 1895282 NIL OMLO (NIL T T) -8 NIL NIL) (-758 1892871 1893018 1893244 "OMEXPR" 1893767 NIL OMEXPR (NIL T) -7 NIL NIL) (-757 1892189 1892417 1892553 "OMERR" 1892755 T OMERR (NIL) -8 NIL NIL) (-756 1891367 1891610 1891770 "OMERRK" 1892049 T OMERRK (NIL) -8 NIL NIL) (-755 1890845 1891044 1891152 "OMENC" 1891279 T OMENC (NIL) -8 NIL NIL) (-754 1884740 1885925 1887096 "OMDEV" 1889694 T OMDEV (NIL) -8 NIL NIL) (-753 1883809 1883980 1884174 "OMCONN" 1884566 T OMCONN (NIL) -8 NIL NIL) (-752 1882424 1883410 1883439 "OINTDOM" 1883444 T OINTDOM (NIL) -9 NIL 1883465) (-751 1878186 1879416 1880131 "OFMONOID" 1881741 NIL OFMONOID (NIL T) -8 NIL NIL) (-750 1877624 1878123 1878168 "ODVAR" 1878173 NIL ODVAR (NIL T) -8 NIL NIL) (-749 1874751 1877123 1877307 "ODR" 1877500 NIL ODR (NIL T T NIL) -8 NIL NIL) (-748 1867057 1874530 1874654 "ODPOL" 1874659 NIL ODPOL (NIL T) -8 NIL NIL) (-747 1860886 1866929 1867034 "ODP" 1867039 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-746 1859652 1859867 1860142 "ODETOOLS" 1860660 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-745 1856621 1857277 1857993 "ODESYS" 1858985 NIL ODESYS (NIL T T) -7 NIL NIL) (-744 1851527 1852435 1853457 "ODERTRIC" 1855697 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-743 1850953 1851035 1851229 "ODERED" 1851439 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-742 1847855 1848403 1849078 "ODERAT" 1850376 NIL ODERAT (NIL T T) -7 NIL NIL) (-741 1844823 1845287 1845883 "ODEPRRIC" 1847384 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-740 1842694 1843261 1843770 "ODEPROB" 1844334 T ODEPROB (NIL) -8 NIL NIL) (-739 1839226 1839709 1840355 "ODEPRIM" 1842173 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-738 1838479 1838581 1838839 "ODEPAL" 1839118 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-737 1834681 1835462 1836316 "ODEPACK" 1837645 T ODEPACK (NIL) -7 NIL NIL) (-736 1833718 1833825 1834053 "ODEINT" 1834570 NIL ODEINT (NIL T T) -7 NIL NIL) (-735 1827819 1829244 1830691 "ODEIFTBL" 1832291 T ODEIFTBL (NIL) -8 NIL NIL) (-734 1823163 1823949 1824907 "ODEEF" 1826978 NIL ODEEF (NIL T T) -7 NIL NIL) (-733 1822500 1822589 1822818 "ODECONST" 1823068 NIL ODECONST (NIL T T T) -7 NIL NIL) (-732 1820657 1821290 1821319 "ODECAT" 1821922 T ODECAT (NIL) -9 NIL 1822451) (-731 1817529 1820369 1820488 "OCT" 1820570 NIL OCT (NIL T) -8 NIL NIL) (-730 1817167 1817210 1817337 "OCTCT2" 1817480 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-729 1812008 1814446 1814487 "OC" 1815583 NIL OC (NIL T) -9 NIL 1816432) (-728 1809235 1809983 1810973 "OC-" 1811067 NIL OC- (NIL T T) -8 NIL NIL) (-727 1808613 1809055 1809084 "OCAMON" 1809089 T OCAMON (NIL) -9 NIL 1809110) (-726 1808066 1808473 1808502 "OASGP" 1808507 T OASGP (NIL) -9 NIL 1808527) (-725 1807353 1807816 1807845 "OAMONS" 1807885 T OAMONS (NIL) -9 NIL 1807928) (-724 1806793 1807200 1807229 "OAMON" 1807234 T OAMON (NIL) -9 NIL 1807254) (-723 1806097 1806589 1806618 "OAGROUP" 1806623 T OAGROUP (NIL) -9 NIL 1806643) (-722 1805787 1805837 1805925 "NUMTUBE" 1806041 NIL NUMTUBE (NIL T) -7 NIL NIL) (-721 1799360 1800878 1802414 "NUMQUAD" 1804271 T NUMQUAD (NIL) -7 NIL NIL) (-720 1795116 1796104 1797129 "NUMODE" 1798355 T NUMODE (NIL) -7 NIL NIL) (-719 1792531 1793373 1793402 "NUMINT" 1794315 T NUMINT (NIL) -9 NIL 1795067) (-718 1791479 1791676 1791894 "NUMFMT" 1792333 T NUMFMT (NIL) -7 NIL NIL) (-717 1777874 1780811 1783333 "NUMERIC" 1788996 NIL NUMERIC (NIL T) -7 NIL NIL) (-716 1772274 1777326 1777421 "NTSCAT" 1777426 NIL NTSCAT (NIL T T T T) -9 NIL 1777464) (-715 1771470 1771635 1771827 "NTPOLFN" 1772114 NIL NTPOLFN (NIL T) -7 NIL NIL) (-714 1759328 1768314 1769123 "NSUP" 1770693 NIL NSUP (NIL T) -8 NIL NIL) (-713 1758964 1759021 1759128 "NSUP2" 1759265 NIL NSUP2 (NIL T T) -7 NIL NIL) (-712 1748926 1758743 1758873 "NSMP" 1758878 NIL NSMP (NIL T T) -8 NIL NIL) (-711 1747358 1747659 1748016 "NREP" 1748614 NIL NREP (NIL T) -7 NIL NIL) (-710 1745949 1746201 1746559 "NPCOEF" 1747101 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-709 1745015 1745130 1745346 "NORMRETR" 1745830 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-708 1743068 1743358 1743765 "NORMPK" 1744723 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-707 1742753 1742781 1742905 "NORMMA" 1743034 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-706 1742580 1742710 1742739 "NONE" 1742744 T NONE (NIL) -8 NIL NIL) (-705 1742369 1742398 1742467 "NONE1" 1742544 NIL NONE1 (NIL T) -7 NIL NIL) (-704 1741854 1741916 1742101 "NODE1" 1742301 NIL NODE1 (NIL T T) -7 NIL NIL) (-703 1740148 1741017 1741272 "NNI" 1741619 T NNI (NIL) -8 NIL NIL) (-702 1738568 1738881 1739245 "NLINSOL" 1739816 NIL NLINSOL (NIL T) -7 NIL NIL) (-701 1734760 1735721 1736637 "NIPROB" 1737672 T NIPROB (NIL) -8 NIL NIL) (-700 1733517 1733751 1734053 "NFINTBAS" 1734522 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-699 1732225 1732456 1732737 "NCODIV" 1733285 NIL NCODIV (NIL T T) -7 NIL NIL) (-698 1731987 1732024 1732099 "NCNTFRAC" 1732182 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-697 1730167 1730531 1730951 "NCEP" 1731612 NIL NCEP (NIL T) -7 NIL NIL) (-696 1729078 1729817 1729846 "NASRING" 1729956 T NASRING (NIL) -9 NIL 1730030) (-695 1728873 1728917 1729011 "NASRING-" 1729016 NIL NASRING- (NIL T) -8 NIL NIL) (-694 1728026 1728525 1728554 "NARNG" 1728671 T NARNG (NIL) -9 NIL 1728762) (-693 1727718 1727785 1727919 "NARNG-" 1727924 NIL NARNG- (NIL T) -8 NIL NIL) (-692 1726597 1726804 1727039 "NAGSP" 1727503 T NAGSP (NIL) -7 NIL NIL) (-691 1718021 1719667 1721302 "NAGS" 1724982 T NAGS (NIL) -7 NIL NIL) (-690 1716585 1716889 1717216 "NAGF07" 1717714 T NAGF07 (NIL) -7 NIL NIL) (-689 1711167 1712447 1713743 "NAGF04" 1715309 T NAGF04 (NIL) -7 NIL NIL) (-688 1704199 1705797 1707414 "NAGF02" 1709570 T NAGF02 (NIL) -7 NIL NIL) (-687 1699463 1700553 1701660 "NAGF01" 1703112 T NAGF01 (NIL) -7 NIL NIL) (-686 1693123 1694681 1696258 "NAGE04" 1697906 T NAGE04 (NIL) -7 NIL NIL) (-685 1684364 1686467 1688579 "NAGE02" 1691031 T NAGE02 (NIL) -7 NIL NIL) (-684 1680357 1681294 1682248 "NAGE01" 1683430 T NAGE01 (NIL) -7 NIL NIL) (-683 1678164 1678695 1679250 "NAGD03" 1679822 T NAGD03 (NIL) -7 NIL NIL) (-682 1669950 1671869 1673814 "NAGD02" 1676239 T NAGD02 (NIL) -7 NIL NIL) (-681 1663809 1665222 1666650 "NAGD01" 1668542 T NAGD01 (NIL) -7 NIL NIL) (-680 1660066 1660876 1661701 "NAGC06" 1663004 T NAGC06 (NIL) -7 NIL NIL) (-679 1658543 1658872 1659225 "NAGC05" 1659733 T NAGC05 (NIL) -7 NIL NIL) (-678 1657927 1658044 1658186 "NAGC02" 1658421 T NAGC02 (NIL) -7 NIL NIL) (-677 1656988 1657545 1657586 "NAALG" 1657665 NIL NAALG (NIL T) -9 NIL 1657726) (-676 1656823 1656852 1656942 "NAALG-" 1656947 NIL NAALG- (NIL T T) -8 NIL NIL) (-675 1650773 1651881 1653068 "MULTSQFR" 1655719 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-674 1650092 1650167 1650351 "MULTFACT" 1650685 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-673 1643234 1647145 1647198 "MTSCAT" 1648258 NIL MTSCAT (NIL T T) -9 NIL 1648771) (-672 1642946 1643000 1643092 "MTHING" 1643174 NIL MTHING (NIL T) -7 NIL NIL) (-671 1642738 1642771 1642831 "MSYSCMD" 1642906 T MSYSCMD (NIL) -7 NIL NIL) (-670 1638850 1641493 1641813 "MSET" 1642451 NIL MSET (NIL T) -8 NIL NIL) (-669 1635945 1638411 1638453 "MSETAGG" 1638458 NIL MSETAGG (NIL T) -9 NIL 1638492) (-668 1631813 1633355 1634090 "MRING" 1635254 NIL MRING (NIL T T) -8 NIL NIL) (-667 1631383 1631450 1631579 "MRF2" 1631740 NIL MRF2 (NIL T T T) -7 NIL NIL) (-666 1631001 1631036 1631180 "MRATFAC" 1631342 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-665 1628613 1628908 1629339 "MPRFF" 1630706 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-664 1622633 1628468 1628564 "MPOLY" 1628569 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-663 1622123 1622158 1622366 "MPCPF" 1622592 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-662 1621639 1621682 1621865 "MPC3" 1622074 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-661 1620840 1620921 1621140 "MPC2" 1621554 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-660 1619141 1619478 1619868 "MONOTOOL" 1620500 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-659 1618265 1618600 1618629 "MONOID" 1618906 T MONOID (NIL) -9 NIL 1619078) (-658 1617643 1617806 1618049 "MONOID-" 1618054 NIL MONOID- (NIL T) -8 NIL NIL) (-657 1608579 1614565 1614625 "MONOGEN" 1615299 NIL MONOGEN (NIL T T) -9 NIL 1615752) (-656 1605797 1606532 1607532 "MONOGEN-" 1607651 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-655 1604656 1605076 1605105 "MONADWU" 1605497 T MONADWU (NIL) -9 NIL 1605735) (-654 1604028 1604187 1604435 "MONADWU-" 1604440 NIL MONADWU- (NIL T) -8 NIL NIL) (-653 1603413 1603631 1603660 "MONAD" 1603867 T MONAD (NIL) -9 NIL 1603979) (-652 1603098 1603176 1603308 "MONAD-" 1603313 NIL MONAD- (NIL T) -8 NIL NIL) (-651 1601349 1602011 1602290 "MOEBIUS" 1602851 NIL MOEBIUS (NIL T) -8 NIL NIL) (-650 1600742 1601120 1601161 "MODULE" 1601166 NIL MODULE (NIL T) -9 NIL 1601192) (-649 1600310 1600406 1600596 "MODULE-" 1600601 NIL MODULE- (NIL T T) -8 NIL NIL) (-648 1597981 1598676 1599002 "MODRING" 1600135 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1594943 1596108 1596622 "MODOP" 1597516 NIL MODOP (NIL T T) -8 NIL NIL) (-646 1593130 1593582 1593923 "MODMONOM" 1594742 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-645 1582852 1591338 1591758 "MODMON" 1592760 NIL MODMON (NIL T T) -8 NIL NIL) (-644 1579978 1581696 1581972 "MODFIELD" 1582727 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-643 1579504 1579547 1579726 "MMAP" 1579929 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-642 1577741 1578518 1578559 "MLO" 1578976 NIL MLO (NIL T) -9 NIL 1579216) (-641 1575108 1575623 1576225 "MLIFT" 1577222 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-640 1574499 1574583 1574737 "MKUCFUNC" 1575019 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-639 1574098 1574168 1574291 "MKRECORD" 1574422 NIL MKRECORD (NIL T T) -7 NIL NIL) (-638 1573146 1573307 1573535 "MKFUNC" 1573909 NIL MKFUNC (NIL T) -7 NIL NIL) (-637 1572534 1572638 1572794 "MKFLCFN" 1573029 NIL MKFLCFN (NIL T) -7 NIL NIL) (-636 1571960 1572327 1572416 "MKCHSET" 1572478 NIL MKCHSET (NIL T) -8 NIL NIL) (-635 1571237 1571339 1571524 "MKBCFUNC" 1571853 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-634 1567921 1570791 1570927 "MINT" 1571121 T MINT (NIL) -8 NIL NIL) (-633 1566733 1566976 1567253 "MHROWRED" 1567676 NIL MHROWRED (NIL T) -7 NIL NIL) (-632 1562004 1565178 1565602 "MFLOAT" 1566329 T MFLOAT (NIL) -8 NIL NIL) (-631 1561361 1561437 1561608 "MFINFACT" 1561916 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-630 1557708 1558547 1559422 "MESH" 1560506 T MESH (NIL) -7 NIL NIL) (-629 1556098 1556410 1556763 "MDDFACT" 1557395 NIL MDDFACT (NIL T) -7 NIL NIL) (-628 1552946 1555257 1555299 "MDAGG" 1555554 NIL MDAGG (NIL T) -9 NIL 1555697) (-627 1542644 1552239 1552446 "MCMPLX" 1552759 T MCMPLX (NIL) -8 NIL NIL) (-626 1541785 1541931 1542131 "MCDEN" 1542493 NIL MCDEN (NIL T T) -7 NIL NIL) (-625 1539675 1539945 1540325 "MCALCFN" 1541515 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-624 1537297 1537820 1538381 "MATSTOR" 1539146 NIL MATSTOR (NIL T) -7 NIL NIL) (-623 1533315 1536676 1536921 "MATRIX" 1537084 NIL MATRIX (NIL T) -8 NIL NIL) (-622 1529090 1529794 1530527 "MATLIN" 1532675 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-621 1519299 1522431 1522508 "MATCAT" 1527346 NIL MATCAT (NIL T T T) -9 NIL 1528757) (-620 1515664 1516677 1518032 "MATCAT-" 1518037 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-619 1514266 1514419 1514750 "MATCAT2" 1515499 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-618 1512378 1512702 1513086 "MAPPKG3" 1513941 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-617 1511359 1511532 1511754 "MAPPKG2" 1512202 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-616 1509858 1510142 1510469 "MAPPKG1" 1511065 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-615 1509469 1509527 1509650 "MAPHACK3" 1509794 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-614 1509061 1509122 1509236 "MAPHACK2" 1509401 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-613 1508499 1508602 1508744 "MAPHACK1" 1508952 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-612 1506607 1507201 1507504 "MAGMA" 1508228 NIL MAGMA (NIL T) -8 NIL NIL) (-611 1503090 1504853 1505312 "M3D" 1506181 NIL M3D (NIL T) -8 NIL NIL) (-610 1497248 1501457 1501499 "LZSTAGG" 1502281 NIL LZSTAGG (NIL T) -9 NIL 1502576) (-609 1493222 1494379 1495836 "LZSTAGG-" 1495841 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-608 1490338 1491115 1491601 "LWORD" 1492768 NIL LWORD (NIL T) -8 NIL NIL) (-607 1483498 1490109 1490243 "LSQM" 1490248 NIL LSQM (NIL NIL T) -8 NIL NIL) (-606 1482722 1482861 1483089 "LSPP" 1483353 NIL LSPP (NIL T T T T) -7 NIL NIL) (-605 1480534 1480835 1481291 "LSMP" 1482411 NIL LSMP (NIL T T T T) -7 NIL NIL) (-604 1477313 1477987 1478717 "LSMP1" 1479836 NIL LSMP1 (NIL T) -7 NIL NIL) (-603 1471236 1476478 1476520 "LSAGG" 1476582 NIL LSAGG (NIL T) -9 NIL 1476660) (-602 1467931 1468855 1470068 "LSAGG-" 1470073 NIL LSAGG- (NIL T T) -8 NIL NIL) (-601 1465557 1467075 1467324 "LPOLY" 1467726 NIL LPOLY (NIL T T) -8 NIL NIL) (-600 1465139 1465224 1465347 "LPEFRAC" 1465466 NIL LPEFRAC (NIL T) -7 NIL NIL) (-599 1463488 1464235 1464487 "LO" 1464972 NIL LO (NIL T T T) -8 NIL NIL) (-598 1463141 1463253 1463282 "LOGIC" 1463393 T LOGIC (NIL) -9 NIL 1463473) (-597 1463003 1463026 1463097 "LOGIC-" 1463102 NIL LOGIC- (NIL T) -8 NIL NIL) (-596 1462196 1462336 1462529 "LODOOPS" 1462859 NIL LODOOPS (NIL T T) -7 NIL NIL) (-595 1459614 1462113 1462178 "LODO" 1462183 NIL LODO (NIL T NIL) -8 NIL NIL) (-594 1458162 1458397 1458747 "LODOF" 1459362 NIL LODOF (NIL T T) -7 NIL NIL) (-593 1454582 1457018 1457059 "LODOCAT" 1457491 NIL LODOCAT (NIL T) -9 NIL 1457701) (-592 1454316 1454374 1454500 "LODOCAT-" 1454505 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-591 1451630 1454157 1454275 "LODO2" 1454280 NIL LODO2 (NIL T T) -8 NIL NIL) (-590 1449059 1451567 1451612 "LODO1" 1451617 NIL LODO1 (NIL T) -8 NIL NIL) (-589 1447922 1448087 1448398 "LODEEF" 1448882 NIL LODEEF (NIL T T T) -7 NIL NIL) (-588 1443206 1446050 1446092 "LNAGG" 1447039 NIL LNAGG (NIL T) -9 NIL 1447482) (-587 1442353 1442567 1442909 "LNAGG-" 1442914 NIL LNAGG- (NIL T T) -8 NIL NIL) (-586 1438518 1439280 1439918 "LMOPS" 1441769 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-585 1437915 1438277 1438318 "LMODULE" 1438378 NIL LMODULE (NIL T) -9 NIL 1438420) (-584 1435167 1437560 1437683 "LMDICT" 1437825 NIL LMDICT (NIL T) -8 NIL NIL) (-583 1428398 1434117 1434413 "LIST" 1434904 NIL LIST (NIL T) -8 NIL NIL) (-582 1427923 1427997 1428136 "LIST3" 1428318 NIL LIST3 (NIL T T T) -7 NIL NIL) (-581 1426930 1427108 1427336 "LIST2" 1427741 NIL LIST2 (NIL T T) -7 NIL NIL) (-580 1425064 1425376 1425775 "LIST2MAP" 1426577 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-579 1423776 1424456 1424497 "LINEXP" 1424750 NIL LINEXP (NIL T) -9 NIL 1424898) (-578 1422423 1422683 1422980 "LINDEP" 1423528 NIL LINDEP (NIL T T) -7 NIL NIL) (-577 1419190 1419909 1420686 "LIMITRF" 1421678 NIL LIMITRF (NIL T) -7 NIL NIL) (-576 1417471 1417765 1418180 "LIMITPS" 1418885 NIL LIMITPS (NIL T T) -7 NIL NIL) (-575 1411930 1416986 1417212 "LIE" 1417294 NIL LIE (NIL T T) -8 NIL NIL) (-574 1410981 1411424 1411465 "LIECAT" 1411605 NIL LIECAT (NIL T) -9 NIL 1411755) (-573 1410822 1410849 1410937 "LIECAT-" 1410942 NIL LIECAT- (NIL T T) -8 NIL NIL) (-572 1403446 1410271 1410436 "LIB" 1410677 T LIB (NIL) -8 NIL NIL) (-571 1399083 1399964 1400899 "LGROBP" 1402563 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-570 1396953 1397226 1397587 "LF" 1398805 NIL LF (NIL T T) -7 NIL NIL) (-569 1395793 1396484 1396513 "LFCAT" 1396720 T LFCAT (NIL) -9 NIL 1396859) (-568 1392705 1393331 1394017 "LEXTRIPK" 1395159 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-567 1389411 1390275 1390778 "LEXP" 1392285 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-566 1387809 1388122 1388523 "LEADCDET" 1389093 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-565 1387005 1387079 1387306 "LAZM3PK" 1387730 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-564 1381928 1385090 1385624 "LAUPOL" 1386521 NIL LAUPOL (NIL T T) -8 NIL NIL) (-563 1381495 1381539 1381706 "LAPLACE" 1381878 NIL LAPLACE (NIL T T) -7 NIL NIL) (-562 1379425 1380598 1380848 "LA" 1381329 NIL LA (NIL T T T) -8 NIL NIL) (-561 1378487 1379081 1379122 "LALG" 1379183 NIL LALG (NIL T) -9 NIL 1379241) (-560 1378202 1378261 1378396 "LALG-" 1378401 NIL LALG- (NIL T T) -8 NIL NIL) (-559 1377112 1377299 1377596 "KOVACIC" 1378002 NIL KOVACIC (NIL T T) -7 NIL NIL) (-558 1376946 1376970 1377012 "KONVERT" 1377074 NIL KONVERT (NIL T) -9 NIL NIL) (-557 1376780 1376804 1376846 "KOERCE" 1376908 NIL KOERCE (NIL T) -9 NIL NIL) (-556 1374516 1375276 1375668 "KERNEL" 1376420 NIL KERNEL (NIL T) -8 NIL NIL) (-555 1374018 1374099 1374229 "KERNEL2" 1374430 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-554 1367633 1372315 1372370 "KDAGG" 1372747 NIL KDAGG (NIL T T) -9 NIL 1372953) (-553 1367162 1367286 1367491 "KDAGG-" 1367496 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-552 1360337 1366823 1366978 "KAFILE" 1367040 NIL KAFILE (NIL T) -8 NIL NIL) (-551 1354796 1359852 1360078 "JORDAN" 1360160 NIL JORDAN (NIL T T) -8 NIL NIL) (-550 1351105 1353005 1353060 "IXAGG" 1353989 NIL IXAGG (NIL T T) -9 NIL 1354444) (-549 1350024 1350330 1350749 "IXAGG-" 1350754 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-548 1345615 1349946 1350005 "IVECTOR" 1350010 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-547 1344381 1344618 1344884 "ITUPLE" 1345382 NIL ITUPLE (NIL T) -8 NIL NIL) (-546 1342817 1342994 1343300 "ITRIGMNP" 1344203 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-545 1341562 1341766 1342049 "ITFUN3" 1342593 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-544 1341194 1341251 1341360 "ITFUN2" 1341499 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-543 1338998 1340069 1340365 "ITAYLOR" 1340930 NIL ITAYLOR (NIL T) -8 NIL NIL) (-542 1327992 1333186 1334344 "ISUPS" 1337872 NIL ISUPS (NIL T) -8 NIL NIL) (-541 1327100 1327239 1327474 "ISUMP" 1327840 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-540 1322364 1326901 1326980 "ISTRING" 1327053 NIL ISTRING (NIL NIL) -8 NIL NIL) (-539 1321577 1321658 1321873 "IRURPK" 1322278 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-538 1320513 1320714 1320954 "IRSN" 1321357 T IRSN (NIL) -7 NIL NIL) (-537 1318550 1318905 1319339 "IRRF2F" 1320152 NIL IRRF2F (NIL T) -7 NIL NIL) (-536 1318297 1318335 1318411 "IRREDFFX" 1318506 NIL IRREDFFX (NIL T) -7 NIL NIL) (-535 1316912 1317171 1317470 "IROOT" 1318030 NIL IROOT (NIL T) -7 NIL NIL) (-534 1313554 1314605 1315293 "IR" 1316256 NIL IR (NIL T) -8 NIL NIL) (-533 1311167 1311662 1312228 "IR2" 1313032 NIL IR2 (NIL T T) -7 NIL NIL) (-532 1310243 1310356 1310576 "IR2F" 1311050 NIL IR2F (NIL T T) -7 NIL NIL) (-531 1310034 1310068 1310128 "IPRNTPK" 1310203 T IPRNTPK (NIL) -7 NIL NIL) (-530 1306588 1309923 1309992 "IPF" 1309997 NIL IPF (NIL NIL) -8 NIL NIL) (-529 1304905 1306513 1306570 "IPADIC" 1306575 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-528 1304404 1304462 1304651 "INVLAPLA" 1304841 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-527 1294053 1296406 1298792 "INTTR" 1302068 NIL INTTR (NIL T T) -7 NIL NIL) (-526 1290415 1291156 1292012 "INTTOOLS" 1293246 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-525 1290001 1290092 1290209 "INTSLPE" 1290318 T INTSLPE (NIL) -7 NIL NIL) (-524 1287951 1289924 1289983 "INTRVL" 1289988 NIL INTRVL (NIL T) -8 NIL NIL) (-523 1285558 1286070 1286644 "INTRF" 1287436 NIL INTRF (NIL T) -7 NIL NIL) (-522 1284973 1285070 1285211 "INTRET" 1285456 NIL INTRET (NIL T) -7 NIL NIL) (-521 1282975 1283364 1283833 "INTRAT" 1284581 NIL INTRAT (NIL T T) -7 NIL NIL) (-520 1280216 1280799 1281420 "INTPM" 1282464 NIL INTPM (NIL T T) -7 NIL NIL) (-519 1276927 1277526 1278269 "INTPAF" 1279603 NIL INTPAF (NIL T T T) -7 NIL NIL) (-518 1272210 1273146 1274171 "INTPACK" 1275922 T INTPACK (NIL) -7 NIL NIL) (-517 1269064 1271939 1272066 "INT" 1272103 T INT (NIL) -8 NIL NIL) (-516 1268316 1268468 1268676 "INTHERTR" 1268906 NIL INTHERTR (NIL T T) -7 NIL NIL) (-515 1267755 1267835 1268023 "INTHERAL" 1268230 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-514 1265601 1266044 1266501 "INTHEORY" 1267318 T INTHEORY (NIL) -7 NIL NIL) (-513 1256926 1258546 1260323 "INTG0" 1263954 NIL INTG0 (NIL T T T) -7 NIL NIL) (-512 1237523 1242307 1247111 "INTFTBL" 1252142 T INTFTBL (NIL) -8 NIL NIL) (-511 1236772 1236910 1237083 "INTFACT" 1237382 NIL INTFACT (NIL T) -7 NIL NIL) (-510 1234163 1234609 1235172 "INTEF" 1236326 NIL INTEF (NIL T T) -7 NIL NIL) (-509 1232624 1233373 1233402 "INTDOM" 1233703 T INTDOM (NIL) -9 NIL 1233910) (-508 1231993 1232167 1232409 "INTDOM-" 1232414 NIL INTDOM- (NIL T) -8 NIL NIL) (-507 1228485 1230417 1230472 "INTCAT" 1231271 NIL INTCAT (NIL T) -9 NIL 1231590) (-506 1227958 1228060 1228188 "INTBIT" 1228377 T INTBIT (NIL) -7 NIL NIL) (-505 1226633 1226787 1227100 "INTALG" 1227803 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-504 1226090 1226180 1226350 "INTAF" 1226537 NIL INTAF (NIL T T) -7 NIL NIL) (-503 1219556 1225900 1226040 "INTABL" 1226045 NIL INTABL (NIL T T T) -8 NIL NIL) (-502 1214506 1217235 1217264 "INS" 1218232 T INS (NIL) -9 NIL 1218913) (-501 1211746 1212517 1213491 "INS-" 1213564 NIL INS- (NIL T) -8 NIL NIL) (-500 1210525 1210752 1211049 "INPSIGN" 1211499 NIL INPSIGN (NIL T T) -7 NIL NIL) (-499 1209643 1209760 1209957 "INPRODPF" 1210405 NIL INPRODPF (NIL T T) -7 NIL NIL) (-498 1208537 1208654 1208891 "INPRODFF" 1209523 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-497 1207537 1207689 1207949 "INNMFACT" 1208373 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-496 1206734 1206831 1207019 "INMODGCD" 1207436 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-495 1205243 1205487 1205811 "INFSP" 1206479 NIL INFSP (NIL T T T) -7 NIL NIL) (-494 1204427 1204544 1204727 "INFPROD0" 1205123 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-493 1201437 1202596 1203087 "INFORM" 1203944 T INFORM (NIL) -8 NIL NIL) (-492 1201047 1201107 1201205 "INFORM1" 1201372 NIL INFORM1 (NIL T) -7 NIL NIL) (-491 1200570 1200659 1200773 "INFINITY" 1200953 T INFINITY (NIL) -7 NIL NIL) (-490 1199188 1199436 1199757 "INEP" 1200318 NIL INEP (NIL T T T) -7 NIL NIL) (-489 1198464 1199085 1199150 "INDE" 1199155 NIL INDE (NIL T) -8 NIL NIL) (-488 1198028 1198096 1198213 "INCRMAPS" 1198391 NIL INCRMAPS (NIL T) -7 NIL NIL) (-487 1193339 1194264 1195208 "INBFF" 1197116 NIL INBFF (NIL T) -7 NIL NIL) (-486 1189840 1193184 1193287 "IMATRIX" 1193292 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-485 1188554 1188677 1188991 "IMATQF" 1189697 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-484 1186776 1187003 1187339 "IMATLIN" 1188311 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-483 1181402 1186700 1186758 "ILIST" 1186763 NIL ILIST (NIL T NIL) -8 NIL NIL) (-482 1179361 1181262 1181375 "IIARRAY2" 1181380 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-481 1174729 1179272 1179336 "IFF" 1179341 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-480 1169778 1174021 1174209 "IFARRAY" 1174586 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-479 1168985 1169682 1169755 "IFAMON" 1169760 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-478 1168568 1168633 1168688 "IEVALAB" 1168895 NIL IEVALAB (NIL T T) -9 NIL NIL) (-477 1168243 1168311 1168471 "IEVALAB-" 1168476 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-476 1167901 1168157 1168220 "IDPO" 1168225 NIL IDPO (NIL T T) -8 NIL NIL) (-475 1167178 1167790 1167865 "IDPOAMS" 1167870 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-474 1166512 1167067 1167142 "IDPOAM" 1167147 NIL IDPOAM (NIL T T) -8 NIL NIL) (-473 1165597 1165847 1165901 "IDPC" 1166314 NIL IDPC (NIL T T) -9 NIL 1166463) (-472 1165093 1165489 1165562 "IDPAM" 1165567 NIL IDPAM (NIL T T) -8 NIL NIL) (-471 1164496 1164985 1165058 "IDPAG" 1165063 NIL IDPAG (NIL T T) -8 NIL NIL) (-470 1160751 1161599 1162494 "IDECOMP" 1163653 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-469 1153627 1154676 1155722 "IDEAL" 1159788 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-468 1152791 1152903 1153102 "ICDEN" 1153511 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-467 1151890 1152271 1152418 "ICARD" 1152664 T ICARD (NIL) -8 NIL NIL) (-466 1149962 1150275 1150678 "IBPTOOLS" 1151567 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-465 1145576 1149582 1149695 "IBITS" 1149881 NIL IBITS (NIL NIL) -8 NIL NIL) (-464 1142299 1142875 1143570 "IBATOOL" 1144993 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-463 1140079 1140540 1141073 "IBACHIN" 1141834 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-462 1137962 1139925 1140028 "IARRAY2" 1140033 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-461 1134121 1137888 1137945 "IARRAY1" 1137950 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-460 1128061 1132539 1133017 "IAN" 1133663 T IAN (NIL) -8 NIL NIL) (-459 1127572 1127629 1127802 "IALGFACT" 1127998 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-458 1127099 1127212 1127241 "HYPCAT" 1127448 T HYPCAT (NIL) -9 NIL NIL) (-457 1126637 1126754 1126940 "HYPCAT-" 1126945 NIL HYPCAT- (NIL T) -8 NIL NIL) (-456 1123323 1124654 1124696 "HOAGG" 1125677 NIL HOAGG (NIL T) -9 NIL 1126349) (-455 1121917 1122316 1122842 "HOAGG-" 1122847 NIL HOAGG- (NIL T T) -8 NIL NIL) (-454 1115748 1121358 1121524 "HEXADEC" 1121771 T HEXADEC (NIL) -8 NIL NIL) (-453 1114496 1114718 1114981 "HEUGCD" 1115525 NIL HEUGCD (NIL T) -7 NIL NIL) (-452 1113599 1114333 1114463 "HELLFDIV" 1114468 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-451 1111833 1113376 1113464 "HEAP" 1113543 NIL HEAP (NIL T) -8 NIL NIL) (-450 1105706 1111748 1111810 "HDP" 1111815 NIL HDP (NIL NIL T) -8 NIL NIL) (-449 1099418 1105343 1105494 "HDMP" 1105607 NIL HDMP (NIL NIL T) -8 NIL NIL) (-448 1098743 1098882 1099046 "HB" 1099274 T HB (NIL) -7 NIL NIL) (-447 1092252 1098589 1098693 "HASHTBL" 1098698 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-446 1090005 1091880 1092059 "HACKPI" 1092093 T HACKPI (NIL) -8 NIL NIL) (-445 1085701 1089859 1089971 "GTSET" 1089976 NIL GTSET (NIL T T T T) -8 NIL NIL) (-444 1079239 1085579 1085677 "GSTBL" 1085682 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-443 1071477 1078277 1078540 "GSERIES" 1079031 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-442 1070499 1070952 1070981 "GROUP" 1071242 T GROUP (NIL) -9 NIL 1071401) (-441 1069615 1069838 1070182 "GROUP-" 1070187 NIL GROUP- (NIL T) -8 NIL NIL) (-440 1067984 1068303 1068690 "GROEBSOL" 1069292 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-439 1066924 1067186 1067238 "GRMOD" 1067767 NIL GRMOD (NIL T T) -9 NIL 1067935) (-438 1066692 1066728 1066856 "GRMOD-" 1066861 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-437 1062032 1063054 1064051 "GRIMAGE" 1065715 T GRIMAGE (NIL) -8 NIL NIL) (-436 1060499 1060759 1061083 "GRDEF" 1061728 T GRDEF (NIL) -7 NIL NIL) (-435 1059943 1060059 1060200 "GRAY" 1060378 T GRAY (NIL) -7 NIL NIL) (-434 1059176 1059556 1059608 "GRALG" 1059761 NIL GRALG (NIL T T) -9 NIL 1059853) (-433 1058837 1058910 1059073 "GRALG-" 1059078 NIL GRALG- (NIL T T T) -8 NIL NIL) (-432 1055645 1058426 1058602 "GPOLSET" 1058744 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-431 1055001 1055058 1055315 "GOSPER" 1055582 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-430 1050760 1051439 1051965 "GMODPOL" 1054700 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-429 1049765 1049949 1050187 "GHENSEL" 1050572 NIL GHENSEL (NIL T T) -7 NIL NIL) (-428 1043831 1044674 1045700 "GENUPS" 1048849 NIL GENUPS (NIL T T) -7 NIL NIL) (-427 1043528 1043579 1043668 "GENUFACT" 1043774 NIL GENUFACT (NIL T) -7 NIL NIL) (-426 1042940 1043017 1043182 "GENPGCD" 1043446 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-425 1042414 1042449 1042662 "GENMFACT" 1042899 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-424 1040982 1041237 1041544 "GENEEZ" 1042157 NIL GENEEZ (NIL T T) -7 NIL NIL) (-423 1034856 1040595 1040756 "GDMP" 1040905 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-422 1024237 1028629 1029734 "GCNAALG" 1033840 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-421 1022658 1023530 1023559 "GCDDOM" 1023814 T GCDDOM (NIL) -9 NIL 1023971) (-420 1022128 1022255 1022470 "GCDDOM-" 1022475 NIL GCDDOM- (NIL T) -8 NIL NIL) (-419 1020802 1020987 1021290 "GB" 1021908 NIL GB (NIL T T T T) -7 NIL NIL) (-418 1009422 1011748 1014140 "GBINTERN" 1018493 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-417 1007259 1007551 1007972 "GBF" 1009097 NIL GBF (NIL T T T T) -7 NIL NIL) (-416 1006040 1006205 1006472 "GBEUCLID" 1007075 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-415 1005389 1005514 1005663 "GAUSSFAC" 1005911 T GAUSSFAC (NIL) -7 NIL NIL) (-414 1003768 1004070 1004382 "GALUTIL" 1005109 NIL GALUTIL (NIL T) -7 NIL NIL) (-413 1002085 1002359 1002682 "GALPOLYU" 1003495 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-412 999474 999764 1000169 "GALFACTU" 1001782 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-411 991280 992779 994387 "GALFACT" 997906 NIL GALFACT (NIL T) -7 NIL NIL) (-410 988667 989325 989354 "FVFUN" 990510 T FVFUN (NIL) -9 NIL 991230) (-409 987932 988114 988143 "FVC" 988434 T FVC (NIL) -9 NIL 988617) (-408 987574 987729 987810 "FUNCTION" 987884 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-407 985244 985795 986284 "FT" 987105 T FT (NIL) -8 NIL NIL) (-406 984062 984545 984748 "FTEM" 985061 T FTEM (NIL) -8 NIL NIL) (-405 982329 982617 983018 "FSUPFACT" 983755 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-404 980726 981015 981347 "FST" 982017 T FST (NIL) -8 NIL NIL) (-403 979901 980007 980201 "FSRED" 980608 NIL FSRED (NIL T T) -7 NIL NIL) (-402 978582 978837 979190 "FSPRMELT" 979617 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-401 975667 976105 976604 "FSPECF" 978145 NIL FSPECF (NIL T T) -7 NIL NIL) (-400 958004 966561 966602 "FS" 970440 NIL FS (NIL T) -9 NIL 972711) (-399 946654 949644 953700 "FS-" 953997 NIL FS- (NIL T T) -8 NIL NIL) (-398 946170 946224 946400 "FSINT" 946595 NIL FSINT (NIL T T) -7 NIL NIL) (-397 944455 945167 945468 "FSERIES" 945951 NIL FSERIES (NIL T T) -8 NIL NIL) (-396 943473 943589 943819 "FSCINT" 944335 NIL FSCINT (NIL T T) -7 NIL NIL) (-395 939709 942419 942461 "FSAGG" 942831 NIL FSAGG (NIL T) -9 NIL 943088) (-394 937471 938072 938868 "FSAGG-" 938963 NIL FSAGG- (NIL T T) -8 NIL NIL) (-393 936513 936656 936883 "FSAGG2" 937324 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-392 934172 934451 935004 "FS2UPS" 936231 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-391 933758 933801 933954 "FS2" 934123 NIL FS2 (NIL T T T T) -7 NIL NIL) (-390 932618 932789 933097 "FS2EXPXP" 933583 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-389 932044 932159 932311 "FRUTIL" 932498 NIL FRUTIL (NIL T) -7 NIL NIL) (-388 923481 927559 928907 "FR" 930728 NIL FR (NIL T) -8 NIL NIL) (-387 918558 921201 921242 "FRNAALG" 922638 NIL FRNAALG (NIL T) -9 NIL 923244) (-386 914237 915307 916582 "FRNAALG-" 917332 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-385 913875 913918 914045 "FRNAAF2" 914188 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-384 912242 912734 913027 "FRMOD" 913689 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-383 909965 910633 910949 "FRIDEAL" 912033 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-382 909164 909251 909538 "FRIDEAL2" 909872 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-381 908423 908831 908873 "FRETRCT" 908878 NIL FRETRCT (NIL T) -9 NIL 909047) (-380 907535 907766 908117 "FRETRCT-" 908122 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-379 904744 905964 906024 "FRAMALG" 906906 NIL FRAMALG (NIL T T) -9 NIL 907198) (-378 902877 903333 903963 "FRAMALG-" 904186 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-377 896789 902362 902633 "FRAC" 902638 NIL FRAC (NIL T) -8 NIL NIL) (-376 896425 896482 896589 "FRAC2" 896726 NIL FRAC2 (NIL T T) -7 NIL NIL) (-375 896061 896118 896225 "FR2" 896362 NIL FR2 (NIL T T) -7 NIL NIL) (-374 890690 893603 893632 "FPS" 894751 T FPS (NIL) -9 NIL 895304) (-373 890139 890248 890412 "FPS-" 890558 NIL FPS- (NIL T) -8 NIL NIL) (-372 887540 889237 889266 "FPC" 889491 T FPC (NIL) -9 NIL 889633) (-371 887333 887373 887470 "FPC-" 887475 NIL FPC- (NIL T) -8 NIL NIL) (-370 886213 886823 886865 "FPATMAB" 886870 NIL FPATMAB (NIL T) -9 NIL 887020) (-369 883913 884389 884815 "FPARFRAC" 885850 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-368 879308 879805 880487 "FORTRAN" 883345 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-367 877024 877524 878063 "FORT" 878789 T FORT (NIL) -7 NIL NIL) (-366 874699 875261 875290 "FORTFN" 876350 T FORTFN (NIL) -9 NIL 876974) (-365 874462 874512 874541 "FORTCAT" 874600 T FORTCAT (NIL) -9 NIL 874662) (-364 872522 873005 873404 "FORMULA" 874083 T FORMULA (NIL) -8 NIL NIL) (-363 872310 872340 872409 "FORMULA1" 872486 NIL FORMULA1 (NIL T) -7 NIL NIL) (-362 871833 871885 872058 "FORDER" 872252 NIL FORDER (NIL T T T T) -7 NIL NIL) (-361 870929 871093 871286 "FOP" 871660 T FOP (NIL) -7 NIL NIL) (-360 869537 870209 870383 "FNLA" 870811 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-359 868205 868594 868623 "FNCAT" 869195 T FNCAT (NIL) -9 NIL 869488) (-358 867771 868164 868192 "FNAME" 868197 T FNAME (NIL) -8 NIL NIL) (-357 866430 867403 867432 "FMTC" 867437 T FMTC (NIL) -9 NIL 867472) (-356 862750 863957 864584 "FMONOID" 865836 NIL FMONOID (NIL T) -8 NIL NIL) (-355 861972 862495 862642 "FM" 862647 NIL FM (NIL T T) -8 NIL NIL) (-354 859395 860041 860070 "FMFUN" 861214 T FMFUN (NIL) -9 NIL 861922) (-353 858663 858844 858873 "FMC" 859163 T FMC (NIL) -9 NIL 859345) (-352 855893 856727 856781 "FMCAT" 857963 NIL FMCAT (NIL T T) -9 NIL 858456) (-351 854788 855661 855760 "FM1" 855838 NIL FM1 (NIL T T) -8 NIL NIL) (-350 852562 852978 853472 "FLOATRP" 854339 NIL FLOATRP (NIL T) -7 NIL NIL) (-349 846049 850218 850848 "FLOAT" 851952 T FLOAT (NIL) -8 NIL NIL) (-348 843487 843987 844565 "FLOATCP" 845516 NIL FLOATCP (NIL T) -7 NIL NIL) (-347 842276 843124 843165 "FLINEXP" 843170 NIL FLINEXP (NIL T) -9 NIL 843262) (-346 841431 841666 841993 "FLINEXP-" 841998 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-345 840507 840651 840875 "FLASORT" 841283 NIL FLASORT (NIL T T) -7 NIL NIL) (-344 837725 838567 838620 "FLALG" 839847 NIL FLALG (NIL T T) -9 NIL 840314) (-343 831516 835212 835254 "FLAGG" 836516 NIL FLAGG (NIL T) -9 NIL 837164) (-342 830242 830581 831071 "FLAGG-" 831076 NIL FLAGG- (NIL T T) -8 NIL NIL) (-341 829284 829427 829654 "FLAGG2" 830095 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-340 826259 827277 827337 "FINRALG" 828465 NIL FINRALG (NIL T T) -9 NIL 828970) (-339 825419 825648 825987 "FINRALG-" 825992 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-338 824825 825038 825067 "FINITE" 825263 T FINITE (NIL) -9 NIL 825370) (-337 817285 819446 819487 "FINAALG" 823154 NIL FINAALG (NIL T) -9 NIL 824606) (-336 812626 813667 814811 "FINAALG-" 816190 NIL FINAALG- (NIL T T) -8 NIL NIL) (-335 812021 812381 812484 "FILE" 812556 NIL FILE (NIL T) -8 NIL NIL) (-334 810705 811017 811072 "FILECAT" 811756 NIL FILECAT (NIL T T) -9 NIL 811972) (-333 808520 810076 810105 "FIELD" 810145 T FIELD (NIL) -9 NIL 810225) (-332 807140 807525 808036 "FIELD-" 808041 NIL FIELD- (NIL T) -8 NIL NIL) (-331 804955 805777 806123 "FGROUP" 806827 NIL FGROUP (NIL T) -8 NIL NIL) (-330 804045 804209 804429 "FGLMICPK" 804787 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-329 799847 803970 804027 "FFX" 804032 NIL FFX (NIL T NIL) -8 NIL NIL) (-328 799448 799509 799644 "FFSLPE" 799780 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-327 795444 796220 797016 "FFPOLY" 798684 NIL FFPOLY (NIL T) -7 NIL NIL) (-326 794948 794984 795193 "FFPOLY2" 795402 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-325 790770 794867 794930 "FFP" 794935 NIL FFP (NIL T NIL) -8 NIL NIL) (-324 786138 790681 790745 "FF" 790750 NIL FF (NIL NIL NIL) -8 NIL NIL) (-323 781234 785481 785671 "FFNBX" 785992 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-322 776144 780369 780627 "FFNBP" 781088 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-321 770747 775428 775639 "FFNB" 775977 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-320 769579 769777 770092 "FFINTBAS" 770544 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-319 765755 767995 768024 "FFIELDC" 768644 T FFIELDC (NIL) -9 NIL 769020) (-318 764418 764788 765285 "FFIELDC-" 765290 NIL FFIELDC- (NIL T) -8 NIL NIL) (-317 763988 764033 764157 "FFHOM" 764360 NIL FFHOM (NIL T T T) -7 NIL NIL) (-316 761686 762170 762687 "FFF" 763503 NIL FFF (NIL T) -7 NIL NIL) (-315 757274 761428 761529 "FFCGX" 761629 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-314 752876 757006 757113 "FFCGP" 757217 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-313 748029 752603 752711 "FFCG" 752812 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-312 729828 738951 739038 "FFCAT" 744203 NIL FFCAT (NIL T T T) -9 NIL 745688) (-311 725026 726073 727387 "FFCAT-" 728617 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-310 724437 724480 724715 "FFCAT2" 724977 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-309 713641 717431 718646 "FEXPR" 723294 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-308 712643 713078 713120 "FEVALAB" 713204 NIL FEVALAB (NIL T) -9 NIL 713462) (-307 711802 712012 712350 "FEVALAB-" 712355 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-306 710395 711185 711388 "FDIV" 711701 NIL FDIV (NIL T T T T) -8 NIL NIL) (-305 707461 708176 708292 "FDIVCAT" 709860 NIL FDIVCAT (NIL T T T T) -9 NIL 710297) (-304 707223 707250 707420 "FDIVCAT-" 707425 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-303 706443 706530 706807 "FDIV2" 707130 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-302 705136 705393 705680 "FCPAK1" 706176 T FCPAK1 (NIL) -7 NIL NIL) (-301 704264 704636 704777 "FCOMP" 705027 NIL FCOMP (NIL T) -8 NIL NIL) (-300 687904 691316 694876 "FC" 700724 T FC (NIL) -8 NIL NIL) (-299 680453 684499 684540 "FAXF" 686342 NIL FAXF (NIL T) -9 NIL 687032) (-298 677732 678387 679212 "FAXF-" 679677 NIL FAXF- (NIL T T) -8 NIL NIL) (-297 672838 677108 677284 "FARRAY" 677589 NIL FARRAY (NIL T) -8 NIL NIL) (-296 668184 670255 670308 "FAMR" 671320 NIL FAMR (NIL T T) -9 NIL 671777) (-295 667075 667377 667811 "FAMR-" 667816 NIL FAMR- (NIL T T T) -8 NIL NIL) (-294 666271 666997 667050 "FAMONOID" 667055 NIL FAMONOID (NIL T) -8 NIL NIL) (-293 664104 664788 664842 "FAMONC" 665783 NIL FAMONC (NIL T T) -9 NIL 666167) (-292 662798 663860 663996 "FAGROUP" 664001 NIL FAGROUP (NIL T) -8 NIL NIL) (-291 660601 660920 661322 "FACUTIL" 662479 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-290 659700 659885 660107 "FACTFUNC" 660411 NIL FACTFUNC (NIL T) -7 NIL NIL) (-289 652023 658951 659163 "EXPUPXS" 659556 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-288 649522 650058 650640 "EXPRTUBE" 651461 T EXPRTUBE (NIL) -7 NIL NIL) (-287 645716 646308 647045 "EXPRODE" 648861 NIL EXPRODE (NIL T T) -7 NIL NIL) (-286 630884 644381 644804 "EXPR" 645325 NIL EXPR (NIL T) -8 NIL NIL) (-285 625312 625899 626711 "EXPR2UPS" 630182 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-284 624948 625005 625112 "EXPR2" 625249 NIL EXPR2 (NIL T T) -7 NIL NIL) (-283 616302 624085 624380 "EXPEXPAN" 624786 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-282 616129 616259 616288 "EXIT" 616293 T EXIT (NIL) -8 NIL NIL) (-281 615756 615818 615931 "EVALCYC" 616061 NIL EVALCYC (NIL T) -7 NIL NIL) (-280 615296 615414 615456 "EVALAB" 615626 NIL EVALAB (NIL T) -9 NIL 615730) (-279 614777 614899 615120 "EVALAB-" 615125 NIL EVALAB- (NIL T T) -8 NIL NIL) (-278 612239 613551 613580 "EUCDOM" 614135 T EUCDOM (NIL) -9 NIL 614485) (-277 610644 611086 611676 "EUCDOM-" 611681 NIL EUCDOM- (NIL T) -8 NIL NIL) (-276 598257 600996 603727 "ESTOOLS" 607933 T ESTOOLS (NIL) -7 NIL NIL) (-275 597893 597950 598057 "ESTOOLS2" 598194 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-274 597644 597686 597766 "ESTOOLS1" 597845 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-273 591583 593307 593336 "ES" 596100 T ES (NIL) -9 NIL 597504) (-272 586531 587817 589634 "ES-" 589798 NIL ES- (NIL T) -8 NIL NIL) (-271 582938 583690 584462 "ESCONT" 585779 T ESCONT (NIL) -7 NIL NIL) (-270 582683 582715 582797 "ESCONT1" 582900 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-269 582358 582408 582508 "ES2" 582627 NIL ES2 (NIL T T) -7 NIL NIL) (-268 581988 582046 582155 "ES1" 582294 NIL ES1 (NIL T T) -7 NIL NIL) (-267 581204 581333 581509 "ERROR" 581832 T ERROR (NIL) -7 NIL NIL) (-266 574719 581063 581154 "EQTBL" 581159 NIL EQTBL (NIL T T) -8 NIL NIL) (-265 567184 570065 571498 "EQ" 573319 NIL -3015 (NIL T) -8 NIL NIL) (-264 566816 566873 566982 "EQ2" 567121 NIL EQ2 (NIL T T) -7 NIL NIL) (-263 562108 563154 564247 "EP" 565755 NIL EP (NIL T) -7 NIL NIL) (-262 561267 561831 561860 "ENTIRER" 561865 T ENTIRER (NIL) -9 NIL 561910) (-261 557723 559222 559592 "EMR" 561066 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-260 556867 557052 557107 "ELTAGG" 557487 NIL ELTAGG (NIL T T) -9 NIL 557697) (-259 556586 556648 556789 "ELTAGG-" 556794 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-258 556374 556403 556458 "ELTAB" 556542 NIL ELTAB (NIL T T) -9 NIL NIL) (-257 555500 555646 555845 "ELFUTS" 556225 NIL ELFUTS (NIL T T) -7 NIL NIL) (-256 555241 555297 555326 "ELEMFUN" 555431 T ELEMFUN (NIL) -9 NIL NIL) (-255 555111 555132 555200 "ELEMFUN-" 555205 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-254 550007 553210 553252 "ELAGG" 554192 NIL ELAGG (NIL T) -9 NIL 554653) (-253 548292 548726 549389 "ELAGG-" 549394 NIL ELAGG- (NIL T T) -8 NIL NIL) (-252 541162 542961 543787 "EFUPXS" 547569 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-251 534614 536415 537224 "EFULS" 540439 NIL EFULS (NIL T T T) -8 NIL NIL) (-250 532045 532403 532881 "EFSTRUC" 534246 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-249 521117 522682 524242 "EF" 530560 NIL EF (NIL T T) -7 NIL NIL) (-248 520218 520602 520751 "EAB" 520988 T EAB (NIL) -8 NIL NIL) (-247 519431 520177 520205 "E04UCFA" 520210 T E04UCFA (NIL) -8 NIL NIL) (-246 518644 519390 519418 "E04NAFA" 519423 T E04NAFA (NIL) -8 NIL NIL) (-245 517857 518603 518631 "E04MBFA" 518636 T E04MBFA (NIL) -8 NIL NIL) (-244 517070 517816 517844 "E04JAFA" 517849 T E04JAFA (NIL) -8 NIL NIL) (-243 516285 517029 517057 "E04GCFA" 517062 T E04GCFA (NIL) -8 NIL NIL) (-242 515500 516244 516272 "E04FDFA" 516277 T E04FDFA (NIL) -8 NIL NIL) (-241 514713 515459 515487 "E04DGFA" 515492 T E04DGFA (NIL) -8 NIL NIL) (-240 508899 510243 511605 "E04AGNT" 513371 T E04AGNT (NIL) -7 NIL NIL) (-239 507625 508105 508146 "DVARCAT" 508621 NIL DVARCAT (NIL T) -9 NIL 508819) (-238 506829 507041 507355 "DVARCAT-" 507360 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-237 499691 506631 506758 "DSMP" 506763 NIL DSMP (NIL T T T) -8 NIL NIL) (-236 494517 495648 496712 "DROPT" 498647 T DROPT (NIL) -8 NIL NIL) (-235 494182 494241 494339 "DROPT1" 494452 NIL DROPT1 (NIL T) -7 NIL NIL) (-234 489304 490428 491563 "DROPT0" 493067 T DROPT0 (NIL) -7 NIL NIL) (-233 487649 487974 488360 "DRAWPT" 488938 T DRAWPT (NIL) -7 NIL NIL) (-232 482324 483223 484278 "DRAW" 486647 NIL DRAW (NIL T) -7 NIL NIL) (-231 481965 482016 482132 "DRAWHACK" 482267 NIL DRAWHACK (NIL T) -7 NIL NIL) (-230 480710 480975 481262 "DRAWCX" 481698 T DRAWCX (NIL) -7 NIL NIL) (-229 480228 480296 480446 "DRAWCURV" 480636 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-228 470832 472754 474833 "DRAWCFUN" 478169 T DRAWCFUN (NIL) -7 NIL NIL) (-227 467651 469527 469569 "DQAGG" 470198 NIL DQAGG (NIL T) -9 NIL 470471) (-226 456111 462849 462932 "DPOLCAT" 464770 NIL DPOLCAT (NIL T T T T) -9 NIL 465313) (-225 450951 452297 454254 "DPOLCAT-" 454259 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-224 445035 450813 450910 "DPMO" 450915 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-223 439022 444816 444982 "DPMM" 444987 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-222 438784 438835 438909 "DOMAIN" 438968 T DOMAIN (NIL) -8 NIL NIL) (-221 432496 438421 438572 "DMP" 438685 NIL DMP (NIL NIL T) -8 NIL NIL) (-220 432096 432152 432296 "DLP" 432434 NIL DLP (NIL T) -7 NIL NIL) (-219 425746 431197 431424 "DLIST" 431901 NIL DLIST (NIL T) -8 NIL NIL) (-218 422599 424602 424644 "DLAGG" 425194 NIL DLAGG (NIL T) -9 NIL 425422) (-217 421261 421953 421982 "DIVRING" 422132 T DIVRING (NIL) -9 NIL 422240) (-216 420249 420502 420895 "DIVRING-" 420900 NIL DIVRING- (NIL T) -8 NIL NIL) (-215 418351 418708 419114 "DISPLAY" 419863 T DISPLAY (NIL) -7 NIL NIL) (-214 412246 418265 418328 "DIRPROD" 418333 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-213 411094 411297 411562 "DIRPROD2" 412039 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-212 400738 406737 406791 "DIRPCAT" 407199 NIL DIRPCAT (NIL NIL T) -9 NIL 408015) (-211 398064 398706 399587 "DIRPCAT-" 399924 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-210 397351 397511 397697 "DIOSP" 397898 T DIOSP (NIL) -7 NIL NIL) (-209 394060 396264 396306 "DIOPS" 396740 NIL DIOPS (NIL T) -9 NIL 396968) (-208 393609 393723 393914 "DIOPS-" 393919 NIL DIOPS- (NIL T T) -8 NIL NIL) (-207 392480 393118 393147 "DIFRING" 393334 T DIFRING (NIL) -9 NIL 393443) (-206 392126 392203 392355 "DIFRING-" 392360 NIL DIFRING- (NIL T) -8 NIL NIL) (-205 389917 391199 391240 "DIFEXT" 391599 NIL DIFEXT (NIL T) -9 NIL 391890) (-204 388203 388631 389296 "DIFEXT-" 389301 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-203 385531 387735 387777 "DIAGG" 387782 NIL DIAGG (NIL T) -9 NIL 387802) (-202 384915 385072 385324 "DIAGG-" 385329 NIL DIAGG- (NIL T T) -8 NIL NIL) (-201 380386 383874 384151 "DHMATRIX" 384684 NIL DHMATRIX (NIL T) -8 NIL NIL) (-200 375998 376907 377917 "DFSFUN" 379396 T DFSFUN (NIL) -7 NIL NIL) (-199 370784 374712 375077 "DFLOAT" 375653 T DFLOAT (NIL) -8 NIL NIL) (-198 369017 369298 369693 "DFINTTLS" 370492 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-197 366050 367052 367450 "DERHAM" 368684 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-196 363905 365825 365914 "DEQUEUE" 365994 NIL DEQUEUE (NIL T) -8 NIL NIL) (-195 363123 363256 363451 "DEGRED" 363767 NIL DEGRED (NIL T T) -7 NIL NIL) (-194 359539 360280 361128 "DEFINTRF" 362355 NIL DEFINTRF (NIL T) -7 NIL NIL) (-193 357078 357545 358141 "DEFINTEF" 359060 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-192 350909 356519 356685 "DECIMAL" 356932 T DECIMAL (NIL) -8 NIL NIL) (-191 348421 348879 349385 "DDFACT" 350453 NIL DDFACT (NIL T T) -7 NIL NIL) (-190 348017 348060 348211 "DBLRESP" 348372 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-189 345727 346061 346430 "DBASE" 347775 NIL DBASE (NIL T) -8 NIL NIL) (-188 344862 345686 345714 "D03FAFA" 345719 T D03FAFA (NIL) -8 NIL NIL) (-187 343998 344821 344849 "D03EEFA" 344854 T D03EEFA (NIL) -8 NIL NIL) (-186 341948 342414 342903 "D03AGNT" 343529 T D03AGNT (NIL) -7 NIL NIL) (-185 341266 341907 341935 "D02EJFA" 341940 T D02EJFA (NIL) -8 NIL NIL) (-184 340584 341225 341253 "D02CJFA" 341258 T D02CJFA (NIL) -8 NIL NIL) (-183 339902 340543 340571 "D02BHFA" 340576 T D02BHFA (NIL) -8 NIL NIL) (-182 339220 339861 339889 "D02BBFA" 339894 T D02BBFA (NIL) -8 NIL NIL) (-181 332419 334006 335612 "D02AGNT" 337634 T D02AGNT (NIL) -7 NIL NIL) (-180 330200 330719 331262 "D01WGTS" 331896 T D01WGTS (NIL) -7 NIL NIL) (-179 329307 330159 330187 "D01TRNS" 330192 T D01TRNS (NIL) -8 NIL NIL) (-178 328414 329266 329294 "D01GBFA" 329299 T D01GBFA (NIL) -8 NIL NIL) (-177 327521 328373 328401 "D01FCFA" 328406 T D01FCFA (NIL) -8 NIL NIL) (-176 326628 327480 327508 "D01ASFA" 327513 T D01ASFA (NIL) -8 NIL NIL) (-175 325735 326587 326615 "D01AQFA" 326620 T D01AQFA (NIL) -8 NIL NIL) (-174 324842 325694 325722 "D01APFA" 325727 T D01APFA (NIL) -8 NIL NIL) (-173 323949 324801 324829 "D01ANFA" 324834 T D01ANFA (NIL) -8 NIL NIL) (-172 323056 323908 323936 "D01AMFA" 323941 T D01AMFA (NIL) -8 NIL NIL) (-171 322163 323015 323043 "D01ALFA" 323048 T D01ALFA (NIL) -8 NIL NIL) (-170 321270 322122 322150 "D01AKFA" 322155 T D01AKFA (NIL) -8 NIL NIL) (-169 320377 321229 321257 "D01AJFA" 321262 T D01AJFA (NIL) -8 NIL NIL) (-168 313709 315251 316803 "D01AGNT" 318845 T D01AGNT (NIL) -7 NIL NIL) (-167 313046 313174 313326 "CYCLOTOM" 313577 T CYCLOTOM (NIL) -7 NIL NIL) (-166 309781 310494 311221 "CYCLES" 312339 T CYCLES (NIL) -7 NIL NIL) (-165 309093 309227 309398 "CVMP" 309642 NIL CVMP (NIL T) -7 NIL NIL) (-164 306875 307132 307507 "CTRIGMNP" 308821 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-163 306249 306348 306501 "CSTTOOLS" 306772 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-162 302048 302705 303463 "CRFP" 305561 NIL CRFP (NIL T T) -7 NIL NIL) (-161 301095 301280 301508 "CRAPACK" 301852 NIL CRAPACK (NIL T) -7 NIL NIL) (-160 300481 300582 300785 "CPMATCH" 300972 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-159 300206 300234 300340 "CPIMA" 300447 NIL CPIMA (NIL T T T) -7 NIL NIL) (-158 296570 297242 297960 "COORDSYS" 299541 NIL COORDSYS (NIL T) -7 NIL NIL) (-157 292431 294573 295065 "CONTFRAC" 296110 NIL CONTFRAC (NIL T) -8 NIL NIL) (-156 291584 292148 292177 "COMRING" 292182 T COMRING (NIL) -9 NIL 292233) (-155 290665 290942 291126 "COMPPROP" 291420 T COMPPROP (NIL) -8 NIL NIL) (-154 290326 290361 290489 "COMPLPAT" 290624 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-153 280309 290137 290245 "COMPLEX" 290250 NIL COMPLEX (NIL T) -8 NIL NIL) (-152 279945 280002 280109 "COMPLEX2" 280246 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-151 279663 279698 279796 "COMPFACT" 279904 NIL COMPFACT (NIL T T) -7 NIL NIL) (-150 263943 274237 274278 "COMPCAT" 275280 NIL COMPCAT (NIL T) -9 NIL 276656) (-149 253459 256382 260009 "COMPCAT-" 260365 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-148 253190 253218 253320 "COMMUPC" 253425 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-147 252985 253018 253077 "COMMONOP" 253151 T COMMONOP (NIL) -7 NIL NIL) (-146 252568 252736 252823 "COMM" 252918 T COMM (NIL) -8 NIL NIL) (-145 251822 252014 252043 "COMBOPC" 252379 T COMBOPC (NIL) -9 NIL 252552) (-144 250718 250928 251170 "COMBINAT" 251612 NIL COMBINAT (NIL T) -7 NIL NIL) (-143 246924 247495 248133 "COMBF" 250142 NIL COMBF (NIL T T) -7 NIL NIL) (-142 245710 246040 246275 "COLOR" 246709 T COLOR (NIL) -8 NIL NIL) (-141 245350 245397 245522 "CMPLXRT" 245657 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-140 240908 241922 242988 "CLIP" 244304 T CLIP (NIL) -7 NIL NIL) (-139 239246 240016 240254 "CLIF" 240736 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-138 235477 237395 237437 "CLAGG" 238366 NIL CLAGG (NIL T) -9 NIL 238899) (-137 233899 234356 234939 "CLAGG-" 234944 NIL CLAGG- (NIL T T) -8 NIL NIL) (-136 233443 233528 233668 "CINTSLPE" 233808 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-135 230944 231415 231963 "CHVAR" 232971 NIL CHVAR (NIL T T T) -7 NIL NIL) (-134 230166 230730 230759 "CHARZ" 230764 T CHARZ (NIL) -9 NIL 230778) (-133 229920 229960 230038 "CHARPOL" 230120 NIL CHARPOL (NIL T) -7 NIL NIL) (-132 229026 229623 229652 "CHARNZ" 229699 T CHARNZ (NIL) -9 NIL 229754) (-131 227049 227716 228051 "CHAR" 228711 T CHAR (NIL) -8 NIL NIL) (-130 226774 226835 226864 "CFCAT" 226975 T CFCAT (NIL) -9 NIL NIL) (-129 226019 226130 226312 "CDEN" 226658 NIL CDEN (NIL T T T) -7 NIL NIL) (-128 222011 225172 225452 "CCLASS" 225759 T CCLASS (NIL) -8 NIL NIL) (-127 217064 218040 218793 "CARTEN" 221314 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-126 216172 216320 216541 "CARTEN2" 216911 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-125 214469 215324 215580 "CARD" 215936 T CARD (NIL) -8 NIL NIL) (-124 213841 214169 214198 "CACHSET" 214330 T CACHSET (NIL) -9 NIL 214407) (-123 213337 213633 213662 "CABMON" 213712 T CABMON (NIL) -9 NIL 213768) (-122 210900 213029 213136 "BTREE" 213263 NIL BTREE (NIL T) -8 NIL NIL) (-121 208404 210548 210670 "BTOURN" 210810 NIL BTOURN (NIL T) -8 NIL NIL) (-120 205828 207875 207917 "BTCAT" 207985 NIL BTCAT (NIL T) -9 NIL 208062) (-119 205495 205575 205724 "BTCAT-" 205729 NIL BTCAT- (NIL T T) -8 NIL NIL) (-118 200685 204556 204585 "BTAGG" 204841 T BTAGG (NIL) -9 NIL 205020) (-117 200108 200252 200482 "BTAGG-" 200487 NIL BTAGG- (NIL T) -8 NIL NIL) (-116 197158 199386 199601 "BSTREE" 199925 NIL BSTREE (NIL T) -8 NIL NIL) (-115 196296 196422 196606 "BRILL" 197014 NIL BRILL (NIL T) -7 NIL NIL) (-114 193004 195025 195067 "BRAGG" 195716 NIL BRAGG (NIL T) -9 NIL 195972) (-113 191533 191939 192494 "BRAGG-" 192499 NIL BRAGG- (NIL T T) -8 NIL NIL) (-112 184741 190879 191063 "BPADICRT" 191381 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-111 183045 184678 184723 "BPADIC" 184728 NIL BPADIC (NIL NIL) -8 NIL NIL) (-110 182745 182775 182888 "BOUNDZRO" 183009 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-109 178260 179351 180218 "BOP" 181898 T BOP (NIL) -8 NIL NIL) (-108 175883 176327 176846 "BOP1" 177774 NIL BOP1 (NIL T) -7 NIL NIL) (-107 174236 174926 175220 "BOOLEAN" 175609 T BOOLEAN (NIL) -8 NIL NIL) (-106 173602 173980 174033 "BMODULE" 174038 NIL BMODULE (NIL T T) -9 NIL 174102) (-105 169412 173400 173473 "BITS" 173549 T BITS (NIL) -8 NIL NIL) (-104 168509 168944 169096 "BINFILE" 169280 T BINFILE (NIL) -8 NIL NIL) (-103 162344 167953 168118 "BINARY" 168364 T BINARY (NIL) -8 NIL NIL) (-102 160177 161599 161641 "BGAGG" 161901 NIL BGAGG (NIL T) -9 NIL 162038) (-101 160008 160040 160131 "BGAGG-" 160136 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 159106 159392 159597 "BFUNCT" 159823 T BFUNCT (NIL) -8 NIL NIL) (-99 157809 157987 158271 "BEZOUT" 158931 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154340 156669 156997 "BBTREE" 157512 NIL BBTREE (NIL T) -8 NIL NIL) (-97 154077 154130 154157 "BASTYPE" 154274 T BASTYPE (NIL) -9 NIL NIL) (-96 153933 153961 154031 "BASTYPE-" 154036 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153371 153447 153597 "BALFACT" 153844 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 152193 152790 152975 "AUTOMOR" 153216 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151918 151923 151950 "ATTREG" 151955 T ATTREG (NIL) -9 NIL NIL) (-92 150197 150615 150967 "ATTRBUT" 151584 T ATTRBUT (NIL) -8 NIL NIL) (-91 149732 149845 149872 "ATRIG" 150073 T ATRIG (NIL) -9 NIL NIL) (-90 149541 149582 149669 "ATRIG-" 149674 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147744 149317 149405 "ASTACK" 149484 NIL ASTACK (NIL T) -8 NIL NIL) (-88 146251 146548 146912 "ASSOCEQ" 147427 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 145283 145910 146034 "ASP9" 146158 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 145047 145231 145270 "ASP8" 145275 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143917 144652 144794 "ASP80" 144936 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142816 143552 143684 "ASP7" 143816 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141772 142493 142611 "ASP78" 142729 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140743 141452 141569 "ASP77" 141686 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139658 140381 140512 "ASP74" 140643 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138559 139293 139425 "ASP73" 139557 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137514 138236 138354 "ASP6" 138472 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136463 137191 137309 "ASP55" 137427 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135413 136137 136256 "ASP50" 136375 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134501 135114 135224 "ASP4" 135334 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133589 134202 134312 "ASP49" 134422 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132374 133128 133296 "ASP42" 133478 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 131152 131907 132077 "ASP41" 132261 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 130104 130829 130947 "ASP35" 131065 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129869 130052 130091 "ASP34" 130096 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129606 129673 129749 "ASP33" 129824 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128502 129241 129373 "ASP31" 129505 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 128267 128450 128489 "ASP30" 128494 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 128002 128071 128147 "ASP29" 128222 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127767 127950 127989 "ASP28" 127994 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127532 127715 127754 "ASP27" 127759 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126616 127230 127341 "ASP24" 127452 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125533 126257 126387 "ASP20" 126517 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124621 125234 125344 "ASP1" 125454 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123565 124295 124414 "ASP19" 124533 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 123302 123369 123445 "ASP12" 123520 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 122155 122901 123045 "ASP10" 123189 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 120060 121999 122090 "ARRAY2" 122095 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115882 119708 119822 "ARRAY1" 119977 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114914 115087 115308 "ARRAY12" 115705 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 109279 111144 111220 "ARR2CAT" 113850 NIL ARR2CAT (NIL T T T) -9 NIL 114608) (-54 106713 107457 108411 "ARR2CAT-" 108416 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105473 105623 105926 "APPRULE" 106551 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 105126 105174 105292 "APPLYORE" 105419 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 104100 104391 104586 "ANY" 104949 T ANY (NIL) -8 NIL NIL) (-50 103378 103501 103658 "ANY1" 103974 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100910 101828 102153 "ANTISYM" 103103 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100737 100869 100896 "ANON" 100901 T ANON (NIL) -8 NIL NIL) (-47 94814 99282 99733 "AN" 100304 T AN (NIL) -8 NIL NIL) (-46 91126 92524 92575 "AMR" 93314 NIL AMR (NIL T T) -9 NIL 93907) (-45 90239 90460 90822 "AMR-" 90827 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74801 90156 90217 "ALIST" 90222 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71638 74395 74564 "ALGSC" 74719 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 68196 68750 69356 "ALGPKG" 71079 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 67473 67574 67758 "ALGMFACT" 68082 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 63230 63911 64561 "ALGMANIP" 67001 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 54549 62856 63006 "ALGFF" 63163 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53745 53876 54055 "ALGFACT" 54407 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52735 53345 53384 "ALGEBRA" 53444 NIL ALGEBRA (NIL T) -9 NIL 53502) (-36 52453 52512 52644 "ALGEBRA-" 52649 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34174 49899 49952 "ALAGG" 50088 NIL ALAGG (NIL T T) -9 NIL 50249) (-34 33709 33822 33849 "AHYP" 34050 T AHYP (NIL) -9 NIL NIL) (-33 32640 32888 32915 "AGG" 33414 T AGG (NIL) -9 NIL 33692) (-32 32074 32236 32450 "AGG-" 32455 NIL AGG- (NIL T) -8 NIL NIL) (-31 29763 30181 30597 "AF" 31718 NIL AF (NIL T T) -7 NIL NIL) (-30 29041 29295 29449 "ACPLOT" 29627 T ACPLOT (NIL) -8 NIL NIL) (-29 18460 26406 26458 "ACFS" 27169 NIL ACFS (NIL T) -9 NIL 27408) (-28 16474 16964 17739 "ACFS-" 17744 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12694 14650 14677 "ACF" 15556 T ACF (NIL) -9 NIL 15968) (-26 11398 11732 12225 "ACF-" 12230 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11192 "ABELSG" 11284 T ABELSG (NIL) -9 NIL 11349) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10232 10493 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9896 9980 10118 "ABELMON-" 10123 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9230 9576 9603 "ABELGRP" 9728 T ABELGRP (NIL) -9 NIL 9810) (-20 8693 8822 9038 "ABELGRP-" 9043 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8029 8069 "A1AGG" 8074 NIL A1AGG (NIL T) -9 NIL 8114) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index f5470b67..9f1e5471 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,2979 +1,2981 @@
 
-(682155 . 3403927926)        
-(((*1 *2 *1) (-12 (-5 *2 (-703)) (-5 *1 (-1062 *3 *4)) (-14 *3 (-843)) (-4 *4 (-961))))) 
-(((*1 *2 *3) (-12 (-4 *4 (-421)) (-4 *5 (-725)) (-4 *6 (-779)) (-5 *2 (-517)) (-5 *1 (-418 *4 *5 *6 *3)) (-4 *3 (-871 *4 *5 *6))))) 
-(((*1 *2 *3 *4) (-12 (-5 *3 (-199)) (-5 *4 (-517)) (-5 *2 (-950)) (-5 *1 (-691))))) 
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-(((*1 *2 *2) (-12 (-5 *2 (-843)) (-5 *1 (-327 *3)) (-4 *3 (-319))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1056)) (-5 *1 (-131)))) ((*1 *1 *2) (-12 (-5 *2 (-517)) (-5 *1 (-131))))) 
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\ No newline at end of file
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(-3899 . 48751) (-3900 . 48670) (-3901 . 48581) (-3902 . 48286) (-3903 . 48213) (-3904 . 48162) (-3905 . 48098) (-3906 . 48008) (-3907 . 47904) (-3908 . 47829) (-3909 . 47713) (-3910 . 47510) (-3911 . 47437) (-3912 . 47242) (-3913 . 46708) (-3914 . 46649) (-3915 . 46566) (-3916 . 46325) (-3917 . 46022) (-3918 . 45887) (-3919 . 45724) (-3920 . 45641) (-3921 . 45610) (-3922 . 45445) (-3923 . 45236) (-3924 . 45034) (-3925 . 44710) (-3926 . 44588) (-3927 . 44392) (-3928 . 44232) (-3929 . 43910) (-3930 . 43836) (-3931 . 43769) (-3932 . 43589) (-3933 . 43511) (-3934 . 43064) (-3935 . 42889) (-3936 . 42174) (-3937 . 42105) (-3938 . 41685) (-3939 . 41535) (-3940 . 41206) (-3941 . 40776) (-3942 . 40161) (-3943 . 39972) (-3944 . 39899) (-3945 . 39798) (-3946 . 39553) (-3947 . 39351) (-3948 . 38734) (-3949 . 38519) (-3950 . 38381) (-3951 . 38309) (-3952 . 38074) (-3953 . 37956) (-3954 . 37648) (-3955 . 37544) (-3956 . 37431) (-3957 . 37378) (-3958 . 37294) (-3959 . 37097) (-3960 . 37024) (-3961 . 36886) (-3962 . 36207) (-3963 . 36154) (-3964 . 35593) (-3965 . 35235) (-3966 . 35136) (-3967 . 35029) (-3968 . 34936) (-3969 . 34884) (-3970 . 34810) (-3971 . 34711) (-3972 . 34601) (-3973 . 34092) (-3974 . 33978) (-3975 . 33819) (-3976 . 33764) (-3977 . 33420) (-3978 . 33350) (-3979 . 33176) (-3980 . 33028) (-3981 . 32940) (-3982 . 32704) (-3983 . 32655) (-3984 . 32506) (-3985 . 32433) (-3986 . 32354) (-3987 . 32225) (-3988 . 31894) (-3989 . 31785) (-3990 . 31702) (-3991 . 31634) (-3992 . 31335) (-3993 . 30417) (-3994 . 30226) (-3995 . 30044) (-3996 . 29946) (-3997 . 29857) (-3998 . 29804) (-3999 . 29726) (-4000 . 29640) (-4001 . 29579) (-4002 . 29475) (-4003 . 29447) (-4004 . 29288) (-4005 . 29218) (-4006 . 29186) (-4007 . 27177) (-4008 . 27068) (-4009 . 26813) (-4010 . 26704) (-4011 . 26583) (-4012 . 26342) (-4013 . 26193) (-4014 . 26043) (-4015 . 25927) (-4016 . 25839) (-4017 . 25720) (-4018 . 25438) (-4019 . 25321) (-4020 . 25001) (-4021 . 24942) (-4022 . 24790) (-4023 . 24738) (-4024 . 24584) (-4025 . 24525) (-4026 . 24432) (-4027 . 24224) (-4028 . 24130) (-4029 . 24054) (-4030 . 23852) (-4031 . 23765) (-4032 . 23631) (-4033 . 23536) (-4034 . 23437) (-4035 . 23362) (-4036 . 23174) (-4037 . 22926) (-4038 . 22687) (-4039 . 22588) (-4040 . 22226) (-4041 . 22129) (-4042 . 21457) (-4043 . 21332) (-4044 . 21199) (-4045 . 21047) (-4046 . 20900) (-4047 . 20529) (-4048 . 20393) (-4049 . 20337) (-4050 . 20032) (-4051 . 19958) (-4052 . 19822) (-4053 . 19492) (-4054 . 19412) (-4055 . 19274) (-4056 . 19208) (-4057 . 19153) (-4058 . 19093) (-4059 . 18915) (-4060 . 18038) (-4061 . 18001) (-4062 . 17901) (-4063 . 17775) (-4064 . 17619) (-4065 . 17192) (-4066 . 17137) (-4067 . 17071) (-4068 . 16974) (-4069 . 16811) (-4070 . 16712) (-4071 . 16655) (-4072 . 16574) (-4073 . 16522) (-4074 . 16494) (-4075 . 16442) (-4076 . 16252) (-4077 . 16200) (-4078 . 15528) (-4079 . 15373) (-4080 . 15211) (-4081 . 15155) (-4082 . 15121) (-4083 . 14882) (-4084 . 14825) (-4085 . 14670) (-4086 . 14577) (-4087 . 14392) (-4088 . 14312) (-4089 . 14177) (-4090 . 14022) (-4091 . 13940) (-4092 . 13764) (-4093 . 13690) (-4094 . 13659) (-4095 . 13504) (-4096 . 13384) (-4097 . 13306) (-4098 . 13216) (-4099 . 13114) (-4100 . 12957) (-4101 . 12755) (-4102 . 12638) (-4103 . 12398) (-4104 . 12327) (-4105 . 12188) (-4106 . 12033) (-4107 . 11971) (-4108 . 11699) (-4109 . 11611) (-4110 . 11553) (-4111 . 11491) (-4112 . 11437) (-4113 . 11269) (-4114 . 11216) (-4115 . 11104) (-4116 . 10954) (-4117 . 10799) (-4118 . 10771) (-4119 . 10696) (-4120 . 10601) (-4121 . 9764) (-4122 . 9531) (-4123 . 8825) (-4124 . 8676) (-4125 . 8570) (-4126 . 8172) (-4127 . 7977) (-4128 . 7441) (-4129 . 7189) (-4130 . 6967) (-4131 . 6858) (-4132 . 6404) (-4133 . 6171) (-4134 . 6016) (-4135 . 5893) (-4136 . 5810) (-4137 . 5527) (-4138 . 5421) (-4139 . 5240) (-4140 . 4942) (-4141 . 4795) (-4142 . 4569) (-4143 . 4512) (-4144 . 4387) (-4145 . 3998) (-4146 . 3873) (-4147 . 3739) (-4148 . 3662) (-4149 . 3589) (-4150 . 3492) (-4151 . 3442) (-4152 . 3086) (-4153 . 2818) (-4154 . 2703) (-4155 . 2495) (-4156 . 2393) (-4157 . 2340) (-4158 . 1705) (-4159 . 1104) (-4160 . 1022) (-4161 . 969) (-4162 . 867) (-4163 . 30)) 
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