* interp/sys-constants.boot ($BuiltinAttributes): Remove

	finiteAggregate and shallowlyMutable.
	* interp/daase.lisp (WRITE-COMPRESS): Do not push strings.

5 files changed, 20208 insertions, 20209 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 35b97233..227263fd 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,4788 +1,4788 @@
 
-(1966230 . 3580478883)       
-(-18 A S) 
+(1966199 . 3581069279)       
+(-15 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the shallowly mutable property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
-(-19 S) 
+(-16 S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the shallowly mutable property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
-(-20 S) 
+(-17 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
 NIL 
 NIL 
-(-21) 
+(-18) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
 NIL 
 NIL 
-(-22 S) 
+(-19 S) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (|opposite?| (((|Boolean|) $ $) "\\spad{opposite?(x,y)} holds if the sum of \\spad{x} and \\spad{y} is \\spad{0}.")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element."))) 
 NIL 
 NIL 
-(-23) 
+(-20) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (|opposite?| (((|Boolean|) $ $) "\\spad{opposite?(x,y)} holds if the sum of \\spad{x} and \\spad{y} is \\spad{0}.")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element."))) 
 NIL 
 NIL 
-(-24 S) 
+(-21 S) 
 ((|constructor| (NIL "the class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-25) 
+(-22) 
 ((|constructor| (NIL "the class of all additive (commutative) semigroups,{} \\spadignore{i.e.} a set with a commutative and associative operation \\spadop{+}. \\blankline")) (* (($ (|PositiveInteger|) $) "\\spad{n*x} computes the left-multiplication of \\spad{x} by the positive integer \\spad{n}. This is equivalent to adding \\spad{x} to itself \\spad{n} times.")) (+ (($ $ $) "\\spad{x+y} computes the sum of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-26 S) 
+(-23 S) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
 NIL 
 NIL 
-(-27) 
+(-24) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-28 S R) 
+(-25 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
 NIL 
 NIL 
-(-29 R) 
+(-26 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3998 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3994 . T) (-3999 . T) (-3993 . T)) 
+((-3994 . T) (-3992 . T) (-3991 . T) ((-3997 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T)) 
 NIL 
-(-30) 
+(-27) 
 ((|refine| (($ $ (|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) 
+(-28) 
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3098) 
+(-29 R -3095) 
 ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-954 (-488))))) 
-(-33 S) 
+((|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+(-30 S) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\"")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
 NIL 
-(-34) 
+(-31) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\"")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
 NIL 
-(-35) 
+(-32) 
 ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-36 |Key| |Entry|) 
+(-33 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table.	It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}."))) 
 NIL 
 NIL 
-(-37 S R) 
+(-34 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
 NIL 
 NIL 
-(-38 R) 
+(-35 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-39 UP) 
+(-36 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3098 UP UPUP -2620) 
+(-37 -3095 UP UPUP -2617) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
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+(-38 R -3095) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
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-(-42 OV E P) 
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+(-39 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
 NIL 
-(-43 R A) 
+(-40 R A) 
 ((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-260)))) 
-(-44 R |n| |ls| |gamma|) 
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+(-41 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
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-(-45 |Key| |Entry|) 
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 ((|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."))) 
 NIL 
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-(-46 S R E) 
+((OR (-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|))) (-11 (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|)))))) 
+(-43 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.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-314)))) 
-(-47 R E) 
+((|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-311)))) 
+(-44 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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.")) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-48) 
+(-45) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| $ (QUOTE (-965))) (|HasCategory| $ (QUOTE (-954 (-488))))) 
-(-49) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+(-46) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) 
 NIL 
 NIL 
-(-50 R |lVar|) 
+(-47 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|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}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-51) 
+(-48) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
 NIL 
 NIL 
-(-52 S) 
+(-49 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}."))) 
 NIL 
 NIL 
-(-53 R M P) 
+(-50 R M P) 
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3098) 
+(-51 |Base| R -3095) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) 
 NIL 
 NIL 
-(-55) 
+(-52) 
 ((|constructor| (NIL "This domain implements the arity of a function or an operator,{} \\spadignore{e.g.} the number of arguments that an operator can take. An arity is either a definition nonnegative integer,{} and the special value `arbitrary',{} signifying that an operation can take any number of arguments.")) (|one?| (((|Boolean|) $) "\\spad{one? a} holds if \\spad{a} is the arity of nullary function.")) (|zero?| (((|Boolean|) $) "\\spad{zero? a} holds if \\spad{a} is the arity of niladic function.")) (|arbitrary| (($) "aribitrary is the arity of a function that accepts any number of arguments."))) 
 NIL 
 NIL 
-(-56 S R |Row| |Col|) 
+(-53 S 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| |#2| |#2| |#2|) $ $ |#2|) "\\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| |#2| |#2| |#2|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#4|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#3|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\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| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|column| ((|#4| $ (|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| ((|#3| $ (|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| ((|#2| $ (|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| ((|#2| $ (|Integer|) (|Integer|) |#2|) "\\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") ((|#2| $ (|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|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#2|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#2|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}"))) 
 NIL 
 NIL 
-(-57 R |Row| |Col|) 
+(-54 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| |#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|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}"))) 
 NIL 
 NIL 
-(-58 S) 
+(-55 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}"))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-59 A B) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-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),...]}."))) 
 NIL 
 NIL 
-(-60 R) 
+(-57 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-61 R L) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-58 R L) 
 ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314)))) 
-(-62 S) 
+((|HasCategory| |#1| (QUOTE (-311)))) 
+(-59 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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-63 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-60 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
 NIL 
-(-64) 
+(-61) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
 NIL 
-(-65 S) 
+(-62 S) 
 ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-66) 
+(-63) 
 ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-67) 
+(-64) 
 ((|constructor| (NIL "This domain represents the syntax of an attribute in \\indented{2}{a category expression.}")) (|name| (((|SpadAst|) $) "\\spad{name(a)} returns the name of the attribute `a'. Note,{} this name may be domain name,{} not just an identifier."))) 
 NIL 
 NIL 
-(-68) 
+(-65) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4003 "*") . T) (-3998 . T) (-3996 . T) (-3995 . T) (-3994 . T) (-3999 . T) (-3993 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3997 . T) (-4000 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3988 . T)) 
+(((-3997 "*") . T) (-3994 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3993 . T) (-3996 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3984 . T)) 
 NIL 
-(-69 R) 
+(-66 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}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-70 R UP) 
+(-67 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
 NIL 
 NIL 
-(-71 S) 
+(-68 S) 
 ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (|before?| (((|Boolean|) $ $) "\\spad{before?(x,y)} holds if the system representation of \\spad{x} comes before that of \\spad{y} in a an implementation defined manner.")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) 
 NIL 
 NIL 
-(-72) 
+(-69) 
 ((|constructor| (NIL "\\spadtype{BasicType} is the basic category for describing a collection of elements with \\spadop{=} (equality).")) (|before?| (((|Boolean|) $ $) "\\spad{before?(x,y)} holds if the system representation of \\spad{x} comes before that of \\spad{y} in a an implementation defined manner.")) (~= (((|Boolean|) $ $) "\\spad{x~=y} tests if \\spad{x} and \\spad{y} are not equal.")) (= (((|Boolean|) $ $) "\\spad{x=y} tests if \\spad{x} and \\spad{y} are equal."))) 
 NIL 
 NIL 
-(-73 S) 
+(-70 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-74 R UP M |Row| |Col|) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-71 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 (-4003 "*")))) 
-(-75 A S) 
+((|HasAttribute| |#1| (QUOTE (-3997 "*")))) 
+(-72 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) 
 NIL 
 NIL 
-(-76 S) 
+(-73 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}."))) 
 NIL 
 NIL 
-(-77) 
+(-74) 
 ((|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."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) 
-(-78) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-117))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-329)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-188))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-259 (-485)))) (|HasCategory| (-485) (QUOTE (-240 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-257))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-115))))) 
+(-75) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
 NIL 
-(-79 T$) 
+(-76 T$) 
 ((|constructor| (NIL "This domain implements binary operations.")) (|binaryOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{binaryOperation f} constructs a binary operation value out of any homogeneous mapping of arity 2."))) 
 NIL 
 NIL 
-(-80 T$) 
+(-77 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement binary operations."))) 
 NIL 
 NIL 
-(-81) 
+(-78) 
 ((|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}"))) 
 NIL 
-((-12 (|HasCategory| (-85) (QUOTE (-262 (-85)))) (|HasCategory| (-85) (QUOTE (-1017)))) (|HasCategory| (-85) (QUOTE (-557 (-477)))) (|HasCategory| (-85) (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-556 (-776)))) (|HasCategory| (-85) (QUOTE (-1017))) (-12 (|HasCategory| $ (QUOTE (-1039 (-85)))) (|HasCategory| (-85) (QUOTE (-760)))) (|HasCategory| $ (QUOTE (-320 (-85)))) (-12 (|HasCategory| $ (QUOTE (-320 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1039 (-85))))) 
-(-82 R S) 
+((-11 (|HasCategory| (-82) (QUOTE (-259 (-82)))) (|HasCategory| (-82) (QUOTE (-1014)))) (|HasCategory| (-82) (QUOTE (-554 (-474)))) (|HasCategory| (-82) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-82) (QUOTE (-69))) (|HasCategory| (-82) (QUOTE (-553 (-773)))) (|HasCategory| (-82) (QUOTE (-1014))) (-11 (|HasCategory| $ (QUOTE (-1036 (-82)))) (|HasCategory| (-82) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-317 (-82)))) (-11 (|HasCategory| $ (QUOTE (-317 (-82)))) (|HasCategory| (-82) (QUOTE (-69)))) (|HasCategory| $ (QUOTE (-1036 (-82))))) 
+(-79 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}"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-83 S) 
+(-80 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
 NIL 
 NIL 
-(-84) 
+(-81) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
 NIL 
 NIL 
-(-85) 
+(-82) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) 
 NIL 
 NIL 
-(-86) 
+(-83) 
 ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Maybe| (|Mapping| (|InputForm|) (|List| (|InputForm|)))) $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \\spad{nothing} otherwise.") (($ $ (|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)}.") (((|Maybe| (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \\spad{nothing} otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If \\spad{op1} and \\spad{op2} have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1} and \\spad{op2} should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) 
 NIL 
 NIL 
-(-87 A) 
+(-84 A) 
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-88 -3098 UP) 
+(-85 -3095 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
-(-89 |p|) 
+(-86 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-90 |p|) 
+(-87 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-825))) (|HasCategory| (-89 |#1|) (QUOTE (-954 (-1094)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-477)))) (|HasCategory| (-89 |#1|) (QUOTE (-937))) (|HasCategory| (-89 |#1|) (QUOTE (-744))) (|HasCategory| (-89 |#1|) (QUOTE (-760))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-744))) (|HasCategory| (-89 |#1|) (QUOTE (-760)))) (|HasCategory| (-89 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-1070))) (|HasCategory| (-89 |#1|) (QUOTE (-800 (-332)))) (|HasCategory| (-89 |#1|) (QUOTE (-800 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-89 |#1|) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-89 |#1|) (QUOTE (-584 (-488)))) (|HasCategory| (-89 |#1|) (QUOTE (-191))) (|HasCategory| (-89 |#1|) (QUOTE (-815 (-1094)))) (|HasCategory| (-89 |#1|) (QUOTE (-192))) (|HasCategory| (-89 |#1|) (QUOTE (-813 (-1094)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -262) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -243) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-260))) (|HasCategory| (-89 |#1|) (QUOTE (-487))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-825)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
-(-91 A S) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-86 |#1|) (QUOTE (-822))) (|HasCategory| (-86 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-86 |#1|) (QUOTE (-115))) (|HasCategory| (-86 |#1|) (QUOTE (-117))) (|HasCategory| (-86 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-86 |#1|) (QUOTE (-934))) (|HasCategory| (-86 |#1|) (QUOTE (-741))) (|HasCategory| (-86 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-86 |#1|) (QUOTE (-741))) (|HasCategory| (-86 |#1|) (QUOTE (-757)))) (|HasCategory| (-86 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-86 |#1|) (QUOTE (-1067))) (|HasCategory| (-86 |#1|) (QUOTE (-797 (-329)))) (|HasCategory| (-86 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-86 |#1|) (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-86 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-86 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-86 |#1|) (QUOTE (-188))) (|HasCategory| (-86 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-86 |#1|) (QUOTE (-189))) (|HasCategory| (-86 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-86 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -86) (|devaluate| |#1|)))) (|HasCategory| (-86 |#1|) (|%list| (QUOTE -259) (|%list| (QUOTE -86) (|devaluate| |#1|)))) (|HasCategory| (-86 |#1|) (|%list| (QUOTE -240) (|%list| (QUOTE -86) (|devaluate| |#1|)) (|%list| (QUOTE -86) (|devaluate| |#1|)))) (|HasCategory| (-86 |#1|) (QUOTE (-257))) (|HasCategory| (-86 |#1|) (QUOTE (-484))) (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-86 |#1|) (QUOTE (-822)))) (OR (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-86 |#1|) (QUOTE (-822)))) (|HasCategory| (-86 |#1|) (QUOTE (-115))))) 
+(-88 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-92 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-89 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
 NIL 
-(-93 UP) 
+(-90 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),{} 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."))) 
 NIL 
 NIL 
-(-94 S) 
+(-91 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"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-95 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-92 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
-(-96) 
+(-93) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
-(-97 A S) 
+(-94 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
 NIL 
 NIL 
-(-98 S) 
+(-95 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
 NIL 
 NIL 
-(-99 S) 
+(-96 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-100 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-97 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."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-101) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-98) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
-(-102) 
+(-99) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
 NIL 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-760)))) (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-1017))))) (|HasCategory| (-101) (QUOTE (-556 (-776)))) (|HasCategory| (-101) (QUOTE (-557 (-477)))) (OR (|HasCategory| (-101) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-1017)))) (|HasCategory| (-101) (QUOTE (-760))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1017))) (-12 (|HasCategory| (-101) (QUOTE (-262 (-101)))) (|HasCategory| (-101) (QUOTE (-1017)))) (-12 (|HasCategory| $ (QUOTE (-320 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-320 (-101)))) (|HasCategory| $ (QUOTE (-1039 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1039 (-101)))) (|HasCategory| (-101) (QUOTE (-760))))) 
-(-103) 
+((OR (-11 (|HasCategory| (-98) (QUOTE (-259 (-98)))) (|HasCategory| (-98) (QUOTE (-757)))) (-11 (|HasCategory| (-98) (QUOTE (-259 (-98)))) (|HasCategory| (-98) (QUOTE (-1014))))) (|HasCategory| (-98) (QUOTE (-553 (-773)))) (|HasCategory| (-98) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-98) (QUOTE (-757))) (|HasCategory| (-98) (QUOTE (-1014)))) (|HasCategory| (-98) (QUOTE (-757))) (OR (|HasCategory| (-98) (QUOTE (-69))) (|HasCategory| (-98) (QUOTE (-757))) (|HasCategory| (-98) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-98) (QUOTE (-69))) (|HasCategory| (-98) (QUOTE (-1014))) (-11 (|HasCategory| (-98) (QUOTE (-259 (-98)))) (|HasCategory| (-98) (QUOTE (-1014)))) (-11 (|HasCategory| $ (QUOTE (-317 (-98)))) (|HasCategory| (-98) (QUOTE (-69)))) (|HasCategory| $ (QUOTE (-317 (-98)))) (|HasCategory| $ (QUOTE (-1036 (-98)))) (-11 (|HasCategory| $ (QUOTE (-1036 (-98)))) (|HasCategory| (-98) (QUOTE (-757))))) 
+(-100) 
 ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) 
 NIL 
 NIL 
-(-104) 
+(-101) 
 ((|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."))) 
 NIL 
 NIL 
-(-105) 
+(-102) 
 ((|constructor| (NIL "A cachable set is a set whose elements keep an integer as part of their structure.")) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) "\\spad{setPosition(x, n)} associates the integer \\spad{n} to \\spad{x}.")) (|position| (((|NonNegativeInteger|) $) "\\spad{position(x)} returns the integer \\spad{n} associated to \\spad{x}."))) 
 NIL 
 NIL 
-(-106) 
+(-103) 
 ((|constructor| (NIL "This domain represents the capsule of a domain definition.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of top level expressions appearing in `c'."))) 
 NIL 
 NIL 
-(-107) 
+(-104) 
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-4003 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-108 |minix| -2627 R) 
+(-105 |minix| -2624 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2627 S T$) 
+(-106 |minix| -2624 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 
-(-110) 
+(-107) 
 ((|constructor| (NIL "This domain represents a `case' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the case expression `e'."))) 
 NIL 
 NIL 
-(-111) 
+(-108) 
 ((|constructor| (NIL "This domain represents the unnamed category defined \\indented{2}{by a list of exported signatures}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of exports in category syntax `c'.")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(c)} returns the kind of unnamed category,{} either 'domain' or 'package'."))) 
 NIL 
 NIL 
-(-112) 
+(-109) 
 ((|constructor| (NIL "This domain provides representations for category constructors."))) 
 NIL 
 NIL 
-(-113) 
+(-110) 
 ((|parents| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{parents(c)} returns the list of all category forms directly extended by the category `c'.")) (|principalAncestors| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{principalAncestors(c)} returns the list of all category forms that are principal ancestors of the the category `c'.")) (|exportedOperators| (((|List| (|OperatorSignature|)) $) "\\spad{exportedOperators(c)} returns the list of all operator signatures exported by the category `c',{} along with their predicates.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: December 20,{} 2008. Date Last Updated: February 16,{} 2008. Basic Operations: coerce Related Constructors: Also See: Type") (((|CategoryConstructor|) $) "\\spad{constructor(c)} returns the category constructor used to instantiate the category object `c'."))) 
 NIL 
 NIL 
-(-114) 
+(-111) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) 
-((-3991 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-322)))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017))))) (|HasCategory| (-117) (QUOTE (-557 (-477)))) (|HasCategory| (-117) (QUOTE (-322))) (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-556 (-776)))) (|HasCategory| (-117) (QUOTE (-1017))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| $ (QUOTE (-320 (-117)))) (-12 (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) 
-(-115 R Q A) 
+((-3987 . T)) 
+((OR (-11 (|HasCategory| (-114) (QUOTE (-259 (-114)))) (|HasCategory| (-114) (QUOTE (-319)))) (-11 (|HasCategory| (-114) (QUOTE (-259 (-114)))) (|HasCategory| (-114) (QUOTE (-1014))))) (|HasCategory| (-114) (QUOTE (-554 (-474)))) (|HasCategory| (-114) (QUOTE (-319))) (|HasCategory| (-114) (QUOTE (-757))) (|HasCategory| (-114) (QUOTE (-69))) (|HasCategory| (-114) (QUOTE (-553 (-773)))) (|HasCategory| (-114) (QUOTE (-1014))) (-11 (|HasCategory| (-114) (QUOTE (-259 (-114)))) (|HasCategory| (-114) (QUOTE (-1014)))) (|HasCategory| $ (QUOTE (-317 (-114)))) (-11 (|HasCategory| $ (QUOTE (-317 (-114)))) (|HasCategory| (-114) (QUOTE (-69))))) 
+(-112 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-116) 
+(-113) 
 ((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n, m)} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note: \\spad{permutation(n,m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note: \\spad{n! = n (n-1)! when n > 0}; also,{} \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\spad{binomial(n,r)} returns the \\spad{(n,r)} binomial coefficient (often denoted in the literature by \\spad{C(n,r)}). Note: \\spad{C(n,r) = n!/(r!(n-r)!)} where \\spad{n >= r >= 0}."))) 
 NIL 
 NIL 
-(-117) 
+(-114) 
 ((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape} designate the escape character.")) (|verticalTab| (($) "\\spad{verticalTab} designates vertical tab.")) (|horizontalTab| (($) "\\spad{horizontalTab} designates horizontal tab.")) (|backspace| (($) "\\spad{backspace} designates the backspace character.")) (|formfeed| (($) "\\spad{formfeed} designates the form feed character.")) (|linefeed| (($) "\\spad{linefeed} designates the line feed character.")) (|carriageReturn| (($) "\\spad{carriageReturn} designates carriage return.")) (|newline| (($) "\\spad{newline} designates the new line character.")) (|underscore| (($) "\\spad{underscore} designates the underbar character.")) (|quote| (($) "\\spad{quote} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}.	It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}."))) 
 NIL 
 NIL 
-(-118) 
+(-115) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-119 R) 
+(-116 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) 
 NIL 
 NIL 
-(-120) 
+(-117) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-121 -3098 UP UPUP) 
+(-118 -3095 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 
-(-122 R CR) 
+(-119 R CR) 
 ((|constructor| (NIL "This package provides the generalized euclidean algorithm which is needed as the basic step for factoring polynomials.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} where (\\spad{fi} relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g} = sum \\spad{ai} prod fj (\\spad{j} \\= \\spad{i}) or equivalently g/prod fj = sum (ai/fi) or returns \"failed\" if no such list exists"))) 
 NIL 
 NIL 
-(-123 A S) 
+(-120 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#2|)))) 
-(-124 S) 
+((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#1| (|%list| (QUOTE -317) (|devaluate| |#2|)))) 
+(-121 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
-(-125 |n| K Q) 
+(-122 |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."))) 
-((-3996 . T) (-3995 . T) (-3998 . T)) 
+((-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-126) 
+(-123) 
 ((|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."))) 
 NIL 
 NIL 
-(-127) 
+(-124) 
 ((|constructor| (NIL "This domain represents list comprehension syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the expression being collected by the list comprehension `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of the iterators of the list comprehension `e'."))) 
 NIL 
 NIL 
-(-128 UP |Par|) 
+(-125 UP |Par|) 
 ((|complexZeros| (((|List| (|Complex| |#2|)) |#1| |#2|) "\\spad{complexZeros(poly, eps)} finds the complex zeros of the univariate polynomial \\spad{poly} to precision eps with solutions returned as complex floats or rationals depending on the type of eps."))) 
 NIL 
 NIL 
-(-129) 
+(-126) 
 ((|constructor| (NIL "This domain represents type specification \\indented{2}{for an identifier or expression.}")) (|rhs| (((|TypeAst|) $) "\\spad{rhs(e)} returns the right hand side of the colon expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the colon expression `e'."))) 
 NIL 
 NIL 
-(-130) 
+(-127) 
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-131 R -3098) 
+(-128 R -3095) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
-(-132 I) 
+(-129 I) 
 ((|stirling2| ((|#1| |#1| |#1|) "\\spad{stirling2(n,m)} returns the Stirling number of the second kind denoted \\spad{SS[n,m]}.")) (|stirling1| ((|#1| |#1| |#1|) "\\spad{stirling1(n,m)} returns the Stirling number of the first kind denoted \\spad{S[n,m]}.")) (|permutation| ((|#1| |#1| |#1|) "\\spad{permutation(n)} returns \\spad{!P(n,r) = n!/(n-r)!}. This is the number of permutations of \\spad{n} objects taken \\spad{r} at a time.")) (|partition| ((|#1| |#1|) "\\spad{partition(n)} returns the number of partitions of the integer \\spad{n}. This is the number of distinct ways that \\spad{n} can be written as a sum of positive integers.")) (|multinomial| ((|#1| |#1| (|List| |#1|)) "\\spad{multinomial(n,[m1,m2,...,mk])} returns the multinomial coefficient \\spad{n!/(m1! m2! ... mk!)}.")) (|factorial| ((|#1| |#1|) "\\spad{factorial(n)} returns \\spad{n!}. this is the product of all integers between 1 and \\spad{n} (inclusive). Note: \\spad{0!} is defined to be 1.")) (|binomial| ((|#1| |#1| |#1|) "\\spad{binomial(n,r)} returns the binomial coefficient \\spad{C(n,r) = n!/(r! (n-r)!)},{} where \\spad{n >= r >= 0}. This is the number of combinations of \\spad{n} objects taken \\spad{r} at a time."))) 
 NIL 
 NIL 
-(-133) 
+(-130) 
 ((|constructor| (NIL "CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.")) (|product| (($ $ (|SegmentBinding| $)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") (($ $ (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| (($ $ (|SegmentBinding| $)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") (($ $ (|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| (($ $ (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") (($ $) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials."))) 
 NIL 
 NIL 
-(-134) 
+(-131) 
 ((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-135) 
+(-132) 
 ((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'."))) 
 NIL 
 NIL 
-(-136) 
+(-133) 
 ((|constructor| (NIL "This package exports the elementary operators,{} with some semantics already attached to them. The semantics that is attached here is not dependent on the set in which the operators will be applied.")) (|operator| (((|BasicOperator|) (|Symbol|)) "\\spad{operator(s)} returns an operator with name \\spad{s},{} with the appropriate semantics if \\spad{s} is known. If \\spad{s} is not known,{} the result has no semantics."))) 
 NIL 
 NIL 
-(-137 R UP UPUP) 
+(-134 R UP UPUP) 
 ((|constructor| (NIL "A package for swapping the order of two variables in a tower of two UnivariatePolynomialCategory extensions.")) (|swap| ((|#3| |#3|) "\\spad{swap(p(x,y))} returns \\spad{p}(\\spad{y},{}\\spad{x})."))) 
 NIL 
 NIL 
-(-138 T$) 
+(-135 T$) 
 ((|constructor| (NIL "This domain implements commutative operations.")) (|commutativeOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{commutativeOperation f} constructs a commutative operation over \\spad{T},{} thus asserting a commutativity property."))) 
-(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3062 (|f| |x| |y|) (|f| |y| |x|)))) . T)) 
+(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3059 (|f| |x| |y|) (|f| |y| |x|)))) . T)) 
 NIL 
-(-139 T$) 
+(-136 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement commutative operations."))) 
-(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3062 (|f| |x| |y|) (|f| |y| |x|)))) . T)) 
+(((|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|)) (-3059 (|f| |x| |y|) (|f| |y| |x|)))) . T)) 
 NIL 
-(-140 S R) 
+(-137 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 (-825))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3997)) (|HasAttribute| |#2| (QUOTE -4000)) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-499)))) 
-(-141 R) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-496)))) 
+(-138 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})"))) 
-((-3994 OR (|has| |#1| (-499)) (-12 (|has| |#1| (-260)) (|has| |#1| (-825)))) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3997 |has| |#1| (-6 -3997)) (-4000 |has| |#1| (-6 -4000)) (-1380 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 OR (|has| |#1| (-496)) (-11 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-142 RR PR) 
+(-139 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."))) 
 NIL 
 NIL 
-(-143) 
+(-140) 
 ((|constructor| (NIL "This package implements a Spad compiler.")) (|elaborate| (((|Maybe| (|Elaboration|)) (|SpadAst|)) "\\spad{elaborate(s)} returns the elaboration of the syntax object \\spad{s} in the empty environement.")) (|macroExpand| (((|SpadAst|) (|SpadAst|) (|Environment|)) "\\spad{macroExpand(s,e)} traverses the syntax object \\spad{s} replacing all (niladic) macro invokations with the corresponding substitution."))) 
 NIL 
 NIL 
-(-144 R) 
+(-141 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}."))) 
-((-3994 OR (|has| |#1| (-499)) (-12 (|has| |#1| (-260)) (|has| |#1| (-825)))) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3997 |has| |#1| (-6 -3997)) (-4000 |has| |#1| (-6 -4000)) (-1380 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
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-(-145 R S) 
+((-3990 OR (|has| |#1| (-496)) (-11 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-298))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-319))) (OR (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-11 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-822)))) (-11 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-974))) (-11 (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-188)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3996)) (-11 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-311)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-142 R S) 
 ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 
 NIL 
 NIL 
-(-146 R S CS) 
+(-143 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 
 NIL 
-(-147) 
+(-144) 
 ((|constructor| (NIL "This domain implements some global properties of subspaces.")) (|copy| (($ $) "\\spad{copy(x)} \\undocumented")) (|solid| (((|Boolean|) $ (|Boolean|)) "\\spad{solid(x,b)} \\undocumented")) (|close| (((|Boolean|) $ (|Boolean|)) "\\spad{close(x,b)} \\undocumented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} \\undocumented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented"))) 
 NIL 
 NIL 
-(-148) 
+(-145) 
 ((|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."))) 
-(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-149) 
+(-146) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
 NIL 
 NIL 
-(-150 R) 
+(-147 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) 
-(((-4003 "*") . T) (-3994 . T) (-3999 . T) (-3993 . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-151) 
+(-148) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
 NIL 
 NIL 
-(-152 R) 
+(-149 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{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(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{(xi,eta,phi)} to \\spad{x = a*sinh(xi)*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(xi)*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(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}."))) 
 NIL 
 NIL 
-(-153 R |PolR| E) 
+(-150 R |PolR| E) 
 ((|constructor| (NIL "This package implements characteristicPolynomials for monogenic algebras using resultants")) (|characteristicPolynomial| ((|#2| |#3|) "\\spad{characteristicPolynomial(e)} returns the characteristic polynomial of \\spad{e} using resultants"))) 
 NIL 
 NIL 
-(-154 R S CS) 
+(-151 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-861 |#2|) (|%list| (QUOTE -800) (|devaluate| |#1|)))) 
-(-155 R) 
+((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+(-152 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-156) 
+(-153) 
 ((|constructor| (NIL "This domain represents `coerce' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-157 R UP) 
+(-154 R UP) 
 ((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken's idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see \\spadfunFrom{digits}{Float}) is not increased when this is necessary to avoid rounding errors. Hence it is the user's responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage's variant of Graeffe's method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in {\\em factors} which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being {\\em 10 ** (-3)} to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal {\\em globalDigits} is set to {\\em ceiling(1/r)**2*10} being {\\em 10**7} by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is {\\em coeffient of \\spad{x**(n-1)}} divided by {\\em n times coefficient of \\spad{x**n}}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em 1+globalEps},{} where {\\em globalEps} is the internal error bound,{} which can be set by {\\em setErrorBound}.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly, eps)} determines a start polynomial {\\em start}\\\\ by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,eps,info)} determines a start polynomial {\\em start} by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} -1\". Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If {\\em info} is {\\em true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note: this function depends on \\spadfunFrom{abs}{Complex}.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost {\\em globalEps},{} the internal error bound,{} which can be set by {\\em setErrorBound}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p, eps)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p, eps, info)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization. If {\\em info} is {\\em true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If {\\em info} is {\\em true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p, eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by {\\em eps}.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant {\\em globalEps} which you may change by {\\em setErrorBound}."))) 
 NIL 
 NIL 
-(-158 S ST) 
+(-155 S ST) 
 ((|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 
-(-159) 
+(-156) 
 ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-160 C) 
+(-157 C) 
 ((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") ((|#1| $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) 
 NIL 
 NIL 
-(-161 S) 
+(-158 S) 
 ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) 
 NIL 
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-(-162) 
+(-159) 
 ((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(\\spad{i+1}) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'."))) 
 NIL 
 NIL 
-(-163) 
+(-160) 
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) 
 NIL 
 NIL 
-(-164 R -3098) 
+(-161 R -3095) 
 ((|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 
-(-165 R) 
+(-162 R) 
 ((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}"))) 
 NIL 
 NIL 
-(-166) 
+(-163) 
 ((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{SFunction(li)} is the \\spad{S}-function of the partition \\spad{li} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|PositiveInteger|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|NonNegativeInteger|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}"))) 
 NIL 
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-(-167) 
+(-164) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-168 N T$) 
+(-165 N T$) 
 ((|constructor| (NIL "This domain provides for a fixed-sized homogeneous data buffer.")) (|qsetelt| ((|#2| $ (|NonNegativeInteger|) |#2|) "setelt(\\spad{b},{}\\spad{i},{}\\spad{x}) sets the \\spad{i}th entry of data buffer `b' to `x'. Indexing is 0-based.")) (|qelt| ((|#2| $ (|NonNegativeInteger|)) "elt(\\spad{b},{}\\spad{i}) returns the \\spad{i}th element in buffer `b'. Indexing is 0-based.")) (|new| (($) "\\spad{new()} returns a fresly allocated data buffer or length \\spad{N}."))) 
 NIL 
 NIL 
-(-169 S) 
+(-166 S) 
 ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) 
 NIL 
 NIL 
-(-170 |vars|) 
+(-167 |vars|) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
 NIL 
 NIL 
-(-171 -3098 UP UPUP R) 
+(-168 -3095 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 
-(-172 -3098 FP) 
+(-169 -3095 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-173) 
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 ((|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."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) 
-(-174) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
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+(-171) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-175 R -3098) 
+(-172 R -3095) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
-(-176 R) 
+(-173 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\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}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|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| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| #1#) (|:| |pole| #2#)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\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 
-(-177 R1 R2) 
+(-174 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-178 S) 
+(-175 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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-179 |CoefRing| |listIndVar|) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-176 |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}.")) (|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}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-180 R -3098) 
+(-177 R -3095) 
 ((|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 
-(-181) 
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 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3773 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-182) 
+(-179) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
 NIL 
 NIL 
-(-183 R) 
+(-180 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}"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499))) (|HasAttribute| |#1| (QUOTE (-4003 "*"))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-184 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-181 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 
-(-185 S) 
+(-182 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 
-(-186 R) 
+(-183 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-187 S T$) 
+(-184 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-188 T$) 
+(-185 T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#1| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#1| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-189 R) 
+(-186 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-190 S) 
+(-187 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-191) 
+(-188) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
 NIL 
 NIL 
-(-192) 
+(-189) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-193) 
+(-190) 
 ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) 
 NIL 
 NIL 
-(-194 A S) 
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 ((|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 
-((|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#2|)))) 
-(-195 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -317) (|devaluate| |#2|)))) 
+(-192 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}."))) 
 NIL 
 NIL 
-(-196) 
+(-193) 
 ((|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 
-(-197 S -2627 R) 
+(-194 S -2624 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-760))) (|HasAttribute| |#3| (QUOTE -3998)) (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#3| (QUOTE (-667))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-965))) (|HasCategory| |#3| (QUOTE (-1017)))) 
-(-198 -2627 R) 
+((|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-18))) (|HasCategory| |#3| (QUOTE (-20))) (|HasCategory| |#3| (QUOTE (-101))) (|HasCategory| |#3| (QUOTE (-22))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) 
+(-195 -2624 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) 
-((-3995 |has| |#2| (-965)) (-3996 |has| |#2| (-965)) (-3998 |has| |#2| (-6 -3998))) 
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
 NIL 
-(-199 -2627 R) 
+(-196 -2624 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."))) 
-((-3995 |has| |#2| (-965)) (-3996 |has| |#2| (-965)) (-3998 |has| |#2| (-6 -3998))) 
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 ((|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 
-(-201) 
+(-198) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
 NIL 
-(-202 S) 
+(-199 S) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
 NIL 
 NIL 
-(-203) 
+(-200) 
 ((|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}."))) 
-((-3994 . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-204 S) 
+(-201 S) 
 ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) 
 NIL 
 NIL 
-(-205 S) 
+(-202 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}"))) 
 NIL 
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-(-206 M) 
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+(-203 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
-(-207 R) 
+(-204 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-208 |vl| R) 
+(-205 |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"))) 
-(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
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-(-209) 
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+(-206) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
 NIL 
-(-210) 
+(-207) 
 ((|constructor| (NIL "This domain provides representations for domains constructors.")) (|functorData| (((|FunctorData|) $) "\\spad{functorData x} returns the functor data associated with the domain constructor \\spad{x}."))) 
 NIL 
 NIL 
-(-211) 
+(-208) 
 ((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
 NIL 
 NIL 
-(-212 |n| R M S) 
+(-209 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-3998 OR (-2568 (|has| |#4| (-965)) (|has| |#4| (-192))) (|has| |#4| (-6 -3998)) (-2568 (|has| |#4| (-965)) (|has| |#4| (-813 (-1094))))) (-3995 |has| |#4| (-965)) (-3996 |has| |#4| (-965))) 
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(-1091))))) (-11 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-189))) (OR (|HasCategory| |#3| (QUOTE (-189))) (-11 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-11 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-11 (|HasCategory| |#3| (QUOTE (-18))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#3| (QUOTE (-1014))))) (OR (-11 (|HasCategory| |#3| (QUOTE (-18))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-11 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#3| (QUOTE (-18))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-11 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-69))) (|HasCategory| (-485) (QUOTE (-757))) (-11 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-962))))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3994)) (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-11 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-18))) (|HasCategory| |#3| (QUOTE (-20))) (|HasCategory| |#3| (QUOTE (-101))) (|HasCategory| |#3| (QUOTE (-22))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (-11 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-11 (|HasCategory| |#3| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#3|)))) 
+(-211 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-192)))) 
-(-215 R S V E) 
+((|HasCategory| |#2| (QUOTE (-189)))) 
+(-212 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-216 S) 
+(-213 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}."))) 
 NIL 
 NIL 
-(-217 |Ex|) 
+(-214 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
 NIL 
 NIL 
-(-218) 
+(-215) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
 NIL 
 NIL 
-(-219 R |Ex|) 
+(-216 R |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,y) = g(x,y),x,y,l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched."))) 
 NIL 
 NIL 
-(-220) 
+(-217) 
 ((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,rRange,iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f, -2..2, -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,rRange,iRange,arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f, 0.3..3, 0..2*\\%pi, false)}} Parameter descriptions: \\indented{2}{f:\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction."))) 
 NIL 
 NIL 
-(-221 R) 
+(-218 R) 
 ((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}."))) 
 NIL 
 NIL 
-(-222) 
+(-219) 
 ((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,lz,l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly,lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,ly,l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}."))) 
 NIL 
 NIL 
-(-223) 
+(-220) 
 ((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,y,z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,y,z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}."))) 
 NIL 
 NIL 
-(-224) 
+(-221) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn't exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned."))) 
 NIL 
 NIL 
-(-225 S) 
+(-222 S) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command."))) 
 NIL 
 NIL 
-(-226 S R) 
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 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-191)))) 
-(-227 R) 
+((|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-188)))) 
+(-224 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
-(-228 R S V) 
+(-225 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"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
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-(-229 A S) 
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+(-226 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
 NIL 
-(-230 S) 
+(-227 S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
 NIL 
-(-231) 
+(-228) 
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-232 R -3098) 
+(-229 R -3095) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the	inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-233 R -3098) 
+(-230 R -3095) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
-(-234 |Coef| UTS ULS) 
+(-231 |Coef| UTS ULS) 
 ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314)))) 
-(-235 |Coef| ULS UPXS EFULS) 
+((|HasCategory| |#1| (QUOTE (-311)))) 
+(-232 |Coef| ULS UPXS EFULS) 
 ((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314)))) 
-(-236) 
+((|HasCategory| |#1| (QUOTE (-311)))) 
+(-233) 
 ((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) 
 NIL 
 NIL 
-(-237) 
+(-234) 
 ((|environment| (((|Environment|) $) "\\spad{environment(x)} returns the environment of the elaboration \\spad{x}.")) (|typeForm| (((|InternalTypeForm|) $) "\\spad{typeForm(x)} returns the type form of the elaboration \\spad{x}.")) (|irForm| (((|InternalRepresentationForm|) $) "\\spad{irForm(x)} returns the internal representation form of the elaboration \\spad{x}.")) (|elaboration| (($ (|InternalRepresentationForm|) (|InternalTypeForm|) (|Environment|)) "\\spad{elaboration(ir,ty,env)} construct an elaboration object for for the internal representation form \\spad{ir},{} with type \\spad{ty},{} and environment \\spad{env}."))) 
 NIL 
 NIL 
-(-238 A S) 
+(-235 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72)))) 
-(-239 S) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69)))) 
+(-236 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}."))) 
 NIL 
 NIL 
-(-240 S) 
+(-237 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-241) 
+(-238) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
 NIL 
 NIL 
-(-242 |Coef| UTS) 
+(-239 |Coef| UTS) 
 ((|constructor| (NIL "The elliptic functions sn,{} sc and dn are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function dn as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function cn as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function sn as a Taylor \\indented{1}{series.}"))) 
 NIL 
 NIL 
-(-243 S T$) 
+(-240 S T$) 
 ((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) 
 NIL 
 NIL 
-(-244 S |Dom| |Im|) 
+(-241 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 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#3|)))) 
-(-245 |Dom| |Im|) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#3|)))) 
+(-242 |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 
-(-246 S R |Mod| -2042 -3524 |exactQuo|) 
+(-243 S R |Mod| -2039 -3521 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-247 S) 
+(-244 S) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
 NIL 
 NIL 
-(-248) 
+(-245) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3994 . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-249) 
+(-246) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
 NIL 
 NIL 
-(-250 R) 
+(-247 R) 
 ((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,m,k,g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable."))) 
 NIL 
 NIL 
-(-251 S) 
+(-248 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|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."))) 
-((-3998 OR (|has| |#1| (-965)) (|has| |#1| (-416))) (-3995 |has| |#1| (-965)) (-3996 |has| |#1| (-965))) 
-((|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (OR (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667)))) (|HasCategory| |#1| (QUOTE (-416))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-1017)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-1029)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-256))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-416)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-667)))) 
-(-252 S R) 
+((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-962)) (-3992 |has| |#1| (-962))) 
+((|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-253))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) 
+(-249 S R) 
 ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) 
 NIL 
 NIL 
-(-253 |Key| |Entry|) 
+(-250 |Key| |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-254) 
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+(-251) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
 NIL 
-(-255 S) 
+(-252 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) 
-(-256) 
+((|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) 
+(-253) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
 NIL 
-(-257 -3098 S) 
+(-254 -3095 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 
-(-258 E -3098) 
+(-255 E -3095) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) 
 NIL 
 NIL 
-(-259 S) 
+(-256 S) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
 NIL 
 NIL 
-(-260) 
+(-257) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-261 S R) 
+(-258 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-262 R) 
+(-259 R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#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 
-(-263 -3098) 
+(-260 -3095) 
 ((|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 
-(-264) 
+(-261) 
 ((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}."))) 
 NIL 
 NIL 
-(-265) 
+(-262) 
 ((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'."))) 
 NIL 
 NIL 
-(-266 R FE |var| |cen|) 
+(-263 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-954 (-1094)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-557 (-477)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-744))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-760))) (OR (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-744))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-760)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-954 (-488)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-1070))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-800 (-332)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-800 (-488)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-584 (-488)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-191))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-815 (-1094)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-192))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-813 (-1094)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -262) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -243) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-260))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-487))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-825)))) (|HasCategory| (-1170 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
-(-267 R) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-115))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-117))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-329)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-188))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -259) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -240) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-257))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-115))))) 
+(-264 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-3998 OR (-12 (|has| |#1| (-499)) (OR (|has| |#1| (-965)) (|has| |#1| (-416)))) (|has| |#1| (-965)) (|has| |#1| (-416))) (-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) ((-4003 "*") |has| |#1| (-499)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-499)) (-3993 |has| |#1| (-499))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-584 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-584 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-584 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-584 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-965))))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-1029)))) (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965)))) (-12 (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1029)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-416))) (|HasCategory| |#1| (QUOTE (-965)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-954 (-488)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| $ (QUOTE (-965))) (|HasCategory| $ (QUOTE (-954 (-488))))) 
-(-268 R S) 
+((-3994 OR (-11 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) ((-3997 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-18))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (-11 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-18)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-22)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485)))))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+(-265 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
 NIL 
-(-269 R FE) 
+(-266 R FE) 
 ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) 
 NIL 
 NIL 
-(-270 R -3098) 
+(-267 R -3095) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
 NIL 
-(-271) 
+(-268) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}."))) 
 NIL 
 NIL 
-(-272 FE |var| |cen|) 
+(-269 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
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-(-273 M) 
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+(-270 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between -k and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}."))) 
 NIL 
 NIL 
-(-275 S) 
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 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-720)))) 
-(-276 S E) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-717)))) 
+(-273 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
 NIL 
-(-277 S) 
+(-274 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-698) (QUOTE (-720)))) 
-(-278 S R E) 
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+(-275 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
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-(-279 R E) 
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+(-276 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-280 S) 
+(-277 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
 NIL 
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-(-281 S -3098) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-278 S -3095) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-322)))) 
-(-282 -3098) 
+((|HasCategory| |#2| (QUOTE (-319)))) 
+(-279 -3095) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-283 E) 
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 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) 
 NIL 
 NIL 
-(-284) 
+(-281) 
 ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) 
 NIL 
 NIL 
-(-285 -3098 UP UPUP R) 
+(-282 -3095 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
-(-286 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+(-283 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-287 S -3098 UP UPUP R) 
+(-284 S -3095 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-288 -3098 UP UPUP R) 
+(-285 -3095 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-289 S R) 
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 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -243) (|devaluate| |#2|) (|devaluate| |#2|)))) 
-(-290 R) 
+((|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -240) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+(-287 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides."))) 
 NIL 
 NIL 
-(-291 |p| |n|) 
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 ((|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}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) 
-(-292 S -3098 UP UPUP) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-115))) (|HasCategory| (-818 |#1|) (QUOTE (-319)))) (|HasCategory| (-818 |#1|) (QUOTE (-117))) (|HasCategory| (-818 |#1|) (QUOTE (-319))) (|HasCategory| (-818 |#1|) (QUOTE (-115)))) 
+(-289 S -3095 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-314)))) 
-(-293 -3098 UP UPUP) 
+((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-311)))) 
+(-290 -3095 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
-((-3994 |has| (-352 |#2|) (-314)) (-3999 |has| (-352 |#2|) (-314)) (-3993 |has| (-352 |#2|) (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 |has| (-349 |#2|) (-311)) (-3995 |has| (-349 |#2|) (-311)) (-3989 |has| (-349 |#2|) (-311)) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-294 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
+(-291 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-295 |p| |extdeg|) 
+(-292 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) 
-(-296 GF |defpol|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-115))) (|HasCategory| (-818 |#1|) (QUOTE (-319)))) (|HasCategory| (-818 |#1|) (QUOTE (-117))) (|HasCategory| (-818 |#1|) (QUOTE (-319))) (|HasCategory| (-818 |#1|) (QUOTE (-115)))) 
+(-293 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-297 GF |extdeg|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-294 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-298 GF) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-295 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
 NIL 
-(-299 F1 GF F2) 
+(-296 F1 GF F2) 
 ((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}GF,{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn't divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn't divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse."))) 
 NIL 
 NIL 
-(-300 S) 
+(-297 S) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
 NIL 
 NIL 
-(-301) 
+(-298) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-302 R UP -3098) 
+(-299 R UP -3095) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-303 |p| |extdeg|) 
+(-300 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| (-821 |#1|) (QUOTE (-118))) (|HasCategory| (-821 |#1|) (QUOTE (-322)))) (|HasCategory| (-821 |#1|) (QUOTE (-120))) (|HasCategory| (-821 |#1|) (QUOTE (-322))) (|HasCategory| (-821 |#1|) (QUOTE (-118)))) 
-(-304 GF |uni|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-115))) (|HasCategory| (-818 |#1|) (QUOTE (-319)))) (|HasCategory| (-818 |#1|) (QUOTE (-117))) (|HasCategory| (-818 |#1|) (QUOTE (-319))) (|HasCategory| (-818 |#1|) (QUOTE (-115)))) 
+(-301 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-305 GF |extdeg|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-302 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-306 GF |defpol|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-303 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-307 GF) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-304 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-308 -3098 GF) 
+(-305 -3095 GF) 
 ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-309 -3098 FP FPP) 
+(-306 -3095 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
-(-310 GF |n|) 
+(-307 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-118)))) 
-(-311 R |ls|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-115)))) 
+(-308 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
 NIL 
 NIL 
-(-312 S) 
+(-309 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-313 S) 
+(-310 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
 NIL 
 NIL 
-(-314) 
+(-311) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-315 S) 
+(-312 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
 NIL 
 NIL 
-(-316 |Name| S) 
+(-313 |Name| S) 
 ((|constructor| (NIL "This category provides an interface to operate on files in the computer's file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) 
 NIL 
 NIL 
-(-317 S R) 
+(-314 S R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-499)))) 
-(-318 R) 
+((|HasCategory| |#2| (QUOTE (-496)))) 
+(-315 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-3998 |has| |#1| (-499)) (-3996 . T) (-3995 . T)) 
+((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
 NIL 
-(-319 A S) 
+(-316 A S) 
 ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\spad{p(x)} is \\spad{true},{} and \\spad{\"failed\"} otherwise.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,x)} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,u,0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. For collections,{}} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\spad{p(x)} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-72)))) 
-(-320 S) 
+((|HasCategory| |#2| (QUOTE (-69)))) 
+(-317 S) 
 ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\spad{p(x)} is \\spad{true},{} and \\spad{\"failed\"} otherwise.")) (|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 \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,x)} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#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 starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,u,0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. For collections,{}} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\spad{p(x)} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) 
 NIL 
 NIL 
-(-321 S) 
+(-318 S) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
 NIL 
 NIL 
-(-322) 
+(-319) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) 
 NIL 
 NIL 
-(-323 S R UP) 
+(-320 S R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-314)))) 
-(-324 R UP) 
+((|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-311)))) 
+(-321 R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-325 A S) 
+(-322 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72)))) 
-(-326 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69)))) 
+(-323 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
 NIL 
-(-327 S A R B) 
+(-324 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-328 |VarSet| R) 
+(-325 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
 NIL 
-(-329 S V) 
+(-326 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
 NIL 
 NIL 
-(-330 S R) 
+(-327 S R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-584 (-488))))) 
-(-331 R) 
+((|HasCategory| |#2| (QUOTE (-581 (-485))))) 
+(-328 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
 NIL 
-(-332) 
+(-329) 
 ((|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3984 . T) (-3992 . T) (-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3981 . T) (-3988 . T) (-3773 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-333 |Par|) 
+(-330 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
 NIL 
 NIL 
-(-334 |Par|) 
+(-331 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in lp,{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-335 R S) 
+(-332 R S) 
 ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-336 R S) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-333 R S) 
 ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-148)))) 
-(-337 R |Basis|) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-145)))) 
+(-334 R |Basis|) 
 ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|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}."))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-338 S) 
+(-335 S) 
 ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
 NIL 
 NIL 
-(-339 S) 
+(-336 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-760)))) 
-(-340) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-337) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
 NIL 
-(-341) 
+(-338) 
 ((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used."))) 
 NIL 
 NIL 
-(-342 |n| |class| R) 
+(-339 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-343 -3098 UP UPUP R) 
+(-340 -3095 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-344 -3098 UP) 
+(-341 -3095 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
-(-345 R) 
+(-342 R) 
 ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) 
 NIL 
 NIL 
-(-346 S) 
+(-343 S) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
 NIL 
 NIL 
-(-347) 
+(-344) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-348 S) 
+(-345 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3992))) 
-(-349) 
+((|HasAttribute| |#1| (QUOTE -3981)) (|HasAttribute| |#1| (QUOTE -3988))) 
+(-346) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-3776 . T) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3773 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-350 R) 
+(-347 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-459 (-1094) $))) (|HasCategory| |#1| (QUOTE (-262 $))) (|HasCategory| |#1| (QUOTE (-243 $ $))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-1138))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-1138)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-395)))) 
-(-351 R S) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-456 (-1091) $))) (|HasCategory| |#1| (QUOTE (-259 $))) (|HasCategory| |#1| (QUOTE (-240 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-392)))) 
+(-348 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
 NIL 
 NIL 
-(-352 S) 
+(-349 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-3988 -12 (|has| |#1| (-6 -3999)) (|has| |#1| (-395)) (|has| |#1| (-6 -3988))) (-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-954 (-1094)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-744))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-744))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-487))) (-12 (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395)))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-353 A B) 
+((-3984 -11 (|has| |#1| (-6 -3995)) (|has| |#1| (-392)) (|has| |#1| (-6 -3984))) (-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-484))) (-11 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392)))) (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-350 A B) 
 ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) 
 NIL 
 NIL 
-(-354 S R UP) 
+(-351 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 NIL 
-(-355 R UP) 
+(-352 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-356 A S) 
+(-353 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488))))) 
-(-357 S) 
+((|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) 
+(-354 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-358 R -3098 UP A) 
+(-355 R -3095 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-359 R1 F1 U1 A1 R2 F2 U2 A2) 
+(-356 R1 F1 U1 A1 R2 F2 U2 A2) 
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-360 R -3098 UP A |ibasis|) 
+(-357 R -3095 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -954) (|devaluate| |#2|)))) 
-(-361 AR R AS S) 
+((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) 
+(-358 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
 NIL 
-(-362 S R) 
+(-359 S R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-314)))) 
-(-363 R) 
+((|HasCategory| |#2| (QUOTE (-311)))) 
+(-360 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3998 |has| |#1| (-499)) (-3996 . T) (-3995 . T)) 
+((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
 NIL 
-(-364 R) 
+(-361 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
 NIL 
 NIL 
-(-365 S R) 
+(-362 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-416))) (|HasCategory| |#2| (QUOTE (-1029))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) 
-(-366 R) 
+((|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-18))) (|HasCategory| |#2| (QUOTE (-22))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
+(-363 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-3998 OR (|has| |#1| (-965)) (|has| |#1| (-416))) (-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) ((-4003 "*") |has| |#1| (-499)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-499)) (-3993 |has| |#1| (-499))) 
+((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) ((-3997 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
 NIL 
-(-367 R A S B) 
+(-364 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) 
 NIL 
 NIL 
-(-368 R FE |x| |cen|) 
+(-365 R FE |x| |cen|) 
 ((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed."))) 
 NIL 
 NIL 
-(-369 R FE |Expon| UPS TRAN |x|) 
+(-366 R FE |Expon| UPS TRAN |x|) 
 ((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series"))) 
 NIL 
 NIL 
-(-370 A S) 
+(-367 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-322)))) 
-(-371 S) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-368 S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3991 . T)) 
+((-3987 . T)) 
 NIL 
-(-372 S A R B) 
+(-369 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-373 R -3098) 
+(-370 R -3095) 
 ((|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 
-(-374 R E) 
+(-371 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) 
-((-3988 -12 (|has| |#1| (-6 -3988)) (|has| |#2| (-6 -3988))) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#2| (QUOTE -3988)))) 
-(-375 R -3098) 
+((-3984 -11 (|has| |#1| (-6 -3984)) (|has| |#2| (-6 -3984))) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-11 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#2| (QUOTE -3984)))) 
+(-372 R -3095) 
 ((|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 
-(-376 R -3098) 
+(-373 R -3095) 
 ((|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 
-(-377 R -3098) 
+(-374 R -3095) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-27)))) 
-(-378 R -3098) 
+((|HasCategory| |#2| (QUOTE (-24)))) 
+(-375 R -3095) 
 ((|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 
-(-379) 
+(-376) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-380 R -3098 UP) 
+(-377 R -3095 UP) 
 ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-954 (-48))))) 
-(-381) 
+((|HasCategory| |#2| (QUOTE (-951 (-45))))) 
+(-378) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
 NIL 
-(-382 |f|) 
+(-379 |f|) 
 ((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-383 S) 
+(-380 S) 
 ((|constructor| (NIL "This category describes the class of structural objects that behave functorially in distinguished class of components.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,x)} returns an object with similar shape and structure as \\spad{x},{} where all \\spad{S}-items \\spad{s} in \\spad{x} have been replacement elementwise by \\spad{f s}."))) 
 NIL 
 NIL 
-(-384) 
+(-381) 
 ((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}."))) 
 NIL 
 NIL 
-(-385 UP) 
+(-382 UP) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-386 R UP -3098) 
+(-383 R UP -3095) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
-(-387 R UP) 
+(-384 R UP) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1)."))) 
 NIL 
 NIL 
-(-388 R) 
+(-385 R) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-349)))) 
-(-389) 
+((|HasCategory| |#1| (QUOTE (-346)))) 
+(-386) 
 ((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer \\spad{zi}."))) 
 NIL 
 NIL 
-(-390 |Dom| |Expon| |VarSet| |Dpol|) 
+(-387 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp, infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314)))) 
-(-391 |Dom| |Expon| |VarSet| |Dpol|) 
+((|HasCategory| |#1| (QUOTE (-311)))) 
+(-388 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp, infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class."))) 
 NIL 
 NIL 
-(-392 |Dom| |Expon| |VarSet| |Dpol|) 
+(-389 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}."))) 
 NIL 
 NIL 
-(-393 |Dom| |Expon| |VarSet| |Dpol|) 
+(-390 |Dom| |Expon| |VarSet| |Dpol|) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented"))) 
 NIL 
 NIL 
-(-394 S) 
+(-391 S) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-395) 
+(-392) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-396 R |n| |ls| |gamma|) 
+(-393 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) 
-((-3998 |has| (-352 (-861 |#1|)) (-499)) (-3996 . T) (-3995 . T)) 
-((|HasCategory| (-352 (-861 |#1|)) (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-352 (-861 |#1|)) (QUOTE (-499)))) 
-(-397 |vl| R E) 
+((-3994 |has| (-349 (-858 |#1|)) (-496)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| (-349 (-858 |#1|)) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-349 (-858 |#1|)) (QUOTE (-496)))) 
+(-394 |vl| R E) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-398 R BP) 
+(((-3997 "*") |has| |#2| (-145)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-496)))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#2| (QUOTE (-115))))) 
+(-395 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) 
 NIL 
 NIL 
-(-399 OV E S R P) 
+(-396 OV E S R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-400 E OV R P) 
+(-397 E OV R P) 
 ((|constructor| (NIL "This package provides operations for GCD computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the GCD of \\spad{p} and \\spad{q}"))) 
 NIL 
 NIL 
-(-401 R) 
+(-398 R) 
 ((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}"))) 
 NIL 
 NIL 
-(-402 R FE) 
+(-399 R FE) 
 ((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}."))) 
 NIL 
 NIL 
-(-403 RP TP) 
+(-400 RP TP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done ."))) 
 NIL 
 NIL 
-(-404 |vl| R IS E |ff| P) 
+(-401 |vl| R IS E |ff| P) 
 ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-405 E V R P Q) 
+(-402 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
 NIL 
 NIL 
-(-406 R E |VarSet| P) 
+(-403 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
 NIL 
-((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) 
-(-407 S R E) 
+((-11 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-11 (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) 
+(-404 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) 
 NIL 
 NIL 
-(-408 R E) 
+(-405 R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) 
 NIL 
 NIL 
-(-409) 
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 ((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(vv) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect."))) 
 NIL 
 NIL 
-(-410) 
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 ((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done."))) 
 NIL 
 NIL 
-(-411) 
+(-408) 
 ((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport."))) 
 NIL 
 NIL 
-(-412 S R E) 
+(-409 S R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
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+(-410 R E) 
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-414 |lv| -3098 R) 
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 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
-(-415 S) 
+(-412 S) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
 NIL 
 NIL 
-(-416) 
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 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-417 |Coef| |var| |cen|) 
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 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) 
-(-418 |Key| |Entry| |Tbl| |dent|) 
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+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-415 |Key| |Entry| |Tbl| |dent|) 
 ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-419 R E V P) 
+((-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-416 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) 
 NIL 
-((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) 
-(-420) 
+((-11 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-11 (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) 
+(-417) 
 ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-421) 
+(-418) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) 
 NIL 
 NIL 
-(-422 |Key| |Entry| |hashfn|) 
+(-419 |Key| |Entry| |hashfn|) 
 ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-423) 
+((-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-420) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
 NIL 
-(-424 |vl| R) 
+(-421 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-425 -2627 S) 
+(((-3997 "*") |has| |#2| (-145)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-496)))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#2| (QUOTE (-115))))) 
+(-422 -2624 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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|#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-11 (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-485) (QUOTE (-757))) (-11 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-11 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-20))) (|HasCategory| |#2| (QUOTE (-101))) (|HasCategory| |#2| (QUOTE (-22))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-423) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
 NIL 
-(-427 S) 
+(-424 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-428 -3098 UP UPUP R) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-425 -3095 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
-(-429 BP) 
+(-426 BP) 
 ((|constructor| (NIL "This package provides the functions for the heuristic integer gcd. Geddes's algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,..,ak])} = gcd of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,..,fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,..fk])} = gcd and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,..fk])} = gcd and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,..,fk])} = gcd of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,..,fk])} = gcd of the polynomials \\spad{fi}."))) 
 NIL 
 NIL 
-(-430) 
+(-427) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) 
-(-431 A S) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
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+(-428 A S) 
 ((|constructor| (NIL "\\indented{2}{A homogeneous aggregate is an aggregate of elements all of the} \\indented{2}{same type,{} and is functorial in stored elements..} In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) 
-(-432 S) 
+((|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) 
+(-429 S) 
 ((|constructor| (NIL "\\indented{2}{A homogeneous aggregate is an aggregate of elements all of the} \\indented{2}{same type,{} and is functorial in stored elements..} In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates."))) 
 NIL 
 NIL 
-(-433 S) 
+(-430 S) 
 ((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A."))) 
 NIL 
 NIL 
-(-434) 
+(-431) 
 ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name `n'."))) 
 NIL 
 NIL 
-(-435 S) 
+(-432 S) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-436) 
+(-433) 
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-437 -3098 UP |AlExt| |AlPol|) 
+(-434 -3095 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
-(-438) 
+(-435) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| $ (QUOTE (-965))) (|HasCategory| $ (QUOTE (-954 (-488))))) 
-(-439 S |mn|) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+(-436 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-440 R |Row| |Col|) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-437 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-441 K R UP) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-438 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) 
 NIL 
 NIL 
-(-442 R UP -3098) 
+(-439 R UP -3095) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-443 |mn|) 
+(-440 |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
 NIL 
-((-12 (|HasCategory| (-85) (QUOTE (-262 (-85)))) (|HasCategory| (-85) (QUOTE (-1017)))) (|HasCategory| (-85) (QUOTE (-557 (-477)))) (|HasCategory| (-85) (QUOTE (-760))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-556 (-776)))) (|HasCategory| (-85) (QUOTE (-1017))) (-12 (|HasCategory| $ (QUOTE (-1039 (-85)))) (|HasCategory| (-85) (QUOTE (-760)))) (|HasCategory| $ (QUOTE (-320 (-85)))) (-12 (|HasCategory| $ (QUOTE (-320 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1039 (-85))))) 
-(-444 K R UP L) 
+((-11 (|HasCategory| (-82) (QUOTE (-259 (-82)))) (|HasCategory| (-82) (QUOTE (-1014)))) (|HasCategory| (-82) (QUOTE (-554 (-474)))) (|HasCategory| (-82) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-82) (QUOTE (-69))) (|HasCategory| (-82) (QUOTE (-553 (-773)))) (|HasCategory| (-82) (QUOTE (-1014))) (-11 (|HasCategory| $ (QUOTE (-1036 (-82)))) (|HasCategory| (-82) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-317 (-82)))) (-11 (|HasCategory| $ (QUOTE (-317 (-82)))) (|HasCategory| (-82) (QUOTE (-69)))) (|HasCategory| $ (QUOTE (-1036 (-82))))) 
+(-441 K R UP L) 
 ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) 
 NIL 
 NIL 
-(-445) 
+(-442) 
 ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) 
 NIL 
 NIL 
-(-446 R Q A B) 
+(-443 R Q A B) 
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-447 -3098 |Expon| |VarSet| |DPoly|) 
+(-444 -3095 |Expon| |VarSet| |DPoly|) 
 ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-557 (-1094))))) 
-(-448 |vl| |nv|) 
+((|HasCategory| |#3| (QUOTE (-554 (-1091))))) 
+(-445 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
 NIL 
-(-449 T$) 
+(-446 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3062 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3059 (|f| |x| |x|) |x|))) . T)) 
 NIL 
-(-450) 
+(-447) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-451 A S) 
+(-448 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-452 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-449 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-453 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-450 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}"))) 
 NIL 
 NIL 
-(-454 A S) 
+(-451 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-455 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-452 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-456 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-453 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) 
-(-457 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+(-454 A S) 
 ((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) 
 NIL 
 NIL 
-(-458 S A B) 
+(-455 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-459 A B) 
+(-456 A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-460 S E |un|) 
+(-457 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-720)))) 
-(-461 S |mn|) 
+((|HasCategory| |#2| (QUOTE (-717)))) 
+(-458 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-462) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-459) 
 ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) 
 NIL 
 NIL 
-(-463 |p| |n|) 
+(-460 |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}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((OR (|HasCategory| (-521 |#1|) (QUOTE (-118))) (|HasCategory| (-521 |#1|) (QUOTE (-322)))) (|HasCategory| (-521 |#1|) (QUOTE (-120))) (|HasCategory| (-521 |#1|) (QUOTE (-322))) (|HasCategory| (-521 |#1|) (QUOTE (-118)))) 
-(-464 R |Row| |Col| M) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-518 |#1|) (QUOTE (-115))) (|HasCategory| (-518 |#1|) (QUOTE (-319)))) (|HasCategory| (-518 |#1|) (QUOTE (-117))) (|HasCategory| (-518 |#1|) (QUOTE (-319))) (|HasCategory| (-518 |#1|) (QUOTE (-115)))) 
+(-461 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-465 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasCategory| |#3| (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-462 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasCategory| |#7| (|%list| (QUOTE -1039) (|devaluate| |#5|)))) 
-(-466) 
+((|HasCategory| |#7| (|%list| (QUOTE -1036) (|devaluate| |#5|)))) 
+(-463) 
 ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) 
 NIL 
 NIL 
-(-467) 
+(-464) 
 ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) 
 NIL 
 NIL 
-(-468 S) 
+(-465 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-469) 
+(-466) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-470 GF) 
+(-467 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) 
 NIL 
 NIL 
-(-471) 
+(-468) 
 ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-472 R) 
+(-469 R) 
 ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) 
 NIL 
 NIL 
-(-473 |Varset|) 
+(-470 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-698) (QUOTE (-1017))))) 
-(-474 K -3098 |Par|) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) 
+(-471 K -3095 |Par|) 
 ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) 
 NIL 
 NIL 
-(-475) 
+(-472) 
 NIL 
 NIL 
 NIL 
-(-476) 
+(-473) 
 ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) 
 NIL 
 NIL 
-(-477) 
+(-474) 
 ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-478 R) 
+(-475 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-479 |Coef| UTS) 
+(-476 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-480 K -3098 |Par|) 
+(-477 K -3095 |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 
-(-481 R BP |pMod| |nextMod|) 
+(-478 R BP |pMod| |nextMod|) 
 ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) 
 NIL 
 NIL 
-(-482 OV E R P) 
+(-479 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) 
 NIL 
 NIL 
-(-483 K UP |Coef| UTS) 
+(-480 K UP |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-484 |Coef| UTS) 
+(-481 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-485 R UP) 
+(-482 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-486 S) 
+(-483 S) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-487) 
+(-484) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
-((-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3995 . T) (-3996 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-488) 
+(-485) 
 ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-489) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-490) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-491) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-492) 
+(-489) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-493 |Key| |Entry| |addDom|) 
+(-490 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-494 R -3098) 
+((-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-491 R -3095) 
 ((|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 
-(-495 R0 -3098 UP UPUP R) 
+(-492 R0 -3095 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 
-(-496) 
+(-493) 
 ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) 
 NIL 
 NIL 
-(-497 R) 
+(-494 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-3776 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3773 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-498 S) 
+(-495 S) 
 ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) 
 NIL 
 NIL 
-(-499) 
+(-496) 
 ((|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."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-500 R -3098) 
+(-497 R -3095) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-501 I) 
+(-498 I) 
 ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) 
 NIL 
 NIL 
-(-502 R -3098 L) 
+(-499 R -3095 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -604) (|devaluate| |#2|)))) 
-(-503) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-500) 
 ((|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 
-(-504 -3098 UP UPUP R) 
+(-501 -3095 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 
-(-505 -3098 UP) 
+(-502 -3095 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 
-(-506 R -3098 L) 
+(-503 R -3095 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -604) (|devaluate| |#2|)))) 
-(-507 R -3098) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-504 R -3095) 
 ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-1057)))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-573))))) 
-(-508 -3098 UP) 
+((-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-570))))) 
+(-505 -3095 UP) 
 ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) 
 NIL 
 NIL 
-(-509 S) 
+(-506 S) 
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-510 -3098) 
+(-507 -3095) 
 ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) 
 NIL 
 NIL 
-(-511 R) 
+(-508 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."))) 
-((-3776 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3773 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-512) 
+(-509) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
-(-513 R -3098) 
+(-510 R -3095) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-241))) (|HasCategory| |#2| (QUOTE (-573))) (|HasCategory| |#2| (QUOTE (-954 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-241)))) (|HasCategory| |#1| (QUOTE (-499)))) 
-(-514 -3098 UP) 
+((-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#1| (QUOTE (-496)))) 
+(-511 -3095 UP) 
 ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) 
 NIL 
 NIL 
-(-515 R -3098) 
+(-512 R -3095) 
 ((|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 
-(-516) 
+(-513) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-517) 
+(-514) 
 ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) 
 NIL 
 NIL 
-(-518) 
+(-515) 
 ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) 
 NIL 
 NIL 
-(-519) 
+(-516) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-520 |p| |unBalanced?|) 
+(-517 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-521 |p|) 
+(-518 |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."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-322)))) 
-(-522) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| $ (QUOTE (-117))) (|HasCategory| $ (QUOTE (-115))) (|HasCategory| $ (QUOTE (-319)))) 
+(-519) 
 ((|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 
-(-523 -3098) 
+(-520 -3095) 
 ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-954 (-1094))))) 
-(-524 E -3098) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-951 (-1091))))) 
+(-521 E -3095) 
 ((|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 
-(-525 R -3098) 
+(-522 R -3095) 
 ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 NIL 
-(-526) 
+(-523) 
 ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) 
 NIL 
 NIL 
-(-527 I) 
+(-524 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
 NIL 
-(-528 GF) 
+(-525 GF) 
 ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) 
 NIL 
 NIL 
-(-529 R) 
+(-526 R) 
 ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-120)))) 
-(-530) 
+((|HasCategory| |#1| (QUOTE (-117)))) 
+(-527) 
 ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) 
 NIL 
 NIL 
-(-531 R E V P TS) 
+(-528 R E V P TS) 
 ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) 
 NIL 
 NIL 
-(-532) 
+(-529) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-533 E V R P) 
+(-530 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-534 |Coef|) 
+(-531 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|)))) (|HasCategory| (-488) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488)))))) 
-(-535 |Coef|) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-311))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) 
+(-532 |Coef|) 
 ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-4003 "*") |has| |#1| (-499)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-499)))) 
-(-536) 
+(((-3997 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-496)))) 
+(-533) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) 
 NIL 
 NIL 
-(-537 A B) 
+(-534 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-538 A B C) 
+(-535 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-539 R -3098 FG) 
+(-536 R -3095 FG) 
 ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) 
 NIL 
 NIL 
-(-540 S) 
+(-537 S) 
 ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}."))) 
 NIL 
 NIL 
-(-541 S |Index| |Entry|) 
+(-538 S |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -320) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) 
-(-542 |Index| |Entry|) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -317) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-69)))) 
+(-539 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
 NIL 
-(-543) 
+(-540) 
 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
-(-544 R A) 
+(-541 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)."))) 
-((-3998 OR (-2568 (|has| |#2| (-318 |#1|)) (|has| |#1| (-499))) (-12 (|has| |#2| (-363 |#1|)) (|has| |#1| (-499)))) (-3996 . T) (-3995 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-545) 
+((-3994 OR (-2565 (|has| |#2| (-315 |#1|)) (|has| |#1| (-496))) (-11 (|has| |#2| (-360 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) 
+(-542) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
 NIL 
-(-546) 
+(-543) 
 ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-547) 
+(-544) 
 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) 
 NIL 
 NIL 
-(-548) 
+(-545) 
 ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-549) 
+(-546) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-550) 
+(-547) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-551 |Entry|) 
+(-548 |Entry|) 
 ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1077) (QUOTE (-760))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (QUOTE (|:| -3867 (-1077))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3867 (-1077)) (|:| |entry| |#1|)) (QUOTE (-72))))) 
-(-552 S |Key| |Entry|) 
+((-11 (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (QUOTE (|:| -3864 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| |#1|)) (QUOTE (-69))))) 
+(-549 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
-(-553 |Key| |Entry|) 
+(-550 |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
-(-554 S) 
+(-551 S) 
 ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#1| (QUOTE (-557 (-804 (-488)))))) 
-(-555 R S) 
+((|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485)))))) 
+(-552 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-556 S) 
+(-553 S) 
 ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-557 S) 
+(-554 S) 
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-558 -3098 UP) 
+(-555 -3095 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
-(-559 S) 
+(-556 S) 
 ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-560) 
+(-557) 
 ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-561 S) 
+(-558 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-562 A R S) 
+(-559 A R S) 
 ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-759)))) 
-(-563 S R) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-560 S R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
 NIL 
 NIL 
-(-564 R) 
+(-561 R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-565 R -3098) 
+(-562 R -3095) 
 ((|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 
-(-566 R UP) 
+(-563 R UP) 
 ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) 
-((-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3994 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) 
-(-567 R E V P TS ST) 
+((-3992 . T) (-3991 . T) ((-3997 "*") . T) (-3990 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+(-564 R E V P TS ST) 
 ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) 
 NIL 
 NIL 
-(-568 OV E Z P) 
+(-565 OV E Z P) 
 ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) 
 NIL 
 NIL 
-(-569) 
+(-566) 
 ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) 
 NIL 
 NIL 
-(-570 |VarSet| R |Order|) 
+(-567 |VarSet| R |Order|) 
 ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-571 R |ls|) 
+(-568 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) 
 NIL 
 NIL 
-(-572 R -3098) 
+(-569 R -3095) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
-(-573) 
+(-570) 
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-574 |lv| -3098) 
+(-571 |lv| -3095) 
 ((|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 
-(-575) 
+(-572) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 NIL 
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-(-576 R A) 
+((-11 (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-259 (-2 (|:| -3864 (-1074)) (|:| |entry| (-48)))))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-1014)))) (OR (|HasCategory| (-48) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-1014)))) (OR (|HasCategory| (-48) (QUOTE (-69))) (|HasCategory| (-48) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-553 (-773)))) (|HasCategory| (-48) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-554 (-474)))) (-11 (|HasCategory| (-48) (QUOTE (-259 (-48)))) (|HasCategory| (-48) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-69))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-48) (QUOTE (-69))) (OR (|HasCategory| (-48) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-69)))) (|HasCategory| (-48) (QUOTE (-1014))) (|HasCategory| (-48) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-1014))) (-11 (|HasCategory| $ (QUOTE (-317 (-2 (|:| -3864 (-1074)) (|:| |entry| (-48)))))) (|HasCategory| (-2 (|:| -3864 (-1074)) (|:| |entry| (-48))) (QUOTE (-69)))) (|HasCategory| $ (QUOTE (-317 (-2 (|:| -3864 (-1074)) (|:| |entry| (-48)))))) (-11 (|HasCategory| $ (QUOTE (-317 (-48)))) (|HasCategory| (-48) (QUOTE (-69)))) (|HasCategory| $ (QUOTE (-1036 (-48))))) 
+(-573 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) 
-((-3998 OR (-2568 (|has| |#2| (-318 |#1|)) (|has| |#1| (-499))) (-12 (|has| |#2| (-363 |#1|)) (|has| |#1| (-499)))) (-3996 . T) (-3995 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (|%list| (QUOTE -363) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-577 S R) 
+((-3994 OR (-2565 (|has| |#2| (-315 |#1|)) (|has| |#1| (-496))) (-11 (|has| |#2| (-360 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -360) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) 
+(-574 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-314)))) 
-(-578 R) 
+((|HasCategory| |#2| (QUOTE (-311)))) 
+(-575 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
 NIL 
-(-579 R FE) 
+(-576 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
 NIL 
 NIL 
-(-580 R) 
+(-577 R) 
 ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) 
 NIL 
 NIL 
-(-581 |vars|) 
+(-578 |vars|) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) 
 NIL 
 NIL 
-(-582 S R) 
+(-579 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-2566 (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-583 K B) 
+((-2563 (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-580 K B) 
 ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) 
-((-3996 . T) (-3995 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| (-581 |#2|) (QUOTE (-1017))))) 
-(-584 R) 
+((-3992 . T) (-3991 . T)) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-578 |#2|) (QUOTE (-1014))))) 
+(-581 R) 
 ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
-(-585 K B) 
+(-582 K B) 
 ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-586 S) 
+(-583 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
-(-587 S) 
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 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-588 A B) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-585 A B) 
 ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) 
 NIL 
 NIL 
-(-589 A B) 
+(-586 A B) 
 ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
 NIL 
 NIL 
-(-590 A B C) 
+(-587 A B C) 
 ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) 
 NIL 
 NIL 
-(-591 T$) 
+(-588 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-592 S) 
+(-589 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-593 S) 
+(-590 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) 
-(-594 R) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-69))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) 
+(-591 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-595 S E |un|) 
+(-592 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) 
 NIL 
 NIL 
-(-596 A S) 
+(-593 A S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-597 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-594 S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-598 M R S) 
+(-595 M R S) 
 ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-718)))) 
-(-599 R -3098 L) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-715)))) 
+(-596 R -3095 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 
-(-600 A -2498) 
+(-597 A -2495) 
 ((|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}}"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-601 A) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-598 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-602 A M) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-599 A M) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-603 S A) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-600 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-314)))) 
-(-604 A) 
+((|HasCategory| |#2| (QUOTE (-311)))) 
+(-601 A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-605 -3098 UP) 
+(-602 -3095 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)))) 
-(-606 A L) 
+((|HasCategory| |#1| (QUOTE (-24)))) 
+(-603 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-607 S) 
+(-604 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spad{x\\/y} returns the logical `join',{} \\spadignore{e.g.} disjunction,{} or \\spad{x} and \\spad{y}.")) (|/\\| (($ $ $) "\\spad {x/\\y} returns the logical `meet',{} \\spadignore{e.g.} conjunction,{} of \\spad{x} and \\spad{y}.")) (~ (($ $) "\\spad{~x} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-608) 
+(-605) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spad{x\\/y} returns the logical `join',{} \\spadignore{e.g.} disjunction,{} or \\spad{x} and \\spad{y}.")) (|/\\| (($ $ $) "\\spad {x/\\y} returns the logical `meet',{} \\spadignore{e.g.} conjunction,{} of \\spad{x} and \\spad{y}.")) (~ (($ $) "\\spad{~x} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-609 R) 
+(-606 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-610 |VarSet| R) 
+(-607 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-3996 . T) (-3995 . T)) 
-((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-611 A S) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-145)))) 
+(-608 A S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
 NIL 
 NIL 
-(-612 S) 
+(-609 S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
 NIL 
 NIL 
-(-613 -3098 |Row| |Col| M) 
+(-610 -3095 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-614 -3098) 
+(-611 -3095) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-615 R E OV P) 
+(-612 R E OV P) 
 ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) 
 NIL 
 NIL 
-(-616 |n| R) 
+(-613 |n| R) 
 ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) 
-((-3998 . T) (-3995 . T) (-3996 . T)) 
-((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasAttribute| |#2| (QUOTE (-4003 #1="*"))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-499))) (OR (|HasAttribute| |#2| (QUOTE (-4003 #1#))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094))))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-617) 
+((-3994 . T) (-3991 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-188))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-145)))) 
+(-614) 
 ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) 
 NIL 
 NIL 
-(-618 |VarSet|) 
+(-615 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-619 A S) 
+(-616 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-620 S) 
+(-617 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-621) 
+(-618) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-622 |VarSet|) 
+(-619 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
 NIL 
-(-623 A) 
+(-620 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) 
 NIL 
 NIL 
-(-624 A C) 
+(-621 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) 
 NIL 
 NIL 
-(-625 A B C) 
+(-622 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) 
 NIL 
 NIL 
-(-626) 
+(-623) 
 ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-627 A) 
+(-624 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) 
 NIL 
 NIL 
-(-628 A C) 
+(-625 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) 
 NIL 
 NIL 
-(-629 A B C) 
+(-626 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) 
 NIL 
 NIL 
-(-630 S R |Row| |Col|) 
+(-627 S R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-4003 "*"))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-499)))) 
-(-631 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3997 "*"))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-496)))) 
+(-628 R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-632 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-633 R |Row| |Col| M) 
+(-630 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that m*n = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499)))) 
-(-634 R) 
+((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-496)))) 
+(-631 R) 
 ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-260))) (|HasCategory| |#1| (QUOTE (-499))) (|HasAttribute| |#1| (QUOTE (-4003 "*"))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) 
-(-635 R) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-69))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
+(-632 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
 NIL 
-(-636 T$) 
+(-633 T$) 
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) 
 NIL 
 NIL 
-(-637 R Q) 
+(-634 R Q) 
 ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) 
 NIL 
 NIL 
-(-638 S) 
+(-635 S) 
 ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) 
 NIL 
 NIL 
-(-639 U) 
+(-636 U) 
 ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
 NIL 
 NIL 
-(-640) 
+(-637) 
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-641 OV E -3098 PG) 
+(-638 OV E -3095 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 
-(-642 R) 
+(-639 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
 NIL 
 NIL 
-(-643 S D1 D2 I) 
+(-640 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
 NIL 
 NIL 
-(-644 S) 
+(-641 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
-(-645 S) 
+(-642 S) 
 ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) 
 NIL 
 NIL 
-(-646 S T$) 
+(-643 S T$) 
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) 
 NIL 
 NIL 
-(-647 S -2675 I) 
+(-644 S -2672 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 
-(-648 E OV R P) 
+(-645 E OV R P) 
 ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) 
 NIL 
 NIL 
-(-649 R) 
+(-646 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)}.}"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-650 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-647 R1 UP1 UPUP1 R2 UP2 UPUP2) 
 ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-651) 
+(-648) 
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-652 R |Mod| -2042 -3524 |exactQuo|) 
+(-649 R |Mod| -2039 -3521 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-653 R P) 
+(-650 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3997 |has| |#1| (-314)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
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-(-654 IS E |ff|) 
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+(-651 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-655 R M) 
+(-652 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-656 R |Mod| -2042 -3524 |exactQuo|) 
+((-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117)))) 
+(-653 R |Mod| -2039 -3521 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-657 S R) 
+(-654 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-658 R) 
+(-655 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-659 -3098) 
+(-656 -3095) 
 ((|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]]}."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-660 S) 
+(-657 S) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-661) 
+(-658) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-662 S) 
+(-659 S) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-663) 
+(-660) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-664 S R UP) 
+(-661 S R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-301))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-322)))) 
-(-665 R UP) 
+((|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-662 R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
-((-3994 |has| |#1| (-314)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 |has| |#1| (-311)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-666 S) 
+(-663 S) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-667) 
+(-664) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-668 T$) 
+(-665 T$) 
 ((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}."))) 
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3062 (|f| |x| (-2417 |f|)) |x|) (|exit| 1 (-3062 (|f| (-2417 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3059 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3059 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-669 T$) 
+(-666 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}."))) 
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3062 (|f| |x| (-2417 |f|)) |x|) (|exit| 1 (-3062 (|f| (-2417 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3059 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3059 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-670 -3098 UP) 
+(-667 -3095 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 
-(-671 |VarSet| E1 E2 R S PR PS) 
+(-668 |VarSet| E1 E2 R S PR PS) 
 ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-672 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-673 E OV R PPR) 
+(-670 E OV R PPR) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-674 |vl| R) 
+(-671 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) 
-(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-825))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-777 |#1|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-777 |#1|) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-675 E OV R PRF) 
+(((-3997 "*") |has| |#2| (-145)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-496)))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#2| (QUOTE (-115))))) 
+(-672 E OV R PRF) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-676 E OV R P) 
+(-673 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) 
 NIL 
 NIL 
-(-677 R S M) 
+(-674 R S M) 
 ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) 
 NIL 
 NIL 
-(-678 R M) 
+(-675 R M) 
 ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|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}."))) 
-((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-760)))) 
-(-679 S) 
+((-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) (-3994 . T)) 
+((-11 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-757)))) 
+(-676 S) 
 ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
-((-3991 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) 
-(-680 S) 
+((-3987 . T)) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) 
+(-677 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-3991 . T)) 
+((-3987 . T)) 
 NIL 
-(-681) 
+(-678) 
 ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) 
 NIL 
 NIL 
-(-682 S) 
+(-679 S) 
 ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) 
 NIL 
 NIL 
-(-683 |Coef| |Var|) 
+(-680 |Coef| |Var|) 
 ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-684 OV E R P) 
+(-681 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) 
 NIL 
 NIL 
-(-685 E OV R P) 
+(-682 E OV R P) 
 ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-686 S R) 
+(-683 S R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
 NIL 
 NIL 
-(-687 R) 
+(-684 R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-688 S) 
+(-685 S) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-689) 
+(-686) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-690 S) 
+(-687 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-691) 
+(-688) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-692 |Par|) 
+(-689 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-693 -3098) 
+(-690 -3095) 
 ((|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 
-(-694 P -3098) 
+(-691 P -3095) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) 
 NIL 
 NIL 
-(-695 T$) 
+(-692 T$) 
 NIL 
 NIL 
 NIL 
-(-696 UP -3098) 
+(-693 UP -3095) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
-(-697 R) 
+(-694 R) 
 ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-698) 
+(-695) 
 ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) 
-(((-4003 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-699 R -3098) 
+(-696 R -3095) 
 ((|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 
-(-700) 
+(-697) 
 ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) 
 NIL 
 NIL 
-(-701 S) 
+(-698 S) 
 ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) 
 NIL 
 NIL 
-(-702 R |PolR| E |PolE|) 
+(-699 R |PolR| E |PolE|) 
 ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) 
 NIL 
 NIL 
-(-703 R E V P TS) 
+(-700 R E V P TS) 
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-704 -3098 |ExtF| |SUEx| |ExtP| |n|) 
+(-701 -3095 |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 
-(-705 BP E OV R P) 
+(-702 BP E OV R P) 
 ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) 
 NIL 
 NIL 
-(-706 |Par|) 
+(-703 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) 
 NIL 
 NIL 
-(-707 R |VarSet|) 
+(-704 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
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-(-708 R) 
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+(-705 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
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-((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-998) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-998) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-998) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-192))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-709 R S) 
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+(-706 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-710 R) 
+(-707 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) 
-(-711 R E V P) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485)))))) 
+(-708 R E V P) 
 ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) 
 NIL 
 NIL 
-(-712 S) 
+(-709 S) 
 ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-713) 
+((-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-145)))) 
+(-710) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
 NIL 
-(-714) 
+(-711) 
 ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) 
 NIL 
 NIL 
-(-715) 
+(-712) 
 ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) 
 NIL 
 NIL 
-(-716 |Curve|) 
+(-713 |Curve|) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-717 S) 
+(-714 S) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-718) 
+(-715) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-719 S) 
+(-716 S) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-720) 
+(-717) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-721) 
+(-718) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-722) 
+(-719) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-723 S R) 
+(-720 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-322)))) 
-(-724 R) 
+((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-319)))) 
+(-721 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-725) 
+(-722) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-726 R) 
+(-723 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-352 (-488)))))) (OR (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-913 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) 
-(-727 OR R OS S) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-349 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-349 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+(-724 OR R OS S) 
 ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-728 R -3098 L) 
+(-725 R -3095 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-729 R -3098) 
+(-726 R -3095) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-730 R -3098) 
+(-727 R -3095) 
 ((|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 
-(-731 -3098 UP UPUP R) 
+(-728 -3095 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 
-(-732 -3098 UP L LQ) 
+(-729 -3095 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
 NIL 
 NIL 
-(-733 -3098 UP L LQ) 
+(-730 -3095 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-734 -3098 UP) 
+(-731 -3095 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-735 -3098 L UP A LO) 
+(-732 -3095 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 
-(-736 -3098 UP) 
+(-733 -3095 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-27)))) 
-(-737 -3098 LO) 
+((|HasCategory| |#1| (QUOTE (-24)))) 
+(-734 -3095 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 
-(-738 -3098 LODO) 
+(-735 -3095 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-739 -2627 S |f|) 
+(-736 -2624 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}."))) 
-((-3995 |has| |#2| (-965)) (-3996 |has| |#2| (-965)) (-3998 |has| |#2| (-6 -3998))) 
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(-11 (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-11 (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-11 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-11 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-20))) (|HasCategory| |#2| (QUOTE (-101))) (|HasCategory| |#2| (QUOTE (-22))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-737 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-742 (-1094)) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-742 (-1094)) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-742 (-1094)) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-742 (-1094)) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-742 (-1094)) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-741 |Kernels| R |var|) 
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+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-739 (-1091)) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-739 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-738 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-4003 "*") |has| |#2| (-314)) (-3994 |has| |#2| (-314)) (-3999 |has| |#2| (-314)) (-3993 |has| |#2| (-314)) (-3998 . T) (-3996 . T) (-3995 . T)) 
-((|HasCategory| |#2| (QUOTE (-314)))) 
-(-742 S) 
+(((-3997 "*") |has| |#2| (-311)) (-3990 |has| |#2| (-311)) (-3995 |has| |#2| (-311)) (-3989 |has| |#2| (-311)) (-3994 . T) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-311)))) 
+(-739 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) 
 NIL 
 NIL 
-(-743 S) 
+(-740 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-760)))) 
-(-744) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-741) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-745 P R) 
+(-742 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-192)))) 
-(-746 S) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-189)))) 
+(-743 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-3991 . T)) 
+((-3987 . T)) 
 NIL 
-(-747 R) 
+(-744 R) 
 ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) 
-((-3998 |has| |#1| (-759))) 
-((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-759)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-487)))) 
-(-748 R S) 
+((-3994 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-18))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-745 R S) 
 ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) 
 NIL 
 NIL 
-(-749 R) 
+(-746 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-750 A S) 
+((-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117)))) 
+(-747 A S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-751 S) 
+(-748 S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-752) 
+(-749) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-753) 
+(-750) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) 
 NIL 
 NIL 
-(-754 R) 
+(-751 R) 
 ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3998 |has| |#1| (-759))) 
-((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-759)))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-487)))) 
-(-755 R S) 
+((-3994 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-18))) (OR (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-752 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-756) 
+(-753) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-757 -2627 S) 
+(-754 -2624 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-758) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-759) 
+(-756) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-760) 
+(-757) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-761 T$ |f|) 
+(-758 T$ |f|) 
 ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-556 (-776))))) 
-(-762 S) 
+((|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-759 S) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-763) 
+(-760) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-764 S R) 
+(-761 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-765 R) 
+((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145)))) 
+(-762 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-766 R C) 
+(-763 R C) 
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) 
-(-767 R |sigma| -3250) 
+((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) 
+(-764 R |sigma| -3247) 
 ((|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."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-768 |x| R |sigma| -3250) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-765 |x| R |sigma| -3247) 
 ((|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}."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-314)))) 
-(-769 R) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-311)))) 
+(-766 R) 
 ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) 
-(-770) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485)))))) 
+(-767) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-771) 
+(-768) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) 
 NIL 
 NIL 
-(-772) 
+(-769) 
 ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-773 S) 
+(-770 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-774) 
+(-771) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-775) 
+(-772) 
 ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-776) 
+(-773) 
 ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) 
 NIL 
 NIL 
-(-777 |VariableList|) 
+(-774 |VariableList|) 
 ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) 
 NIL 
 NIL 
-(-778) 
+(-775) 
 ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) 
 NIL 
 NIL 
-(-779 R |vl| |wl| |wtlevel|) 
+(-776 R |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-780 R PS UP) 
+((-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-777 R PS UP) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-781 R |x| |pt|) 
+(-778 R |x| |pt|) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-782 |p|) 
+(-779 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-783 |p|) 
+(-780 |p|) 
 ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-784 |p|) 
+(-781 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-782 |#1|) (QUOTE (-825))) (|HasCategory| (-782 |#1|) (QUOTE (-954 (-1094)))) (|HasCategory| (-782 |#1|) (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-120))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-477)))) (|HasCategory| (-782 |#1|) (QUOTE (-937))) (|HasCategory| (-782 |#1|) (QUOTE (-744))) (|HasCategory| (-782 |#1|) (QUOTE (-760))) (OR (|HasCategory| (-782 |#1|) (QUOTE (-744))) (|HasCategory| (-782 |#1|) (QUOTE (-760)))) (|HasCategory| (-782 |#1|) (QUOTE (-954 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-1070))) (|HasCategory| (-782 |#1|) (QUOTE (-800 (-332)))) (|HasCategory| (-782 |#1|) (QUOTE (-800 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-782 |#1|) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-782 |#1|) (QUOTE (-584 (-488)))) (|HasCategory| (-782 |#1|) (QUOTE (-191))) (|HasCategory| (-782 |#1|) (QUOTE (-815 (-1094)))) (|HasCategory| (-782 |#1|) (QUOTE (-192))) (|HasCategory| (-782 |#1|) (QUOTE (-813 (-1094)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -262) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (|%list| (QUOTE -243) (|%list| (QUOTE -782) (|devaluate| |#1|)) (|%list| (QUOTE -782) (|devaluate| |#1|)))) (|HasCategory| (-782 |#1|) (QUOTE (-260))) (|HasCategory| (-782 |#1|) (QUOTE (-487))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-782 |#1|) (QUOTE (-825)))) (|HasCategory| (-782 |#1|) (QUOTE (-118))))) 
-(-785 |p| PADIC) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-115))) (|HasCategory| (-779 |#1|) (QUOTE (-117))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-1067))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-329)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-188))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -259) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -240) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-257))) (|HasCategory| (-779 |#1|) (QUOTE (-484))) (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-115))))) 
+(-782 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-954 (-1094)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760))) (OR (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760)))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -243) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-487))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-786 S T$) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -240) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-484))) (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#2| (QUOTE (-115))))) 
+(-783 S T$) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1017))))) (-12 (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776)))))) 
-(-787) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-11 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) 
+(-784) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) 
 NIL 
 NIL 
-(-788) 
+(-785) 
 ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) 
 NIL 
 NIL 
-(-789) 
+(-786) 
 ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) 
 NIL 
 NIL 
-(-790 CF1 CF2) 
+(-787 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-791 |ComponentFunction|) 
+(-788 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) 
 NIL 
 NIL 
-(-792 CF1 CF2) 
+(-789 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-793 |ComponentFunction|) 
+(-790 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-794) 
+(-791) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) 
 NIL 
 NIL 
-(-795 CF1 CF2) 
+(-792 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-796 |ComponentFunction|) 
+(-793 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-797) 
+(-794) 
 ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-798 R) 
+(-795 R) 
 ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) 
 NIL 
 NIL 
-(-799 R S L) 
+(-796 R S L) 
 ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-800 S) 
+(-797 S) 
 ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) 
 NIL 
 NIL 
-(-801 |Base| |Subject| |Pat|) 
+(-798 |Base| |Subject| |Pat|) 
 ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) 
 NIL 
-((-12 (-2566 (|HasCategory| |#2| (QUOTE (-954 (-1094))))) (-2566 (|HasCategory| |#2| (QUOTE (-965))))) (-12 (|HasCategory| |#2| (QUOTE (-965))) (-2566 (|HasCategory| |#2| (QUOTE (-954 (-1094)))))) (|HasCategory| |#2| (QUOTE (-954 (-1094))))) 
-(-802 R S) 
+((-11 (-2563 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2563 (|HasCategory| |#2| (QUOTE (-962))))) (-11 (|HasCategory| |#2| (QUOTE (-962))) (-2563 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) 
+(-799 R S) 
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-803 R A B) 
+(-800 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-804 R) 
+(-801 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) (|One| (($) "1")) (|Zero| (($) "0"))) 
 NIL 
 NIL 
-(-805 R -2675) 
+(-802 R -2672) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
-(-806 R S) 
+(-803 R S) 
 ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) 
 NIL 
 NIL 
-(-807 |VarSet|) 
+(-804 |VarSet|) 
 ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) (|One| (($) "\\spad{1} returns the empty list."))) 
 NIL 
 NIL 
-(-808 UP R) 
+(-805 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-809 A T$ S) 
+(-806 A T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-810 T$ S) 
+(-807 T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-811 UP -3098) 
+(-808 UP -3095) 
 ((|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 
-(-812 R S) 
+(-809 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-813 S) 
+(-810 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-814 A S) 
+(-811 A S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-815 S) 
+(-812 S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-816 S) 
+(-813 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-817 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-814 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-760)))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-760)))) 
-(-818 |n| R) 
+((-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-757)))) 
+(-815 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
 NIL 
-(-819 S) 
+(-816 S) 
 ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-820 S) 
+(-817 S) 
 ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-821 |p|) 
+(-818 |p|) 
 ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-322)))) 
-(-822 R E |VarSet| S) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| $ (QUOTE (-117))) (|HasCategory| $ (QUOTE (-115))) (|HasCategory| $ (QUOTE (-319)))) 
+(-819 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-823 R S) 
+(-820 R S) 
 ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-824 S) 
+(-821 S) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-118)))) 
-(-825) 
+((|HasCategory| |#1| (QUOTE (-115)))) 
+(-822) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-826 R0 -3098 UP UPUP R) 
+(-823 R0 -3095 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 
-(-827 UP UPUP R) 
+(-824 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-828 UP UPUP) 
+(-825 UP UPUP) 
 ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) 
 NIL 
 NIL 
-(-829 R) 
+(-826 R) 
 ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} ``p-adically'' in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-830 R) 
+(-827 R) 
 ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) 
 NIL 
 NIL 
-(-831 E OV R P) 
+(-828 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-832) 
+(-829) 
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) 
 NIL 
 NIL 
-(-833 -3098) 
+(-830 -3095) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
-(-834) 
+(-831) 
 ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) 
-(((-4003 "*") . T)) 
+(((-3997 "*") . T)) 
 NIL 
-(-835 R) 
+(-832 R) 
 ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) 
 NIL 
 NIL 
-(-836) 
+(-833) 
 ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-837 |xx| -3098) 
+(-834 |xx| -3095) 
 ((|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 
-(-838 -3098 P) 
+(-835 -3095 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-839 R |Var| |Expon| GR) 
+(-836 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) 
 NIL 
 NIL 
-(-840) 
+(-837) 
 ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) 
 NIL 
 NIL 
-(-841 S) 
+(-838 S) 
 ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) 
 NIL 
 NIL 
-(-842) 
+(-839) 
 ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) 
 NIL 
 NIL 
-(-843) 
+(-840) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-844) 
+(-841) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-845 R -3098) 
+(-842 R -3095) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-846 S A B) 
+(-843 S A B) 
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-847 S R -3098) 
+(-844 S R -3095) 
 ((|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 
-(-848 I) 
+(-845 I) 
 ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-849 S E) 
+(-846 S E) 
 ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-850 S R L) 
+(-847 S R L) 
 ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-851 S E V R P) 
+(-848 S E V R P) 
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -800) (|devaluate| |#1|)))) 
-(-852 -2675) 
+((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+(-849 -2672) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-853 R -3098 -2675) 
+(-850 R -3095 -2672) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-854 S R Q) 
+(-851 S R Q) 
 ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-855 S) 
+(-852 S) 
 ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) 
 NIL 
 NIL 
-(-856 S R P) 
+(-853 S R P) 
 ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) 
 NIL 
 NIL 
-(-857) 
+(-854) 
 ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) 
 NIL 
 NIL 
-(-858 R) 
+(-855 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
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-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-965))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-859 |lv| R) 
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+(-856 |lv| R) 
 ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) 
 NIL 
 NIL 
-(-860 |TheField| |ThePols|) 
+(-857 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-759)))) 
-(-861 R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-858 R) 
 ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-1094) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-1094) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-1094) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-1094) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-1094) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-862 R S) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| (-1091) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-859 R S) 
 ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-863 |x| R) 
+(-860 |x| R) 
 ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) 
 NIL 
 NIL 
-(-864 S R E |VarSet|) 
+(-861 S R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-825))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#4| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| |#4| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| |#4| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#4| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) 
-(-865 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#4| (QUOTE (-797 (-329)))) (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
+(-862 R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-866 E V R P -3098) 
+(-863 E V R P -3095) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-867 E |Vars| R P S) 
+(-864 E |Vars| R P S) 
 ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) 
 NIL 
 NIL 
-(-868 E V R P -3098) 
+(-865 E V R P -3095) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-395)))) 
-(-869) 
+((|HasCategory| |#3| (QUOTE (-392)))) 
+(-866) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-870) 
+(-867) 
 ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-871 R E) 
+(-868 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3999))) 
-(-872 R L) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-101)))) (|HasAttribute| |#1| (QUOTE -3995))) 
+(-869 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-873 S) 
+(-870 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-874 A B) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-871 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
-(-875) 
+(-872) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) 
 NIL 
 NIL 
-(-876 -3098) 
+(-873 -3095) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-877 I) 
+(-874 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-878) 
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 ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) 
 NIL 
 NIL 
-(-879 A B) 
+(-876 A B) 
 ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) 
-((-3998 -12 (|has| |#2| (-416)) (|has| |#1| (-416)))) 
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-(-880) 
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+(-877) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-881 T$) 
+(-878 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-882 T$) 
+(-879 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-883 S T$) 
+(-880 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-884) 
+(-881) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-885 S) 
+(-882 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) 
 NIL 
 NIL 
-(-886 R |polR|) 
+(-883 R |polR|) 
 ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{semiSubResultantGcdEuclidean2}}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.fr}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the gcd of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-395)))) 
-(-887) 
+((|HasCategory| |#1| (QUOTE (-392)))) 
+(-884) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-888) 
+(-885) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-889 S |Coef| |Expon| |Var|) 
+(-886 S |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
 NIL 
 NIL 
-(-890 |Coef| |Expon| |Var|) 
+(-887 |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-891) 
+(-888) 
 ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-892 S R E |VarSet| P) 
+(-889 S R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-499)))) 
-(-893 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-496)))) 
+(-890 R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
 NIL 
-(-894 R E V P) 
+(-891 R E V P) 
 ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) 
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-((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-260)))) (|HasCategory| |#1| (QUOTE (-395)))) 
-(-895 K) 
+((-11 (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-257)))) (|HasCategory| |#1| (QUOTE (-392)))) 
+(-892 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
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-(-896 |VarSet| E RC P) 
+(-893 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
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-(-897 R) 
+(-894 R) 
 ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) 
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-(-898 R1 R2) 
+(-895 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
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-(-899 R) 
+(-896 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
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-(-900 K) 
+(-897 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-901 R E OV PPR) 
+(-898 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-902 K R UP -3098) 
+(-899 K R UP -3095) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-903 R |Var| |Expon| |Dpoly|) 
+(-900 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-260))))) 
-(-904 |vl| |nv|) 
+((-11 (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-257))))) 
+(-901 |vl| |nv|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) 
 NIL 
 NIL 
-(-905 R E V P TS) 
+(-902 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-906) 
+(-903) 
 ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) 
 NIL 
 NIL 
-(-907 A S) 
+(-904 A S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-954 (-1094)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-744))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-1070)))) 
-(-908 S) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) 
+(-905 S) 
 ((|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}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-909 A B R S) 
+(-906 A B R S) 
 ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) 
 NIL 
 NIL 
-(-910 |n| K) 
+(-907 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-911) 
+(-908) 
 ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) 
 NIL 
 NIL 
-(-912 S) 
+(-909 S) 
 ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) 
 NIL 
 NIL 
-(-913 R) 
+(-910 R) 
 ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) 
-((-3994 |has| |#1| (-248)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-248))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-248))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (|%list| (QUOTE -459) (QUOTE (-1094)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -243) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-487)))) 
-(-914 S R) 
+((-3990 |has| |#1| (-245)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -240) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-911 S R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-248)))) 
-(-915 R) 
+((|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-245)))) 
+(-912 R) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3994 |has| |#1| (-248)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 |has| |#1| (-245)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-916 QR R QS S) 
+(-913 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-917 S) 
+(-914 S) 
 ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-918 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-915 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-919) 
+(-916) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-920 -3098 UP UPUP |radicnd| |n|) 
+(-917 -3095 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-3994 |has| (-352 |#2|) (-314)) (-3999 |has| (-352 |#2|) (-314)) (-3993 |has| (-352 |#2|) (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-352 |#2|) (QUOTE (-118))) (|HasCategory| (-352 |#2|) (QUOTE (-120))) (|HasCategory| (-352 |#2|) (QUOTE (-301))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-322))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (|HasCategory| (-352 |#2|) (QUOTE (-301)))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-301))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) (OR (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094)))))) (|HasCategory| (-352 |#2|) (QUOTE (-584 (-488)))) (OR (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488)))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-352 |#2|) (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-191))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-815 (-1094))))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-192))) (|HasCategory| (-352 |#2|) (QUOTE (-314)))) (-12 (|HasCategory| (-352 |#2|) (QUOTE (-314))) (|HasCategory| (-352 |#2|) (QUOTE (-813 (-1094)))))) 
-(-921 |bb|) 
+((-3990 |has| (-349 |#2|) (-311)) (-3995 |has| (-349 |#2|) (-311)) (-3989 |has| (-349 |#2|) (-311)) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-349 |#2|) (QUOTE (-115))) (|HasCategory| (-349 |#2|) (QUOTE (-117))) (|HasCategory| (-349 |#2|) (QUOTE (-298))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-298)))) (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-319))) (OR (-11 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-311)))) (|HasCategory| (-349 |#2|) (QUOTE (-298)))) (OR (-11 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-311)))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-188))) (|HasCategory| (-349 |#2|) (QUOTE (-311)))) (|HasCategory| (-349 |#2|) (QUOTE (-298)))) (OR (-11 (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-810 (-1091))))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-298))) (|HasCategory| (-349 |#2|) (QUOTE (-810 (-1091)))))) (OR (-11 (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-810 (-1091))))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-349 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-951 (-349 (-485)))))) (|HasCategory| (-349 |#2|) (QUOTE (-951 (-349 (-485))))) (|HasCategory| (-349 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-319))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-188))) (|HasCategory| (-349 |#2|) (QUOTE (-311)))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-812 (-1091))))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-189))) (|HasCategory| (-349 |#2|) (QUOTE (-311)))) (-11 (|HasCategory| (-349 |#2|) (QUOTE (-311))) (|HasCategory| (-349 |#2|) (QUOTE (-810 (-1091)))))) 
+(-918 |bb|) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-488) (QUOTE (-825))) (|HasCategory| (-488) (QUOTE (-954 (-1094)))) (|HasCategory| (-488) (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-120))) (|HasCategory| (-488) (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-937))) (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760))) (OR (|HasCategory| (-488) (QUOTE (-744))) (|HasCategory| (-488) (QUOTE (-760)))) (|HasCategory| (-488) (QUOTE (-954 (-488)))) (|HasCategory| (-488) (QUOTE (-1070))) (|HasCategory| (-488) (QUOTE (-800 (-332)))) (|HasCategory| (-488) (QUOTE (-800 (-488)))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-488) (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-488) (QUOTE (-191))) (|HasCategory| (-488) (QUOTE (-815 (-1094)))) (|HasCategory| (-488) (QUOTE (-192))) (|HasCategory| (-488) (QUOTE (-813 (-1094)))) (|HasCategory| (-488) (QUOTE (-459 (-1094) (-488)))) (|HasCategory| (-488) (QUOTE (-262 (-488)))) (|HasCategory| (-488) (QUOTE (-243 (-488) (-488)))) (|HasCategory| (-488) (QUOTE (-260))) (|HasCategory| (-488) (QUOTE (-487))) (|HasCategory| (-488) (QUOTE (-584 (-488)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-488) (QUOTE (-825)))) (|HasCategory| (-488) (QUOTE (-118))))) 
-(-922) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-117))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-329)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-188))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-259 (-485)))) (|HasCategory| (-485) (QUOTE (-240 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-257))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-11 (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-115))))) 
+(-919) 
 ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) 
 NIL 
 NIL 
-(-923) 
+(-920) 
 ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) 
 NIL 
 NIL 
-(-924 RP) 
+(-921 RP) 
 ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) 
 NIL 
 NIL 
-(-925 S) 
+(-922 S) 
 ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) 
 NIL 
 NIL 
-(-926 A S) 
+(-923 A S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) 
-(-927 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-69)))) 
+(-924 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
 NIL 
-(-928 S) 
+(-925 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-929) 
+(-926) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
-((-3994 . T) (-3999 . T) (-3993 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3998 . T)) 
+((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3997 "*") . T) (-3994 . T)) 
 NIL 
-(-930 R -3098) 
+(-927 R -3095) 
 ((|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 
-(-931 R -3098) 
+(-928 R -3095) 
 ((|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 
-(-932 -3098 UP) 
+(-929 -3095 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 
-(-933 -3098 UP) 
+(-930 -3095 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 
-(-934 S) 
+(-931 S) 
 ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-935 F1 UP UPUP R F2) 
+(-932 F1 UP UPUP R F2) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) 
 NIL 
 NIL 
-(-936) 
+(-933) 
 ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) 
 NIL 
 NIL 
-(-937) 
+(-934) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-938 |Pol|) 
+(-935 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-939 |Pol|) 
+(-936 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-940) 
+(-937) 
 ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-941 |TheField|) 
+(-938 |TheField|) 
 ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) 
-((-3994 . T) (-3999 . T) (-3993 . T) (-3996 . T) (-3995 . T) ((-4003 "*") . T) (-3998 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-352 (-488)) (QUOTE (-954 (-488))))) 
-(-942 -3098 L) 
+((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3997 "*") . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-349 (-485)) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-349 (-485)) (QUOTE (-951 (-349 (-485))))) (|HasCategory| (-349 (-485)) (QUOTE (-951 (-485))))) 
+(-939 -3095 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
-(-943 S) 
+(-940 S) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) 
 NIL 
 NIL 
-(-944 R E V P) 
+(-941 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
-((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) 
-(-945) 
+((-11 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-11 (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) 
+(-942) 
 ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) 
 NIL 
 NIL 
-(-946 R) 
+(-943 R) 
 ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-4003 "*")))) 
-(-947 R) 
+((|HasAttribute| |#1| (QUOTE (-3997 "*")))) 
+(-944 R) 
 ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-260)))) 
-(-948 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-319)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257)))) 
+(-945 S) 
 ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-949 S) 
+(-946 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-950 S) 
+(-947 S) 
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-951 -3098 |Expon| |VarSet| |FPol| |LFPol|) 
+(-948 -3095 |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"))) 
-(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-952) 
+(-949) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-953 A S) 
+(-950 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-954 S) 
+(-951 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-955 Q R) 
+(-952 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-956 R) 
+(-953 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-957) 
+(-954) 
 ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) 
 NIL 
 NIL 
-(-958 UP) 
+(-955 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-959 R) 
+(-956 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) 
 NIL 
 NIL 
-(-960 T$) 
+(-957 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-961 T$) 
+(-958 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-962 R |ls|) 
+(-959 R |ls|) 
 ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) 
 NIL 
-((-12 (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-1017))) (|HasCategory| (-707 |#1| (-777 |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|)))))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-557 (-477)))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-777 |#2|) (QUOTE (-322))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|))))) (|HasCategory| (-707 |#1| (-777 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -707) (|devaluate| |#1|) (|%list| (QUOTE -777) (|devaluate| |#2|)))))) 
-(-963) 
+((-11 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-319))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) 
+(-960) 
 ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-964 S) 
+(-961 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-965) 
+(-962) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
-((-3998 . T)) 
+((-3994 . T)) 
 NIL 
-(-966 |xx| -3098) 
+(-963 |xx| -3095) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-967 S) 
+(-964 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-968 S |m| |n| R |Row| |Col|) 
+(-965 S |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-260))) (|HasCategory| |#4| (QUOTE (-314))) (|HasCategory| |#4| (QUOTE (-499))) (|HasCategory| |#4| (QUOTE (-148)))) 
-(-969 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-257))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-145)))) 
+(-966 |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.")) (|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."))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-970 |m| |n| R) 
+(-967 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-3996 . T) (-3995 . T)) 
-((|HasCategory| |#3| (QUOTE (-148))) (OR (-12 (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#3| (QUOTE (-148))) (|HasCategory| |#3| (QUOTE (-314)))) (|HasCategory| |#3| (QUOTE (-314))) (|HasCategory| |#3| (QUOTE (-260))) (|HasCategory| |#3| (QUOTE (-499))) (-12 (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (|%list| (QUOTE -262) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1017))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-556 (-776))))) 
-(-971 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#3| (QUOTE (-145))) (OR (-11 (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-11 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-11 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-311)))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-257))) (|HasCategory| |#3| (QUOTE (-496))) (-11 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-69))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) 
+(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-972 R) 
+(-969 R) 
 ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-973 S) 
+(-970 S) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-974) 
+(-971) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-975 S T$) 
+(-972 S T$) 
 ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1017)))) 
-(-976 S) 
+((|HasCategory| |#1| (QUOTE (-1014)))) 
+(-973 S) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-977) 
+(-974) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-978 |TheField| |ThePolDom|) 
+(-975 |TheField| |ThePolDom|) 
 ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-979) 
+(-976) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) 
-((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-980 S R E V) 
+(-977 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-38 (-488)))) (|HasCategory| |#2| (QUOTE (-908 (-488)))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#4| (QUOTE (-557 (-1094))))) 
-(-981 R E V) 
+((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-35 (-485)))) (|HasCategory| |#2| (QUOTE (-905 (-485)))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-1091))))) 
+(-978 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-982) 
+(-979) 
 ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) 
 NIL 
 NIL 
-(-983 S |TheField| |ThePols|) 
+(-980 S |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-984 |TheField| |ThePols|) 
+(-981 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-985 R E V P TS) 
+(-982 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-986 S R E V P) 
+(-983 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-987 R E V P) 
+(-984 R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-988 R E V P TS) 
+(-985 R E V P TS) 
 ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}ts,{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-989) 
+(-986) 
 ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-990) 
+(-987) 
 ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) 
 NIL 
 NIL 
-(-991 |Base| R -3098) 
+(-988 |Base| R -3095) 
 ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) 
 NIL 
 NIL 
-(-992 |f|) 
+(-989 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-993 |Base| R -3098) 
+(-990 |Base| R -3095) 
 ((|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 
-(-994 R |ls|) 
+(-991 R |ls|) 
 ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) 
 NIL 
 NIL 
-(-995 R UP M) 
+(-992 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."))) 
-((-3994 |has| |#1| (-314)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-301))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-301)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-322))) (OR (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (|HasCategory| |#1| (QUOTE (-301)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-815 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-314)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))))) 
-(-996 UP SAE UPA) 
+((-3990 |has| |#1| (-311)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-298))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-319))) (OR (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-11 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-311)))) (-11 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) 
+(-993 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-997 UP SAE UPA) 
+(-994 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-998) 
+(-995) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-999) 
+(-996) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-1000 S) 
+(-997 S) 
 ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) 
 NIL 
 NIL 
-(-1001) 
+(-998) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-1002 R) 
+(-999 R) 
 ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) 
 NIL 
 NIL 
-(-1003 R) 
+(-1000 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"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-1004 (-1094)) (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-192))) (|HasCategory| |#1| (QUOTE (-191))) (|HasCategory| |#1| (QUOTE (-815 (-1094)))) (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1004 S) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-188))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-1001 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) 
 NIL 
 NIL 
-(-1005 S) 
+(-1002 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-1017)))) 
-(-1006 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
+(-1003 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-759)))) 
-(-1007) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1004) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1008 S) 
+(-1005 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1005 |#1|) (QUOTE (-1017)))) 
-(-1009 R S) 
+((|HasCategory| (-1002 |#1|) (QUOTE (-1014)))) 
+(-1006 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1010 S) 
+(-1007 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
 NIL 
 NIL 
-(-1011 S L) 
+(-1008 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) 
 NIL 
 NIL 
-(-1012) 
+(-1009) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1013 S) 
+(-1010 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the members function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) 
-((-3991 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#1| (QUOTE (-322))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) 
-(-1014 A S) 
+((-3987 . T)) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) 
+(-1011 A S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1015 S) 
+(-1012 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
-((-3991 . T)) 
+((-3987 . T)) 
 NIL 
-(-1016 S) 
+(-1013 S) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1017) 
+(-1014) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1018 |m| |n|) 
+(-1015 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1019) 
+(-1016) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1020 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1017 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1021 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1018 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1022 R E V P TS) 
+(-1019 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1023 R E V P TS) 
+(-1020 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1024 R E V P) 
+(-1021 R E V P) 
 ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(ts,{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1025) 
+(-1022) 
 ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) 
 NIL 
 NIL 
-(-1026 T$) 
+(-1023 T$) 
 ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) 
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1027 T$) 
+(-1024 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) 
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3062 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3059 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1028 S) 
+(-1025 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1029) 
+(-1026) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1030 |dimtot| |dim1| S) 
+(-1027 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-3995 |has| |#3| (-965)) (-3996 |has| |#3| (-965)) (-3998 |has| |#3| (-6 -3998))) 
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(-11 (|HasCategory| |#3| (QUOTE (-188))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-11 (|HasCategory| |#3| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3994)) (-11 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-11 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-145))) (|HasCategory| |#3| (QUOTE (-20))) (|HasCategory| |#3| (QUOTE (-101))) (|HasCategory| |#3| (QUOTE (-22))) (-11 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-11 (|HasCategory| |#3| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#3|)))) 
+(-1028 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-395)))) 
-(-1032) 
+((|HasCategory| |#1| (QUOTE (-392)))) 
+(-1029) 
 ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) 
 NIL 
 NIL 
-(-1033) 
+(-1030) 
 ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) 
 NIL 
 NIL 
-(-1034 R -3098) 
+(-1031 R -3095) 
 ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1035 R) 
+(-1032 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1036) 
+(-1033) 
 ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) 
 NIL 
 NIL 
-(-1037) 
+(-1034) 
 ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) 
-((-3989 . T) (-3993 . T) (-3988 . T) (-3999 . T) (-4000 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1038 S) 
+(-1035 S) 
 ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\#s}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
 NIL 
 NIL 
-(-1039 S) 
+(-1036 S) 
 ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) 
 NIL 
 NIL 
-(-1040 S |ndim| R |Row| |Col|) 
+(-1037 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-314))) (|HasAttribute| |#3| (QUOTE (-4003 "*"))) (|HasCategory| |#3| (QUOTE (-148)))) 
-(-1041 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-311))) (|HasAttribute| |#3| (QUOTE (-3997 "*"))) (|HasCategory| |#3| (QUOTE (-145)))) 
+(-1038 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1042 R |Row| |Col| M) 
+(-1039 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-1043 R |VarSet|) 
+(-1040 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."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-825))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-825)))) (OR (|HasCategory| |#1| (QUOTE (-395))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-332)))) (|HasCategory| |#2| (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#1| (QUOTE (-800 (-488)))) (|HasCategory| |#2| (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-332))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-804 (-488))))) (|HasCategory| |#2| (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-557 (-477))))) (|HasCategory| |#1| (QUOTE (-584 (-488)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3999)) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1044 |Coef| |Var| SMP) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-329)))) (|HasCategory| |#2| (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-329))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-1041 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-1045 R E V P) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-1042 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}"))) 
 NIL 
 NIL 
-(-1046 UP -3098) 
+(-1043 UP -3095) 
 ((|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 
-(-1047 R) 
+(-1044 R) 
 ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) 
 NIL 
 NIL 
-(-1048 R) 
+(-1045 R) 
 ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1049 R) 
+(-1046 R) 
 ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) 
 NIL 
 NIL 
-(-1050 S A) 
+(-1047 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-760)))) 
-(-1051 R) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1048 R) 
 ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) 
 NIL 
 NIL 
-(-1052 R) 
+(-1049 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1053) 
+(-1050) 
 ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) 
 NIL 
 NIL 
-(-1054) 
+(-1051) 
 ((|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 
-(-1055) 
+(-1052) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) 
 NIL 
 NIL 
-(-1056) 
+(-1053) 
 ((|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 
-(-1057) 
+(-1054) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1058 V C) 
+(-1055 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1059 V C) 
+(-1056 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
 NIL 
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-(-1060 |ndim| R) 
+((-11 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -259) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-69))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|))))) 
+(-1057 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) 
-((-3998 . T) (-3990 |has| |#2| (-6 (-4003 "*"))) (-3995 . T) (-3996 . T)) 
-((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-191))) (|HasAttribute| |#2| (QUOTE (-4003 #1="*"))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| |#2| (QUOTE (-260))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-314))) (OR (|HasAttribute| |#2| (QUOTE (-4003 #1#))) (|HasCategory| |#2| (QUOTE (-192))) (|HasCategory| |#2| (QUOTE (-813 (-1094))))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-148)))) 
-(-1061 S) 
+((-3994 . T) (-3986 |has| |#2| (-6 (-3997 "*"))) (-3991 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-188))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-311))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-145)))) 
+(-1058 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1062) 
+(-1059) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1063 R E V P TS) 
+(-1060 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1064 R E V P) 
+(-1061 R E V P) 
 ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
-((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) 
-(-1065) 
+((-11 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-11 (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) 
+(-1062) 
 ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) 
 NIL 
 NIL 
-(-1066 S) 
+(-1063 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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1067 A S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69)))) 
+(-1064 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1068 S) 
+(-1065 S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1069 |Key| |Ent| |dent|) 
+(-1066 |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."))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-1070) 
+((-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-1067) 
 ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) 
 NIL 
 NIL 
-(-1071) 
+(-1068) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1072 |Coef|) 
+(-1069 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1073 S) 
+(-1070 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-1074 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-1071 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 
-(-1075 A B) 
+(-1072 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 
-(-1076 A B C) 
+(-1073 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 
-(-1077) 
+(-1074) 
 ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) 
 NIL 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-760)))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017))))) (|HasCategory| (-117) (QUOTE (-556 (-776)))) (|HasCategory| (-117) (QUOTE (-557 (-477)))) (OR (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| (-117) (QUOTE (-760))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1017))) (-12 (|HasCategory| (-117) (QUOTE (-262 (-117)))) (|HasCategory| (-117) (QUOTE (-1017)))) (-12 (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-320 (-117)))) (|HasCategory| $ (QUOTE (-1039 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1039 (-117)))) (|HasCategory| (-117) (QUOTE (-760))))) 
-(-1078 |Entry|) 
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+(-1075 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 NIL 
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-(-1079 A) 
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+(-1076 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) 
-(-1080 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485)))))) 
+(-1077 |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 
-(-1081 |Coef|) 
+(-1078 |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 
-(-1082 R UP) 
+(-1079 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 (-260)))) 
-(-1083 |n| R) 
+((|HasCategory| |#1| (QUOTE (-257)))) 
+(-1080 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1084 S1 S2) 
+(-1081 S1 S2) 
 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) 
 NIL 
 NIL 
-(-1085) 
+(-1082) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1086 |Coef| |var| |cen|) 
+(-1083 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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-(-1087 R -3098) 
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(-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-484)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-257)))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-115))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-741)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-741)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-145)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-188)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-757)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-117)))) (|HasCategory| |#1| (QUOTE (-117)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-115)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-115))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-115))))) 
+(-1084 R -3095) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
 NIL 
-(-1088 R) 
+(-1085 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 
-(-1089 R) 
+(-1086 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1090 R S) 
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+(-1087 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 
-(-1091 E OV R P) 
+(-1088 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 
-(-1092 |Coef| |var| |cen|) 
+(-1089 |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."))) 
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-(-1093 |Coef| |var| |cen|) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1090 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|)))) (|HasCategory| (-698) (QUOTE (-1029))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasCategory| |#1| (QUOTE (-314))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) 
-(-1094) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1091) 
 ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) 
 NIL 
 NIL 
-(-1095 R) 
+(-1092 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1096 R) 
+(-1093 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-6 -3999)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#1| (QUOTE (-954 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-954 (-488)))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-395))) (-12 (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| (-888) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3999))) 
-(-1097) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-392))) (-11 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-885) (QUOTE (-101)))) (|HasAttribute| |#1| (QUOTE -3995))) 
+(-1094) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
 NIL 
-(-1098) 
+(-1095) 
 ((|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 
-(-1099) 
+(-1096) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1100 N) 
+(-1097 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1101 N) 
+(-1098 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) 
 NIL 
 NIL 
-(-1102) 
+(-1099) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1103 R) 
+(-1100 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 
-(-1104) 
+(-1101) 
 ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) 
 NIL 
 NIL 
-(-1105 S) 
+(-1102 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1106 |Key| |Entry|) 
+(-1103 |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}"))) 
 NIL 
-((-12 (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -262) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017)))) (OR (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| |#2| (QUOTE (-556 (-776))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-557 (-477)))) (-12 (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (|%list| (QUOTE -262) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-556 (-776)))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-1017))) (-12 (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3867 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -320) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-1107 S) 
+((-11 (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-11 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-69))) (OR (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-11 (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (QUOTE (-69)))) (|HasCategory| $ (|%list| (QUOTE -317) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3864) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-11 (|HasCategory| |#2| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-1104 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 
-(-1108 S) 
+(-1105 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
 NIL 
-(-1109 R) 
+(-1106 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1110 S |Key| |Entry|) 
+(-1107 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}."))) 
 NIL 
 NIL 
-(-1111 |Key| |Entry|) 
+(-1108 |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}."))) 
 NIL 
 NIL 
-(-1112 |Key| |Entry|) 
+(-1109 |Key| |Entry|) 
 ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) 
 NIL 
 NIL 
-(-1113) 
+(-1110) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1114 S) 
+(-1111 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 
-(-1115) 
+(-1112) 
 ((|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 
-(-1116 R) 
+(-1113 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 
-(-1117) 
+(-1114) 
 ((|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 
-(-1118 S) 
+(-1115 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1119) 
+(-1116) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1120 S) 
+(-1117 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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1017))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|)))) 
-(-1121 S) 
+((-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-1118 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1122) 
+(-1119) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1123 R -3098) 
+(-1120 R -3095) 
 ((|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 
-(-1124 R |Row| |Col| M) 
+(-1121 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 
-(-1125 R -3098) 
+(-1122 R -3095) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -557) (|%list| (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -800) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -557) (|%list| (QUOTE -804) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -800) (|devaluate| |#1|))))) 
-(-1126 |Coef|) 
+((-11 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) 
+(-1123 |Coef|) 
 ((|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}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-1127 S R E V P) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-117))) (|HasCategory| |#1| (QUOTE (-115))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-1124 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-322)))) 
-(-1128 R E V P) 
+((|HasCategory| |#4| (QUOTE (-319)))) 
+(-1125 R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
 NIL 
-(-1129 |Curve|) 
+(-1126 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 
-(-1130) 
+(-1127) 
 ((|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 
-(-1131 S) 
+(-1128 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-556 (-776))))) 
-(-1132 -3098) 
+((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-1129 -3095) 
 ((|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 
-(-1133) 
+(-1130) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1134) 
+(-1131) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1135 S) 
+(-1132 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-760)))) 
-(-1136) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1133) 
 ((|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 
-(-1137 S) 
+(-1134 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 
-(-1138) 
+(-1135) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1139) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1140) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1141) 
+(-1138) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1142) 
+(-1139) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1143 |Coef| |var| |cen|) 
+(-1140 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-744)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-813 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-815 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-192)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-192)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-191)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-488)) (|devaluate| |#1|))))) (|HasCategory| (-488) (QUOTE (-1029))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-314))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-825)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) 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|#3|) (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (|%list| (QUOTE -243) (|%list| (QUOTE -1173) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1173) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (|%list| (QUOTE -262) (|%list| (QUOTE -1173) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (|%list| (QUOTE -459) (QUOTE (-1094)) (|%list| (QUOTE -1173) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-584 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-800 (-332))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-488))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE 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(QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-760)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-825)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1173 |#1| |#2| |#3|) (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1144 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
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+(-1141 |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 
-(-1145 |Coef|) 
+(-1142 |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree <= \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
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 NIL 
-(-1146 S |Coef| UTS) 
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 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
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-(-1147 |Coef| UTS) 
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 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
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 NIL 
-(-1148 |Coef| UTS) 
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 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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(-488)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-815 (-1094))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-191)))) (OR (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-120))))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-118)))))) 
-(-1149 ZP) 
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(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-188))))) (|HasCategory| (-485) (QUOTE (-1026))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-311))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-741)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-741)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757))))) (OR (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1067)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -240) (|devaluate| |#2|) (|devaluate| |#2|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-797 (-329))))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-822))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-484)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-257)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-115))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-188))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-812 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-812 (-1091))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-188)))) (OR (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-117))))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#1| (QUOTE (-115))) (-11 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-115)))))) 
+(-1146 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 
-(-1150 S) 
+(-1147 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 (-759))) (|HasCategory| |#1| (QUOTE (-1017)))) 
-(-1151 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
+(-1148 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 (-759)))) 
-(-1152 |x| R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1149 |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}"))) 
-(((-4003 "*") |has| |#2| (-148)) (-3994 |has| |#2| (-499)) (-3997 |has| |#2| (-314)) (-3999 |has| |#2| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-332)))) (|HasCategory| (-998) (QUOTE (-800 (-332))))) (-12 (|HasCategory| |#2| (QUOTE (-800 (-488)))) (|HasCategory| (-998) (QUOTE (-800 (-488))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-332))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-332)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-804 (-488))))) (|HasCategory| (-998) (QUOTE (-557 (-804 (-488)))))) (-12 (|HasCategory| |#2| (QUOTE (-557 (-477)))) (|HasCategory| (-998) (QUOTE (-557 (-477))))) (|HasCategory| |#2| (QUOTE (-584 (-488)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-488)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488)))))) (|HasCategory| |#2| (QUOTE (-954 (-352 (-488))))) (OR (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-825)))) (OR (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-815 (-1094)))) (|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasCategory| |#2| (QUOTE (-191))) (|HasCategory| |#2| (QUOTE (-192))) (|HasAttribute| |#2| (QUOTE -3999)) (|HasCategory| |#2| (QUOTE (-395))) (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1153 |x| R |y| S) 
+(((-3997 "*") |has| |#2| (-145)) (-3990 |has| |#2| (-496)) (-3993 |has| |#2| (-311)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-496)))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-329)))) (|HasCategory| (-995) (QUOTE (-797 (-329))))) (-11 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-329))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-329)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-11 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-117))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-349 (-485))))) (OR (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-188))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (OR (-11 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-115)))) (|HasCategory| |#2| (QUOTE (-115))))) 
+(-1150 |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 
-(-1154 R Q UP) 
+(-1151 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1155 R UP) 
+(-1152 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1156 R UP) 
+(-1153 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 
-(-1157 R U) 
+(-1154 R U) 
 ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) 
 NIL 
 NIL 
-(-1158 S R) 
+(-1155 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314))) (|HasCategory| |#2| (QUOTE (-395))) (|HasCategory| |#2| (QUOTE (-499))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1070)))) 
-(-1159 R) 
+((|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1067)))) 
+(-1156 R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3997 |has| |#1| (-314)) (-3999 |has| |#1| (-6 -3999)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-311)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1160 R PR S PS) 
+(-1157 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 
-(-1161 S |Coef| |Expon|) 
+(-1158 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-813 (-1094)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1029))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#2|) (QUOTE (-1094)))))) 
-(-1162 |Coef| |Expon|) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) 
+(-1159 |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1163 RC P) 
+(-1160 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1164 |Coef| |var| |cen|) 
+(-1161 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) 
-(-1165 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1162 |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 
-(-1166 |Coef|) 
+(-1163 |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."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1167 S |Coef| ULS) 
+(-1164 S |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
 NIL 
 NIL 
-(-1168 |Coef| ULS) 
+(-1165 |Coef| ULS) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1169 |Coef| ULS) 
+(-1166 |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)}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3999 |has| |#1| (-314)) (-3993 |has| |#1| (-314)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#1| (QUOTE (-148))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488))) (|devaluate| |#1|)))) (|HasCategory| (-352 (-488)) (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-314))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (OR (|HasCategory| |#1| (QUOTE (-314))) (|HasCategory| |#1| (QUOTE (-499)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -352) (QUOTE (-488)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-352 (-488)))))) 
-(-1170 R FE |var| |cen|) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-145))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-349 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-496)))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -349) (QUOTE (-485)))))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-35 (-349 (-485)))))) 
+(-1167 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))}."))) 
-(((-4003 "*") |has| (-1164 |#2| |#3| |#4|) (-148)) (-3994 |has| (-1164 |#2| |#3| |#4|) (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-38 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-148))) (OR (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-38 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-352 (-488)))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-352 (-488))))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-954 (-488)))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-314))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-395))) (|HasCategory| (-1164 |#2| |#3| |#4|) (QUOTE (-499)))) 
-(-1171 A S) 
+(((-3997 "*") |has| (-1161 |#2| |#3| |#4|) (-145)) (-3990 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-35 (-349 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-115))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-117))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-145))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-35 (-349 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-349 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-349 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) 
+(-1168 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1039) (|devaluate| |#2|)))) 
-(-1172 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-1169 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1173 |Coef| |var| |cen|) 
+(-1170 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-499))) (OR (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-813 (-1094)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-698)) (|devaluate| |#1|)))) (|HasCategory| (-698) (QUOTE (-1029))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasSignature| |#1| (|%list| (QUOTE -3953) (|%list| (|devaluate| |#1|) (QUOTE (-1094)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-698))))) (|HasCategory| |#1| (QUOTE (-314))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#1| (QUOTE (-29 (-488)))) (|HasCategory| |#1| (QUOTE (-875))) (|HasCategory| |#1| (QUOTE (-1119)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-352 (-488))))) (|HasSignature| |#1| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1094))))) (|HasSignature| |#1| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#1|))))))) 
-(-1174 |Coef1| |Coef2| UTS1 UTS2) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-115))) (|HasCategory| |#1| (QUOTE (-117))) (-11 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-11 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3950) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#1| (QUOTE (-26 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-11 (|HasCategory| |#1| (QUOTE (-35 (-349 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1171 |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 
-(-1175 S |Coef|) 
+(-1172 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-29 (-488)))) (|HasCategory| |#2| (QUOTE (-875))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasSignature| |#2| (|%list| (QUOTE -3087) (|%list| (|%list| (QUOTE -587) (QUOTE (-1094))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3818) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1094))))) (|HasCategory| |#2| (QUOTE (-38 (-352 (-488))))) (|HasCategory| |#2| (QUOTE (-314)))) 
-(-1176 |Coef|) 
+((|HasCategory| |#2| (QUOTE (-26 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3084) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3815) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-35 (-349 (-485))))) (|HasCategory| |#2| (QUOTE (-311)))) 
+(-1173 |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."))) 
-(((-4003 "*") |has| |#1| (-148)) (-3994 |has| |#1| (-499)) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") |has| |#1| (-145)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1177 |Coef| UTS) 
+(-1174 |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 
-(-1178 -3098 UP L UTS) 
+(-1175 -3095 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 (-499)))) 
-(-1179) 
+((|HasCategory| |#1| (QUOTE (-496)))) 
+(-1176) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
 NIL 
 NIL 
-(-1180 |sym|) 
+(-1177 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1181 S R) 
+(-1178 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-919))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-667))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1182 R) 
+((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-18))) (|HasCategory| |#2| (QUOTE (-20))) (|HasCategory| |#2| (QUOTE (-22)))) 
+(-1179 R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
 NIL 
-(-1183 R) 
+(-1180 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
 NIL 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-556 (-776)))) (|HasCategory| |#1| (QUOTE (-557 (-477)))) (OR (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| |#1| (QUOTE (-760))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-1017)))) (|HasCategory| (-488) (QUOTE (-760))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-667))) (|HasCategory| |#1| (QUOTE (-965))) (-12 (|HasCategory| |#1| (QUOTE (-919))) (|HasCategory| |#1| (QUOTE (-965)))) (|HasCategory| |#1| (QUOTE (-1017))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (|%list| (QUOTE -262) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-760))) (|HasCategory| $ (|%list| (QUOTE -1039) (|devaluate| |#1|))))) 
-(-1184 A B) 
+((OR (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-22))) (|HasCategory| |#1| (QUOTE (-20))) (|HasCategory| |#1| (QUOTE (-18))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-11 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-11 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-11 (|HasCategory| |#1| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-11 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-1181 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 
-(-1185) 
+(-1182) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1186) 
+(-1183) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1187) 
+(-1184) 
 ((|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 
-(-1188) 
+(-1185) 
 ((|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 
-(-1189) 
+(-1186) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1190 A S) 
+(-1187 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1191 S) 
+(-1188 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}."))) 
-((-3996 . T) (-3995 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1192 R) 
+(-1189 R) 
 ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) 
 NIL 
 NIL 
-(-1193 K R UP -3098) 
+(-1190 K R UP -3095) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-1194) 
+(-1191) 
 ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) 
 NIL 
 NIL 
-(-1195) 
+(-1192) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1196 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1193 R |VarSet| E P |vl| |wl| |wtlevel|) 
 ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: NB: previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) 
-((-3996 |has| |#1| (-148)) (-3995 |has| |#1| (-148)) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314)))) 
-(-1197 R E V P) 
+((-3992 |has| |#1| (-145)) (-3991 |has| |#1| (-145)) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-1194 R E V P) 
 ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) 
 NIL 
-((-12 (|HasCategory| |#4| (QUOTE (-1017))) (|HasCategory| |#4| (|%list| (QUOTE -262) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-557 (-477)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-499))) (|HasCategory| |#3| (QUOTE (-322))) (|HasCategory| |#4| (QUOTE (-556 (-776)))) (|HasCategory| |#4| (QUOTE (-1017))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -320) (|devaluate| |#4|)))) 
-(-1198 R) 
+((-11 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-11 (|HasCategory| |#4| (QUOTE (-69))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -317) (|devaluate| |#4|)))) 
+(-1195 R) 
 ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) 
-((-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1199 |vl| R) 
+(-1196 |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."))) 
-((-3998 . T) (-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T)) 
-((|HasCategory| |#2| (QUOTE (-148))) (|HasAttribute| |#2| (QUOTE -3994))) 
-(-1200 R |VarSet| XPOLY) 
+((-3994 . T) (-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-145))) (|HasAttribute| |#2| (QUOTE -3990))) 
+(-1197 R |VarSet| XPOLY) 
 ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) 
 NIL 
 NIL 
-(-1201 S -3098) 
+(-1198 S -3095) 
 ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-322))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1202 -3098) 
+((|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-115))) (|HasCategory| |#2| (QUOTE (-117)))) 
+(-1199 -3095) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3993 . T) (-3999 . T) (-3994 . T) ((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1203 |vl| R) 
+(-1200 |vl| R) 
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|sh| (($ $ (|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1204 |VarSet| R) 
+(-1201 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) 
-((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-658 (-352 (-488))))) (|HasAttribute| |#2| (QUOTE -3994))) 
-(-1205 R) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-655 (-349 (-485))))) (|HasAttribute| |#2| (QUOTE -3990))) 
+(-1202 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."))) 
-((-3994 |has| |#1| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-1206 |vl| R) 
+((-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasAttribute| |#1| (QUOTE -3990))) 
+(-1203 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1207 R E) 
+(-1204 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-3998 . T) (-3999 |has| |#1| (-6 -3999)) (-3994 |has| |#1| (-6 -3994)) (-3996 . T) (-3995 . T)) 
-((|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-314))) (|HasAttribute| |#1| (QUOTE -3998)) (|HasAttribute| |#1| (QUOTE -3999)) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-1208 |VarSet| R) 
+((-3994 . T) (-3995 |has| |#1| (-6 -3995)) (-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3990))) 
+(-1205 |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."))) 
-((-3994 |has| |#2| (-6 -3994)) (-3996 . T) (-3995 . T) (-3998 . T)) 
-((|HasCategory| |#2| (QUOTE (-148))) (|HasAttribute| |#2| (QUOTE -3994))) 
-(-1209) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-145))) (|HasAttribute| |#2| (QUOTE -3990))) 
+(-1206) 
 ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) 
 NIL 
 NIL 
-(-1210 A) 
+(-1207 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 
-(-1211 R |ls| |ls2|) 
+(-1208 R |ls| |ls2|) 
 ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1212 R) 
+(-1209 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1213 |p|) 
+(-1210 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-4003 "*") . T) (-3995 . T) (-3996 . T) (-3998 . T)) 
+(((-3997 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4800,4 +4800,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1966210 1966215 1966220 1966225) (-2 NIL 1966190 1966195 1966200 1966205) (-1 NIL 1966170 1966175 1966180 1966185) (0 NIL 1966150 1966155 1966160 1966165) (-1213 "ZMOD.spad" 1965959 1965972 1966088 1966145) (-1212 "ZLINDEP.spad" 1965057 1965068 1965949 1965954) (-1211 "ZDSOLVE.spad" 1955018 1955040 1965047 1965052) (-1210 "YSTREAM.spad" 1954513 1954524 1955008 1955013) (-1209 "YDIAGRAM.spad" 1954147 1954156 1954503 1954508) (-1208 "XRPOLY.spad" 1953367 1953387 1954003 1954072) (-1207 "XPR.spad" 1951295 1951308 1953085 1953184) (-1206 "XPOLYC.spad" 1950614 1950630 1951221 1951290) (-1205 "XPOLY.spad" 1950169 1950180 1950470 1950539) (-1204 "XPBWPOLY.spad" 1948640 1948660 1949975 1950044) (-1203 "XFALG.spad" 1945821 1945837 1948566 1948635) (-1202 "XF.spad" 1944284 1944299 1945723 1945816) (-1201 "XF.spad" 1942727 1942744 1944168 1944173) (-1200 "XEXPPKG.spad" 1941986 1942012 1942717 1942722) (-1199 "XDPOLY.spad" 1941600 1941616 1941842 1941911) (-1198 "XALG.spad" 1941268 1941279 1941556 1941595) (-1197 "WUTSET.spad" 1937132 1937149 1940763 1940768) (-1196 "WP.spad" 1936339 1936383 1936990 1937057) (-1195 "WHILEAST.spad" 1936137 1936146 1936329 1936334) (-1194 "WHEREAST.spad" 1935808 1935817 1936127 1936132) (-1193 "WFFINTBS.spad" 1933471 1933493 1935798 1935803) (-1192 "WEIER.spad" 1931693 1931704 1933461 1933466) (-1191 "VSPACE.spad" 1931366 1931377 1931661 1931688) (-1190 "VSPACE.spad" 1931059 1931072 1931356 1931361) (-1189 "VOID.spad" 1930736 1930745 1931049 1931054) (-1188 "VIEWDEF.spad" 1925937 1925946 1930726 1930731) (-1187 "VIEW3D.spad" 1909898 1909907 1925927 1925932) (-1186 "VIEW2D.spad" 1897797 1897806 1909888 1909893) (-1185 "VIEW.spad" 1895517 1895526 1897787 1897792) (-1184 "VECTOR2.spad" 1894156 1894169 1895507 1895512) (-1183 "VECTOR.spad" 1892572 1892583 1892823 1892828) (-1182 "VECTCAT.spad" 1890506 1890517 1892562 1892567) (-1181 "VECTCAT.spad" 1888227 1888240 1890285 1890290) (-1180 "VARIABLE.spad" 1888007 1888022 1888217 1888222) (-1179 "UTYPE.spad" 1887651 1887660 1887997 1888002) (-1178 "UTSODETL.spad" 1886946 1886970 1887607 1887612) (-1177 "UTSODE.spad" 1885162 1885182 1886936 1886941) (-1176 "UTSCAT.spad" 1882641 1882657 1885060 1885157) (-1175 "UTSCAT.spad" 1879788 1879806 1882209 1882214) (-1174 "UTS2.spad" 1879383 1879418 1879778 1879783) (-1173 "UTS.spad" 1874395 1874423 1877915 1878012) (-1172 "URAGG.spad" 1869116 1869127 1874385 1874390) (-1171 "URAGG.spad" 1863773 1863786 1869044 1869049) (-1170 "UPXSSING.spad" 1861541 1861567 1862977 1863110) (-1169 "UPXSCONS.spad" 1859359 1859379 1859732 1859881) (-1168 "UPXSCCA.spad" 1857930 1857950 1859205 1859354) (-1167 "UPXSCCA.spad" 1856643 1856665 1857920 1857925) (-1166 "UPXSCAT.spad" 1855232 1855248 1856489 1856638) (-1165 "UPXS2.spad" 1854775 1854828 1855222 1855227) (-1164 "UPXS.spad" 1852130 1852158 1852966 1853115) (-1163 "UPSQFREE.spad" 1850545 1850559 1852120 1852125) (-1162 "UPSCAT.spad" 1848340 1848364 1850443 1850540) (-1161 "UPSCAT.spad" 1845836 1845862 1847941 1847946) (-1160 "UPOLYC2.spad" 1845307 1845326 1845826 1845831) (-1159 "UPOLYC.spad" 1840387 1840398 1845149 1845302) (-1158 "UPOLYC.spad" 1835385 1835398 1840149 1840154) (-1157 "UPMP.spad" 1834317 1834330 1835375 1835380) (-1156 "UPDIVP.spad" 1833882 1833896 1834307 1834312) (-1155 "UPDECOMP.spad" 1832143 1832157 1833872 1833877) (-1154 "UPCDEN.spad" 1831360 1831376 1832133 1832138) (-1153 "UP2.spad" 1830724 1830745 1831350 1831355) (-1152 "UP.spad" 1828194 1828209 1828581 1828734) (-1151 "UNISEG2.spad" 1827691 1827704 1828150 1828155) (-1150 "UNISEG.spad" 1827044 1827055 1827610 1827615) (-1149 "UNIFACT.spad" 1826147 1826159 1827034 1827039) (-1148 "ULSCONS.spad" 1819993 1820013 1820363 1820512) (-1147 "ULSCCAT.spad" 1817730 1817750 1819839 1819988) (-1146 "ULSCCAT.spad" 1815575 1815597 1817686 1817691) (-1145 "ULSCAT.spad" 1813815 1813831 1815421 1815570) (-1144 "ULS2.spad" 1813329 1813382 1813805 1813810) (-1143 "ULS.spad" 1805362 1805390 1806307 1806730) (-1142 "UINT8.spad" 1805239 1805248 1805352 1805357) (-1141 "UINT64.spad" 1805115 1805124 1805229 1805234) (-1140 "UINT32.spad" 1804991 1805000 1805105 1805110) (-1139 "UINT16.spad" 1804867 1804876 1804981 1804986) (-1138 "UFD.spad" 1803932 1803941 1804793 1804862) (-1137 "UFD.spad" 1803059 1803070 1803922 1803927) (-1136 "UDVO.spad" 1801940 1801949 1803049 1803054) (-1135 "UDPO.spad" 1799521 1799532 1801896 1801901) (-1134 "TYPEAST.spad" 1799440 1799449 1799511 1799516) (-1133 "TYPE.spad" 1799372 1799381 1799430 1799435) (-1132 "TWOFACT.spad" 1798024 1798039 1799362 1799367) (-1131 "TUPLE.spad" 1797531 1797542 1797936 1797941) (-1130 "TUBETOOL.spad" 1794398 1794407 1797521 1797526) (-1129 "TUBE.spad" 1793045 1793062 1794388 1794393) (-1128 "TSETCAT.spad" 1781138 1781155 1793035 1793040) (-1127 "TSETCAT.spad" 1769195 1769214 1781094 1781099) (-1126 "TS.spad" 1767823 1767839 1768789 1768886) (-1125 "TRMANIP.spad" 1762187 1762204 1767511 1767516) (-1124 "TRIMAT.spad" 1761150 1761175 1762177 1762182) (-1123 "TRIGMNIP.spad" 1759677 1759694 1761140 1761145) (-1122 "TRIGCAT.spad" 1759189 1759198 1759667 1759672) (-1121 "TRIGCAT.spad" 1758699 1758710 1759179 1759184) (-1120 "TREE.spad" 1757300 1757311 1758332 1758337) (-1119 "TRANFUN.spad" 1757139 1757148 1757290 1757295) (-1118 "TRANFUN.spad" 1756976 1756987 1757129 1757134) (-1117 "TOPSP.spad" 1756650 1756659 1756966 1756971) (-1116 "TOOLSIGN.spad" 1756313 1756324 1756640 1756645) (-1115 "TEXTFILE.spad" 1754874 1754883 1756303 1756308) (-1114 "TEX1.spad" 1754430 1754441 1754864 1754869) (-1113 "TEX.spad" 1751624 1751633 1754420 1754425) (-1112 "TBCMPPK.spad" 1749725 1749748 1751614 1751619) (-1111 "TBAGG.spad" 1748990 1749013 1749715 1749720) (-1110 "TBAGG.spad" 1748253 1748278 1748980 1748985) (-1109 "TANEXP.spad" 1747661 1747672 1748243 1748248) (-1108 "TALGOP.spad" 1747385 1747396 1747651 1747656) (-1107 "TABLEAU.spad" 1746866 1746877 1747375 1747380) (-1106 "TABLE.spad" 1744576 1744599 1744846 1744851) (-1105 "TABLBUMP.spad" 1741355 1741366 1744566 1744571) (-1104 "SYSTEM.spad" 1740583 1740592 1741345 1741350) (-1103 "SYSSOLP.spad" 1738066 1738077 1740573 1740578) (-1102 "SYSPTR.spad" 1737965 1737974 1738056 1738061) (-1101 "SYSNNI.spad" 1737188 1737199 1737955 1737960) (-1100 "SYSINT.spad" 1736592 1736603 1737178 1737183) (-1099 "SYNTAX.spad" 1732926 1732935 1736582 1736587) (-1098 "SYMTAB.spad" 1730994 1731003 1732916 1732921) (-1097 "SYMS.spad" 1727023 1727032 1730984 1730989) (-1096 "SYMPOLY.spad" 1726156 1726167 1726238 1726365) (-1095 "SYMFUNC.spad" 1725657 1725668 1726146 1726151) (-1094 "SYMBOL.spad" 1723152 1723161 1725647 1725652) (-1093 "SUTS.spad" 1720265 1720293 1721684 1721781) (-1092 "SUPXS.spad" 1717607 1717635 1718456 1718605) (-1091 "SUPFRACF.spad" 1716712 1716730 1717597 1717602) (-1090 "SUP2.spad" 1716104 1716117 1716702 1716707) (-1089 "SUP.spad" 1713188 1713199 1713961 1714114) (-1088 "SUMRF.spad" 1712162 1712173 1713178 1713183) (-1087 "SUMFS.spad" 1711791 1711808 1712152 1712157) (-1086 "SULS.spad" 1703811 1703839 1704769 1705192) (-1085 "syntax.spad" 1703580 1703589 1703801 1703806) (-1084 "SUCH.spad" 1703270 1703285 1703570 1703575) (-1083 "SUBSPACE.spad" 1695401 1695416 1703260 1703265) (-1082 "SUBRESP.spad" 1694571 1694585 1695357 1695362) (-1081 "STTFNC.spad" 1691039 1691055 1694561 1694566) (-1080 "STTF.spad" 1687138 1687154 1691029 1691034) (-1079 "STTAYLOR.spad" 1679815 1679826 1687045 1687050) (-1078 "STRTBL.spad" 1677688 1677705 1677837 1677842) (-1077 "STRING.spad" 1676329 1676338 1676714 1676719) (-1076 "STREAM3.spad" 1675902 1675917 1676319 1676324) (-1075 "STREAM2.spad" 1675030 1675043 1675892 1675897) (-1074 "STREAM1.spad" 1674736 1674747 1675020 1675025) (-1073 "STREAM.spad" 1671696 1671707 1674187 1674192) (-1072 "STINPROD.spad" 1670632 1670648 1671686 1671691) (-1071 "STEPAST.spad" 1669866 1669875 1670622 1670627) (-1070 "STEP.spad" 1669183 1669192 1669856 1669861) (-1069 "STBL.spad" 1666996 1667024 1667163 1667168) (-1068 "STAGG.spad" 1665695 1665706 1666986 1666991) (-1067 "STAGG.spad" 1664392 1664405 1665685 1665690) (-1066 "STACK.spad" 1663836 1663847 1664086 1664091) (-1065 "SRING.spad" 1663596 1663605 1663826 1663831) (-1064 "SREGSET.spad" 1661189 1661206 1663091 1663096) (-1063 "SRDCMPK.spad" 1659766 1659786 1661179 1661184) (-1062 "SRAGG.spad" 1654971 1654980 1659756 1659761) (-1061 "SRAGG.spad" 1650174 1650185 1654961 1654966) (-1060 "SQMATRIX.spad" 1647863 1647881 1648779 1648854) (-1059 "SPLTREE.spad" 1642523 1642536 1647319 1647324) (-1058 "SPLNODE.spad" 1639143 1639156 1642513 1642518) (-1057 "SPFCAT.spad" 1637952 1637961 1639133 1639138) (-1056 "SPECOUT.spad" 1636504 1636513 1637942 1637947) (-1055 "SPADXPT.spad" 1628595 1628604 1636494 1636499) (-1054 "spad-parser.spad" 1628060 1628069 1628585 1628590) (-1053 "SPADAST.spad" 1627761 1627770 1628050 1628055) (-1052 "SPACEC.spad" 1611976 1611987 1627751 1627756) (-1051 "SPACE3.spad" 1611752 1611763 1611966 1611971) (-1050 "SORTPAK.spad" 1611301 1611314 1611708 1611713) (-1049 "SOLVETRA.spad" 1609064 1609075 1611291 1611296) (-1048 "SOLVESER.spad" 1607520 1607531 1609054 1609059) (-1047 "SOLVERAD.spad" 1603546 1603557 1607510 1607515) (-1046 "SOLVEFOR.spad" 1602008 1602026 1603536 1603541) (-1045 "SNTSCAT.spad" 1601630 1601647 1601998 1602003) (-1044 "SMTS.spad" 1599947 1599973 1601224 1601321) (-1043 "SMP.spad" 1597755 1597775 1598145 1598272) (-1042 "SMITH.spad" 1596600 1596625 1597745 1597750) (-1041 "SMATCAT.spad" 1594730 1594760 1596556 1596595) (-1040 "SMATCAT.spad" 1592780 1592812 1594608 1594613) (-1039 "aggcat.spad" 1592466 1592477 1592770 1592775) (-1038 "SKAGG.spad" 1591457 1591468 1592456 1592461) (-1037 "SINT.spad" 1590756 1590765 1591323 1591452) (-1036 "SIMPAN.spad" 1590484 1590493 1590746 1590751) (-1035 "SIGNRF.spad" 1589609 1589620 1590474 1590479) (-1034 "SIGNEF.spad" 1588895 1588912 1589599 1589604) (-1033 "syntax.spad" 1588312 1588321 1588885 1588890) (-1032 "SIG.spad" 1587674 1587683 1588302 1588307) (-1031 "SHP.spad" 1585618 1585633 1587630 1587635) (-1030 "SHDP.spad" 1574961 1574988 1575478 1575563) (-1029 "SGROUP.spad" 1574569 1574578 1574951 1574956) (-1028 "SGROUP.spad" 1574175 1574186 1574559 1574564) (-1027 "catdef.spad" 1573885 1573897 1573996 1574170) (-1026 "catdef.spad" 1573441 1573453 1573706 1573880) (-1025 "SGCF.spad" 1566580 1566589 1573431 1573436) (-1024 "SFRTCAT.spad" 1565548 1565565 1566570 1566575) (-1023 "SFRGCD.spad" 1564611 1564631 1565538 1565543) (-1022 "SFQCMPK.spad" 1559424 1559444 1564601 1564606) (-1021 "SEXOF.spad" 1559267 1559307 1559414 1559419) (-1020 "SEXCAT.spad" 1557095 1557135 1559257 1559262) (-1019 "SEX.spad" 1556987 1556996 1557085 1557090) (-1018 "SETMN.spad" 1555447 1555464 1556977 1556982) (-1017 "SETCAT.spad" 1554932 1554941 1555437 1555442) (-1016 "SETCAT.spad" 1554415 1554426 1554922 1554927) (-1015 "SETAGG.spad" 1550964 1550975 1554395 1554410) (-1014 "SETAGG.spad" 1547521 1547534 1550954 1550959) (-1013 "SET.spad" 1545691 1545702 1546790 1546805) (-1012 "syntax.spad" 1545394 1545403 1545681 1545686) (-1011 "SEGXCAT.spad" 1544550 1544563 1545384 1545389) (-1010 "SEGCAT.spad" 1543475 1543486 1544540 1544545) (-1009 "SEGBIND2.spad" 1543173 1543186 1543465 1543470) (-1008 "SEGBIND.spad" 1542931 1542942 1543120 1543125) (-1007 "SEGAST.spad" 1542661 1542670 1542921 1542926) (-1006 "SEG2.spad" 1542096 1542109 1542617 1542622) (-1005 "SEG.spad" 1541909 1541920 1542015 1542020) (-1004 "SDVAR.spad" 1541185 1541196 1541899 1541904) (-1003 "SDPOL.spad" 1538877 1538888 1539168 1539295) (-1002 "SCPKG.spad" 1536966 1536977 1538867 1538872) (-1001 "SCOPE.spad" 1536143 1536152 1536956 1536961) (-1000 "SCACHE.spad" 1534839 1534850 1536133 1536138) (-999 "SASTCAT.spad" 1534749 1534757 1534829 1534834) (-998 "SAOS.spad" 1534622 1534630 1534739 1534744) (-997 "SAERFFC.spad" 1534336 1534355 1534612 1534617) (-996 "SAEFACT.spad" 1534038 1534057 1534326 1534331) (-995 "SAE.spad" 1531689 1531704 1532299 1532434) (-994 "RURPK.spad" 1529349 1529364 1531679 1531684) (-993 "RULESET.spad" 1528803 1528826 1529339 1529344) (-992 "RULECOLD.spad" 1528656 1528668 1528793 1528798) (-991 "RULE.spad" 1526905 1526928 1528646 1528651) (-990 "RTVALUE.spad" 1526641 1526649 1526895 1526900) (-989 "syntax.spad" 1526359 1526367 1526631 1526636) (-988 "RSETGCD.spad" 1522802 1522821 1526349 1526354) (-987 "RSETCAT.spad" 1512793 1512809 1522792 1522797) (-986 "RSETCAT.spad" 1502782 1502800 1512783 1512788) (-985 "RSDCMPK.spad" 1501283 1501302 1502772 1502777) (-984 "RRCC.spad" 1499668 1499697 1501273 1501278) (-983 "RRCC.spad" 1498051 1498082 1499658 1499663) (-982 "RPTAST.spad" 1497754 1497762 1498041 1498046) (-981 "RPOLCAT.spad" 1477259 1477273 1497622 1497749) (-980 "RPOLCAT.spad" 1456557 1456573 1476922 1476927) (-979 "ROMAN.spad" 1455886 1455894 1456423 1456552) (-978 "ROIRC.spad" 1454967 1454998 1455876 1455881) (-977 "RNS.spad" 1453944 1453952 1454869 1454962) (-976 "RNS.spad" 1453007 1453017 1453934 1453939) (-975 "RNGBIND.spad" 1452168 1452181 1452962 1452967) (-974 "RNG.spad" 1451777 1451785 1452158 1452163) (-973 "RNG.spad" 1451384 1451394 1451767 1451772) (-972 "RMODULE.spad" 1451166 1451176 1451374 1451379) (-971 "RMCAT2.spad" 1450587 1450643 1451156 1451161) (-970 "RMATRIX.spad" 1449409 1449427 1449751 1449778) (-969 "RMATCAT.spad" 1445191 1445221 1449377 1449404) (-968 "RMATCAT.spad" 1440851 1440883 1445039 1445044) (-967 "RLINSET.spad" 1440556 1440566 1440841 1440846) (-966 "RINTERP.spad" 1440445 1440464 1440546 1440551) (-965 "RING.spad" 1439916 1439924 1440425 1440440) (-964 "RING.spad" 1439395 1439405 1439906 1439911) (-963 "RIDIST.spad" 1438788 1438796 1439385 1439390) (-962 "RGCHAIN.spad" 1437055 1437070 1437948 1437953) (-961 "RGBCSPC.spad" 1436845 1436856 1437045 1437050) (-960 "RGBCMDL.spad" 1436408 1436419 1436835 1436840) (-959 "RFFACTOR.spad" 1435871 1435881 1436398 1436403) (-958 "RFFACT.spad" 1435607 1435618 1435861 1435866) (-957 "RFDIST.spad" 1434604 1434612 1435597 1435602) (-956 "RF.spad" 1432279 1432289 1434594 1434599) (-955 "RETSOL.spad" 1431699 1431711 1432269 1432274) (-954 "RETRACT.spad" 1431128 1431138 1431689 1431694) (-953 "RETRACT.spad" 1430555 1430567 1431118 1431123) (-952 "RETAST.spad" 1430368 1430376 1430545 1430550) (-951 "RESRING.spad" 1429716 1429762 1430306 1430363) (-950 "RESLATC.spad" 1429041 1429051 1429706 1429711) (-949 "REPSQ.spad" 1428773 1428783 1429031 1429036) (-948 "REPDB.spad" 1428481 1428491 1428763 1428768) (-947 "REP2.spad" 1418196 1418206 1428323 1428328) (-946 "REP1.spad" 1412417 1412427 1418146 1418151) (-945 "REP.spad" 1409972 1409980 1412407 1412412) (-944 "REGSET.spad" 1407659 1407675 1409467 1409472) (-943 "REF.spad" 1407178 1407188 1407649 1407654) (-942 "REDORDER.spad" 1406385 1406401 1407168 1407173) (-941 "RECLOS.spad" 1405282 1405301 1405985 1406078) (-940 "REALSOLV.spad" 1404423 1404431 1405272 1405277) (-939 "REAL0Q.spad" 1401722 1401736 1404413 1404418) (-938 "REAL0.spad" 1398567 1398581 1401712 1401717) (-937 "REAL.spad" 1398440 1398448 1398557 1398562) (-936 "RDUCEAST.spad" 1398162 1398170 1398430 1398435) (-935 "RDIV.spad" 1397818 1397842 1398152 1398157) (-934 "RDIST.spad" 1397386 1397396 1397808 1397813) (-933 "RDETRS.spad" 1396251 1396268 1397376 1397381) (-932 "RDETR.spad" 1394391 1394408 1396241 1396246) (-931 "RDEEFS.spad" 1393491 1393507 1394381 1394386) (-930 "RDEEF.spad" 1392502 1392518 1393481 1393486) (-929 "RCFIELD.spad" 1389721 1389729 1392404 1392497) (-928 "RCFIELD.spad" 1387026 1387036 1389711 1389716) (-927 "RCAGG.spad" 1384963 1384973 1387016 1387021) (-926 "RCAGG.spad" 1382801 1382813 1384856 1384861) (-925 "RATRET.spad" 1382162 1382172 1382791 1382796) (-924 "RATFACT.spad" 1381855 1381866 1382152 1382157) (-923 "RANDSRC.spad" 1381175 1381183 1381845 1381850) (-922 "RADUTIL.spad" 1380932 1380940 1381165 1381170) (-921 "RADIX.spad" 1377977 1377990 1379522 1379615) (-920 "RADFF.spad" 1375894 1375930 1376012 1376168) (-919 "RADCAT.spad" 1375490 1375498 1375884 1375889) (-918 "RADCAT.spad" 1375084 1375094 1375480 1375485) (-917 "QUEUE.spad" 1374520 1374530 1374778 1374783) (-916 "QUATCT2.spad" 1374141 1374159 1374510 1374515) (-915 "QUATCAT.spad" 1372312 1372322 1374071 1374136) (-914 "QUATCAT.spad" 1370248 1370260 1372009 1372014) (-913 "QUAT.spad" 1368855 1368865 1369197 1369262) (-912 "QUAGG.spad" 1367711 1367721 1368845 1368850) (-911 "QQUTAST.spad" 1367480 1367488 1367701 1367706) (-910 "QFORM.spad" 1367099 1367113 1367470 1367475) (-909 "QFCAT2.spad" 1366792 1366808 1367089 1367094) (-908 "QFCAT.spad" 1365495 1365505 1366694 1366787) (-907 "QFCAT.spad" 1363831 1363843 1365032 1365037) (-906 "QEQUAT.spad" 1363390 1363398 1363821 1363826) (-905 "QCMPACK.spad" 1358305 1358324 1363380 1363385) (-904 "QALGSET2.spad" 1356301 1356319 1358295 1358300) (-903 "QALGSET.spad" 1352406 1352438 1356215 1356220) (-902 "PWFFINTB.spad" 1349822 1349843 1352396 1352401) (-901 "PUSHVAR.spad" 1349161 1349180 1349812 1349817) (-900 "PTRANFN.spad" 1345297 1345307 1349151 1349156) (-899 "PTPACK.spad" 1342385 1342395 1345287 1345292) (-898 "PTFUNC2.spad" 1342208 1342222 1342375 1342380) (-897 "PTCAT.spad" 1341485 1341495 1342198 1342203) (-896 "PSQFR.spad" 1340800 1340824 1341475 1341480) (-895 "PSEUDLIN.spad" 1339686 1339696 1340790 1340795) (-894 "PSETPK.spad" 1326391 1326407 1339564 1339569) (-893 "PSETCAT.spad" 1320801 1320824 1326381 1326386) (-892 "PSETCAT.spad" 1315175 1315200 1320757 1320762) (-891 "PSCURVE.spad" 1314174 1314182 1315165 1315170) (-890 "PSCAT.spad" 1312957 1312986 1314072 1314169) (-889 "PSCAT.spad" 1311830 1311861 1312947 1312952) (-888 "PRTITION.spad" 1310528 1310536 1311820 1311825) (-887 "PRTDAST.spad" 1310247 1310255 1310518 1310523) (-886 "PRS.spad" 1299865 1299882 1310203 1310208) (-885 "PRQAGG.spad" 1299322 1299332 1299855 1299860) (-884 "PROPLOG.spad" 1298926 1298934 1299312 1299317) (-883 "PROPFUN2.spad" 1298549 1298562 1298916 1298921) (-882 "PROPFUN1.spad" 1297955 1297966 1298539 1298544) (-881 "PROPFRML.spad" 1296523 1296534 1297945 1297950) (-880 "PROPERTY.spad" 1296019 1296027 1296513 1296518) (-879 "PRODUCT.spad" 1293716 1293728 1294000 1294055) (-878 "PRINT.spad" 1293468 1293476 1293706 1293711) (-877 "PRIMES.spad" 1291729 1291739 1293458 1293463) (-876 "PRIMELT.spad" 1289850 1289864 1291719 1291724) (-875 "PRIMCAT.spad" 1289493 1289501 1289840 1289845) (-874 "PRIMARR2.spad" 1288260 1288272 1289483 1289488) (-873 "PRIMARR.spad" 1287012 1287022 1287182 1287187) (-872 "PREASSOC.spad" 1286394 1286406 1287002 1287007) (-871 "PR.spad" 1284912 1284924 1285611 1285738) (-870 "PPCURVE.spad" 1284049 1284057 1284902 1284907) (-869 "PORTNUM.spad" 1283840 1283848 1284039 1284044) (-868 "POLYROOT.spad" 1282689 1282711 1283796 1283801) (-867 "POLYLIFT.spad" 1281954 1281977 1282679 1282684) (-866 "POLYCATQ.spad" 1280080 1280102 1281944 1281949) (-865 "POLYCAT.spad" 1273582 1273603 1279948 1280075) (-864 "POLYCAT.spad" 1266604 1266627 1272972 1272977) (-863 "POLY2UP.spad" 1266056 1266070 1266594 1266599) (-862 "POLY2.spad" 1265653 1265665 1266046 1266051) (-861 "POLY.spad" 1263321 1263331 1263836 1263963) (-860 "POLUTIL.spad" 1262286 1262315 1263277 1263282) (-859 "POLTOPOL.spad" 1261034 1261049 1262276 1262281) (-858 "POINT.spad" 1259614 1259624 1259701 1259706) (-857 "PNTHEORY.spad" 1256316 1256324 1259604 1259609) (-856 "PMTOOLS.spad" 1255091 1255105 1256306 1256311) (-855 "PMSYM.spad" 1254640 1254650 1255081 1255086) (-854 "PMQFCAT.spad" 1254231 1254245 1254630 1254635) (-853 "PMPREDFS.spad" 1253693 1253715 1254221 1254226) (-852 "PMPRED.spad" 1253180 1253194 1253683 1253688) (-851 "PMPLCAT.spad" 1252257 1252275 1253109 1253114) (-850 "PMLSAGG.spad" 1251842 1251856 1252247 1252252) (-849 "PMKERNEL.spad" 1251421 1251433 1251832 1251837) (-848 "PMINS.spad" 1251001 1251011 1251411 1251416) (-847 "PMFS.spad" 1250578 1250596 1250991 1250996) (-846 "PMDOWN.spad" 1249868 1249882 1250568 1250573) (-845 "PMASSFS.spad" 1248843 1248859 1249858 1249863) (-844 "PMASS.spad" 1247861 1247869 1248833 1248838) (-843 "PLOTTOOL.spad" 1247641 1247649 1247851 1247856) (-842 "PLOT3D.spad" 1244105 1244113 1247631 1247636) (-841 "PLOT1.spad" 1243278 1243288 1244095 1244100) (-840 "PLOT.spad" 1238201 1238209 1243268 1243273) (-839 "PLEQN.spad" 1225603 1225630 1238191 1238196) (-838 "PINTERPA.spad" 1225387 1225403 1225593 1225598) (-837 "PINTERP.spad" 1225009 1225028 1225377 1225382) (-836 "PID.spad" 1223983 1223991 1224935 1225004) (-835 "PICOERCE.spad" 1223640 1223650 1223973 1223978) (-834 "PI.spad" 1223257 1223265 1223614 1223635) (-833 "PGROEB.spad" 1221866 1221880 1223247 1223252) (-832 "PGE.spad" 1213539 1213547 1221856 1221861) (-831 "PGCD.spad" 1212493 1212510 1213529 1213534) (-830 "PFRPAC.spad" 1211642 1211652 1212483 1212488) (-829 "PFR.spad" 1208345 1208355 1211544 1211637) (-828 "PFOTOOLS.spad" 1207603 1207619 1208335 1208340) (-827 "PFOQ.spad" 1206973 1206991 1207593 1207598) (-826 "PFO.spad" 1206392 1206419 1206963 1206968) (-825 "PFECAT.spad" 1204102 1204110 1206318 1206387) (-824 "PFECAT.spad" 1201840 1201850 1204058 1204063) (-823 "PFBRU.spad" 1199728 1199740 1201830 1201835) (-822 "PFBR.spad" 1197288 1197311 1199718 1199723) (-821 "PF.spad" 1196862 1196874 1197093 1197186) (-820 "PERMGRP.spad" 1191632 1191642 1196852 1196857) (-819 "PERMCAT.spad" 1190293 1190303 1191612 1191627) (-818 "PERMAN.spad" 1188849 1188863 1190283 1190288) (-817 "PERM.spad" 1184659 1184669 1188682 1188697) (-816 "PENDTREE.spad" 1184012 1184022 1184292 1184297) (-815 "PDSPC.spad" 1182825 1182835 1184002 1184007) (-814 "PDSPC.spad" 1181636 1181648 1182815 1182820) (-813 "PDRING.spad" 1181478 1181488 1181616 1181631) (-812 "PDMOD.spad" 1181294 1181306 1181446 1181473) (-811 "PDECOMP.spad" 1180764 1180781 1181284 1181289) (-810 "PDDOM.spad" 1180202 1180215 1180754 1180759) (-809 "PDDOM.spad" 1179638 1179653 1180192 1180197) (-808 "PCOMP.spad" 1179491 1179504 1179628 1179633) (-807 "PBWLB.spad" 1178089 1178106 1179481 1179486) (-806 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1108919 1108924) (-750 "OPERCAT.spad" 1107859 1107871 1108385 1108390) (-749 "OP.spad" 1107601 1107611 1107681 1107748) (-748 "ONECOMP2.spad" 1107025 1107037 1107591 1107596) (-747 "ONECOMP.spad" 1105831 1105841 1106633 1106662) (-746 "OMSAGG.spad" 1105643 1105653 1105811 1105826) (-745 "OMLO.spad" 1105076 1105088 1105529 1105568) (-744 "OINTDOM.spad" 1104839 1104847 1105002 1105071) (-743 "OFMONOID.spad" 1102978 1102988 1104795 1104800) (-742 "ODVAR.spad" 1102239 1102249 1102968 1102973) (-741 "ODR.spad" 1101883 1101909 1102051 1102200) (-740 "ODPOL.spad" 1099531 1099541 1099871 1099998) (-739 "ODP.spad" 1089018 1089038 1089391 1089476) (-738 "ODETOOLS.spad" 1087667 1087686 1089008 1089013) (-737 "ODESYS.spad" 1085361 1085378 1087657 1087662) (-736 "ODERTRIC.spad" 1081394 1081411 1085318 1085323) (-735 "ODERED.spad" 1080793 1080817 1081384 1081389) (-734 "ODERAT.spad" 1078426 1078443 1080783 1080788) (-733 "ODEPRRIC.spad" 1075519 1075541 1078416 1078421) (-732 "ODEPRIM.spad" 1072917 1072939 1075509 1075514) (-731 "ODEPAL.spad" 1072303 1072327 1072907 1072912) (-730 "ODEINT.spad" 1071738 1071754 1072293 1072298) (-729 "ODEEF.spad" 1067233 1067249 1071728 1071733) (-728 "ODECONST.spad" 1066778 1066796 1067223 1067228) (-727 "OCTCT2.spad" 1066419 1066437 1066768 1066773) (-726 "OCT.spad" 1064734 1064744 1065448 1065487) (-725 "OCAMON.spad" 1064582 1064590 1064724 1064729) (-724 "OC.spad" 1062378 1062388 1064538 1064577) (-723 "OC.spad" 1059913 1059925 1062075 1062080) (-722 "OASGP.spad" 1059728 1059736 1059903 1059908) (-721 "OAMONS.spad" 1059250 1059258 1059718 1059723) (-720 "OAMON.spad" 1059008 1059016 1059240 1059245) (-719 "OAMON.spad" 1058764 1058774 1058998 1059003) (-718 "OAGROUP.spad" 1058302 1058310 1058754 1058759) (-717 "OAGROUP.spad" 1057838 1057848 1058292 1058297) (-716 "NUMTUBE.spad" 1057429 1057445 1057828 1057833) (-715 "NUMQUAD.spad" 1045405 1045413 1057419 1057424) (-714 "NUMODE.spad" 1036757 1036765 1045395 1045400) (-713 "NUMFMT.spad" 1035597 1035605 1036747 1036752) (-712 "NUMERIC.spad" 1027712 1027722 1035403 1035408) (-711 "NTSCAT.spad" 1026242 1026258 1027702 1027707) (-710 "NTPOLFN.spad" 1025819 1025829 1026185 1026190) (-709 "NSUP2.spad" 1025211 1025223 1025809 1025814) (-708 "NSUP.spad" 1018648 1018658 1023068 1023221) (-707 "NSMP.spad" 1015560 1015579 1015852 1015979) (-706 "NREP.spad" 1013962 1013976 1015550 1015555) (-705 "NPCOEF.spad" 1013208 1013228 1013952 1013957) (-704 "NORMRETR.spad" 1012806 1012845 1013198 1013203) (-703 "NORMPK.spad" 1010748 1010767 1012796 1012801) (-702 "NORMMA.spad" 1010436 1010462 1010738 1010743) (-701 "NONE1.spad" 1010112 1010122 1010426 1010431) (-700 "NONE.spad" 1009853 1009861 1010102 1010107) (-699 "NODE1.spad" 1009340 1009356 1009843 1009848) (-698 "NNI.spad" 1008235 1008243 1009314 1009335) (-697 "NLINSOL.spad" 1006861 1006871 1008225 1008230) (-696 "NFINTBAS.spad" 1004421 1004438 1006851 1006856) (-695 "NETCLT.spad" 1004395 1004406 1004411 1004416) (-694 "NCODIV.spad" 1002619 1002635 1004385 1004390) (-693 "NCNTFRAC.spad" 1002261 1002275 1002609 1002614) (-692 "NCEP.spad" 1000427 1000441 1002251 1002256) (-691 "NASRING.spad" 1000031 1000039 1000417 1000422) (-690 "NASRING.spad" 999633 999643 1000021 1000026) (-689 "NARNG.spad" 999033 999041 999623 999628) (-688 "NARNG.spad" 998431 998441 999023 999028) (-687 "NAALG.spad" 997996 998006 998399 998426) (-686 "NAALG.spad" 997581 997593 997986 997991) (-685 "MULTSQFR.spad" 994539 994556 997571 997576) (-684 "MULTFACT.spad" 993922 993939 994529 994534) (-683 "MTSCAT.spad" 992016 992037 993820 993917) (-682 "MTHING.spad" 991675 991685 992006 992011) (-681 "MSYSCMD.spad" 991109 991117 991665 991670) (-680 "MSETAGG.spad" 990966 990976 991089 991104) (-679 "MSET.spad" 988776 988786 990523 990538) (-678 "MRING.spad" 985898 985910 988484 988551) (-677 "MRF2.spad" 985460 985474 985888 985893) (-676 "MRATFAC.spad" 985006 985023 985450 985455) (-675 "MPRFF.spad" 983046 983065 984996 985001) (-674 "MPOLY.spad" 980850 980865 981209 981336) (-673 "MPCPF.spad" 980114 980133 980840 980845) (-672 "MPC3.spad" 979931 979971 980104 980109) (-671 "MPC2.spad" 979585 979618 979921 979926) (-670 "MONOTOOL.spad" 977936 977953 979575 979580) (-669 "catdef.spad" 977369 977380 977590 977931) (-668 "catdef.spad" 976767 976778 977023 977364) (-667 "MONOID.spad" 976088 976096 976757 976762) (-666 "MONOID.spad" 975407 975417 976078 976083) (-665 "MONOGEN.spad" 974155 974168 975267 975402) (-664 "MONOGEN.spad" 972925 972940 974039 974044) (-663 "MONADWU.spad" 971005 971013 972915 972920) (-662 "MONADWU.spad" 969083 969093 970995 971000) (-661 "MONAD.spad" 968243 968251 969073 969078) (-660 "MONAD.spad" 967401 967411 968233 968238) (-659 "MOEBIUS.spad" 966137 966151 967381 967396) (-658 "MODULE.spad" 966007 966017 966105 966132) (-657 "MODULE.spad" 965897 965909 965997 966002) (-656 "MODRING.spad" 965232 965271 965877 965892) (-655 "MODOP.spad" 963889 963901 965054 965121) (-654 "MODMONOM.spad" 963620 963638 963879 963884) (-653 "MODMON.spad" 960690 960702 961405 961558) (-652 "MODFIELD.spad" 960052 960091 960592 960685) (-651 "MMLFORM.spad" 958912 958920 960042 960047) (-650 "MMAP.spad" 958654 958688 958902 958907) (-649 "MLO.spad" 957113 957123 958610 958649) (-648 "MLIFT.spad" 955725 955742 957103 957108) (-647 "MKUCFUNC.spad" 955260 955278 955715 955720) (-646 "MKRECORD.spad" 954848 954861 955250 955255) (-645 "MKFUNC.spad" 954255 954265 954838 954843) (-644 "MKFLCFN.spad" 953223 953233 954245 954250) (-643 "MKBCFUNC.spad" 952718 952736 953213 953218) (-642 "MHROWRED.spad" 951229 951239 952708 952713) (-641 "MFINFACT.spad" 950629 950651 951219 951224) (-640 "MESH.spad" 948424 948432 950619 950624) (-639 "MDDFACT.spad" 946643 946653 948414 948419) (-638 "MDAGG.spad" 945944 945954 946633 946638) (-637 "MCDEN.spad" 945154 945166 945934 945939) (-636 "MAYBE.spad" 944454 944465 945144 945149) (-635 "MATSTOR.spad" 941770 941780 944444 944449) (-634 "MATRIX.spad" 940571 940581 941055 941060) (-633 "MATLIN.spad" 937939 937963 940455 940460) (-632 "MATCAT2.spad" 937221 937269 937929 937934) (-631 "MATCAT.spad" 928939 928961 937211 937216) (-630 "MATCAT.spad" 920507 920531 928781 928786) (-629 "MAPPKG3.spad" 919422 919436 920497 920502) (-628 "MAPPKG2.spad" 918760 918772 919412 919417) (-627 "MAPPKG1.spad" 917588 917598 918750 918755) (-626 "MAPPAST.spad" 916927 916935 917578 917583) (-625 "MAPHACK3.spad" 916739 916753 916917 916922) (-624 "MAPHACK2.spad" 916508 916520 916729 916734) (-623 "MAPHACK1.spad" 916152 916162 916498 916503) (-622 "MAGMA.spad" 913958 913975 916142 916147) (-621 "MACROAST.spad" 913553 913561 913948 913953) (-620 "LZSTAGG.spad" 910807 910817 913543 913548) (-619 "LZSTAGG.spad" 908059 908071 910797 910802) (-618 "LWORD.spad" 904804 904821 908049 908054) (-617 "LSTAST.spad" 904588 904596 904794 904799) (-616 "LSQM.spad" 902878 902892 903272 903311) (-615 "LSPP.spad" 902413 902430 902868 902873) (-614 "LSMP1.spad" 900256 900270 902403 902408) (-613 "LSMP.spad" 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(-592 "LLINSET.spad" 875308 875318 875591 875596) (-591 "LITERAL.spad" 875214 875225 875298 875303) (-590 "LIST3.spad" 874525 874539 875204 875209) (-589 "LIST2MAP.spad" 871452 871464 874515 874520) (-588 "LIST2.spad" 870154 870166 871442 871447) (-587 "LIST.spad" 867733 867743 869076 869081) (-586 "LINSET.spad" 867512 867522 867723 867728) (-585 "LINFORM.spad" 866975 866987 867480 867507) (-584 "LINEXP.spad" 865718 865728 866965 866970) (-583 "LINELT.spad" 865089 865101 865601 865628) (-582 "LINDEP.spad" 863938 863950 865001 865006) (-581 "LINBASIS.spad" 863574 863589 863928 863933) (-580 "LIMITRF.spad" 861521 861531 863564 863569) (-579 "LIMITPS.spad" 860431 860444 861511 861516) (-578 "LIECAT.spad" 859915 859925 860357 860426) (-577 "LIECAT.spad" 859427 859439 859871 859876) (-576 "LIE.spad" 857431 857443 858705 858847) (-575 "LIB.spad" 855254 855262 855700 855705) (-574 "LGROBP.spad" 852607 852626 855244 855249) (-573 "LFCAT.spad" 851666 851674 852597 852602) (-572 "LF.spad" 850621 850637 851656 851661) (-571 "LEXTRIPK.spad" 846244 846259 850611 850616) (-570 "LEXP.spad" 844263 844290 846224 846239) (-569 "LETAST.spad" 843962 843970 844253 844258) (-568 "LEADCDET.spad" 842368 842385 843952 843957) (-567 "LAZM3PK.spad" 841112 841134 842358 842363) (-566 "LAUPOL.spad" 839779 839792 840679 840748) (-565 "LAPLACE.spad" 839362 839378 839769 839774) (-564 "LALG.spad" 839138 839148 839342 839357) (-563 "LALG.spad" 838922 838934 839128 839133) (-562 "LA.spad" 838362 838376 838844 838883) (-561 "KVTFROM.spad" 838105 838115 838352 838357) (-560 "KTVLOGIC.spad" 837649 837657 838095 838100) (-559 "KRCFROM.spad" 837395 837405 837639 837644) (-558 "KOVACIC.spad" 836126 836143 837385 837390) (-557 "KONVERT.spad" 835848 835858 836116 836121) (-556 "KOERCE.spad" 835585 835595 835838 835843) (-555 "KERNEL2.spad" 835288 835300 835575 835580) (-554 "KERNEL.spad" 834008 834018 835137 835142) (-553 "KDAGG.spad" 833127 833149 833998 834003) (-552 "KDAGG.spad" 832244 832268 833117 833122) (-551 "KAFILE.spad" 830620 830636 830855 830860) (-550 "JVMOP.spad" 830533 830541 830610 830615) (-549 "JVMMDACC.spad" 829587 829595 830523 830528) (-548 "JVMFDACC.spad" 828903 828911 829577 829582) (-547 "JVMCSTTG.spad" 827632 827640 828893 828898) (-546 "JVMCFACC.spad" 827078 827086 827622 827627) (-545 "JVMBCODE.spad" 826989 826997 827068 827073) (-544 "JORDAN.spad" 824806 824818 826267 826409) (-543 "JOINAST.spad" 824508 824516 824796 824801) (-542 "IXAGG.spad" 822641 822665 824498 824503) (-541 "IXAGG.spad" 820576 820602 822435 822440) (-540 "ITUPLE.spad" 819868 819878 820566 820571) (-539 "ITRIGMNP.spad" 818715 818734 819858 819863) (-538 "ITFUN3.spad" 818221 818235 818705 818710) (-537 "ITFUN2.spad" 817965 817977 818211 818216) (-536 "ITFORM.spad" 817320 817328 817955 817960) (-535 "ITAYLOR.spad" 815314 815329 817184 817281) (-534 "ISUPS.spad" 807763 807778 814300 814397) (-533 "ISUMP.spad" 807264 807280 807753 807758) (-532 "ISAST.spad" 806983 806991 807254 807259) 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691671) (-429 "HEUGCD.spad" 690304 690315 691203 691208) (-428 "HELLFDIV.spad" 689910 689934 690294 690299) (-427 "HEAP.spad" 689389 689399 689604 689609) (-426 "HEADAST.spad" 688930 688938 689379 689384) (-425 "HDP.spad" 678413 678429 678790 678875) (-424 "HDMP.spad" 675960 675975 676576 676703) (-423 "HB.spad" 674235 674243 675950 675955) (-422 "HASHTBL.spad" 672004 672035 672215 672220) (-421 "HASAST.spad" 671720 671728 671994 671999) (-420 "HACKPI.spad" 671211 671219 671622 671715) (-419 "GTSET.spad" 669999 670015 670706 670711) (-418 "GSTBL.spad" 667805 667840 667979 667984) (-417 "GSERIES.spad" 665177 665204 665996 666145) (-416 "GROUP.spad" 664450 664458 665157 665172) (-415 "GROUP.spad" 663731 663741 664440 664445) (-414 "GROEBSOL.spad" 662225 662246 663721 663726) (-413 "GRMOD.spad" 660806 660818 662215 662220) (-412 "GRMOD.spad" 659385 659399 660796 660801) (-411 "GRIMAGE.spad" 652298 652306 659375 659380) (-410 "GRDEF.spad" 650677 650685 652288 652293) (-409 "GRAY.spad" 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614005 614010) (-388 "GALUTIL.spad" 611654 611664 613284 613289) (-387 "GALPOLYU.spad" 610108 610121 611644 611649) (-386 "GALFACTU.spad" 608321 608340 610098 610103) (-385 "GALFACT.spad" 598534 598545 608311 608316) (-384 "FUNDESC.spad" 598212 598220 598524 598529) (-383 "catdef.spad" 597823 597833 598202 598207) (-382 "FUNCTION.spad" 597672 597684 597813 597818) (-381 "FT.spad" 595972 595980 597662 597667) (-380 "FSUPFACT.spad" 594886 594905 595922 595927) (-379 "FST.spad" 592972 592980 594876 594881) (-378 "FSRED.spad" 592452 592468 592962 592967) (-377 "FSPRMELT.spad" 591318 591334 592409 592414) (-376 "FSPECF.spad" 589409 589425 591308 591313) (-375 "FSINT.spad" 589069 589085 589399 589404) (-374 "FSERIES.spad" 588260 588272 588889 588988) (-373 "FSCINT.spad" 587577 587593 588250 588255) (-372 "FSAGG2.spad" 586312 586328 587567 587572) (-371 "FSAGG.spad" 585453 585463 586292 586307) (-370 "FSAGG.spad" 584532 584544 585373 585378) (-369 "FS2UPS.spad" 579047 579081 584522 584527) 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(-224 "DROPT0.spad" 287548 287556 292673 292678) (-223 "DROPT.spad" 281507 281515 287538 287543) (-222 "DRAWPT.spad" 279680 279688 281497 281502) (-221 "DRAWHACK.spad" 278988 278998 279670 279675) (-220 "DRAWCX.spad" 276466 276474 278978 278983) (-219 "DRAWCURV.spad" 276013 276028 276456 276461) (-218 "DRAWCFUN.spad" 265545 265553 276003 276008) (-217 "DRAW.spad" 258421 258434 265535 265540) (-216 "DQAGG.spad" 256621 256631 258411 258416) (-215 "DPOLCAT.spad" 251978 251994 256489 256616) (-214 "DPOLCAT.spad" 247421 247439 251934 251939) (-213 "DPMO.spad" 239974 239990 240112 240306) (-212 "DPMM.spad" 232540 232558 232665 232859) (-211 "DOMTMPLT.spad" 232311 232319 232530 232535) (-210 "DOMCTOR.spad" 232066 232074 232301 232306) (-209 "DOMAIN.spad" 231177 231185 232056 232061) (-208 "DMP.spad" 228770 228785 229340 229467) (-207 "DMEXT.spad" 228637 228647 228738 228765) (-206 "DLP.spad" 227997 228007 228627 228632) (-205 "DLIST.spad" 226315 226325 226919 226924) (-204 "DLAGG.spad" 224732 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201184 201189) (-183 "DHMATRIX.spad" 199231 199241 200376 200381) (-182 "DFSFUN.spad" 192871 192879 199221 199226) (-181 "DFLOAT.spad" 189478 189486 192761 192866) (-180 "DFINTTLS.spad" 187709 187725 189468 189473) (-179 "DERHAM.spad" 185796 185828 187689 187704) (-178 "DEQUEUE.spad" 185207 185217 185490 185495) (-177 "DEGRED.spad" 184824 184838 185197 185202) (-176 "DEFINTRF.spad" 182406 182416 184814 184819) (-175 "DEFINTEF.spad" 180944 180960 182396 182401) (-174 "DEFAST.spad" 180328 180336 180934 180939) (-173 "DECIMAL.spad" 178557 178565 178918 179011) (-172 "DDFACT.spad" 176378 176395 178547 178552) (-171 "DBLRESP.spad" 175978 176002 176368 176373) (-170 "DBASIS.spad" 175604 175619 175968 175973) (-169 "DBASE.spad" 174268 174278 175594 175599) (-168 "DATAARY.spad" 173754 173767 174258 174263) (-167 "CYCLOTOM.spad" 173260 173268 173744 173749) (-166 "CYCLES.spad" 170043 170051 173250 173255) (-165 "CVMP.spad" 169460 169470 170033 170038) (-164 "CTRIGMNP.spad" 167960 167976 169450 169455) (-163 "CTORKIND.spad" 167563 167571 167950 167955) (-162 "CTORCAT.spad" 166804 166812 167553 167558) (-161 "CTORCAT.spad" 166043 166053 166794 166799) (-160 "CTORCALL.spad" 165632 165642 166033 166038) (-159 "CTOR.spad" 165323 165331 165622 165627) (-158 "CSTTOOLS.spad" 164568 164581 165313 165318) (-157 "CRFP.spad" 158340 158353 164558 164563) (-156 "CRCEAST.spad" 158060 158068 158330 158335) (-155 "CRAPACK.spad" 157127 157137 158050 158055) (-154 "CPMATCH.spad" 156628 156643 157049 157054) (-153 "CPIMA.spad" 156333 156352 156618 156623) (-152 "COORDSYS.spad" 151342 151352 156323 156328) (-151 "CONTOUR.spad" 150769 150777 151332 151337) (-150 "CONTFRAC.spad" 146519 146529 150671 150764) (-149 "CONDUIT.spad" 146277 146285 146509 146514) (-148 "COMRING.spad" 145951 145959 146215 146272) (-147 "COMPPROP.spad" 145469 145477 145941 145946) (-146 "COMPLPAT.spad" 145236 145251 145459 145464) (-145 "COMPLEX2.spad" 144951 144963 145226 145231) (-144 "COMPLEX.spad" 140657 140667 140901 141159) (-143 "COMPILER.spad" 140206 140214 140647 140652) (-142 "COMPFACT.spad" 139808 139822 140196 140201) (-141 "COMPCAT.spad" 137883 137893 139545 139803) (-140 "COMPCAT.spad" 135699 135711 137363 137368) (-139 "catdef.spad" 135442 135453 135555 135694) (-138 "/home/gdr/build/1.5.x/x86_64-unknown-linux-gnu/src/algebra/catdef.spad" 135028 135039 135298 135437) (-137 "COMMUPC.spad" 134776 134794 135018 135023) (-136 "COMMONOP.spad" 134309 134317 134766 134771) (-135 "COMMAAST.spad" 134072 134080 134299 134304) (-134 "COMM.spad" 133883 133891 134062 134067) (-133 "COMBOPC.spad" 132806 132814 133873 133878) (-132 "COMBINAT.spad" 131573 131583 132796 132801) (-131 "COMBF.spad" 128995 129011 131563 131568) (-130 "COLOR.spad" 127832 127840 128985 128990) (-129 "COLONAST.spad" 127498 127506 127822 127827) (-128 "CMPLXRT.spad" 127209 127226 127488 127493) (-127 "CLLCTAST.spad" 126871 126879 127199 127204) (-126 "CLIP.spad" 122979 122987 126861 126866) (-125 "CLIF.spad" 121634 121650 122935 122974) (-124 "CLAGG.spad" 119840 119850 121624 121629) (-123 "CLAGG.spad" 117905 117917 119691 119696) (-122 "CINTSLPE.spad" 117260 117273 117895 117900) (-121 "CHVAR.spad" 115398 115420 117250 117255) (-120 "CHARZ.spad" 115313 115321 115378 115393) (-119 "CHARPOL.spad" 114839 114849 115303 115308) (-118 "CHARNZ.spad" 114601 114609 114819 114834) (-117 "CHAR.spad" 111969 111977 114591 114596) (-116 "CFCAT.spad" 111297 111305 111959 111964) (-115 "CDEN.spad" 110517 110531 111287 111292) (-114 "CCLASS.spad" 108598 108606 109860 109875) (-113 "CATEGORY.spad" 107672 107680 108588 108593) (-112 "CATCTOR.spad" 107563 107571 107662 107667) (-111 "CATAST.spad" 107189 107197 107553 107558) (-110 "CASEAST.spad" 106903 106911 107179 107184) (-109 "CARTEN2.spad" 106293 106320 106893 106898) (-108 "CARTEN.spad" 102045 102069 106283 106288) (-107 "CARD.spad" 99340 99348 102019 102040) (-106 "CAPSLAST.spad" 99122 99130 99330 99335) (-105 "CACHSET.spad" 98746 98754 99112 99117) (-104 "CABMON.spad" 98301 98309 98736 98741) (-103 "BYTEORD.spad" 97976 97984 98291 98296) (-102 "BYTEBUF.spad" 95796 95804 97002 97007) (-101 "BYTE.spad" 95271 95279 95786 95791) (-100 "BTREE.spad" 94370 94380 94904 94909) (-99 "BTOURN.spad" 93402 93411 94003 94008) (-98 "BTCAT.spad" 92982 92991 93392 93397) (-97 "BTCAT.spad" 92560 92571 92972 92977) (-96 "BTAGG.spad" 92049 92056 92550 92555) (-95 "BTAGG.spad" 91536 91545 92039 92044) (-94 "BSTREE.spad" 90304 90313 91169 91174) (-93 "BRILL.spad" 88510 88520 90294 90299) (-92 "BRAGG.spad" 87467 87476 88500 88505) (-91 "BRAGG.spad" 86360 86371 87395 87400) (-90 "BPADICRT.spad" 84420 84431 84666 84759) (-89 "BPADIC.spad" 84093 84104 84346 84415) (-88 "BOUNDZRO.spad" 83750 83766 84083 84088) (-87 "BOP1.spad" 81209 81218 83740 83745) (-86 "BOP.spad" 76352 76359 81199 81204) (-85 "BOOLEAN.spad" 75901 75908 76342 76347) (-84 "BOOLE.spad" 75552 75559 75891 75896) (-83 "BOOLE.spad" 75201 75210 75542 75547) (-82 "BMODULE.spad" 74914 74925 75169 75196) (-81 "BITS.spad" 74125 74132 74339 74344) (-80 "catdef.spad" 74008 74018 74115 74120) (-79 "catdef.spad" 73759 73769 73998 74003) (-78 "BINDING.spad" 73181 73188 73749 73754) (-77 "BINARY.spad" 71416 71423 71771 71864) (-76 "BGAGG.spad" 70746 70755 71406 71411) (-75 "BGAGG.spad" 70074 70085 70736 70741) (-74 "BEZOUT.spad" 69215 69241 70024 70029) (-73 "BBTREE.spad" 66119 66128 68848 68853) (-72 "BASTYPE.spad" 65619 65626 66109 66114) (-71 "BASTYPE.spad" 65117 65126 65609 65614) (-70 "BALFACT.spad" 64577 64589 65107 65112) (-69 "AUTOMOR.spad" 64028 64037 64557 64572) (-68 "ATTREG.spad" 61160 61167 63804 64023) (-67 "ATTRAST.spad" 60877 60884 61150 61155) (-66 "ATRIG.spad" 60347 60354 60867 60872) (-65 "ATRIG.spad" 59815 59824 60337 60342) (-64 "ASTCAT.spad" 59719 59726 59805 59810) (-63 "ASTCAT.spad" 59621 59630 59709 59714) (-62 "ASTACK.spad" 59047 59056 59315 59320) (-61 "ASSOCEQ.spad" 57881 57892 59003 59008) (-60 "ARRAY2.spad" 57426 57435 57575 57580) (-59 "ARRAY12.spad" 56139 56150 57416 57421) (-58 "ARRAY1.spad" 54715 54724 55061 55066) (-57 "ARR2CAT.spad" 51024 51045 54705 54710) (-56 "ARR2CAT.spad" 47331 47354 51014 51019) (-55 "ARITY.spad" 46703 46710 47321 47326) (-54 "APPRULE.spad" 45987 46009 46693 46698) (-53 "APPLYORE.spad" 45606 45619 45977 45982) (-52 "ANY1.spad" 44677 44686 45596 45601) (-51 "ANY.spad" 43528 43535 44667 44672) (-50 "ANTISYM.spad" 42101 42117 43508 43523) (-49 "ANON.spad" 41810 41817 42091 42096) (-48 "AN.spad" 40278 40285 41641 41734) (-47 "AMR.spad" 38608 38619 40176 40273) (-46 "AMR.spad" 36801 36814 38371 38376) (-45 "ALIST.spad" 33046 33067 33396 33401) (-44 "ALGSC.spad" 32181 32207 32918 32971) (-43 "ALGPKG.spad" 27964 27975 32137 32142) (-42 "ALGMFACT.spad" 27157 27171 27954 27959) (-41 "ALGMANIP.spad" 24658 24673 27001 27006) (-40 "ALGFF.spad" 22476 22503 22693 22849) (-39 "ALGFACT.spad" 21595 21605 22466 22471) (-38 "ALGEBRA.spad" 21428 21437 21551 21590) (-37 "ALGEBRA.spad" 21293 21304 21418 21423) (-36 "ALAGG.spad" 20831 20852 21283 21288) (-35 "AHYP.spad" 20212 20219 20821 20826) (-34 "AGG.spad" 19119 19126 20202 20207) (-33 "AGG.spad" 18024 18033 19109 19114) (-32 "AF.spad" 16469 16484 17973 17978) (-31 "ADDAST.spad" 16155 16162 16459 16464) (-30 "ACPLOT.spad" 15032 15039 16145 16150) (-29 "ACFS.spad" 12889 12898 14934 15027) (-28 "ACFS.spad" 10832 10843 12879 12884) (-27 "ACF.spad" 7586 7593 10734 10827) (-26 "ACF.spad" 4426 4435 7576 7581) (-25 "ABELSG.spad" 3967 3974 4416 4421) (-24 "ABELSG.spad" 3506 3515 3957 3962) (-23 "ABELMON.spad" 2934 2941 3496 3501) (-22 "ABELMON.spad" 2360 2369 2924 2929) (-21 "ABELGRP.spad" 2025 2032 2350 2355) (-20 "ABELGRP.spad" 1688 1697 2015 2020) (-19 "A1AGG.spad" 860 869 1678 1683) (-18 "A1AGG.spad" 30 41 850 855)) 
\ No newline at end of file
+((-3 NIL 1966179 1966184 1966189 1966194) (-2 NIL 1966159 1966164 1966169 1966174) (-1 NIL 1966139 1966144 1966149 1966154) (0 NIL 1966119 1966124 1966129 1966134) (-1210 "ZMOD.spad" 1965928 1965941 1966057 1966114) (-1209 "ZLINDEP.spad" 1965026 1965037 1965918 1965923) (-1208 "ZDSOLVE.spad" 1954987 1955009 1965016 1965021) (-1207 "YSTREAM.spad" 1954482 1954493 1954977 1954982) (-1206 "YDIAGRAM.spad" 1954116 1954125 1954472 1954477) (-1205 "XRPOLY.spad" 1953336 1953356 1953972 1954041) (-1204 "XPR.spad" 1951264 1951277 1953054 1953153) (-1203 "XPOLYC.spad" 1950583 1950599 1951190 1951259) (-1202 "XPOLY.spad" 1950138 1950149 1950439 1950508) (-1201 "XPBWPOLY.spad" 1948609 1948629 1949944 1950013) (-1200 "XFALG.spad" 1945790 1945806 1948535 1948604) (-1199 "XF.spad" 1944253 1944268 1945692 1945785) (-1198 "XF.spad" 1942696 1942713 1944137 1944142) (-1197 "XEXPPKG.spad" 1941955 1941981 1942686 1942691) (-1196 "XDPOLY.spad" 1941569 1941585 1941811 1941880) (-1195 "XALG.spad" 1941237 1941248 1941525 1941564) (-1194 "WUTSET.spad" 1937101 1937118 1940732 1940737) (-1193 "WP.spad" 1936308 1936352 1936959 1937026) (-1192 "WHILEAST.spad" 1936106 1936115 1936298 1936303) (-1191 "WHEREAST.spad" 1935777 1935786 1936096 1936101) (-1190 "WFFINTBS.spad" 1933440 1933462 1935767 1935772) (-1189 "WEIER.spad" 1931662 1931673 1933430 1933435) (-1188 "VSPACE.spad" 1931335 1931346 1931630 1931657) (-1187 "VSPACE.spad" 1931028 1931041 1931325 1931330) (-1186 "VOID.spad" 1930705 1930714 1931018 1931023) (-1185 "VIEWDEF.spad" 1925906 1925915 1930695 1930700) (-1184 "VIEW3D.spad" 1909867 1909876 1925896 1925901) (-1183 "VIEW2D.spad" 1897766 1897775 1909857 1909862) (-1182 "VIEW.spad" 1895486 1895495 1897756 1897761) (-1181 "VECTOR2.spad" 1894125 1894138 1895476 1895481) (-1180 "VECTOR.spad" 1892541 1892552 1892792 1892797) (-1179 "VECTCAT.spad" 1890475 1890486 1892531 1892536) (-1178 "VECTCAT.spad" 1888196 1888209 1890254 1890259) (-1177 "VARIABLE.spad" 1887976 1887991 1888186 1888191) (-1176 "UTYPE.spad" 1887620 1887629 1887966 1887971) (-1175 "UTSODETL.spad" 1886915 1886939 1887576 1887581) (-1174 "UTSODE.spad" 1885131 1885151 1886905 1886910) (-1173 "UTSCAT.spad" 1882610 1882626 1885029 1885126) (-1172 "UTSCAT.spad" 1879757 1879775 1882178 1882183) (-1171 "UTS2.spad" 1879352 1879387 1879747 1879752) (-1170 "UTS.spad" 1874364 1874392 1877884 1877981) (-1169 "URAGG.spad" 1869085 1869096 1874354 1874359) (-1168 "URAGG.spad" 1863742 1863755 1869013 1869018) (-1167 "UPXSSING.spad" 1861510 1861536 1862946 1863079) (-1166 "UPXSCONS.spad" 1859328 1859348 1859701 1859850) (-1165 "UPXSCCA.spad" 1857899 1857919 1859174 1859323) (-1164 "UPXSCCA.spad" 1856612 1856634 1857889 1857894) (-1163 "UPXSCAT.spad" 1855201 1855217 1856458 1856607) (-1162 "UPXS2.spad" 1854744 1854797 1855191 1855196) (-1161 "UPXS.spad" 1852099 1852127 1852935 1853084) (-1160 "UPSQFREE.spad" 1850514 1850528 1852089 1852094) (-1159 "UPSCAT.spad" 1848309 1848333 1850412 1850509) (-1158 "UPSCAT.spad" 1845805 1845831 1847910 1847915) (-1157 "UPOLYC2.spad" 1845276 1845295 1845795 1845800) (-1156 "UPOLYC.spad" 1840356 1840367 1845118 1845271) (-1155 "UPOLYC.spad" 1835354 1835367 1840118 1840123) (-1154 "UPMP.spad" 1834286 1834299 1835344 1835349) (-1153 "UPDIVP.spad" 1833851 1833865 1834276 1834281) (-1152 "UPDECOMP.spad" 1832112 1832126 1833841 1833846) (-1151 "UPCDEN.spad" 1831329 1831345 1832102 1832107) (-1150 "UP2.spad" 1830693 1830714 1831319 1831324) (-1149 "UP.spad" 1828163 1828178 1828550 1828703) (-1148 "UNISEG2.spad" 1827660 1827673 1828119 1828124) (-1147 "UNISEG.spad" 1827013 1827024 1827579 1827584) (-1146 "UNIFACT.spad" 1826116 1826128 1827003 1827008) (-1145 "ULSCONS.spad" 1819962 1819982 1820332 1820481) (-1144 "ULSCCAT.spad" 1817699 1817719 1819808 1819957) (-1143 "ULSCCAT.spad" 1815544 1815566 1817655 1817660) (-1142 "ULSCAT.spad" 1813784 1813800 1815390 1815539) (-1141 "ULS2.spad" 1813298 1813351 1813774 1813779) (-1140 "ULS.spad" 1805331 1805359 1806276 1806699) (-1139 "UINT8.spad" 1805208 1805217 1805321 1805326) (-1138 "UINT64.spad" 1805084 1805093 1805198 1805203) (-1137 "UINT32.spad" 1804960 1804969 1805074 1805079) (-1136 "UINT16.spad" 1804836 1804845 1804950 1804955) (-1135 "UFD.spad" 1803901 1803910 1804762 1804831) (-1134 "UFD.spad" 1803028 1803039 1803891 1803896) (-1133 "UDVO.spad" 1801909 1801918 1803018 1803023) (-1132 "UDPO.spad" 1799490 1799501 1801865 1801870) (-1131 "TYPEAST.spad" 1799409 1799418 1799480 1799485) (-1130 "TYPE.spad" 1799341 1799350 1799399 1799404) (-1129 "TWOFACT.spad" 1797993 1798008 1799331 1799336) (-1128 "TUPLE.spad" 1797500 1797511 1797905 1797910) (-1127 "TUBETOOL.spad" 1794367 1794376 1797490 1797495) (-1126 "TUBE.spad" 1793014 1793031 1794357 1794362) (-1125 "TSETCAT.spad" 1781107 1781124 1793004 1793009) (-1124 "TSETCAT.spad" 1769164 1769183 1781063 1781068) (-1123 "TS.spad" 1767792 1767808 1768758 1768855) (-1122 "TRMANIP.spad" 1762156 1762173 1767480 1767485) (-1121 "TRIMAT.spad" 1761119 1761144 1762146 1762151) (-1120 "TRIGMNIP.spad" 1759646 1759663 1761109 1761114) (-1119 "TRIGCAT.spad" 1759158 1759167 1759636 1759641) (-1118 "TRIGCAT.spad" 1758668 1758679 1759148 1759153) (-1117 "TREE.spad" 1757269 1757280 1758301 1758306) (-1116 "TRANFUN.spad" 1757108 1757117 1757259 1757264) (-1115 "TRANFUN.spad" 1756945 1756956 1757098 1757103) (-1114 "TOPSP.spad" 1756619 1756628 1756935 1756940) (-1113 "TOOLSIGN.spad" 1756282 1756293 1756609 1756614) (-1112 "TEXTFILE.spad" 1754843 1754852 1756272 1756277) (-1111 "TEX1.spad" 1754399 1754410 1754833 1754838) (-1110 "TEX.spad" 1751593 1751602 1754389 1754394) (-1109 "TBCMPPK.spad" 1749694 1749717 1751583 1751588) (-1108 "TBAGG.spad" 1748959 1748982 1749684 1749689) (-1107 "TBAGG.spad" 1748222 1748247 1748949 1748954) (-1106 "TANEXP.spad" 1747630 1747641 1748212 1748217) (-1105 "TALGOP.spad" 1747354 1747365 1747620 1747625) (-1104 "TABLEAU.spad" 1746835 1746846 1747344 1747349) (-1103 "TABLE.spad" 1744545 1744568 1744815 1744820) (-1102 "TABLBUMP.spad" 1741324 1741335 1744535 1744540) (-1101 "SYSTEM.spad" 1740552 1740561 1741314 1741319) (-1100 "SYSSOLP.spad" 1738035 1738046 1740542 1740547) (-1099 "SYSPTR.spad" 1737934 1737943 1738025 1738030) (-1098 "SYSNNI.spad" 1737157 1737168 1737924 1737929) (-1097 "SYSINT.spad" 1736561 1736572 1737147 1737152) (-1096 "SYNTAX.spad" 1732895 1732904 1736551 1736556) (-1095 "SYMTAB.spad" 1730963 1730972 1732885 1732890) (-1094 "SYMS.spad" 1726992 1727001 1730953 1730958) (-1093 "SYMPOLY.spad" 1726125 1726136 1726207 1726334) (-1092 "SYMFUNC.spad" 1725626 1725637 1726115 1726120) (-1091 "SYMBOL.spad" 1723121 1723130 1725616 1725621) (-1090 "SUTS.spad" 1720234 1720262 1721653 1721750) (-1089 "SUPXS.spad" 1717576 1717604 1718425 1718574) (-1088 "SUPFRACF.spad" 1716681 1716699 1717566 1717571) (-1087 "SUP2.spad" 1716073 1716086 1716671 1716676) (-1086 "SUP.spad" 1713157 1713168 1713930 1714083) (-1085 "SUMRF.spad" 1712131 1712142 1713147 1713152) (-1084 "SUMFS.spad" 1711760 1711777 1712121 1712126) (-1083 "SULS.spad" 1703780 1703808 1704738 1705161) (-1082 "syntax.spad" 1703549 1703558 1703770 1703775) (-1081 "SUCH.spad" 1703239 1703254 1703539 1703544) (-1080 "SUBSPACE.spad" 1695370 1695385 1703229 1703234) (-1079 "SUBRESP.spad" 1694540 1694554 1695326 1695331) (-1078 "STTFNC.spad" 1691008 1691024 1694530 1694535) (-1077 "STTF.spad" 1687107 1687123 1690998 1691003) (-1076 "STTAYLOR.spad" 1679784 1679795 1687014 1687019) (-1075 "STRTBL.spad" 1677657 1677674 1677806 1677811) (-1074 "STRING.spad" 1676298 1676307 1676683 1676688) (-1073 "STREAM3.spad" 1675871 1675886 1676288 1676293) (-1072 "STREAM2.spad" 1674999 1675012 1675861 1675866) (-1071 "STREAM1.spad" 1674705 1674716 1674989 1674994) (-1070 "STREAM.spad" 1671665 1671676 1674156 1674161) (-1069 "STINPROD.spad" 1670601 1670617 1671655 1671660) (-1068 "STEPAST.spad" 1669835 1669844 1670591 1670596) (-1067 "STEP.spad" 1669152 1669161 1669825 1669830) (-1066 "STBL.spad" 1666965 1666993 1667132 1667137) (-1065 "STAGG.spad" 1665664 1665675 1666955 1666960) (-1064 "STAGG.spad" 1664361 1664374 1665654 1665659) (-1063 "STACK.spad" 1663805 1663816 1664055 1664060) (-1062 "SRING.spad" 1663565 1663574 1663795 1663800) (-1061 "SREGSET.spad" 1661158 1661175 1663060 1663065) (-1060 "SRDCMPK.spad" 1659735 1659755 1661148 1661153) (-1059 "SRAGG.spad" 1654940 1654949 1659725 1659730) (-1058 "SRAGG.spad" 1650143 1650154 1654930 1654935) (-1057 "SQMATRIX.spad" 1647832 1647850 1648748 1648823) (-1056 "SPLTREE.spad" 1642492 1642505 1647288 1647293) (-1055 "SPLNODE.spad" 1639112 1639125 1642482 1642487) (-1054 "SPFCAT.spad" 1637921 1637930 1639102 1639107) (-1053 "SPECOUT.spad" 1636473 1636482 1637911 1637916) (-1052 "SPADXPT.spad" 1628564 1628573 1636463 1636468) (-1051 "spad-parser.spad" 1628029 1628038 1628554 1628559) (-1050 "SPADAST.spad" 1627730 1627739 1628019 1628024) (-1049 "SPACEC.spad" 1611945 1611956 1627720 1627725) (-1048 "SPACE3.spad" 1611721 1611732 1611935 1611940) (-1047 "SORTPAK.spad" 1611270 1611283 1611677 1611682) (-1046 "SOLVETRA.spad" 1609033 1609044 1611260 1611265) (-1045 "SOLVESER.spad" 1607489 1607500 1609023 1609028) (-1044 "SOLVERAD.spad" 1603515 1603526 1607479 1607484) (-1043 "SOLVEFOR.spad" 1601977 1601995 1603505 1603510) (-1042 "SNTSCAT.spad" 1601599 1601616 1601967 1601972) (-1041 "SMTS.spad" 1599916 1599942 1601193 1601290) (-1040 "SMP.spad" 1597724 1597744 1598114 1598241) (-1039 "SMITH.spad" 1596569 1596594 1597714 1597719) (-1038 "SMATCAT.spad" 1594699 1594729 1596525 1596564) (-1037 "SMATCAT.spad" 1592749 1592781 1594577 1594582) (-1036 "aggcat.spad" 1592435 1592446 1592739 1592744) (-1035 "SKAGG.spad" 1591426 1591437 1592425 1592430) (-1034 "SINT.spad" 1590725 1590734 1591292 1591421) (-1033 "SIMPAN.spad" 1590453 1590462 1590715 1590720) (-1032 "SIGNRF.spad" 1589578 1589589 1590443 1590448) (-1031 "SIGNEF.spad" 1588864 1588881 1589568 1589573) (-1030 "syntax.spad" 1588281 1588290 1588854 1588859) (-1029 "SIG.spad" 1587643 1587652 1588271 1588276) (-1028 "SHP.spad" 1585587 1585602 1587599 1587604) (-1027 "SHDP.spad" 1574930 1574957 1575447 1575532) (-1026 "SGROUP.spad" 1574538 1574547 1574920 1574925) (-1025 "SGROUP.spad" 1574144 1574155 1574528 1574533) (-1024 "catdef.spad" 1573854 1573866 1573965 1574139) (-1023 "catdef.spad" 1573410 1573422 1573675 1573849) (-1022 "SGCF.spad" 1566549 1566558 1573400 1573405) (-1021 "SFRTCAT.spad" 1565517 1565534 1566539 1566544) (-1020 "SFRGCD.spad" 1564580 1564600 1565507 1565512) (-1019 "SFQCMPK.spad" 1559393 1559413 1564570 1564575) (-1018 "SEXOF.spad" 1559236 1559276 1559383 1559388) (-1017 "SEXCAT.spad" 1557064 1557104 1559226 1559231) (-1016 "SEX.spad" 1556956 1556965 1557054 1557059) (-1015 "SETMN.spad" 1555416 1555433 1556946 1556951) (-1014 "SETCAT.spad" 1554901 1554910 1555406 1555411) (-1013 "SETCAT.spad" 1554384 1554395 1554891 1554896) (-1012 "SETAGG.spad" 1550933 1550944 1554364 1554379) (-1011 "SETAGG.spad" 1547490 1547503 1550923 1550928) (-1010 "SET.spad" 1545660 1545671 1546759 1546774) (-1009 "syntax.spad" 1545363 1545372 1545650 1545655) (-1008 "SEGXCAT.spad" 1544519 1544532 1545353 1545358) (-1007 "SEGCAT.spad" 1543444 1543455 1544509 1544514) (-1006 "SEGBIND2.spad" 1543142 1543155 1543434 1543439) (-1005 "SEGBIND.spad" 1542900 1542911 1543089 1543094) (-1004 "SEGAST.spad" 1542630 1542639 1542890 1542895) (-1003 "SEG2.spad" 1542065 1542078 1542586 1542591) (-1002 "SEG.spad" 1541878 1541889 1541984 1541989) (-1001 "SDVAR.spad" 1541154 1541165 1541868 1541873) (-1000 "SDPOL.spad" 1538846 1538857 1539137 1539264) (-999 "SCPKG.spad" 1536936 1536946 1538836 1538841) (-998 "SCOPE.spad" 1536114 1536122 1536926 1536931) (-997 "SCACHE.spad" 1534811 1534821 1536104 1536109) (-996 "SASTCAT.spad" 1534721 1534729 1534801 1534806) (-995 "SAOS.spad" 1534594 1534602 1534711 1534716) (-994 "SAERFFC.spad" 1534308 1534327 1534584 1534589) (-993 "SAEFACT.spad" 1534010 1534029 1534298 1534303) (-992 "SAE.spad" 1531661 1531676 1532271 1532406) (-991 "RURPK.spad" 1529321 1529336 1531651 1531656) (-990 "RULESET.spad" 1528775 1528798 1529311 1529316) (-989 "RULECOLD.spad" 1528628 1528640 1528765 1528770) (-988 "RULE.spad" 1526877 1526900 1528618 1528623) (-987 "RTVALUE.spad" 1526613 1526621 1526867 1526872) (-986 "syntax.spad" 1526331 1526339 1526603 1526608) (-985 "RSETGCD.spad" 1522774 1522793 1526321 1526326) (-984 "RSETCAT.spad" 1512765 1512781 1522764 1522769) (-983 "RSETCAT.spad" 1502754 1502772 1512755 1512760) (-982 "RSDCMPK.spad" 1501255 1501274 1502744 1502749) (-981 "RRCC.spad" 1499640 1499669 1501245 1501250) (-980 "RRCC.spad" 1498023 1498054 1499630 1499635) (-979 "RPTAST.spad" 1497726 1497734 1498013 1498018) (-978 "RPOLCAT.spad" 1477231 1477245 1497594 1497721) (-977 "RPOLCAT.spad" 1456529 1456545 1476894 1476899) (-976 "ROMAN.spad" 1455858 1455866 1456395 1456524) (-975 "ROIRC.spad" 1454939 1454970 1455848 1455853) (-974 "RNS.spad" 1453916 1453924 1454841 1454934) (-973 "RNS.spad" 1452979 1452989 1453906 1453911) (-972 "RNGBIND.spad" 1452140 1452153 1452934 1452939) (-971 "RNG.spad" 1451749 1451757 1452130 1452135) (-970 "RNG.spad" 1451356 1451366 1451739 1451744) (-969 "RMODULE.spad" 1451138 1451148 1451346 1451351) (-968 "RMCAT2.spad" 1450559 1450615 1451128 1451133) (-967 "RMATRIX.spad" 1449381 1449399 1449723 1449750) (-966 "RMATCAT.spad" 1445163 1445193 1449349 1449376) (-965 "RMATCAT.spad" 1440823 1440855 1445011 1445016) (-964 "RLINSET.spad" 1440528 1440538 1440813 1440818) (-963 "RINTERP.spad" 1440417 1440436 1440518 1440523) (-962 "RING.spad" 1439888 1439896 1440397 1440412) (-961 "RING.spad" 1439367 1439377 1439878 1439883) (-960 "RIDIST.spad" 1438760 1438768 1439357 1439362) (-959 "RGCHAIN.spad" 1437027 1437042 1437920 1437925) (-958 "RGBCSPC.spad" 1436817 1436828 1437017 1437022) (-957 "RGBCMDL.spad" 1436380 1436391 1436807 1436812) (-956 "RFFACTOR.spad" 1435843 1435853 1436370 1436375) (-955 "RFFACT.spad" 1435579 1435590 1435833 1435838) (-954 "RFDIST.spad" 1434576 1434584 1435569 1435574) (-953 "RF.spad" 1432251 1432261 1434566 1434571) (-952 "RETSOL.spad" 1431671 1431683 1432241 1432246) (-951 "RETRACT.spad" 1431100 1431110 1431661 1431666) (-950 "RETRACT.spad" 1430527 1430539 1431090 1431095) (-949 "RETAST.spad" 1430340 1430348 1430517 1430522) (-948 "RESRING.spad" 1429688 1429734 1430278 1430335) (-947 "RESLATC.spad" 1429013 1429023 1429678 1429683) (-946 "REPSQ.spad" 1428745 1428755 1429003 1429008) (-945 "REPDB.spad" 1428453 1428463 1428735 1428740) (-944 "REP2.spad" 1418168 1418178 1428295 1428300) (-943 "REP1.spad" 1412389 1412399 1418118 1418123) (-942 "REP.spad" 1409944 1409952 1412379 1412384) (-941 "REGSET.spad" 1407631 1407647 1409439 1409444) (-940 "REF.spad" 1407150 1407160 1407621 1407626) (-939 "REDORDER.spad" 1406357 1406373 1407140 1407145) (-938 "RECLOS.spad" 1405254 1405273 1405957 1406050) (-937 "REALSOLV.spad" 1404395 1404403 1405244 1405249) (-936 "REAL0Q.spad" 1401694 1401708 1404385 1404390) (-935 "REAL0.spad" 1398539 1398553 1401684 1401689) (-934 "REAL.spad" 1398412 1398420 1398529 1398534) (-933 "RDUCEAST.spad" 1398134 1398142 1398402 1398407) (-932 "RDIV.spad" 1397790 1397814 1398124 1398129) (-931 "RDIST.spad" 1397358 1397368 1397780 1397785) (-930 "RDETRS.spad" 1396223 1396240 1397348 1397353) (-929 "RDETR.spad" 1394363 1394380 1396213 1396218) (-928 "RDEEFS.spad" 1393463 1393479 1394353 1394358) (-927 "RDEEF.spad" 1392474 1392490 1393453 1393458) (-926 "RCFIELD.spad" 1389693 1389701 1392376 1392469) (-925 "RCFIELD.spad" 1386998 1387008 1389683 1389688) (-924 "RCAGG.spad" 1384935 1384945 1386988 1386993) (-923 "RCAGG.spad" 1382773 1382785 1384828 1384833) (-922 "RATRET.spad" 1382134 1382144 1382763 1382768) (-921 "RATFACT.spad" 1381827 1381838 1382124 1382129) (-920 "RANDSRC.spad" 1381147 1381155 1381817 1381822) (-919 "RADUTIL.spad" 1380904 1380912 1381137 1381142) (-918 "RADIX.spad" 1377949 1377962 1379494 1379587) (-917 "RADFF.spad" 1375866 1375902 1375984 1376140) (-916 "RADCAT.spad" 1375462 1375470 1375856 1375861) (-915 "RADCAT.spad" 1375056 1375066 1375452 1375457) (-914 "QUEUE.spad" 1374492 1374502 1374750 1374755) (-913 "QUATCT2.spad" 1374113 1374131 1374482 1374487) (-912 "QUATCAT.spad" 1372284 1372294 1374043 1374108) (-911 "QUATCAT.spad" 1370220 1370232 1371981 1371986) (-910 "QUAT.spad" 1368827 1368837 1369169 1369234) (-909 "QUAGG.spad" 1367683 1367693 1368817 1368822) (-908 "QQUTAST.spad" 1367452 1367460 1367673 1367678) (-907 "QFORM.spad" 1367071 1367085 1367442 1367447) (-906 "QFCAT2.spad" 1366764 1366780 1367061 1367066) (-905 "QFCAT.spad" 1365467 1365477 1366666 1366759) (-904 "QFCAT.spad" 1363803 1363815 1365004 1365009) (-903 "QEQUAT.spad" 1363362 1363370 1363793 1363798) (-902 "QCMPACK.spad" 1358277 1358296 1363352 1363357) (-901 "QALGSET2.spad" 1356273 1356291 1358267 1358272) (-900 "QALGSET.spad" 1352378 1352410 1356187 1356192) (-899 "PWFFINTB.spad" 1349794 1349815 1352368 1352373) (-898 "PUSHVAR.spad" 1349133 1349152 1349784 1349789) (-897 "PTRANFN.spad" 1345269 1345279 1349123 1349128) (-896 "PTPACK.spad" 1342357 1342367 1345259 1345264) (-895 "PTFUNC2.spad" 1342180 1342194 1342347 1342352) (-894 "PTCAT.spad" 1341457 1341467 1342170 1342175) (-893 "PSQFR.spad" 1340772 1340796 1341447 1341452) (-892 "PSEUDLIN.spad" 1339658 1339668 1340762 1340767) (-891 "PSETPK.spad" 1326363 1326379 1339536 1339541) (-890 "PSETCAT.spad" 1320773 1320796 1326353 1326358) (-889 "PSETCAT.spad" 1315147 1315172 1320729 1320734) (-888 "PSCURVE.spad" 1314146 1314154 1315137 1315142) (-887 "PSCAT.spad" 1312929 1312958 1314044 1314141) (-886 "PSCAT.spad" 1311802 1311833 1312919 1312924) (-885 "PRTITION.spad" 1310500 1310508 1311792 1311797) (-884 "PRTDAST.spad" 1310219 1310227 1310490 1310495) (-883 "PRS.spad" 1299837 1299854 1310175 1310180) (-882 "PRQAGG.spad" 1299294 1299304 1299827 1299832) (-881 "PROPLOG.spad" 1298898 1298906 1299284 1299289) (-880 "PROPFUN2.spad" 1298521 1298534 1298888 1298893) (-879 "PROPFUN1.spad" 1297927 1297938 1298511 1298516) (-878 "PROPFRML.spad" 1296495 1296506 1297917 1297922) (-877 "PROPERTY.spad" 1295991 1295999 1296485 1296490) (-876 "PRODUCT.spad" 1293688 1293700 1293972 1294027) (-875 "PRINT.spad" 1293440 1293448 1293678 1293683) (-874 "PRIMES.spad" 1291701 1291711 1293430 1293435) (-873 "PRIMELT.spad" 1289822 1289836 1291691 1291696) (-872 "PRIMCAT.spad" 1289465 1289473 1289812 1289817) (-871 "PRIMARR2.spad" 1288232 1288244 1289455 1289460) (-870 "PRIMARR.spad" 1286984 1286994 1287154 1287159) (-869 "PREASSOC.spad" 1286366 1286378 1286974 1286979) (-868 "PR.spad" 1284884 1284896 1285583 1285710) (-867 "PPCURVE.spad" 1284021 1284029 1284874 1284879) (-866 "PORTNUM.spad" 1283812 1283820 1284011 1284016) (-865 "POLYROOT.spad" 1282661 1282683 1283768 1283773) (-864 "POLYLIFT.spad" 1281926 1281949 1282651 1282656) (-863 "POLYCATQ.spad" 1280052 1280074 1281916 1281921) (-862 "POLYCAT.spad" 1273554 1273575 1279920 1280047) (-861 "POLYCAT.spad" 1266576 1266599 1272944 1272949) (-860 "POLY2UP.spad" 1266028 1266042 1266566 1266571) (-859 "POLY2.spad" 1265625 1265637 1266018 1266023) (-858 "POLY.spad" 1263293 1263303 1263808 1263935) (-857 "POLUTIL.spad" 1262258 1262287 1263249 1263254) (-856 "POLTOPOL.spad" 1261006 1261021 1262248 1262253) (-855 "POINT.spad" 1259586 1259596 1259673 1259678) (-854 "PNTHEORY.spad" 1256288 1256296 1259576 1259581) (-853 "PMTOOLS.spad" 1255063 1255077 1256278 1256283) (-852 "PMSYM.spad" 1254612 1254622 1255053 1255058) (-851 "PMQFCAT.spad" 1254203 1254217 1254602 1254607) (-850 "PMPREDFS.spad" 1253665 1253687 1254193 1254198) (-849 "PMPRED.spad" 1253152 1253166 1253655 1253660) (-848 "PMPLCAT.spad" 1252229 1252247 1253081 1253086) (-847 "PMLSAGG.spad" 1251814 1251828 1252219 1252224) (-846 "PMKERNEL.spad" 1251393 1251405 1251804 1251809) (-845 "PMINS.spad" 1250973 1250983 1251383 1251388) (-844 "PMFS.spad" 1250550 1250568 1250963 1250968) (-843 "PMDOWN.spad" 1249840 1249854 1250540 1250545) (-842 "PMASSFS.spad" 1248815 1248831 1249830 1249835) (-841 "PMASS.spad" 1247833 1247841 1248805 1248810) (-840 "PLOTTOOL.spad" 1247613 1247621 1247823 1247828) (-839 "PLOT3D.spad" 1244077 1244085 1247603 1247608) (-838 "PLOT1.spad" 1243250 1243260 1244067 1244072) (-837 "PLOT.spad" 1238173 1238181 1243240 1243245) (-836 "PLEQN.spad" 1225575 1225602 1238163 1238168) (-835 "PINTERPA.spad" 1225359 1225375 1225565 1225570) (-834 "PINTERP.spad" 1224981 1225000 1225349 1225354) (-833 "PID.spad" 1223955 1223963 1224907 1224976) (-832 "PICOERCE.spad" 1223612 1223622 1223945 1223950) (-831 "PI.spad" 1223229 1223237 1223586 1223607) (-830 "PGROEB.spad" 1221838 1221852 1223219 1223224) (-829 "PGE.spad" 1213511 1213519 1221828 1221833) (-828 "PGCD.spad" 1212465 1212482 1213501 1213506) (-827 "PFRPAC.spad" 1211614 1211624 1212455 1212460) (-826 "PFR.spad" 1208317 1208327 1211516 1211609) (-825 "PFOTOOLS.spad" 1207575 1207591 1208307 1208312) (-824 "PFOQ.spad" 1206945 1206963 1207565 1207570) (-823 "PFO.spad" 1206364 1206391 1206935 1206940) (-822 "PFECAT.spad" 1204074 1204082 1206290 1206359) (-821 "PFECAT.spad" 1201812 1201822 1204030 1204035) (-820 "PFBRU.spad" 1199700 1199712 1201802 1201807) (-819 "PFBR.spad" 1197260 1197283 1199690 1199695) (-818 "PF.spad" 1196834 1196846 1197065 1197158) (-817 "PERMGRP.spad" 1191604 1191614 1196824 1196829) (-816 "PERMCAT.spad" 1190265 1190275 1191584 1191599) (-815 "PERMAN.spad" 1188821 1188835 1190255 1190260) (-814 "PERM.spad" 1184631 1184641 1188654 1188669) (-813 "PENDTREE.spad" 1183984 1183994 1184264 1184269) (-812 "PDSPC.spad" 1182797 1182807 1183974 1183979) (-811 "PDSPC.spad" 1181608 1181620 1182787 1182792) (-810 "PDRING.spad" 1181450 1181460 1181588 1181603) (-809 "PDMOD.spad" 1181266 1181278 1181418 1181445) (-808 "PDECOMP.spad" 1180736 1180753 1181256 1181261) (-807 "PDDOM.spad" 1180174 1180187 1180726 1180731) (-806 "PDDOM.spad" 1179610 1179625 1180164 1180169) (-805 "PCOMP.spad" 1179463 1179476 1179600 1179605) (-804 "PBWLB.spad" 1178061 1178078 1179453 1179458) (-803 "PATTERN2.spad" 1177799 1177811 1178051 1178056) (-802 "PATTERN1.spad" 1176143 1176159 1177789 1177794) (-801 "PATTERN.spad" 1170718 1170728 1176133 1176138) (-800 "PATRES2.spad" 1170390 1170404 1170708 1170713) (-799 "PATRES.spad" 1167973 1167985 1170380 1170385) (-798 "PATMATCH.spad" 1166214 1166245 1167725 1167730) (-797 "PATMAB.spad" 1165643 1165653 1166204 1166209) (-796 "PATLRES.spad" 1164729 1164743 1165633 1165638) (-795 "PATAB.spad" 1164493 1164503 1164719 1164724) (-794 "PARTPERM.spad" 1162549 1162557 1164483 1164488) (-793 "PARSURF.spad" 1161983 1162011 1162539 1162544) (-792 "PARSU2.spad" 1161780 1161796 1161973 1161978) (-791 "script-parser.spad" 1161300 1161308 1161770 1161775) (-790 "PARSCURV.spad" 1160734 1160762 1161290 1161295) (-789 "PARSC2.spad" 1160525 1160541 1160724 1160729) (-788 "PARPCURV.spad" 1159987 1160015 1160515 1160520) (-787 "PARPC2.spad" 1159778 1159794 1159977 1159982) (-786 "PARAMAST.spad" 1158906 1158914 1159768 1159773) (-785 "PAN2EXPR.spad" 1158318 1158326 1158896 1158901) (-784 "PALETTE.spad" 1157432 1157440 1158308 1158313) (-783 "PAIR.spad" 1156506 1156519 1157075 1157080) (-782 "PADICRC.spad" 1153911 1153929 1155074 1155167) (-781 "PADICRAT.spad" 1151971 1151983 1152184 1152277) (-780 "PADICCT.spad" 1150520 1150532 1151897 1151966) (-779 "PADIC.spad" 1150223 1150235 1150446 1150515) (-778 "PADEPAC.spad" 1148912 1148931 1150213 1150218) (-777 "PADE.spad" 1147664 1147680 1148902 1148907) (-776 "OWP.spad" 1146912 1146942 1147522 1147589) (-775 "OVERSET.spad" 1146485 1146493 1146902 1146907) (-774 "OVAR.spad" 1146266 1146289 1146475 1146480) (-773 "OUTFORM.spad" 1135674 1135682 1146256 1146261) (-772 "OUTBFILE.spad" 1135108 1135116 1135664 1135669) (-771 "OUTBCON.spad" 1134178 1134186 1135098 1135103) (-770 "OUTBCON.spad" 1133246 1133256 1134168 1134173) (-769 "OUT.spad" 1132364 1132372 1133236 1133241) (-768 "OSI.spad" 1131839 1131847 1132354 1132359) (-767 "OSGROUP.spad" 1131757 1131765 1131829 1131834) (-766 "ORTHPOL.spad" 1130268 1130278 1131700 1131705) (-765 "OREUP.spad" 1129762 1129790 1129989 1130028) (-764 "ORESUP.spad" 1129104 1129128 1129483 1129522) (-763 "OREPCTO.spad" 1126993 1127005 1129024 1129029) (-762 "OREPCAT.spad" 1121180 1121190 1126949 1126988) (-761 "OREPCAT.spad" 1115257 1115269 1121028 1121033) (-760 "ORDTYPE.spad" 1114494 1114502 1115247 1115252) (-759 "ORDTYPE.spad" 1113729 1113739 1114484 1114489) (-758 "ORDSTRCT.spad" 1113515 1113530 1113678 1113683) (-757 "ORDSET.spad" 1113215 1113223 1113505 1113510) (-756 "ORDRING.spad" 1113032 1113040 1113195 1113210) (-755 "ORDMON.spad" 1112887 1112895 1113022 1113027) (-754 "ORDFUNS.spad" 1112019 1112035 1112877 1112882) (-753 "ORDFIN.spad" 1111839 1111847 1112009 1112014) (-752 "ORDCOMP2.spad" 1111132 1111144 1111829 1111834) (-751 "ORDCOMP.spad" 1109658 1109668 1110740 1110769) (-750 "OPSIG.spad" 1109320 1109328 1109648 1109653) (-749 "OPQUERY.spad" 1108901 1108909 1109310 1109315) (-748 "OPERCAT.spad" 1108367 1108377 1108891 1108896) (-747 "OPERCAT.spad" 1107831 1107843 1108357 1108362) (-746 "OP.spad" 1107573 1107583 1107653 1107720) (-745 "ONECOMP2.spad" 1106997 1107009 1107563 1107568) (-744 "ONECOMP.spad" 1105803 1105813 1106605 1106634) (-743 "OMSAGG.spad" 1105615 1105625 1105783 1105798) (-742 "OMLO.spad" 1105048 1105060 1105501 1105540) (-741 "OINTDOM.spad" 1104811 1104819 1104974 1105043) (-740 "OFMONOID.spad" 1102950 1102960 1104767 1104772) (-739 "ODVAR.spad" 1102211 1102221 1102940 1102945) (-738 "ODR.spad" 1101855 1101881 1102023 1102172) (-737 "ODPOL.spad" 1099503 1099513 1099843 1099970) (-736 "ODP.spad" 1088990 1089010 1089363 1089448) (-735 "ODETOOLS.spad" 1087639 1087658 1088980 1088985) (-734 "ODESYS.spad" 1085333 1085350 1087629 1087634) (-733 "ODERTRIC.spad" 1081366 1081383 1085290 1085295) (-732 "ODERED.spad" 1080765 1080789 1081356 1081361) (-731 "ODERAT.spad" 1078398 1078415 1080755 1080760) (-730 "ODEPRRIC.spad" 1075491 1075513 1078388 1078393) (-729 "ODEPRIM.spad" 1072889 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(-589 "LLINSET.spad" 875280 875290 875563 875568) (-588 "LITERAL.spad" 875186 875197 875270 875275) (-587 "LIST3.spad" 874497 874511 875176 875181) (-586 "LIST2MAP.spad" 871424 871436 874487 874492) (-585 "LIST2.spad" 870126 870138 871414 871419) (-584 "LIST.spad" 867705 867715 869048 869053) (-583 "LINSET.spad" 867484 867494 867695 867700) (-582 "LINFORM.spad" 866947 866959 867452 867479) (-581 "LINEXP.spad" 865690 865700 866937 866942) (-580 "LINELT.spad" 865061 865073 865573 865600) (-579 "LINDEP.spad" 863910 863922 864973 864978) (-578 "LINBASIS.spad" 863546 863561 863900 863905) (-577 "LIMITRF.spad" 861493 861503 863536 863541) (-576 "LIMITPS.spad" 860403 860416 861483 861488) (-575 "LIECAT.spad" 859887 859897 860329 860398) (-574 "LIECAT.spad" 859399 859411 859843 859848) (-573 "LIE.spad" 857403 857415 858677 858819) (-572 "LIB.spad" 855226 855234 855672 855677) (-571 "LGROBP.spad" 852579 852598 855216 855221) (-570 "LFCAT.spad" 851638 851646 852569 852574) (-569 "LF.spad" 850593 850609 851628 851633) (-568 "LEXTRIPK.spad" 846216 846231 850583 850588) (-567 "LEXP.spad" 844235 844262 846196 846211) (-566 "LETAST.spad" 843934 843942 844225 844230) (-565 "LEADCDET.spad" 842340 842357 843924 843929) (-564 "LAZM3PK.spad" 841084 841106 842330 842335) (-563 "LAUPOL.spad" 839751 839764 840651 840720) (-562 "LAPLACE.spad" 839334 839350 839741 839746) (-561 "LALG.spad" 839110 839120 839314 839329) (-560 "LALG.spad" 838894 838906 839100 839105) (-559 "LA.spad" 838334 838348 838816 838855) (-558 "KVTFROM.spad" 838077 838087 838324 838329) (-557 "KTVLOGIC.spad" 837621 837629 838067 838072) (-556 "KRCFROM.spad" 837367 837377 837611 837616) (-555 "KOVACIC.spad" 836098 836115 837357 837362) (-554 "KONVERT.spad" 835820 835830 836088 836093) (-553 "KOERCE.spad" 835557 835567 835810 835815) (-552 "KERNEL2.spad" 835260 835272 835547 835552) (-551 "KERNEL.spad" 833980 833990 835109 835114) (-550 "KDAGG.spad" 833099 833121 833970 833975) (-549 "KDAGG.spad" 832216 832240 833089 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diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 5b6b753c..fc3ceb42 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
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((-1197 . -557) 201414) ((-1197 . -320) 201398) ((-1197 . -893) 201367) ((-1196 . -965) T) ((-1196 . -667) T) ((-1196 . -1065) T) ((-1196 . -1029) T) ((-1196 . -974) T) ((-1196 . -21) T) ((-1196 . -592) 201312) ((-1196 . -23) T) ((-1196 . -1017) T) ((-1196 . -556) 201281) ((-1196 . -1133) T) ((-1196 . -13) T) ((-1196 . -72) T) ((-1196 . -25) T) ((-1196 . -104) T) ((-1196 . -594) 201241) ((-1196 . -559) 201183) ((-1196 . -433) 201167) ((-1196 . -38) 201137) ((-1196 . -82) 201102) ((-1196 . -967) 201072) ((-1196 . -972) 201042) ((-1196 . -586) 201012) ((-1196 . -658) 200982) ((-1195 . -999) T) ((-1195 . -433) 200963) ((-1195 . -556) 200929) ((-1195 . -559) 200910) ((-1195 . -1017) T) ((-1195 . -1133) T) ((-1195 . -13) T) ((-1195 . -72) T) ((-1195 . -64) T) ((-1194 . -999) T) ((-1194 . -433) 200891) ((-1194 . -556) 200857) ((-1194 . -559) 200838) ((-1194 . -1017) T) ((-1194 . -1133) T) ((-1194 . -13) T) ((-1194 . -72) T) ((-1194 . -64) T) ((-1189 . -556) 200820) ((-1187 . -1017) T) ((-1187 . -556) 200802) ((-1187 . -1133) T) ((-1187 . -13) T) ((-1187 . -72) T) ((-1186 . -1017) T) ((-1186 . -556) 200784) ((-1186 . -1133) T) ((-1186 . -13) T) ((-1186 . -72) T) ((-1183 . -1182) 200768) ((-1183 . -326) 200752) ((-1183 . -763) 200731) ((-1183 . -760) 200710) ((-1183 . -124) 200694) ((-1183 . -557) 200655) ((-1183 . -243) 200607) ((-1183 . -542) 200584) ((-1183 . -245) 200561) ((-1183 . -597) 200545) ((-1183 . -432) 200529) ((-1183 . -1017) 200482) ((-1183 . -383) 200466) ((-1183 . -459) 200399) ((-1183 . -262) 200337) ((-1183 . -556) 200252) ((-1183 . -72) 200186) ((-1183 . -1133) T) ((-1183 . -13) T) ((-1183 . -34) T) ((-1183 . -320) 200170) ((-1183 . -1039) 200154) ((-1183 . -19) 200138) ((-1180 . -1017) T) ((-1180 . -556) 200104) ((-1180 . -1133) T) ((-1180 . -13) T) ((-1180 . -72) T) ((-1173 . -1176) 200088) ((-1173 . -192) 200047) ((-1173 . -559) 199929) ((-1173 . -594) 199854) ((-1173 . -592) 199764) ((-1173 . -104) T) ((-1173 . -25) T) ((-1173 . -72) T) ((-1173 . -556) 199746) ((-1173 . -1017) T) ((-1173 . -23) T) ((-1173 . -21) T) ((-1173 . -974) T) ((-1173 . -1029) T) ((-1173 . -1065) T) ((-1173 . -667) T) ((-1173 . -965) T) ((-1173 . -188) 199699) ((-1173 . -13) T) ((-1173 . -1133) T) ((-1173 . -191) 199658) ((-1173 . -243) 199623) ((-1173 . -813) 199536) ((-1173 . -810) 199424) ((-1173 . -815) 199337) ((-1173 . -890) 199307) ((-1173 . -38) 199204) ((-1173 . -82) 199069) ((-1173 . -967) 198955) ((-1173 . -972) 198841) ((-1173 . -586) 198738) ((-1173 . -658) 198635) ((-1173 . -118) 198614) ((-1173 . -120) 198593) ((-1173 . -148) 198547) ((-1173 . -383) 198531) ((-1173 . -499) 198510) ((-1173 . -248) 198489) ((-1173 . -47) 198466) ((-1173 . -1162) 198443) ((-1173 . -35) 198409) ((-1173 . -66) 198375) ((-1173 . -241) 198341) ((-1173 . -436) 198307) ((-1173 . -1122) 198273) ((-1173 . -1119) 198239) ((-1173 . -919) 198205) ((-1170 . -279) 198149) ((-1170 . -954) 198115) ((-1170 . -357) 198081) ((-1170 . -38) 197938) ((-1170 . -559) 197812) ((-1170 . -594) 197701) ((-1170 . -592) 197575) ((-1170 . -974) T) ((-1170 . -1029) T) ((-1170 . -1065) T) ((-1170 . -667) T) ((-1170 . -965) T) ((-1170 . -82) 197425) ((-1170 . -967) 197314) ((-1170 . -972) 197203) ((-1170 . -21) T) ((-1170 . -23) T) ((-1170 . -1017) T) ((-1170 . -556) 197185) ((-1170 . -1133) T) ((-1170 . -13) T) ((-1170 . -72) T) ((-1170 . -25) T) ((-1170 . -104) T) ((-1170 . -586) 197042) ((-1170 . -658) 196899) ((-1170 . -118) 196860) ((-1170 . -120) 196821) ((-1170 . -148) T) ((-1170 . -383) 196787) ((-1170 . -499) T) ((-1170 . -248) T) ((-1170 . -47) 196731) ((-1169 . -1168) 196710) ((-1169 . -314) 196689) ((-1169 . -1138) 196668) ((-1169 . -836) 196647) ((-1169 . -499) 196601) ((-1169 . -148) 196535) ((-1169 . -559) 196354) ((-1169 . -658) 196201) ((-1169 . -586) 196048) ((-1169 . -38) 195895) ((-1169 . -395) 195874) ((-1169 . -260) 195853) ((-1169 . -594) 195753) ((-1169 . -592) 195638) ((-1169 . -974) T) ((-1169 . -1029) T) ((-1169 . -1065) T) ((-1169 . -667) T) ((-1169 . -965) T) ((-1169 . -82) 195458) ((-1169 . -967) 195299) ((-1169 . -972) 195140) ((-1169 . -21) T) ((-1169 . -23) T) ((-1169 . -1017) T) ((-1169 . -556) 195122) ((-1169 . -1133) T) ((-1169 . -13) T) ((-1169 . -72) T) ((-1169 . -25) T) ((-1169 . -104) T) ((-1169 . -248) 195076) ((-1169 . -203) 195055) ((-1169 . -919) 195021) ((-1169 . -1119) 194987) ((-1169 . -1122) 194953) ((-1169 . -436) 194919) ((-1169 . -241) 194885) ((-1169 . -66) 194851) ((-1169 . -35) 194817) ((-1169 . -1162) 194787) ((-1169 . -47) 194757) ((-1169 . -383) 194741) ((-1169 . -120) 194720) ((-1169 . -118) 194699) ((-1169 . -890) 194662) ((-1169 . -815) 194568) ((-1169 . -810) 194472) ((-1169 . -813) 194378) ((-1169 . -243) 194336) ((-1169 . -191) 194288) ((-1169 . -188) 194234) ((-1169 . -192) 194186) ((-1169 . -1166) 194170) ((-1169 . -954) 194154) ((-1164 . -1168) 194115) ((-1164 . -314) 194094) ((-1164 . -1138) 194073) ((-1164 . -836) 194052) ((-1164 . -499) 194006) ((-1164 . -148) 193940) ((-1164 . -559) 193689) ((-1164 . -658) 193536) ((-1164 . -586) 193383) ((-1164 . -38) 193230) ((-1164 . -395) 193209) ((-1164 . -260) 193188) ((-1164 . -594) 193088) ((-1164 . -592) 192973) ((-1164 . -974) T) ((-1164 . -1029) T) ((-1164 . -1065) T) ((-1164 . -667) T) ((-1164 . -965) T) ((-1164 . -82) 192793) ((-1164 . -967) 192634) ((-1164 . -972) 192475) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1017) T) ((-1164 . -556) 192457) ((-1164 . -1133) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -248) 192411) ((-1164 . -203) 192390) ((-1164 . -919) 192356) ((-1164 . -1119) 192322) ((-1164 . -1122) 192288) ((-1164 . -436) 192254) ((-1164 . -241) 192220) ((-1164 . -66) 192186) ((-1164 . -35) 192152) ((-1164 . -1162) 192122) ((-1164 . -47) 192092) ((-1164 . -383) 192076) ((-1164 . -120) 192055) ((-1164 . -118) 192034) ((-1164 . -890) 191997) ((-1164 . -815) 191903) ((-1164 . -810) 191784) ((-1164 . -813) 191690) ((-1164 . -243) 191648) ((-1164 . -191) 191600) ((-1164 . -188) 191546) ((-1164 . -192) 191498) ((-1164 . -1166) 191482) ((-1164 . -954) 191417) ((-1152 . -1159) 191401) ((-1152 . -1070) 191379) ((-1152 . -557) NIL) ((-1152 . -262) 191366) ((-1152 . -459) 191314) ((-1152 . -279) 191291) ((-1152 . -954) 191174) ((-1152 . -357) 191158) ((-1152 . -38) 190990) ((-1152 . -82) 190795) ((-1152 . -967) 190621) ((-1152 . -972) 190447) ((-1152 . -592) 190357) ((-1152 . -594) 190246) ((-1152 . -586) 190078) ((-1152 . -658) 189910) ((-1152 . -559) 189666) ((-1152 . -118) 189645) ((-1152 . -120) 189624) ((-1152 . -383) 189608) ((-1152 . -47) 189585) ((-1152 . -331) 189569) ((-1152 . -584) 189517) ((-1152 . -813) 189461) ((-1152 . -810) 189368) ((-1152 . -815) 189279) ((-1152 . -800) NIL) ((-1152 . -825) 189258) ((-1152 . -1138) 189237) ((-1152 . -865) 189207) ((-1152 . -836) 189186) ((-1152 . -499) 189100) ((-1152 . -248) 189014) ((-1152 . -148) 188908) ((-1152 . -395) 188842) ((-1152 . -260) 188821) ((-1152 . -243) 188748) ((-1152 . -192) T) ((-1152 . -104) T) ((-1152 . -25) T) ((-1152 . -72) T) ((-1152 . -556) 188730) ((-1152 . -1017) T) ((-1152 . -23) T) ((-1152 . -21) T) ((-1152 . -974) T) ((-1152 . -1029) T) ((-1152 . -1065) T) ((-1152 . -667) T) ((-1152 . -965) T) ((-1152 . -188) 188717) ((-1152 . -13) T) ((-1152 . -1133) T) ((-1152 . -191) T) ((-1152 . -227) 188701) ((-1152 . -186) 188685) ((-1150 . -1010) 188669) ((-1150 . -561) 188653) ((-1150 . -1017) 188631) ((-1150 . -556) 188598) ((-1150 . -1133) 188576) ((-1150 . -13) 188554) ((-1150 . -72) 188532) ((-1150 . -1011) 188489) ((-1148 . -1147) 188468) ((-1148 . -919) 188434) ((-1148 . -1119) 188400) ((-1148 . -1122) 188366) ((-1148 . -436) 188332) ((-1148 . -241) 188298) ((-1148 . -66) 188264) ((-1148 . -35) 188230) ((-1148 . -1162) 188207) ((-1148 . -47) 188184) ((-1148 . -383) 188141) ((-1148 . -559) 187896) ((-1148 . -658) 187716) ((-1148 . -586) 187536) ((-1148 . -594) 187347) ((-1148 . -592) 187205) ((-1148 . -972) 187019) ((-1148 . -967) 186833) ((-1148 . -82) 186621) ((-1148 . -38) 186441) ((-1148 . -890) 186411) ((-1148 . -243) 186311) ((-1148 . -1145) 186295) ((-1148 . -974) T) ((-1148 . -1029) T) ((-1148 . -1065) T) ((-1148 . -667) T) ((-1148 . -965) T) ((-1148 . -21) T) ((-1148 . -23) T) ((-1148 . -1017) T) ((-1148 . -556) 186277) ((-1148 . -1133) T) ((-1148 . -13) T) ((-1148 . -72) T) ((-1148 . -25) T) ((-1148 . -104) T) ((-1148 . -118) 186205) ((-1148 . -120) 186087) ((-1148 . -557) 185760) ((-1148 . -186) 185730) ((-1148 . -813) 185584) ((-1148 . -815) 185384) ((-1148 . -810) 185182) ((-1148 . -227) 185152) ((-1148 . -191) 185014) ((-1148 . -188) 184870) ((-1148 . -192) 184778) ((-1148 . -314) 184757) ((-1148 . -1138) 184736) ((-1148 . -836) 184715) ((-1148 . -499) 184669) ((-1148 . -148) 184603) ((-1148 . -395) 184582) ((-1148 . -260) 184561) ((-1148 . -248) 184515) ((-1148 . -203) 184494) ((-1148 . -290) 184464) ((-1148 . -459) 184324) ((-1148 . -262) 184263) ((-1148 . -331) 184233) ((-1148 . -584) 184141) ((-1148 . -345) 184111) ((-1148 . -800) 183984) ((-1148 . -744) 183937) ((-1148 . -718) 183890) ((-1148 . -720) 183843) ((-1148 . -760) 183745) ((-1148 . -763) 183647) ((-1148 . -722) 183600) ((-1148 . -725) 183553) ((-1148 . -759) 183506) ((-1148 . -798) 183476) ((-1148 . -825) 183429) ((-1148 . -937) 183382) ((-1148 . -954) 183171) ((-1148 . -1070) 183123) ((-1148 . -908) 183093) ((-1143 . -1147) 183054) ((-1143 . -919) 183020) ((-1143 . -1119) 182986) ((-1143 . -1122) 182952) ((-1143 . -436) 182918) ((-1143 . -241) 182884) ((-1143 . -66) 182850) ((-1143 . -35) 182816) ((-1143 . -1162) 182793) ((-1143 . -47) 182770) ((-1143 . -383) 182709) ((-1143 . -559) 182510) ((-1143 . -658) 182312) ((-1143 . -586) 182114) ((-1143 . -594) 181969) ((-1143 . -592) 181809) ((-1143 . -972) 181605) ((-1143 . -967) 181401) ((-1143 . -82) 181153) ((-1143 . -38) 180955) ((-1143 . -890) 180925) ((-1143 . -243) 180753) ((-1143 . -1145) 180737) ((-1143 . -974) T) ((-1143 . -1029) T) ((-1143 . -1065) T) ((-1143 . -667) T) ((-1143 . -965) T) ((-1143 . -21) T) ((-1143 . -23) T) ((-1143 . -1017) T) ((-1143 . -556) 180719) ((-1143 . -1133) T) ((-1143 . -13) T) ((-1143 . -72) T) ((-1143 . -25) T) ((-1143 . -104) T) ((-1143 . -118) 180629) ((-1143 . -120) 180539) ((-1143 . -557) NIL) ((-1143 . -186) 180491) ((-1143 . -813) 180327) ((-1143 . -815) 180091) ((-1143 . -810) 179830) ((-1143 . -227) 179782) ((-1143 . -191) 179608) ((-1143 . -188) 179428) ((-1143 . -192) 179318) ((-1143 . -314) 179297) ((-1143 . -1138) 179276) ((-1143 . -836) 179255) ((-1143 . -499) 179209) ((-1143 . -148) 179143) ((-1143 . -395) 179122) ((-1143 . -260) 179101) ((-1143 . -248) 179055) ((-1143 . -203) 179034) ((-1143 . -290) 178986) ((-1143 . -459) 178720) ((-1143 . -262) 178605) ((-1143 . -331) 178557) ((-1143 . -584) 178509) ((-1143 . -345) 178461) ((-1143 . -800) NIL) ((-1143 . -744) NIL) ((-1143 . -718) NIL) ((-1143 . -720) NIL) ((-1143 . -760) NIL) ((-1143 . -763) NIL) ((-1143 . -722) NIL) ((-1143 . -725) NIL) ((-1143 . -759) NIL) ((-1143 . -798) 178413) ((-1143 . -825) NIL) ((-1143 . -937) NIL) ((-1143 . -954) 178379) ((-1143 . -1070) NIL) ((-1143 . -908) 178331) ((-1142 . -756) T) ((-1142 . -763) T) ((-1142 . -760) T) ((-1142 . -1017) T) ((-1142 . -556) 178313) ((-1142 . -1133) T) ((-1142 . -13) T) ((-1142 . -72) T) ((-1142 . -322) T) ((-1142 . -608) T) ((-1141 . -756) T) ((-1141 . -763) T) ((-1141 . -760) T) ((-1141 . -1017) T) ((-1141 . -556) 178295) ((-1141 . -1133) T) ((-1141 . -13) T) ((-1141 . -72) T) ((-1141 . -322) T) ((-1141 . -608) T) ((-1140 . -756) T) ((-1140 . -763) T) ((-1140 . -760) T) ((-1140 . -1017) T) ((-1140 . -556) 178277) ((-1140 . -1133) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -322) T) ((-1140 . -608) T) ((-1139 . -756) T) ((-1139 . -763) T) ((-1139 . -760) T) ((-1139 . -1017) T) ((-1139 . -556) 178259) ((-1139 . -1133) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -322) T) ((-1139 . -608) T) ((-1134 . -999) T) ((-1134 . -433) 178240) ((-1134 . -556) 178206) ((-1134 . -559) 178187) ((-1134 . -1017) T) ((-1134 . -1133) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -64) T) ((-1131 . -433) 178164) ((-1131 . -556) 178105) ((-1131 . -559) 178082) ((-1131 . -1017) 178060) ((-1131 . -1133) 178038) ((-1131 . -13) 178016) ((-1131 . -72) 177994) ((-1126 . -683) 177970) ((-1126 . -35) 177936) ((-1126 . -66) 177902) ((-1126 . -241) 177868) ((-1126 . -436) 177834) ((-1126 . -1122) 177800) ((-1126 . -1119) 177766) ((-1126 . -919) 177732) ((-1126 . -47) 177701) ((-1126 . -38) 177598) ((-1126 . -586) 177495) ((-1126 . -658) 177392) ((-1126 . -559) 177274) ((-1126 . -248) 177253) ((-1126 . -499) 177232) ((-1126 . -383) 177216) ((-1126 . -82) 177081) ((-1126 . -967) 176967) ((-1126 . -972) 176853) ((-1126 . -148) 176807) ((-1126 . -120) 176786) ((-1126 . -118) 176765) ((-1126 . -594) 176690) ((-1126 . -592) 176600) ((-1126 . -890) 176561) ((-1126 . -815) 176542) ((-1126 . -1133) T) ((-1126 . -13) T) ((-1126 . -810) 176521) ((-1126 . -965) T) ((-1126 . -667) T) ((-1126 . -1065) T) ((-1126 . -1029) T) ((-1126 . -974) T) ((-1126 . -21) T) ((-1126 . -23) T) ((-1126 . -1017) T) ((-1126 . -556) 176503) ((-1126 . -72) T) ((-1126 . -25) T) ((-1126 . -104) T) ((-1126 . -813) 176484) ((-1126 . -459) 176451) ((-1126 . -262) 176438) ((-1120 . -927) 176422) ((-1120 . -34) T) ((-1120 . -13) T) ((-1120 . -1133) T) ((-1120 . -72) 176376) ((-1120 . -556) 176311) ((-1120 . -262) 176249) ((-1120 . -459) 176182) ((-1120 . -383) 176166) ((-1120 . -1017) 176144) ((-1120 . -432) 176128) ((-1120 . -320) 176112) ((-1120 . -1039) 176096) ((-1115 . -316) 176070) ((-1115 . -72) T) ((-1115 . -13) T) ((-1115 . -1133) T) ((-1115 . -556) 176052) ((-1115 . -1017) T) ((-1113 . -1017) T) ((-1113 . -556) 176034) ((-1113 . -1133) T) ((-1113 . -13) T) ((-1113 . -72) T) ((-1113 . -559) 176016) ((-1108 . -751) 176000) ((-1108 . -72) T) ((-1108 . -13) T) ((-1108 . -1133) T) ((-1108 . -556) 175982) ((-1108 . -1017) T) ((-1106 . -1111) 175961) ((-1106 . -185) 175909) ((-1106 . -76) 175857) ((-1106 . -1039) 175792) ((-1106 . -124) 175740) ((-1106 . -557) NIL) ((-1106 . -195) 175688) ((-1106 . -542) 175667) ((-1106 . -262) 175465) ((-1106 . -459) 175217) ((-1106 . -383) 175152) ((-1106 . -432) 175087) ((-1106 . -243) 175066) ((-1106 . -245) 175045) ((-1106 . -553) 175024) ((-1106 . -1017) T) ((-1106 . -556) 175006) ((-1106 . -72) T) ((-1106 . -1133) T) ((-1106 . -13) T) ((-1106 . -34) T) ((-1106 . -320) 174954) ((-1102 . -1017) T) ((-1102 . -556) 174936) ((-1102 . -1133) T) ((-1102 . -13) T) ((-1102 . -72) T) ((-1101 . -756) T) ((-1101 . -763) T) ((-1101 . -760) T) ((-1101 . -1017) T) ((-1101 . -556) 174918) ((-1101 . -1133) T) ((-1101 . -13) T) ((-1101 . -72) T) ((-1101 . -322) T) ((-1101 . -608) T) ((-1100 . -756) T) ((-1100 . -763) T) ((-1100 . -760) T) ((-1100 . -1017) T) ((-1100 . -556) 174900) ((-1100 . -1133) T) ((-1100 . -13) T) ((-1100 . -72) T) ((-1100 . -322) T) ((-1099 . -1179) T) ((-1099 . -1017) T) ((-1099 . -556) 174867) ((-1099 . -1133) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1099 . -954) 174803) ((-1099 . -559) 174739) ((-1098 . -556) 174721) ((-1097 . -556) 174703) ((-1096 . -279) 174680) ((-1096 . -954) 174578) ((-1096 . -357) 174562) ((-1096 . -38) 174459) ((-1096 . -559) 174316) ((-1096 . -594) 174241) ((-1096 . -592) 174151) ((-1096 . -974) T) ((-1096 . -1029) T) ((-1096 . -1065) T) ((-1096 . -667) T) ((-1096 . -965) T) ((-1096 . -82) 174016) ((-1096 . -967) 173902) ((-1096 . -972) 173788) ((-1096 . -21) T) ((-1096 . -23) T) ((-1096 . -1017) T) ((-1096 . -556) 173770) ((-1096 . -1133) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -25) T) ((-1096 . -104) T) ((-1096 . -586) 173667) ((-1096 . -658) 173564) ((-1096 . -118) 173543) ((-1096 . -120) 173522) ((-1096 . -148) 173476) ((-1096 . -383) 173460) ((-1096 . -499) 173439) ((-1096 . -248) 173418) ((-1096 . -47) 173395) ((-1094 . -760) T) ((-1094 . -556) 173377) ((-1094 . -1017) T) ((-1094 . -72) T) ((-1094 . -13) T) ((-1094 . -1133) T) ((-1094 . -763) T) ((-1094 . -557) 173299) ((-1094 . -559) 173265) ((-1094 . -954) 173247) ((-1094 . -800) 173214) ((-1093 . -1176) 173198) ((-1093 . -192) 173157) ((-1093 . -559) 173039) ((-1093 . -594) 172964) ((-1093 . -592) 172874) ((-1093 . -104) T) ((-1093 . -25) T) ((-1093 . -72) T) ((-1093 . -556) 172856) ((-1093 . -1017) T) ((-1093 . -23) T) ((-1093 . -21) T) ((-1093 . -974) T) ((-1093 . -1029) T) ((-1093 . -1065) T) ((-1093 . -667) T) ((-1093 . -965) T) ((-1093 . -188) 172809) ((-1093 . -13) T) ((-1093 . -1133) T) ((-1093 . -191) 172768) ((-1093 . -243) 172733) ((-1093 . -813) 172646) ((-1093 . -810) 172534) ((-1093 . -815) 172447) ((-1093 . -890) 172417) ((-1093 . -38) 172314) ((-1093 . -82) 172179) ((-1093 . -967) 172065) ((-1093 . -972) 171951) ((-1093 . -586) 171848) ((-1093 . -658) 171745) ((-1093 . -118) 171724) ((-1093 . -120) 171703) ((-1093 . -148) 171657) ((-1093 . -383) 171641) ((-1093 . -499) 171620) ((-1093 . -248) 171599) ((-1093 . -47) 171576) ((-1093 . -1162) 171553) ((-1093 . -35) 171519) ((-1093 . -66) 171485) ((-1093 . -241) 171451) ((-1093 . -436) 171417) ((-1093 . -1122) 171383) ((-1093 . -1119) 171349) ((-1093 . -919) 171315) ((-1092 . -1168) 171276) ((-1092 . -314) 171255) ((-1092 . -1138) 171234) ((-1092 . -836) 171213) ((-1092 . -499) 171167) ((-1092 . -148) 171101) ((-1092 . -559) 170850) ((-1092 . -658) 170697) ((-1092 . -586) 170544) ((-1092 . -38) 170391) ((-1092 . -395) 170370) ((-1092 . -260) 170349) ((-1092 . -594) 170249) ((-1092 . -592) 170134) ((-1092 . -974) T) ((-1092 . -1029) T) ((-1092 . -1065) T) ((-1092 . -667) T) ((-1092 . -965) T) ((-1092 . -82) 169954) ((-1092 . -967) 169795) ((-1092 . -972) 169636) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1017) T) ((-1092 . -556) 169618) ((-1092 . -1133) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -248) 169572) ((-1092 . -203) 169551) ((-1092 . -919) 169517) ((-1092 . -1119) 169483) ((-1092 . -1122) 169449) ((-1092 . -436) 169415) ((-1092 . -241) 169381) ((-1092 . -66) 169347) ((-1092 . -35) 169313) ((-1092 . -1162) 169283) ((-1092 . -47) 169253) ((-1092 . -383) 169237) ((-1092 . -120) 169216) ((-1092 . -118) 169195) ((-1092 . -890) 169158) ((-1092 . -815) 169064) ((-1092 . -810) 168945) ((-1092 . -813) 168851) ((-1092 . -243) 168809) ((-1092 . -191) 168761) ((-1092 . -188) 168707) ((-1092 . -192) 168659) ((-1092 . -1166) 168643) ((-1092 . -954) 168578) ((-1089 . -1159) 168562) ((-1089 . -1070) 168540) ((-1089 . -557) NIL) ((-1089 . -262) 168527) ((-1089 . -459) 168475) ((-1089 . -279) 168452) ((-1089 . -954) 168335) ((-1089 . -357) 168319) ((-1089 . -38) 168151) ((-1089 . -82) 167956) ((-1089 . -967) 167782) ((-1089 . -972) 167608) ((-1089 . -592) 167518) ((-1089 . -594) 167407) ((-1089 . -586) 167239) ((-1089 . -658) 167071) ((-1089 . -559) 166848) ((-1089 . -118) 166827) ((-1089 . -120) 166806) ((-1089 . -383) 166790) ((-1089 . -47) 166767) ((-1089 . -331) 166751) ((-1089 . -584) 166699) ((-1089 . -813) 166643) ((-1089 . -810) 166550) ((-1089 . -815) 166461) ((-1089 . -800) NIL) ((-1089 . -825) 166440) ((-1089 . -1138) 166419) ((-1089 . -865) 166389) ((-1089 . -836) 166368) ((-1089 . -499) 166282) ((-1089 . -248) 166196) ((-1089 . -148) 166090) ((-1089 . -395) 166024) ((-1089 . -260) 166003) ((-1089 . -243) 165930) ((-1089 . -192) T) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -556) 165912) ((-1089 . -1017) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -974) T) ((-1089 . -1029) T) ((-1089 . -1065) T) ((-1089 . -667) T) ((-1089 . -965) T) ((-1089 . -188) 165899) ((-1089 . -13) T) ((-1089 . -1133) T) ((-1089 . -191) T) ((-1089 . -227) 165883) ((-1089 . -186) 165867) ((-1086 . -1147) 165828) ((-1086 . -919) 165794) ((-1086 . -1119) 165760) ((-1086 . -1122) 165726) ((-1086 . -436) 165692) ((-1086 . -241) 165658) ((-1086 . -66) 165624) ((-1086 . -35) 165590) ((-1086 . -1162) 165567) ((-1086 . -47) 165544) ((-1086 . -383) 165483) ((-1086 . -559) 165284) ((-1086 . -658) 165086) ((-1086 . -586) 164888) ((-1086 . -594) 164743) ((-1086 . -592) 164583) ((-1086 . -972) 164379) ((-1086 . -967) 164175) ((-1086 . -82) 163927) ((-1086 . -38) 163729) ((-1086 . -890) 163699) ((-1086 . -243) 163527) ((-1086 . -1145) 163511) ((-1086 . -974) T) ((-1086 . -1029) T) ((-1086 . -1065) T) ((-1086 . -667) T) ((-1086 . -965) T) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1017) T) ((-1086 . -556) 163493) ((-1086 . -1133) T) ((-1086 . -13) T) ((-1086 . -72) T) ((-1086 . -25) T) ((-1086 . -104) T) ((-1086 . -118) 163403) ((-1086 . -120) 163313) ((-1086 . -557) NIL) ((-1086 . -186) 163265) ((-1086 . -813) 163101) ((-1086 . -815) 162865) ((-1086 . -810) 162604) ((-1086 . -227) 162556) ((-1086 . -191) 162382) ((-1086 . -188) 162202) ((-1086 . -192) 162092) ((-1086 . -314) 162071) ((-1086 . -1138) 162050) ((-1086 . -836) 162029) ((-1086 . -499) 161983) ((-1086 . -148) 161917) ((-1086 . -395) 161896) ((-1086 . -260) 161875) ((-1086 . -248) 161829) ((-1086 . -203) 161808) ((-1086 . -290) 161760) ((-1086 . -459) 161494) ((-1086 . -262) 161379) ((-1086 . -331) 161331) ((-1086 . -584) 161283) ((-1086 . -345) 161235) ((-1086 . -800) NIL) ((-1086 . -744) NIL) ((-1086 . -718) NIL) ((-1086 . -720) NIL) ((-1086 . -760) NIL) ((-1086 . -763) NIL) ((-1086 . -722) NIL) ((-1086 . -725) NIL) ((-1086 . -759) NIL) ((-1086 . -798) 161187) ((-1086 . -825) NIL) ((-1086 . -937) NIL) ((-1086 . -954) 161153) ((-1086 . -1070) NIL) ((-1086 . -908) 161105) ((-1085 . -999) T) ((-1085 . -433) 161086) ((-1085 . -556) 161052) ((-1085 . -559) 161033) ((-1085 . -1017) T) ((-1085 . -1133) T) ((-1085 . -13) T) ((-1085 . -72) T) ((-1085 . -64) T) ((-1084 . -1017) T) ((-1084 . -556) 161015) ((-1084 . -1133) T) ((-1084 . -13) T) ((-1084 . -72) T) ((-1083 . -1017) T) ((-1083 . -556) 160997) ((-1083 . -1133) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1078 . -1111) 160973) ((-1078 . -185) 160918) ((-1078 . -76) 160863) ((-1078 . -1039) 160795) ((-1078 . -124) 160740) ((-1078 . -557) NIL) ((-1078 . -195) 160685) ((-1078 . -542) 160661) ((-1078 . -262) 160450) ((-1078 . -459) 160190) ((-1078 . -383) 160122) ((-1078 . -432) 160054) ((-1078 . -243) 160030) ((-1078 . -245) 160006) ((-1078 . -553) 159982) ((-1078 . -1017) T) ((-1078 . -556) 159964) ((-1078 . -72) T) ((-1078 . -1133) T) ((-1078 . -13) T) ((-1078 . -34) T) ((-1078 . -320) 159909) ((-1077 . -1062) T) ((-1077 . -326) 159891) ((-1077 . -763) T) ((-1077 . -760) T) ((-1077 . -124) 159873) ((-1077 . -557) NIL) ((-1077 . -243) 159823) ((-1077 . -542) 159798) ((-1077 . -245) 159773) ((-1077 . -597) 159755) ((-1077 . -432) 159737) ((-1077 . -1017) T) ((-1077 . -383) 159719) ((-1077 . -459) NIL) ((-1077 . -262) NIL) ((-1077 . -556) 159701) ((-1077 . -72) T) ((-1077 . -1133) T) ((-1077 . -13) T) ((-1077 . -34) T) ((-1077 . -320) 159683) ((-1077 . -1039) 159665) ((-1077 . -19) 159647) ((-1073 . -620) 159631) ((-1073 . -597) 159615) ((-1073 . -245) 159592) ((-1073 . -243) 159544) ((-1073 . -542) 159521) ((-1073 . -557) 159482) ((-1073 . -432) 159466) ((-1073 . -1017) 159444) ((-1073 . -383) 159428) ((-1073 . -459) 159361) ((-1073 . -262) 159299) ((-1073 . -556) 159234) ((-1073 . -72) 159188) ((-1073 . -1133) T) ((-1073 . -13) T) ((-1073 . -34) T) ((-1073 . -124) 159172) ((-1073 . -1172) 159156) ((-1073 . -927) 159140) ((-1073 . -1068) 159124) ((-1073 . -559) 159101) ((-1073 . -1039) 159085) ((-1071 . -999) T) ((-1071 . -433) 159066) ((-1071 . -556) 159032) ((-1071 . -559) 159013) ((-1071 . -1017) T) ((-1071 . -1133) T) ((-1071 . -13) T) ((-1071 . -72) T) ((-1071 . -64) T) ((-1069 . -1111) 158992) ((-1069 . -185) 158940) ((-1069 . -76) 158888) ((-1069 . -1039) 158823) ((-1069 . -124) 158771) ((-1069 . -557) NIL) ((-1069 . -195) 158719) ((-1069 . -542) 158698) ((-1069 . -262) 158496) ((-1069 . -459) 158248) ((-1069 . -383) 158183) ((-1069 . -432) 158118) ((-1069 . -243) 158097) ((-1069 . -245) 158076) ((-1069 . -553) 158055) ((-1069 . -1017) T) ((-1069 . -556) 158037) ((-1069 . -72) T) ((-1069 . -1133) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -320) 157985) ((-1066 . -1038) 157969) ((-1066 . -320) 157953) ((-1066 . -432) 157937) ((-1066 . -1017) 157915) ((-1066 . -383) 157899) ((-1066 . -459) 157832) ((-1066 . -262) 157770) ((-1066 . -556) 157705) ((-1066 . -72) 157659) ((-1066 . -1133) T) ((-1066 . -13) T) ((-1066 . -34) T) ((-1066 . -1039) 157643) ((-1066 . -76) 157627) ((-1064 . -1024) 157596) ((-1064 . -1128) 157565) ((-1064 . -1039) 157549) ((-1064 . -556) 157511) ((-1064 . -124) 157495) ((-1064 . -34) T) ((-1064 . -13) T) ((-1064 . -1133) T) ((-1064 . -72) T) ((-1064 . -262) 157433) ((-1064 . -459) 157366) ((-1064 . -383) 157350) ((-1064 . -1017) T) ((-1064 . -432) 157334) ((-1064 . -557) 157295) ((-1064 . -320) 157279) ((-1064 . -893) 157248) ((-1064 . -987) 157217) ((-1060 . -1041) 157162) ((-1060 . -320) 157146) ((-1060 . -34) T) ((-1060 . -262) 157084) ((-1060 . -459) 157017) ((-1060 . -383) 157001) ((-1060 . -432) 156985) ((-1060 . -969) 156925) ((-1060 . -954) 156823) ((-1060 . -559) 156742) ((-1060 . -357) 156726) ((-1060 . -584) 156674) ((-1060 . -594) 156612) ((-1060 . -331) 156596) ((-1060 . -192) 156575) ((-1060 . -188) 156523) ((-1060 . -191) 156477) ((-1060 . -227) 156461) ((-1060 . -810) 156385) ((-1060 . -815) 156311) ((-1060 . -813) 156270) ((-1060 . -186) 156254) ((-1060 . -658) 156189) ((-1060 . -586) 156124) ((-1060 . -592) 156083) ((-1060 . -104) T) ((-1060 . -25) T) ((-1060 . -72) T) ((-1060 . -13) T) ((-1060 . -1133) T) ((-1060 . -556) 156045) ((-1060 . -1017) T) ((-1060 . -23) T) ((-1060 . -21) T) ((-1060 . -972) 156029) ((-1060 . -967) 156013) ((-1060 . -82) 155992) ((-1060 . -965) T) ((-1060 . -667) T) ((-1060 . -1065) T) ((-1060 . -1029) T) ((-1060 . -974) T) ((-1060 . -38) 155952) ((-1060 . -557) 155913) ((-1059 . -927) 155884) ((-1059 . -34) T) ((-1059 . -13) T) ((-1059 . -1133) T) ((-1059 . -72) T) ((-1059 . -556) 155866) ((-1059 . -262) 155792) ((-1059 . -459) 155700) ((-1059 . -383) 155671) ((-1059 . -1017) T) ((-1059 . -432) 155642) ((-1059 . -320) 155613) ((-1059 . -1039) 155584) ((-1058 . -1017) T) ((-1058 . -556) 155566) ((-1058 . -1133) T) ((-1058 . -13) T) ((-1058 . -72) T) ((-1053 . -1055) T) ((-1053 . -1179) T) ((-1053 . -64) T) ((-1053 . -72) T) ((-1053 . -13) T) ((-1053 . -1133) T) ((-1053 . -556) 155532) ((-1053 . -1017) T) ((-1053 . -559) 155513) ((-1053 . -433) 155494) ((-1053 . -999) T) ((-1051 . -1052) 155478) ((-1051 . -72) T) ((-1051 . -13) T) ((-1051 . -1133) T) ((-1051 . -556) 155460) ((-1051 . -1017) T) ((-1044 . -683) 155439) ((-1044 . -35) 155405) ((-1044 . -66) 155371) ((-1044 . -241) 155337) ((-1044 . -436) 155303) ((-1044 . -1122) 155269) ((-1044 . -1119) 155235) ((-1044 . -919) 155201) ((-1044 . -47) 155173) ((-1044 . -38) 155070) ((-1044 . -586) 154967) ((-1044 . -658) 154864) ((-1044 . -559) 154746) ((-1044 . -248) 154725) ((-1044 . -499) 154704) ((-1044 . -383) 154688) ((-1044 . -82) 154553) ((-1044 . -967) 154439) ((-1044 . -972) 154325) ((-1044 . -148) 154279) ((-1044 . -120) 154258) ((-1044 . -118) 154237) ((-1044 . -594) 154162) ((-1044 . -592) 154072) ((-1044 . -890) 154039) ((-1044 . -815) 154023) ((-1044 . -1133) T) ((-1044 . -13) T) ((-1044 . -810) 154005) ((-1044 . -965) T) ((-1044 . -667) T) ((-1044 . -1065) T) ((-1044 . -1029) T) ((-1044 . -974) T) ((-1044 . -21) T) ((-1044 . -23) T) ((-1044 . -1017) T) ((-1044 . -556) 153987) ((-1044 . -72) T) ((-1044 . -25) T) ((-1044 . -104) T) ((-1044 . -813) 153971) ((-1044 . -459) 153941) ((-1044 . -262) 153928) ((-1043 . -865) 153895) ((-1043 . -559) 153694) ((-1043 . -954) 153579) ((-1043 . -1138) 153558) ((-1043 . -825) 153537) ((-1043 . -800) 153396) ((-1043 . -815) 153380) ((-1043 . -810) 153362) ((-1043 . -813) 153346) ((-1043 . -459) 153298) ((-1043 . -395) 153252) ((-1043 . -584) 153200) ((-1043 . -594) 153089) ((-1043 . -331) 153073) ((-1043 . -47) 153045) ((-1043 . -38) 152897) ((-1043 . -586) 152749) ((-1043 . -658) 152601) ((-1043 . -248) 152535) ((-1043 . -499) 152469) ((-1043 . -383) 152453) ((-1043 . 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. -82) 139833) ((-979 . -38) 139820) ((-979 . -395) T) ((-979 . -260) T) ((-979 . -191) T) ((-979 . -188) 139807) ((-979 . -192) T) ((-979 . -116) T) ((-979 . -965) T) ((-979 . -667) T) ((-979 . -1065) T) ((-979 . -1029) T) ((-979 . -974) T) ((-979 . -21) T) ((-979 . -592) 139779) ((-979 . -23) T) ((-979 . -1017) T) ((-979 . -556) 139761) ((-979 . -1133) T) ((-979 . -13) T) ((-979 . -72) T) ((-979 . -25) T) ((-979 . -104) T) ((-979 . -120) T) ((-979 . -561) 139742) ((-978 . -984) 139721) ((-978 . -72) T) ((-978 . -13) T) ((-978 . -1133) T) ((-978 . -556) 139703) ((-978 . -1017) T) ((-975 . -1133) T) ((-975 . -13) T) ((-975 . -1017) 139681) ((-975 . -556) 139648) ((-975 . -72) 139626) ((-970 . -969) 139566) ((-970 . -586) 139511) ((-970 . -658) 139456) ((-970 . -432) 139440) ((-970 . -383) 139424) ((-970 . -459) 139357) ((-970 . -262) 139295) ((-970 . -34) T) ((-970 . -320) 139279) ((-970 . -594) 139263) ((-970 . -592) 139232) ((-970 . -104) T) ((-970 . -25) T) ((-970 . -72) T) ((-970 . 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. -720) T) ((-921 . -718) T) ((-921 . -744) T) ((-921 . -800) 136591) ((-921 . -345) 136573) ((-921 . -584) 136555) ((-921 . -331) 136537) ((-921 . -243) NIL) ((-921 . -262) NIL) ((-921 . -459) NIL) ((-921 . -383) 136519) ((-921 . -290) 136501) ((-921 . -203) T) ((-921 . -82) 136428) ((-921 . -967) 136378) ((-921 . -972) 136328) ((-921 . -248) T) ((-921 . -658) 136278) ((-921 . -586) 136228) ((-921 . -594) 136178) ((-921 . -592) 136128) ((-921 . -38) 136078) ((-921 . -260) T) ((-921 . -395) T) ((-921 . -148) T) ((-921 . -499) T) ((-921 . -836) T) ((-921 . -1138) T) ((-921 . -314) T) ((-921 . -192) T) ((-921 . -188) 136065) ((-921 . -191) T) ((-921 . -227) 136047) ((-921 . -810) NIL) ((-921 . -815) NIL) ((-921 . -813) NIL) ((-921 . -186) 136029) ((-921 . -120) T) ((-921 . -118) NIL) ((-921 . -104) T) ((-921 . -25) T) ((-921 . -72) T) ((-921 . -13) T) ((-921 . -1133) T) ((-921 . -556) 135989) ((-921 . -1017) T) ((-921 . -23) T) ((-921 . -21) T) ((-921 . -965) T) ((-921 . -667) T) ((-921 . -1065) T) ((-921 . -1029) T) ((-921 . -974) T) ((-920 . -293) 135963) ((-920 . -148) T) ((-920 . -559) 135893) ((-920 . -974) T) ((-920 . -1029) T) ((-920 . -1065) T) ((-920 . -667) T) ((-920 . -965) T) ((-920 . -594) 135795) ((-920 . -592) 135725) ((-920 . -104) T) ((-920 . -25) T) ((-920 . -72) T) ((-920 . -13) T) ((-920 . -1133) T) ((-920 . -556) 135707) ((-920 . -1017) T) ((-920 . -23) T) ((-920 . -21) T) ((-920 . -972) 135652) ((-920 . -967) 135597) ((-920 . -82) 135514) ((-920 . -557) 135498) ((-920 . -186) 135475) ((-920 . -813) 135427) ((-920 . -815) 135339) ((-920 . -810) 135249) ((-920 . -227) 135226) ((-920 . -191) 135166) ((-920 . -188) 135100) ((-920 . -192) 135072) ((-920 . -314) T) ((-920 . -1138) T) ((-920 . -836) T) ((-920 . -499) T) ((-920 . -658) 135017) ((-920 . -586) 134962) ((-920 . -38) 134907) ((-920 . -395) T) ((-920 . -260) T) ((-920 . -248) T) ((-920 . -203) T) ((-920 . -322) NIL) ((-920 . -301) NIL) ((-920 . -1070) NIL) ((-920 . -118) 134879) ((-920 . -347) NIL) ((-920 . -355) 134851) ((-920 . -120) 134823) ((-920 . -324) 134795) ((-920 . -331) 134772) ((-920 . -584) 134706) ((-920 . -357) 134683) ((-920 . -954) 134560) ((-920 . -665) 134532) ((-917 . -912) 134516) ((-917 . -320) 134500) ((-917 . -432) 134484) ((-917 . -1017) 134462) ((-917 . -383) 134446) ((-917 . -459) 134379) ((-917 . -262) 134317) ((-917 . -556) 134252) ((-917 . -72) 134206) ((-917 . -1133) T) ((-917 . -13) T) ((-917 . -34) T) ((-917 . -1039) 134190) ((-917 . -76) 134174) ((-913 . -915) 134158) ((-913 . -763) 134137) ((-913 . -760) 134116) ((-913 . -954) 134014) ((-913 . -357) 133998) ((-913 . -584) 133946) ((-913 . -594) 133848) ((-913 . -331) 133832) ((-913 . -243) 133790) ((-913 . -262) 133755) ((-913 . -459) 133667) ((-913 . -383) 133651) ((-913 . -290) 133635) ((-913 . -38) 133583) ((-913 . -82) 133461) ((-913 . -967) 133360) ((-913 . -972) 133259) ((-913 . -592) 133182) ((-913 . -586) 133130) ((-913 . -658) 133078) ((-913 . -559) 132972) ((-913 . -248) 132926) ((-913 . -203) 132905) ((-913 . -192) 132884) ((-913 . -188) 132832) ((-913 . -191) 132786) ((-913 . -227) 132770) ((-913 . -810) 132694) ((-913 . -815) 132620) ((-913 . -813) 132579) ((-913 . -186) 132563) ((-913 . -557) 132524) ((-913 . -120) 132503) ((-913 . -118) 132482) ((-913 . -104) T) ((-913 . -25) T) ((-913 . -72) T) ((-913 . -13) T) ((-913 . -1133) T) ((-913 . -556) 132464) ((-913 . -1017) T) ((-913 . -23) T) ((-913 . -21) T) ((-913 . -965) T) ((-913 . -667) T) ((-913 . -1065) T) ((-913 . -1029) T) ((-913 . -974) T) ((-911 . -999) T) ((-911 . -433) 132445) ((-911 . -556) 132411) ((-911 . -559) 132392) ((-911 . -1017) T) ((-911 . -1133) T) ((-911 . -13) T) ((-911 . -72) T) ((-911 . -64) T) ((-910 . -21) T) ((-910 . -592) 132374) ((-910 . -23) T) ((-910 . -1017) T) ((-910 . -556) 132356) ((-910 . -1133) T) ((-910 . -13) T) ((-910 . -72) T) ((-910 . -25) T) ((-910 . -104) T) ((-910 . -243) 132323) ((-906 . -556) 132305) ((-903 . -1017) T) ((-903 . -556) 132287) ((-903 . -1133) T) ((-903 . -13) T) ((-903 . -72) T) ((-888 . -725) T) ((-888 . -722) T) ((-888 . -763) T) ((-888 . -760) T) ((-888 . -720) T) ((-888 . -23) T) ((-888 . -1017) T) ((-888 . -556) 132247) ((-888 . -1133) T) ((-888 . -13) T) ((-888 . -72) T) ((-888 . -25) T) ((-888 . -104) T) ((-887 . -999) T) ((-887 . -433) 132228) ((-887 . -556) 132194) ((-887 . -559) 132175) ((-887 . -1017) T) ((-887 . -1133) T) ((-887 . -13) T) ((-887 . -72) T) ((-887 . -64) T) ((-881 . -884) T) ((-881 . -72) T) ((-881 . -556) 132157) ((-881 . -1017) T) ((-881 . -608) T) ((-881 . -13) T) ((-881 . -1133) T) ((-881 . -84) T) ((-881 . -559) 132141) ((-880 . -556) 132123) ((-879 . -1017) T) ((-879 . -556) 132105) ((-879 . -1133) T) ((-879 . -13) T) ((-879 . -72) T) ((-879 . -322) 132058) ((-879 . -667) 131960) ((-879 . -1029) 131862) ((-879 . -23) 131676) ((-879 . -25) 131490) ((-879 . -104) 131348) ((-879 . -416) 131301) ((-879 . -21) 131256) ((-879 . -592) 131200) ((-879 . -721) 131153) ((-879 . -720) 131106) ((-879 . -760) 131008) ((-879 . -763) 130910) ((-879 . -722) 130863) ((-879 . -725) 130816) ((-873 . -19) 130800) ((-873 . -1039) 130784) ((-873 . -320) 130768) ((-873 . -34) T) ((-873 . -13) T) ((-873 . -1133) T) ((-873 . -72) 130702) ((-873 . -556) 130617) ((-873 . -262) 130555) ((-873 . -459) 130488) ((-873 . -383) 130472) ((-873 . -1017) 130425) ((-873 . -432) 130409) ((-873 . -597) 130393) ((-873 . -245) 130370) ((-873 . -243) 130322) ((-873 . -542) 130299) ((-873 . -557) 130260) ((-873 . -124) 130244) ((-873 . -760) 130223) ((-873 . -763) 130202) ((-873 . -326) 130186) ((-871 . -279) 130165) ((-871 . -954) 130063) ((-871 . -357) 130047) ((-871 . -38) 129944) ((-871 . -559) 129801) ((-871 . -594) 129726) ((-871 . -592) 129636) ((-871 . -974) T) ((-871 . -1029) T) ((-871 . -1065) T) ((-871 . -667) T) ((-871 . -965) T) ((-871 . -82) 129501) ((-871 . -967) 129387) ((-871 . -972) 129273) ((-871 . -21) T) ((-871 . -23) T) ((-871 . -1017) T) ((-871 . -556) 129255) ((-871 . -1133) T) ((-871 . -13) T) ((-871 . -72) T) ((-871 . -25) T) ((-871 . -104) T) ((-871 . -586) 129152) ((-871 . -658) 129049) ((-871 . -118) 129028) ((-871 . -120) 129007) ((-871 . -148) 128961) ((-871 . -383) 128945) ((-871 . -499) 128924) ((-871 . -248) 128903) ((-871 . -47) 128882) ((-869 . -1017) T) ((-869 . -556) 128848) ((-869 . -1133) T) ((-869 . -13) T) ((-869 . -72) T) ((-861 . -865) 128809) ((-861 . -559) 128605) ((-861 . -954) 128487) ((-861 . -1138) 128466) ((-861 . -825) 128445) ((-861 . -800) 128370) ((-861 . -815) 128351) ((-861 . -810) 128330) ((-861 . -813) 128311) ((-861 . -459) 128257) ((-861 . -395) 128211) ((-861 . -584) 128159) ((-861 . -594) 128048) ((-861 . -331) 128032) ((-861 . -47) 128001) ((-861 . -38) 127853) ((-861 . -586) 127705) ((-861 . -658) 127557) ((-861 . -248) 127491) ((-861 . -499) 127425) ((-861 . -383) 127409) ((-861 . -82) 127234) ((-861 . -967) 127080) ((-861 . -972) 126926) ((-861 . -148) 126840) ((-861 . -120) 126819) ((-861 . -118) 126798) ((-861 . -592) 126708) ((-861 . -104) T) ((-861 . -25) T) ((-861 . -72) T) ((-861 . -13) T) ((-861 . -1133) T) ((-861 . -556) 126690) ((-861 . -1017) T) ((-861 . -23) T) ((-861 . -21) T) ((-861 . -965) T) ((-861 . -667) T) ((-861 . -1065) T) ((-861 . -1029) T) ((-861 . -974) T) ((-861 . -357) 126674) ((-861 . -279) 126643) ((-861 . -262) 126630) ((-861 . -557) 126491) ((-858 . -897) 126475) ((-858 . -19) 126459) ((-858 . -1039) 126443) ((-858 . -320) 126427) ((-858 . -34) T) ((-858 . -13) T) ((-858 . -1133) T) ((-858 . -72) 126361) ((-858 . -556) 126276) ((-858 . -262) 126214) ((-858 . -459) 126147) ((-858 . -383) 126131) ((-858 . -1017) 126084) ((-858 . -432) 126068) ((-858 . -597) 126052) ((-858 . -245) 126029) ((-858 . -243) 125981) ((-858 . -542) 125958) ((-858 . -557) 125919) ((-858 . -124) 125903) ((-858 . -760) 125882) ((-858 . -763) 125861) ((-858 . -326) 125845) ((-858 . -1182) 125829) ((-858 . -561) 125806) ((-842 . -891) T) ((-842 . -556) 125788) ((-840 . -870) T) ((-840 . -556) 125770) ((-834 . -722) T) ((-834 . -763) T) ((-834 . -760) T) ((-834 . -1017) T) ((-834 . -556) 125752) ((-834 . -1133) T) ((-834 . -13) T) ((-834 . -72) T) ((-834 . -25) T) ((-834 . -667) T) ((-834 . -1029) T) ((-829 . -314) T) ((-829 . -1138) T) ((-829 . -836) T) ((-829 . -499) T) ((-829 . -148) T) ((-829 . -559) 125689) ((-829 . -658) 125641) ((-829 . -586) 125593) ((-829 . -38) 125545) ((-829 . -395) T) ((-829 . -260) T) ((-829 . -594) 125497) ((-829 . -592) 125434) ((-829 . -974) T) ((-829 . -1029) T) ((-829 . -1065) T) ((-829 . -667) T) ((-829 . -965) T) ((-829 . -82) 125365) ((-829 . -967) 125317) ((-829 . -972) 125269) ((-829 . -21) T) ((-829 . -23) T) ((-829 . -1017) T) ((-829 . -556) 125251) ((-829 . -1133) T) ((-829 . -13) T) ((-829 . -72) T) ((-829 . -25) T) ((-829 . -104) T) ((-829 . -248) T) ((-829 . -203) T) ((-821 . -301) T) ((-821 . -1070) T) ((-821 . -322) T) ((-821 . -118) T) ((-821 . -314) T) ((-821 . -1138) T) ((-821 . -836) T) ((-821 . -499) T) ((-821 . -148) T) ((-821 . -559) 125201) ((-821 . -658) 125166) ((-821 . -586) 125131) ((-821 . -38) 125096) ((-821 . -395) T) ((-821 . -260) T) ((-821 . -82) 125045) ((-821 . -967) 125010) ((-821 . -972) 124975) ((-821 . -592) 124925) ((-821 . -594) 124890) ((-821 . -248) T) ((-821 . -203) T) ((-821 . -347) T) ((-821 . -191) T) ((-821 . -1133) T) ((-821 . -13) T) ((-821 . -188) 124877) ((-821 . -965) T) ((-821 . -667) T) ((-821 . -1065) T) ((-821 . -1029) T) ((-821 . -974) T) ((-821 . -21) T) ((-821 . -23) T) ((-821 . -1017) T) ((-821 . -556) 124859) ((-821 . -72) T) ((-821 . -25) T) ((-821 . -104) T) ((-821 . -192) T) ((-821 . -282) 124846) ((-821 . -120) 124828) ((-821 . -954) 124815) ((-821 . -1191) 124802) ((-821 . -1202) 124789) ((-821 . -557) 124771) ((-820 . -1017) T) ((-820 . -556) 124753) ((-820 . -1133) T) ((-820 . -13) T) ((-820 . -72) T) ((-817 . -819) 124737) ((-817 . -763) 124691) ((-817 . -760) 124645) ((-817 . -667) T) ((-817 . -1017) T) ((-817 . -556) 124627) ((-817 . -72) T) ((-817 . -1029) T) ((-817 . -416) T) ((-817 . -1133) T) ((-817 . -13) T) ((-817 . -243) 124606) ((-816 . -92) 124590) ((-816 . -432) 124574) ((-816 . -1017) 124552) ((-816 . -383) 124536) ((-816 . -459) 124469) ((-816 . -262) 124407) ((-816 . -556) 124321) ((-816 . -72) 124275) ((-816 . -1133) T) ((-816 . -13) T) ((-816 . -34) T) ((-816 . -927) 124259) ((-807 . -760) T) ((-807 . -556) 124241) ((-807 . -1017) T) ((-807 . -72) T) ((-807 . -13) T) ((-807 . -1133) T) ((-807 . -763) T) ((-807 . -954) 124218) ((-807 . -559) 124195) ((-804 . -1017) T) ((-804 . -556) 124177) ((-804 . -1133) T) ((-804 . -13) T) ((-804 . -72) T) ((-804 . -954) 124145) ((-804 . -559) 124113) ((-802 . -1017) T) ((-802 . -556) 124095) ((-802 . -1133) T) ((-802 . -13) T) ((-802 . -72) T) ((-799 . -1017) T) ((-799 . -556) 124077) ((-799 . -1133) T) ((-799 . -13) T) ((-799 . -72) T) ((-789 . -999) T) ((-789 . -433) 124058) ((-789 . -556) 124024) ((-789 . -559) 124005) ((-789 . -1017) T) ((-789 . -1133) T) ((-789 . -13) T) ((-789 . -72) T) ((-789 . -64) T) ((-789 . -1179) T) ((-787 . -1017) T) ((-787 . -556) 123987) ((-787 . -1133) T) ((-787 . -13) T) ((-787 . -72) T) ((-787 . -559) 123969) ((-786 . -1133) T) ((-786 . -13) T) ((-786 . -556) 123844) ((-786 . -1017) 123795) ((-786 . -72) 123746) ((-785 . -908) 123730) ((-785 . -1070) 123708) ((-785 . -954) 123575) ((-785 . -559) 123474) ((-785 . -557) 123277) ((-785 . -937) 123256) ((-785 . -825) 123235) ((-785 . -798) 123219) ((-785 . -759) 123198) ((-785 . -725) 123177) ((-785 . -722) 123156) ((-785 . -763) 123110) ((-785 . -760) 123064) ((-785 . -720) 123043) ((-785 . -718) 123022) ((-785 . -744) 123001) ((-785 . -800) 122926) ((-785 . -345) 122910) ((-785 . -584) 122858) ((-785 . -594) 122774) ((-785 . -331) 122758) ((-785 . -243) 122716) ((-785 . -262) 122681) ((-785 . -459) 122593) ((-785 . -383) 122577) ((-785 . -290) 122561) ((-785 . -203) T) ((-785 . -82) 122492) ((-785 . -967) 122444) ((-785 . -972) 122396) ((-785 . -248) T) ((-785 . -658) 122348) ((-785 . -586) 122300) ((-785 . -592) 122237) ((-785 . -38) 122189) ((-785 . -260) T) ((-785 . -395) T) ((-785 . -148) T) ((-785 . -499) T) ((-785 . -836) T) ((-785 . -1138) T) ((-785 . -314) T) ((-785 . -192) 122168) ((-785 . -188) 122116) ((-785 . -191) 122070) ((-785 . -227) 122054) ((-785 . -810) 121978) ((-785 . -815) 121904) ((-785 . -813) 121863) ((-785 . -186) 121847) ((-785 . -120) 121801) ((-785 . -118) 121780) ((-785 . -104) T) ((-785 . -25) T) ((-785 . -72) T) ((-785 . -13) T) ((-785 . -1133) T) ((-785 . -556) 121762) ((-785 . -1017) T) ((-785 . -23) T) ((-785 . -21) T) ((-785 . -965) T) ((-785 . -667) T) ((-785 . -1065) T) ((-785 . -1029) T) ((-785 . -974) T) ((-784 . -908) 121739) ((-784 . -1070) NIL) ((-784 . -954) 121716) ((-784 . -559) 121646) ((-784 . -557) NIL) ((-784 . -937) NIL) ((-784 . -825) NIL) ((-784 . -798) 121623) ((-784 . -759) NIL) ((-784 . -725) NIL) ((-784 . -722) NIL) ((-784 . -763) NIL) ((-784 . -760) NIL) ((-784 . -720) NIL) ((-784 . -718) NIL) ((-784 . -744) NIL) ((-784 . -800) NIL) ((-784 . -345) 121600) ((-784 . -584) 121577) ((-784 . -594) 121522) ((-784 . -331) 121499) ((-784 . -243) 121429) ((-784 . -262) 121373) ((-784 . -459) 121236) ((-784 . -383) 121213) ((-784 . -290) 121190) ((-784 . -203) T) ((-784 . -82) 121107) ((-784 . -967) 121052) ((-784 . -972) 120997) ((-784 . -248) T) ((-784 . -658) 120942) ((-784 . -586) 120887) ((-784 . -592) 120817) ((-784 . -38) 120762) ((-784 . -260) T) ((-784 . -395) T) ((-784 . -148) T) ((-784 . -499) T) ((-784 . -836) T) ((-784 . -1138) T) ((-784 . -314) T) ((-784 . -192) NIL) ((-784 . -188) NIL) ((-784 . -191) NIL) ((-784 . -227) 120739) ((-784 . -810) NIL) ((-784 . -815) NIL) ((-784 . -813) NIL) ((-784 . -186) 120716) ((-784 . -120) T) ((-784 . -118) NIL) ((-784 . -104) T) ((-784 . -25) T) ((-784 . -72) T) ((-784 . -13) T) ((-784 . -1133) T) ((-784 . -556) 120698) ((-784 . -1017) T) ((-784 . -23) T) ((-784 . -21) T) ((-784 . -965) T) ((-784 . -667) T) ((-784 . -1065) T) ((-784 . -1029) T) ((-784 . -974) T) ((-782 . -783) 120682) ((-782 . -836) T) ((-782 . -499) T) ((-782 . -248) T) ((-782 . -148) T) ((-782 . -559) 120654) ((-782 . -658) 120641) ((-782 . -586) 120628) ((-782 . -972) 120615) ((-782 . -967) 120602) ((-782 . -82) 120587) ((-782 . -38) 120574) ((-782 . -395) T) ((-782 . -260) T) ((-782 . -965) T) ((-782 . -667) T) ((-782 . -1065) T) ((-782 . -1029) T) ((-782 . -974) T) ((-782 . -21) T) ((-782 . -592) 120546) ((-782 . -23) T) ((-782 . -1017) T) ((-782 . -556) 120528) ((-782 . -1133) T) ((-782 . -13) T) ((-782 . -72) T) ((-782 . -25) T) ((-782 . -104) T) ((-782 . -594) 120515) ((-782 . -120) T) ((-779 . -965) T) ((-779 . -667) T) ((-779 . -1065) T) ((-779 . -1029) T) ((-779 . -974) T) ((-779 . -21) T) ((-779 . -592) 120460) ((-779 . -23) T) ((-779 . -1017) T) ((-779 . -556) 120422) ((-779 . -1133) T) ((-779 . -13) T) ((-779 . -72) T) ((-779 . -25) T) ((-779 . -104) T) ((-779 . -594) 120382) ((-779 . -559) 120317) ((-779 . -433) 120294) ((-779 . -38) 120264) ((-779 . -82) 120229) ((-779 . -967) 120199) ((-779 . -972) 120169) ((-779 . -586) 120139) ((-779 . -658) 120109) ((-778 . -1017) T) ((-778 . -556) 120091) ((-778 . -1133) T) ((-778 . -13) T) ((-778 . -72) T) ((-777 . -756) T) ((-777 . -763) T) ((-777 . -760) T) ((-777 . -1017) T) ((-777 . -556) 120073) ((-777 . -1133) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -322) T) ((-777 . -557) 119995) ((-776 . -1017) T) ((-776 . -556) 119977) ((-776 . -1133) T) ((-776 . -13) T) ((-776 . -72) T) ((-775 . -774) T) ((-775 . -149) T) ((-775 . -556) 119959) ((-771 . -760) T) ((-771 . -556) 119941) ((-771 . -1017) T) ((-771 . -72) T) ((-771 . -13) T) ((-771 . -1133) T) ((-771 . -763) T) ((-768 . -765) 119925) ((-768 . -954) 119823) ((-768 . -559) 119721) ((-768 . -357) 119705) ((-768 . -658) 119675) ((-768 . -586) 119645) ((-768 . -594) 119619) ((-768 . -592) 119578) ((-768 . -104) T) ((-768 . -25) T) ((-768 . -72) T) ((-768 . -13) T) ((-768 . -1133) T) ((-768 . -556) 119560) ((-768 . -1017) T) ((-768 . -23) T) ((-768 . -21) T) ((-768 . -972) 119544) ((-768 . -967) 119528) ((-768 . -82) 119507) ((-768 . -965) T) ((-768 . -667) T) ((-768 . -1065) T) ((-768 . -1029) T) ((-768 . -974) T) ((-768 . -38) 119477) ((-767 . -765) 119461) ((-767 . -954) 119359) ((-767 . -559) 119278) ((-767 . -357) 119262) ((-767 . -658) 119232) ((-767 . -586) 119202) ((-767 . -594) 119176) ((-767 . -592) 119135) ((-767 . -104) T) ((-767 . -25) T) ((-767 . -72) T) ((-767 . -13) T) ((-767 . -1133) T) ((-767 . -556) 119117) ((-767 . -1017) T) ((-767 . -23) T) ((-767 . -21) T) ((-767 . -972) 119101) ((-767 . -967) 119085) ((-767 . -82) 119064) ((-767 . -965) T) ((-767 . -667) T) ((-767 . -1065) T) ((-767 . -1029) T) ((-767 . -974) T) ((-767 . -38) 119034) ((-761 . -763) T) ((-761 . -1133) T) ((-761 . -13) T) ((-761 . -72) T) ((-761 . -433) 119018) ((-761 . -556) 118966) ((-761 . -559) 118950) ((-754 . -1017) T) ((-754 . -556) 118932) ((-754 . -1133) T) ((-754 . -13) T) ((-754 . -72) T) 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. -120) 117861) ((-749 . -118) 117840) ((-749 . -38) 117810) ((-749 . -82) 117775) ((-749 . -967) 117745) ((-749 . -972) 117715) ((-749 . -586) 117685) ((-749 . -658) 117655) ((-747 . -1017) T) ((-747 . -556) 117637) ((-747 . -1133) T) ((-747 . -13) T) ((-747 . -72) T) ((-747 . -357) 117621) ((-747 . -559) 117494) ((-747 . -954) 117392) ((-747 . -21) 117347) ((-747 . -592) 117267) ((-747 . -23) 117222) ((-747 . -25) 117177) ((-747 . -104) 117132) ((-747 . -759) 117111) ((-747 . -725) 117090) ((-747 . -722) 117069) ((-747 . -763) 117048) ((-747 . -760) 117027) ((-747 . -720) 117006) ((-747 . -718) 116985) ((-747 . -965) 116964) ((-747 . -667) 116943) ((-747 . -1065) 116922) ((-747 . -1029) 116901) ((-747 . -974) 116880) ((-747 . -594) 116853) ((-747 . -120) 116832) ((-745 . -649) 116816) ((-745 . -559) 116771) ((-745 . -658) 116741) ((-745 . -586) 116711) ((-745 . -594) 116685) ((-745 . -592) 116644) ((-745 . -104) T) ((-745 . -25) T) ((-745 . -72) T) ((-745 . -13) T) ((-745 . -1133) T) 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116071) ((-741 . -1133) T) ((-741 . -13) T) ((-741 . -72) T) ((-741 . -25) T) ((-741 . -104) T) ((-741 . -594) 116022) ((-741 . -192) T) ((-741 . -559) 115931) ((-741 . -974) T) ((-741 . -1029) T) ((-741 . -1065) T) ((-741 . -667) T) ((-741 . -965) T) ((-741 . -188) 115918) ((-741 . -191) T) ((-741 . -433) 115902) ((-741 . -314) 115881) ((-741 . -1138) 115860) ((-741 . -836) 115839) ((-741 . -499) 115818) ((-741 . -148) 115797) ((-741 . -658) 115734) ((-741 . -586) 115671) ((-741 . -38) 115608) ((-741 . -395) 115587) ((-741 . -260) 115566) ((-741 . -248) 115545) ((-741 . -203) 115524) ((-740 . -215) 115463) ((-740 . -559) 115207) ((-740 . -954) 115037) ((-740 . -557) NIL) ((-740 . -279) 114999) ((-740 . -357) 114983) ((-740 . -38) 114835) ((-740 . -82) 114660) ((-740 . -967) 114506) ((-740 . -972) 114352) ((-740 . -592) 114262) ((-740 . -594) 114151) ((-740 . -586) 114003) ((-740 . -658) 113855) ((-740 . -118) 113834) ((-740 . -120) 113813) ((-740 . -148) 113727) ((-740 . -383) 113711) 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-542) 112327) ((-739 . -954) 112156) ((-739 . -559) 111960) ((-739 . -357) 111929) ((-739 . -584) 111837) ((-739 . -594) 111676) ((-739 . -331) 111646) ((-739 . -432) 111630) ((-739 . -383) 111614) ((-739 . -459) 111547) ((-739 . -262) 111485) ((-739 . -34) T) ((-739 . -320) 111469) ((-739 . -322) 111448) ((-739 . -192) 111401) ((-739 . -592) 111189) ((-739 . -974) 111168) ((-739 . -1029) 111147) ((-739 . -1065) 111126) ((-739 . -667) 111105) ((-739 . -965) 111084) ((-739 . -188) 110980) ((-739 . -191) 110882) ((-739 . -227) 110852) ((-739 . -810) 110724) ((-739 . -815) 110598) ((-739 . -813) 110531) ((-739 . -186) 110501) ((-739 . -556) 110198) ((-739 . -972) 110123) ((-739 . -967) 110028) ((-739 . -82) 109948) ((-739 . -104) 109823) ((-739 . -25) 109660) ((-739 . -72) 109397) ((-739 . -13) T) ((-739 . -1133) T) ((-739 . -1017) 109153) ((-739 . -23) 109009) ((-739 . -21) 108924) ((-726 . -724) 108908) ((-726 . -763) 108887) ((-726 . -760) 108866) ((-726 . -954) 108659) ((-726 . -559) 108512) ((-726 . -357) 108476) ((-726 . -243) 108434) ((-726 . -262) 108399) ((-726 . -459) 108311) ((-726 . -383) 108295) ((-726 . -290) 108279) ((-726 . -322) 108258) ((-726 . -557) 108219) ((-726 . -120) 108198) ((-726 . -118) 108177) ((-726 . -658) 108161) ((-726 . -586) 108145) ((-726 . -594) 108119) ((-726 . -592) 108078) ((-726 . -104) T) ((-726 . -25) T) ((-726 . -72) T) ((-726 . -13) T) ((-726 . -1133) T) ((-726 . -556) 108060) ((-726 . -1017) T) ((-726 . -23) T) ((-726 . -21) T) ((-726 . -972) 108044) ((-726 . -967) 108028) ((-726 . -82) 108007) ((-726 . -965) T) ((-726 . -667) T) ((-726 . -1065) T) ((-726 . -1029) T) ((-726 . -974) T) ((-726 . -38) 107991) ((-708 . -1159) 107975) ((-708 . -1070) 107953) ((-708 . -557) NIL) ((-708 . -262) 107940) ((-708 . -459) 107888) ((-708 . -279) 107865) ((-708 . -954) 107727) ((-708 . -357) 107711) ((-708 . -38) 107543) ((-708 . -82) 107348) ((-708 . -967) 107174) ((-708 . -972) 107000) ((-708 . -592) 106910) ((-708 . -594) 106799) 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101953) ((-678 . -559) 101909) ((-678 . -954) 101880) ((-678 . -383) 101864) ((-678 . -120) 101843) ((-678 . -118) 101822) ((-678 . -38) 101792) ((-678 . -82) 101757) ((-678 . -967) 101727) ((-678 . -972) 101697) ((-678 . -586) 101667) ((-678 . -658) 101637) ((-678 . -322) 101590) ((-674 . -865) 101543) ((-674 . -559) 101335) ((-674 . -954) 101213) ((-674 . -1138) 101192) ((-674 . -825) 101171) ((-674 . -800) NIL) ((-674 . -815) 101148) ((-674 . -810) 101123) ((-674 . -813) 101100) ((-674 . -459) 101038) ((-674 . -395) 100992) ((-674 . -584) 100940) ((-674 . -594) 100829) ((-674 . -331) 100813) ((-674 . -47) 100778) ((-674 . -38) 100630) ((-674 . -586) 100482) ((-674 . -658) 100334) ((-674 . -248) 100268) ((-674 . -499) 100202) ((-674 . -383) 100186) ((-674 . -82) 100011) ((-674 . -967) 99857) ((-674 . -972) 99703) ((-674 . -148) 99617) ((-674 . -120) 99596) ((-674 . -118) 99575) ((-674 . -592) 99485) ((-674 . -104) T) ((-674 . -25) T) ((-674 . -72) T) ((-674 . -13) T) ((-674 . -1133) T) ((-674 . -556) 99467) ((-674 . -1017) T) ((-674 . -23) T) ((-674 . -21) T) ((-674 . -965) T) ((-674 . -667) T) ((-674 . -1065) T) ((-674 . -1029) T) ((-674 . -974) T) ((-674 . -357) 99451) ((-674 . -279) 99416) ((-674 . -262) 99403) ((-674 . -557) 99264) ((-668 . -669) 99248) ((-668 . -80) 99232) ((-668 . -1133) T) ((-668 . |MappingCategory|) 99206) ((-668 . -1027) 99190) ((-668 . -1017) T) ((-668 . -556) 99151) ((-668 . -13) T) ((-668 . -72) T) ((-659 . -416) T) ((-659 . -1029) T) ((-659 . -72) T) ((-659 . -13) T) ((-659 . -1133) T) ((-659 . -556) 99133) ((-659 . -1017) T) ((-659 . -667) T) ((-656 . -965) T) ((-656 . -667) T) ((-656 . -1065) T) ((-656 . -1029) T) ((-656 . -974) T) ((-656 . -21) T) ((-656 . -592) 99105) ((-656 . -23) T) ((-656 . -1017) T) ((-656 . -556) 99087) ((-656 . -1133) T) ((-656 . -13) T) ((-656 . -72) T) ((-656 . -25) T) ((-656 . -104) T) ((-656 . -594) 99074) ((-656 . -559) 99056) ((-655 . -965) T) ((-655 . -667) T) ((-655 . -1065) T) ((-655 . -1029) T) 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95555) ((-652 . -395) T) ((-652 . -260) T) ((-652 . -594) 95520) ((-652 . -592) 95470) ((-652 . -974) T) ((-652 . -1029) T) ((-652 . -1065) T) ((-652 . -667) T) ((-652 . -965) T) ((-652 . -82) 95419) ((-652 . -967) 95384) ((-652 . -972) 95349) ((-652 . -21) T) ((-652 . -23) T) ((-652 . -1017) T) ((-652 . -556) 95331) ((-652 . -1133) T) ((-652 . -13) T) ((-652 . -72) T) ((-652 . -25) T) ((-652 . -104) T) ((-652 . -248) T) ((-652 . -203) T) ((-651 . -1017) T) ((-651 . -556) 95313) ((-651 . -1133) T) ((-651 . -13) T) ((-651 . -72) T) ((-636 . -1179) T) ((-636 . -954) 95297) ((-636 . -559) 95281) ((-636 . -556) 95263) ((-634 . -631) 95221) ((-634 . -320) 95205) ((-634 . -34) T) ((-634 . -13) T) ((-634 . -1133) T) ((-634 . -72) 95159) ((-634 . -556) 95094) ((-634 . -262) 95032) ((-634 . -459) 94965) ((-634 . -383) 94949) ((-634 . -1017) 94927) ((-634 . -432) 94911) ((-634 . -1039) 94895) ((-634 . -57) 94853) ((-634 . -557) 94814) ((-626 . -999) T) ((-626 . -433) 94795) ((-626 . -556) 94745) 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. -1133) T) ((-147 . -13) T) ((-147 . -72) T) ((-144 . -141) 14999) ((-144 . -35) 14977) ((-144 . -66) 14955) ((-144 . -241) 14933) ((-144 . -436) 14911) ((-144 . -1122) 14889) ((-144 . -1119) 14867) ((-144 . -919) 14819) ((-144 . -825) 14772) ((-144 . -557) 14540) ((-144 . -798) 14524) ((-144 . -322) 14478) ((-144 . -301) 14457) ((-144 . -1070) 14436) ((-144 . -347) 14415) ((-144 . -355) 14386) ((-144 . -38) 14220) ((-144 . -82) 14112) ((-144 . -967) 14025) ((-144 . -972) 13938) ((-144 . -586) 13772) ((-144 . -658) 13606) ((-144 . -324) 13577) ((-144 . -665) 13548) ((-144 . -954) 13446) ((-144 . -559) 13231) ((-144 . -357) 13215) ((-144 . -800) 13140) ((-144 . -345) 13124) ((-144 . -584) 13072) ((-144 . -594) 12949) ((-144 . -592) 12847) ((-144 . -331) 12831) ((-144 . -243) 12789) ((-144 . -262) 12754) ((-144 . -459) 12666) ((-144 . -383) 12650) ((-144 . -290) 12634) ((-144 . -203) 12588) ((-144 . -1138) 12496) ((-144 . -314) 12450) ((-144 . -836) 12384) ((-144 . -499) 12298) ((-144 . 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. -594) 4292) ((-50 . -592) 4251) ((-50 . -974) T) ((-50 . -1029) T) ((-50 . -1065) T) ((-50 . -667) T) ((-50 . -965) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1017) T) ((-50 . -556) 4233) ((-50 . -1133) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -954) 4217) ((-50 . -383) 4201) ((-49 . -1017) T) ((-49 . -556) 4183) ((-49 . -1133) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -256) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1133) T) ((-48 . -556) 4165) ((-48 . -1017) T) ((-48 . -559) 4066) ((-48 . -954) 4009) ((-48 . -459) 3975) ((-48 . -262) 3962) ((-48 . -27) T) ((-48 . -919) T) ((-48 . -203) T) ((-48 . -82) 3911) ((-48 . -967) 3876) ((-48 . -972) 3841) ((-48 . -248) T) ((-48 . -658) 3806) ((-48 . -586) 3771) ((-48 . -594) 3721) ((-48 . -592) 3671) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -965) T) ((-48 . -667) T) ((-48 . -1065) T) ((-48 . -1029) T) ((-48 . -974) T) ((-48 . -38) 3636) ((-48 . -260) T) ((-48 . -395) T) 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\ No newline at end of file
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191581) ((-1161 . -185) 191527) ((-1161 . -189) 191479) ((-1161 . -1163) 191463) ((-1161 . -951) 191398) ((-1149 . -1156) 191382) ((-1149 . -1067) 191360) ((-1149 . -554) NIL) ((-1149 . -259) 191347) ((-1149 . -456) 191295) ((-1149 . -276) 191272) ((-1149 . -951) 191155) ((-1149 . -354) 191139) ((-1149 . -35) 190971) ((-1149 . -79) 190776) ((-1149 . -964) 190602) ((-1149 . -969) 190428) ((-1149 . -589) 190338) ((-1149 . -591) 190227) ((-1149 . -583) 190059) ((-1149 . -655) 189891) ((-1149 . -556) 189647) ((-1149 . -115) 189626) ((-1149 . -117) 189605) ((-1149 . -380) 189589) ((-1149 . -44) 189566) ((-1149 . -328) 189550) ((-1149 . -581) 189498) ((-1149 . -810) 189442) ((-1149 . -807) 189349) ((-1149 . -812) 189260) ((-1149 . -797) NIL) ((-1149 . -822) 189239) ((-1149 . -1135) 189218) ((-1149 . -862) 189188) ((-1149 . -833) 189167) ((-1149 . -496) 189081) ((-1149 . -245) 188995) ((-1149 . -145) 188889) ((-1149 . -392) 188823) ((-1149 . -257) 188802) ((-1149 . -240) 188729) ((-1149 . -189) T) ((-1149 . -101) T) ((-1149 . -22) T) ((-1149 . -69) T) ((-1149 . -553) 188711) ((-1149 . -1014) T) ((-1149 . -20) T) ((-1149 . -18) T) ((-1149 . -971) T) ((-1149 . -1026) T) ((-1149 . -1062) T) ((-1149 . -664) T) ((-1149 . -962) T) ((-1149 . -185) 188698) ((-1149 . -12) T) ((-1149 . -1130) T) ((-1149 . -188) T) ((-1149 . -224) 188682) ((-1149 . -183) 188666) ((-1147 . -1007) 188650) ((-1147 . -558) 188634) ((-1147 . -1014) 188612) ((-1147 . -553) 188579) ((-1147 . -1130) 188557) ((-1147 . -12) 188535) ((-1147 . -69) 188513) ((-1147 . -1008) 188470) ((-1145 . -1144) 188449) ((-1145 . -916) 188415) ((-1145 . -1116) 188381) ((-1145 . -1119) 188347) ((-1145 . -433) 188313) ((-1145 . -238) 188279) ((-1145 . -63) 188245) ((-1145 . -32) 188211) ((-1145 . -1159) 188188) ((-1145 . -44) 188165) ((-1145 . -380) 188122) ((-1145 . -556) 187877) ((-1145 . -655) 187697) ((-1145 . -583) 187517) ((-1145 . -591) 187328) ((-1145 . -589) 187186) ((-1145 . -969) 187000) ((-1145 . -964) 186814) ((-1145 . -79) 186602) ((-1145 . -35) 186422) ((-1145 . -887) 186392) ((-1145 . -240) 186292) ((-1145 . -1142) 186276) ((-1145 . -971) T) ((-1145 . -1026) T) ((-1145 . -1062) T) ((-1145 . -664) T) ((-1145 . -962) T) ((-1145 . -18) T) ((-1145 . -20) T) ((-1145 . -1014) T) ((-1145 . -553) 186258) ((-1145 . -1130) T) ((-1145 . -12) T) ((-1145 . -69) T) ((-1145 . -22) T) ((-1145 . -101) T) ((-1145 . -115) 186186) ((-1145 . -117) 186068) ((-1145 . -554) 185741) ((-1145 . -183) 185711) ((-1145 . -810) 185565) ((-1145 . -812) 185365) ((-1145 . -807) 185163) ((-1145 . -224) 185133) ((-1145 . -188) 184995) ((-1145 . -185) 184851) ((-1145 . -189) 184759) ((-1145 . -311) 184738) ((-1145 . -1135) 184717) ((-1145 . -833) 184696) ((-1145 . -496) 184650) ((-1145 . -145) 184584) ((-1145 . -392) 184563) ((-1145 . -257) 184542) ((-1145 . -245) 184496) ((-1145 . -200) 184475) ((-1145 . -287) 184445) ((-1145 . -456) 184305) ((-1145 . -259) 184244) ((-1145 . -328) 184214) ((-1145 . -581) 184122) ((-1145 . -342) 184092) ((-1145 . -797) 183965) ((-1145 . -741) 183918) ((-1145 . -715) 183871) ((-1145 . -717) 183824) ((-1145 . -757) 183726) ((-1145 . -760) 183628) ((-1145 . -719) 183581) ((-1145 . -722) 183534) ((-1145 . -756) 183487) ((-1145 . -795) 183457) ((-1145 . -822) 183410) ((-1145 . -934) 183363) ((-1145 . -951) 183152) ((-1145 . -1067) 183104) ((-1145 . -905) 183074) ((-1140 . -1144) 183035) ((-1140 . -916) 183001) ((-1140 . -1116) 182967) ((-1140 . -1119) 182933) ((-1140 . -433) 182899) ((-1140 . -238) 182865) ((-1140 . -63) 182831) ((-1140 . -32) 182797) ((-1140 . -1159) 182774) ((-1140 . -44) 182751) ((-1140 . -380) 182690) ((-1140 . -556) 182491) ((-1140 . -655) 182293) ((-1140 . -583) 182095) ((-1140 . -591) 181950) ((-1140 . -589) 181790) ((-1140 . -969) 181586) ((-1140 . -964) 181382) ((-1140 . -79) 181134) ((-1140 . -35) 180936) ((-1140 . -887) 180906) ((-1140 . -240) 180734) ((-1140 . -1142) 180718) ((-1140 . -971) T) ((-1140 . -1026) T) ((-1140 . -1062) T) ((-1140 . -664) T) ((-1140 . -962) T) ((-1140 . -18) T) ((-1140 . -20) T) ((-1140 . -1014) T) ((-1140 . -553) 180700) ((-1140 . -1130) T) ((-1140 . -12) T) ((-1140 . -69) T) ((-1140 . -22) T) ((-1140 . -101) T) ((-1140 . -115) 180610) ((-1140 . -117) 180520) ((-1140 . -554) NIL) ((-1140 . -183) 180472) ((-1140 . -810) 180308) ((-1140 . -812) 180072) ((-1140 . -807) 179811) ((-1140 . -224) 179763) ((-1140 . -188) 179589) ((-1140 . -185) 179409) ((-1140 . -189) 179299) ((-1140 . -311) 179278) ((-1140 . -1135) 179257) ((-1140 . -833) 179236) ((-1140 . -496) 179190) ((-1140 . -145) 179124) ((-1140 . -392) 179103) ((-1140 . -257) 179082) ((-1140 . -245) 179036) ((-1140 . -200) 179015) ((-1140 . -287) 178967) ((-1140 . -456) 178701) ((-1140 . -259) 178586) ((-1140 . -328) 178538) ((-1140 . -581) 178490) ((-1140 . -342) 178442) ((-1140 . -797) NIL) ((-1140 . -741) NIL) ((-1140 . -715) NIL) ((-1140 . -717) NIL) ((-1140 . -757) NIL) ((-1140 . -760) NIL) ((-1140 . -719) NIL) ((-1140 . -722) NIL) ((-1140 . -756) NIL) ((-1140 . -795) 178394) ((-1140 . -822) NIL) ((-1140 . -934) NIL) ((-1140 . -951) 178360) ((-1140 . -1067) NIL) ((-1140 . -905) 178312) ((-1139 . -753) T) ((-1139 . -760) T) ((-1139 . -757) T) ((-1139 . -1014) T) ((-1139 . -553) 178294) ((-1139 . -1130) T) ((-1139 . -12) T) ((-1139 . -69) T) ((-1139 . -319) T) ((-1139 . -605) T) ((-1138 . -753) T) ((-1138 . -760) T) ((-1138 . -757) T) ((-1138 . -1014) T) ((-1138 . -553) 178276) ((-1138 . -1130) T) ((-1138 . -12) T) ((-1138 . -69) T) ((-1138 . -319) T) ((-1138 . -605) T) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1014) T) ((-1137 . -553) 178258) ((-1137 . -1130) T) ((-1137 . -12) T) ((-1137 . -69) T) ((-1137 . -319) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1014) T) ((-1136 . -553) 178240) ((-1136 . -1130) T) ((-1136 . -12) T) ((-1136 . -69) T) ((-1136 . -319) T) ((-1136 . -605) T) ((-1131 . -996) T) ((-1131 . -430) 178221) ((-1131 . -553) 178187) ((-1131 . -556) 178168) ((-1131 . -1014) T) ((-1131 . -1130) T) ((-1131 . -12) T) ((-1131 . -69) T) ((-1131 . -61) T) ((-1128 . -430) 178145) ((-1128 . -553) 178086) ((-1128 . -556) 178063) ((-1128 . -1014) 178041) ((-1128 . -1130) 178019) ((-1128 . -12) 177997) ((-1128 . -69) 177975) ((-1123 . -680) 177951) ((-1123 . -32) 177917) ((-1123 . -63) 177883) ((-1123 . -238) 177849) ((-1123 . -433) 177815) ((-1123 . -1119) 177781) ((-1123 . -1116) 177747) ((-1123 . -916) 177713) ((-1123 . -44) 177682) ((-1123 . -35) 177579) ((-1123 . -583) 177476) ((-1123 . -655) 177373) ((-1123 . -556) 177255) ((-1123 . -245) 177234) ((-1123 . -496) 177213) ((-1123 . -380) 177197) ((-1123 . -79) 177062) ((-1123 . -964) 176948) ((-1123 . -969) 176834) ((-1123 . -145) 176788) ((-1123 . -117) 176767) ((-1123 . -115) 176746) ((-1123 . -591) 176671) ((-1123 . -589) 176581) ((-1123 . -887) 176542) ((-1123 . -812) 176523) ((-1123 . -1130) T) ((-1123 . -12) T) ((-1123 . -807) 176502) ((-1123 . -962) T) ((-1123 . -664) T) ((-1123 . -1062) T) ((-1123 . -1026) T) ((-1123 . -971) T) ((-1123 . -18) T) ((-1123 . -20) T) ((-1123 . -1014) T) ((-1123 . -553) 176484) ((-1123 . -69) T) ((-1123 . -22) T) ((-1123 . -101) T) ((-1123 . -810) 176465) ((-1123 . -456) 176432) ((-1123 . -259) 176419) ((-1117 . -924) 176403) ((-1117 . -31) T) ((-1117 . -12) T) ((-1117 . -1130) T) ((-1117 . -69) 176357) ((-1117 . -553) 176292) ((-1117 . -259) 176230) ((-1117 . -456) 176163) ((-1117 . -380) 176147) ((-1117 . -1014) 176125) ((-1117 . -429) 176109) ((-1117 . -317) 176093) ((-1117 . -1036) 176077) ((-1112 . -313) 176051) ((-1112 . -69) T) ((-1112 . -12) T) ((-1112 . -1130) T) ((-1112 . -553) 176033) ((-1112 . -1014) T) ((-1110 . -1014) T) ((-1110 . -553) 176015) ((-1110 . -1130) T) ((-1110 . -12) T) ((-1110 . -69) T) ((-1110 . -556) 175997) ((-1105 . -748) 175981) ((-1105 . -69) T) ((-1105 . -12) T) ((-1105 . -1130) T) ((-1105 . -553) 175963) ((-1105 . -1014) T) ((-1103 . -1108) 175942) ((-1103 . -182) 175890) ((-1103 . -73) 175838) ((-1103 . -1036) 175773) ((-1103 . -121) 175721) ((-1103 . -554) NIL) ((-1103 . -192) 175669) ((-1103 . -539) 175648) ((-1103 . -259) 175446) ((-1103 . -456) 175198) ((-1103 . -380) 175133) ((-1103 . -429) 175068) ((-1103 . -240) 175047) ((-1103 . -242) 175026) ((-1103 . -550) 175005) ((-1103 . -1014) T) ((-1103 . -553) 174987) ((-1103 . -69) T) ((-1103 . -1130) T) ((-1103 . -12) T) ((-1103 . -31) T) ((-1103 . -317) 174935) ((-1099 . -1014) T) ((-1099 . -553) 174917) ((-1099 . -1130) T) ((-1099 . -12) T) ((-1099 . -69) T) ((-1098 . -753) T) ((-1098 . -760) T) ((-1098 . -757) T) ((-1098 . -1014) T) ((-1098 . -553) 174899) ((-1098 . -1130) T) ((-1098 . -12) T) ((-1098 . -69) T) ((-1098 . -319) T) ((-1098 . -605) T) ((-1097 . -753) T) ((-1097 . -760) T) ((-1097 . -757) T) ((-1097 . -1014) T) ((-1097 . -553) 174881) ((-1097 . -1130) T) ((-1097 . -12) T) ((-1097 . -69) T) ((-1097 . -319) T) ((-1096 . -1176) T) ((-1096 . -1014) T) ((-1096 . -553) 174848) ((-1096 . -1130) T) ((-1096 . -12) T) ((-1096 . -69) T) ((-1096 . -951) 174784) ((-1096 . -556) 174720) ((-1095 . -553) 174702) ((-1094 . -553) 174684) ((-1093 . -276) 174661) ((-1093 . -951) 174559) ((-1093 . -354) 174543) ((-1093 . -35) 174440) ((-1093 . -556) 174297) ((-1093 . -591) 174222) ((-1093 . -589) 174132) ((-1093 . -971) T) ((-1093 . -1026) T) ((-1093 . -1062) T) ((-1093 . -664) T) ((-1093 . -962) T) ((-1093 . -79) 173997) ((-1093 . -964) 173883) ((-1093 . -969) 173769) ((-1093 . -18) T) ((-1093 . -20) T) ((-1093 . -1014) T) ((-1093 . -553) 173751) ((-1093 . -1130) T) ((-1093 . -12) T) ((-1093 . -69) T) ((-1093 . -22) T) ((-1093 . -101) T) ((-1093 . -583) 173648) ((-1093 . -655) 173545) ((-1093 . -115) 173524) ((-1093 . -117) 173503) ((-1093 . -145) 173457) ((-1093 . -380) 173441) ((-1093 . -496) 173420) ((-1093 . -245) 173399) ((-1093 . -44) 173376) ((-1091 . -757) T) ((-1091 . -553) 173358) ((-1091 . -1014) T) ((-1091 . -69) T) ((-1091 . -12) T) ((-1091 . -1130) T) ((-1091 . -760) T) ((-1091 . -554) 173280) ((-1091 . -556) 173246) ((-1091 . -951) 173228) ((-1091 . -797) 173195) ((-1090 . -1173) 173179) ((-1090 . -189) 173138) ((-1090 . -556) 173020) ((-1090 . -591) 172945) ((-1090 . -589) 172855) ((-1090 . -101) T) ((-1090 . -22) T) ((-1090 . -69) T) ((-1090 . -553) 172837) ((-1090 . -1014) T) ((-1090 . -20) T) ((-1090 . -18) T) ((-1090 . -971) T) ((-1090 . -1026) T) ((-1090 . -1062) T) ((-1090 . -664) T) ((-1090 . -962) T) ((-1090 . -185) 172790) ((-1090 . -12) T) ((-1090 . -1130) T) ((-1090 . -188) 172749) ((-1090 . -240) 172714) ((-1090 . -810) 172627) ((-1090 . -807) 172515) ((-1090 . -812) 172428) ((-1090 . -887) 172398) ((-1090 . -35) 172295) ((-1090 . -79) 172160) ((-1090 . -964) 172046) ((-1090 . -969) 171932) ((-1090 . -583) 171829) ((-1090 . -655) 171726) ((-1090 . -115) 171705) ((-1090 . -117) 171684) ((-1090 . -145) 171638) ((-1090 . -380) 171622) ((-1090 . -496) 171601) ((-1090 . -245) 171580) ((-1090 . -44) 171557) ((-1090 . -1159) 171534) ((-1090 . -32) 171500) ((-1090 . -63) 171466) ((-1090 . -238) 171432) ((-1090 . -433) 171398) ((-1090 . -1119) 171364) ((-1090 . -1116) 171330) ((-1090 . -916) 171296) ((-1089 . -1165) 171257) ((-1089 . -311) 171236) ((-1089 . -1135) 171215) ((-1089 . -833) 171194) ((-1089 . -496) 171148) ((-1089 . -145) 171082) ((-1089 . -556) 170831) ((-1089 . -655) 170678) ((-1089 . -583) 170525) ((-1089 . -35) 170372) ((-1089 . -392) 170351) ((-1089 . -257) 170330) ((-1089 . -591) 170230) ((-1089 . -589) 170115) ((-1089 . -971) T) ((-1089 . -1026) T) ((-1089 . -1062) T) ((-1089 . -664) T) ((-1089 . -962) T) ((-1089 . -79) 169935) ((-1089 . -964) 169776) ((-1089 . -969) 169617) ((-1089 . -18) T) ((-1089 . -20) T) ((-1089 . -1014) T) ((-1089 . -553) 169599) ((-1089 . -1130) T) ((-1089 . -12) T) ((-1089 . -69) T) ((-1089 . -22) T) ((-1089 . -101) T) ((-1089 . -245) 169553) ((-1089 . -200) 169532) ((-1089 . -916) 169498) ((-1089 . -1116) 169464) ((-1089 . -1119) 169430) ((-1089 . -433) 169396) ((-1089 . -238) 169362) ((-1089 . -63) 169328) ((-1089 . -32) 169294) ((-1089 . -1159) 169264) ((-1089 . -44) 169234) ((-1089 . -380) 169218) ((-1089 . -117) 169197) ((-1089 . -115) 169176) ((-1089 . -887) 169139) ((-1089 . -812) 169045) ((-1089 . -807) 168926) ((-1089 . -810) 168832) ((-1089 . -240) 168790) ((-1089 . -188) 168742) ((-1089 . -185) 168688) ((-1089 . -189) 168640) ((-1089 . -1163) 168624) ((-1089 . -951) 168559) ((-1086 . -1156) 168543) ((-1086 . -1067) 168521) ((-1086 . -554) NIL) ((-1086 . -259) 168508) ((-1086 . -456) 168456) ((-1086 . -276) 168433) ((-1086 . -951) 168316) ((-1086 . -354) 168300) ((-1086 . -35) 168132) ((-1086 . -79) 167937) ((-1086 . -964) 167763) ((-1086 . -969) 167589) ((-1086 . -589) 167499) ((-1086 . -591) 167388) ((-1086 . -583) 167220) ((-1086 . -655) 167052) ((-1086 . -556) 166829) ((-1086 . -115) 166808) ((-1086 . -117) 166787) ((-1086 . -380) 166771) ((-1086 . -44) 166748) ((-1086 . -328) 166732) ((-1086 . -581) 166680) ((-1086 . -810) 166624) ((-1086 . -807) 166531) ((-1086 . -812) 166442) ((-1086 . -797) NIL) ((-1086 . -822) 166421) ((-1086 . -1135) 166400) ((-1086 . -862) 166370) ((-1086 . -833) 166349) ((-1086 . -496) 166263) ((-1086 . -245) 166177) ((-1086 . -145) 166071) ((-1086 . -392) 166005) ((-1086 . -257) 165984) ((-1086 . -240) 165911) ((-1086 . -189) T) ((-1086 . -101) T) ((-1086 . -22) T) ((-1086 . -69) T) ((-1086 . -553) 165893) ((-1086 . -1014) T) ((-1086 . -20) T) ((-1086 . -18) T) ((-1086 . -971) T) ((-1086 . -1026) T) ((-1086 . -1062) T) ((-1086 . -664) T) ((-1086 . -962) T) ((-1086 . -185) 165880) ((-1086 . -12) T) ((-1086 . -1130) T) ((-1086 . -188) T) ((-1086 . -224) 165864) ((-1086 . -183) 165848) ((-1083 . -1144) 165809) ((-1083 . -916) 165775) ((-1083 . -1116) 165741) ((-1083 . -1119) 165707) ((-1083 . -433) 165673) ((-1083 . -238) 165639) ((-1083 . -63) 165605) ((-1083 . -32) 165571) ((-1083 . -1159) 165548) ((-1083 . -44) 165525) ((-1083 . -380) 165464) ((-1083 . -556) 165265) ((-1083 . -655) 165067) ((-1083 . -583) 164869) ((-1083 . -591) 164724) ((-1083 . -589) 164564) ((-1083 . -969) 164360) ((-1083 . -964) 164156) ((-1083 . -79) 163908) ((-1083 . -35) 163710) ((-1083 . -887) 163680) ((-1083 . -240) 163508) ((-1083 . -1142) 163492) ((-1083 . -971) T) ((-1083 . -1026) T) ((-1083 . -1062) T) ((-1083 . -664) T) ((-1083 . -962) T) ((-1083 . -18) T) ((-1083 . -20) T) ((-1083 . -1014) T) ((-1083 . -553) 163474) ((-1083 . -1130) T) ((-1083 . -12) T) ((-1083 . -69) T) ((-1083 . -22) T) ((-1083 . -101) T) ((-1083 . -115) 163384) ((-1083 . -117) 163294) ((-1083 . -554) NIL) ((-1083 . -183) 163246) ((-1083 . -810) 163082) ((-1083 . -812) 162846) ((-1083 . -807) 162585) ((-1083 . -224) 162537) ((-1083 . -188) 162363) ((-1083 . -185) 162183) ((-1083 . -189) 162073) ((-1083 . -311) 162052) ((-1083 . -1135) 162031) ((-1083 . -833) 162010) ((-1083 . -496) 161964) ((-1083 . -145) 161898) ((-1083 . -392) 161877) ((-1083 . -257) 161856) ((-1083 . -245) 161810) ((-1083 . -200) 161789) ((-1083 . -287) 161741) ((-1083 . -456) 161475) ((-1083 . -259) 161360) ((-1083 . -328) 161312) ((-1083 . -581) 161264) ((-1083 . -342) 161216) ((-1083 . -797) NIL) ((-1083 . -741) NIL) ((-1083 . -715) NIL) ((-1083 . -717) NIL) ((-1083 . -757) NIL) ((-1083 . -760) NIL) ((-1083 . -719) NIL) ((-1083 . -722) NIL) ((-1083 . -756) NIL) ((-1083 . -795) 161168) ((-1083 . -822) NIL) ((-1083 . -934) NIL) ((-1083 . -951) 161134) ((-1083 . -1067) NIL) ((-1083 . -905) 161086) ((-1082 . -996) T) ((-1082 . -430) 161067) ((-1082 . -553) 161033) ((-1082 . -556) 161014) ((-1082 . -1014) T) ((-1082 . -1130) T) ((-1082 . -12) T) ((-1082 . -69) T) ((-1082 . -61) T) ((-1081 . -1014) T) ((-1081 . -553) 160996) ((-1081 . -1130) T) ((-1081 . -12) T) ((-1081 . -69) T) ((-1080 . -1014) T) ((-1080 . -553) 160978) ((-1080 . -1130) T) ((-1080 . -12) T) ((-1080 . -69) T) ((-1075 . -1108) 160954) ((-1075 . -182) 160899) ((-1075 . -73) 160844) ((-1075 . -1036) 160776) ((-1075 . -121) 160721) ((-1075 . -554) NIL) ((-1075 . -192) 160666) ((-1075 . -539) 160642) ((-1075 . -259) 160431) ((-1075 . -456) 160171) ((-1075 . -380) 160103) ((-1075 . -429) 160035) ((-1075 . -240) 160011) ((-1075 . -242) 159987) ((-1075 . -550) 159963) ((-1075 . -1014) T) ((-1075 . -553) 159945) ((-1075 . -69) T) ((-1075 . -1130) T) ((-1075 . -12) T) ((-1075 . -31) T) ((-1075 . -317) 159890) ((-1074 . -1059) T) ((-1074 . -323) 159872) ((-1074 . -760) T) ((-1074 . -757) T) ((-1074 . -121) 159854) ((-1074 . -554) NIL) ((-1074 . -240) 159804) ((-1074 . -539) 159779) ((-1074 . -242) 159754) ((-1074 . -594) 159736) ((-1074 . -429) 159718) ((-1074 . -1014) T) ((-1074 . -380) 159700) ((-1074 . -456) NIL) ((-1074 . -259) NIL) ((-1074 . -553) 159682) ((-1074 . -69) T) ((-1074 . -1130) T) ((-1074 . -12) T) ((-1074 . -31) T) ((-1074 . -317) 159664) ((-1074 . -1036) 159646) ((-1074 . -16) 159628) ((-1070 . -617) 159612) ((-1070 . -594) 159596) ((-1070 . -242) 159573) ((-1070 . -240) 159525) ((-1070 . -539) 159502) ((-1070 . -554) 159463) ((-1070 . -429) 159447) ((-1070 . -1014) 159425) ((-1070 . -380) 159409) ((-1070 . -456) 159342) ((-1070 . -259) 159280) ((-1070 . -553) 159215) ((-1070 . -69) 159169) ((-1070 . -1130) T) ((-1070 . -12) T) ((-1070 . -31) T) ((-1070 . -121) 159153) ((-1070 . -1169) 159137) ((-1070 . -924) 159121) ((-1070 . -1065) 159105) ((-1070 . -556) 159082) ((-1070 . -1036) 159066) ((-1068 . -996) T) ((-1068 . -430) 159047) ((-1068 . -553) 159013) ((-1068 . -556) 158994) ((-1068 . -1014) T) ((-1068 . -1130) T) ((-1068 . -12) T) ((-1068 . -69) T) ((-1068 . -61) T) ((-1066 . -1108) 158973) ((-1066 . -182) 158921) ((-1066 . -73) 158869) ((-1066 . -1036) 158804) ((-1066 . -121) 158752) ((-1066 . -554) NIL) ((-1066 . -192) 158700) ((-1066 . -539) 158679) ((-1066 . -259) 158477) ((-1066 . -456) 158229) ((-1066 . -380) 158164) ((-1066 . -429) 158099) ((-1066 . -240) 158078) ((-1066 . -242) 158057) ((-1066 . -550) 158036) ((-1066 . -1014) T) ((-1066 . -553) 158018) ((-1066 . -69) T) ((-1066 . -1130) T) ((-1066 . -12) T) ((-1066 . -31) T) ((-1066 . -317) 157966) ((-1063 . -1035) 157950) ((-1063 . -317) 157934) ((-1063 . -429) 157918) ((-1063 . -1014) 157896) ((-1063 . -380) 157880) ((-1063 . -456) 157813) ((-1063 . -259) 157751) ((-1063 . -553) 157686) ((-1063 . -69) 157640) ((-1063 . -1130) T) ((-1063 . -12) T) ((-1063 . -31) T) ((-1063 . -1036) 157624) ((-1063 . -73) 157608) ((-1061 . -1021) 157577) ((-1061 . -1125) 157546) ((-1061 . -1036) 157530) ((-1061 . -553) 157492) ((-1061 . -121) 157476) ((-1061 . -31) T) ((-1061 . -12) T) ((-1061 . -1130) T) ((-1061 . -69) T) ((-1061 . -259) 157414) ((-1061 . -456) 157347) ((-1061 . -380) 157331) ((-1061 . -1014) T) ((-1061 . -429) 157315) ((-1061 . -554) 157276) ((-1061 . -317) 157260) ((-1061 . -890) 157229) ((-1061 . -984) 157198) ((-1057 . -1038) 157143) ((-1057 . -317) 157127) ((-1057 . -31) T) ((-1057 . -259) 157065) ((-1057 . -456) 156998) ((-1057 . -380) 156982) ((-1057 . -429) 156966) ((-1057 . -966) 156906) ((-1057 . -951) 156804) ((-1057 . -556) 156723) ((-1057 . -354) 156707) ((-1057 . -581) 156655) ((-1057 . -591) 156593) ((-1057 . -328) 156577) ((-1057 . -189) 156556) ((-1057 . -185) 156504) ((-1057 . -188) 156458) ((-1057 . -224) 156442) ((-1057 . -807) 156366) ((-1057 . -812) 156292) ((-1057 . -810) 156251) ((-1057 . -183) 156235) ((-1057 . -655) 156170) ((-1057 . -583) 156105) ((-1057 . -589) 156064) ((-1057 . -101) T) ((-1057 . -22) T) ((-1057 . -69) T) ((-1057 . -12) T) ((-1057 . -1130) T) ((-1057 . -553) 156026) ((-1057 . -1014) T) ((-1057 . -20) T) ((-1057 . -18) T) ((-1057 . -969) 156010) ((-1057 . -964) 155994) ((-1057 . -79) 155973) ((-1057 . -962) T) ((-1057 . -664) T) ((-1057 . -1062) T) ((-1057 . -1026) T) ((-1057 . -971) T) ((-1057 . -35) 155933) ((-1057 . -554) 155894) ((-1056 . -924) 155865) ((-1056 . -31) T) ((-1056 . -12) T) ((-1056 . -1130) T) ((-1056 . -69) T) ((-1056 . -553) 155847) ((-1056 . -259) 155773) ((-1056 . -456) 155681) ((-1056 . -380) 155652) ((-1056 . -1014) T) ((-1056 . -429) 155623) ((-1056 . -317) 155594) ((-1056 . -1036) 155565) ((-1055 . -1014) T) ((-1055 . -553) 155547) ((-1055 . -1130) T) ((-1055 . -12) T) ((-1055 . -69) T) ((-1050 . -1052) T) ((-1050 . -1176) T) ((-1050 . -61) T) ((-1050 . -69) T) ((-1050 . -12) T) ((-1050 . -1130) T) ((-1050 . -553) 155513) ((-1050 . -1014) T) ((-1050 . -556) 155494) ((-1050 . -430) 155475) ((-1050 . -996) T) ((-1048 . -1049) 155459) ((-1048 . -69) T) ((-1048 . -12) T) ((-1048 . -1130) T) ((-1048 . -553) 155441) ((-1048 . -1014) T) ((-1041 . -680) 155420) ((-1041 . -32) 155386) ((-1041 . -63) 155352) ((-1041 . -238) 155318) ((-1041 . -433) 155284) ((-1041 . -1119) 155250) ((-1041 . -1116) 155216) ((-1041 . -916) 155182) ((-1041 . -44) 155154) ((-1041 . -35) 155051) ((-1041 . -583) 154948) ((-1041 . -655) 154845) ((-1041 . -556) 154727) ((-1041 . -245) 154706) ((-1041 . -496) 154685) ((-1041 . -380) 154669) ((-1041 . -79) 154534) ((-1041 . -964) 154420) ((-1041 . -969) 154306) ((-1041 . -145) 154260) ((-1041 . -117) 154239) ((-1041 . -115) 154218) ((-1041 . -591) 154143) ((-1041 . -589) 154053) ((-1041 . -887) 154020) ((-1041 . -812) 154004) ((-1041 . -1130) T) ((-1041 . -12) T) ((-1041 . -807) 153986) ((-1041 . -962) T) ((-1041 . -664) T) ((-1041 . -1062) T) ((-1041 . -1026) T) ((-1041 . -971) T) ((-1041 . -18) T) ((-1041 . -20) T) ((-1041 . -1014) T) ((-1041 . -553) 153968) ((-1041 . -69) T) ((-1041 . -22) T) ((-1041 . -101) T) ((-1041 . -810) 153952) ((-1041 . -456) 153922) ((-1041 . -259) 153909) ((-1040 . -862) 153876) ((-1040 . -556) 153675) ((-1040 . -951) 153560) ((-1040 . -1135) 153539) ((-1040 . -822) 153518) ((-1040 . -797) 153377) ((-1040 . -812) 153361) ((-1040 . -807) 153343) ((-1040 . -810) 153327) ((-1040 . -456) 153279) ((-1040 . -392) 153233) ((-1040 . -581) 153181) ((-1040 . -591) 153070) ((-1040 . -328) 153054) ((-1040 . -44) 153026) ((-1040 . -35) 152878) ((-1040 . -583) 152730) ((-1040 . -655) 152582) ((-1040 . -245) 152516) ((-1040 . -496) 152450) ((-1040 . -380) 152434) ((-1040 . -79) 152259) ((-1040 . -964) 152105) ((-1040 . -969) 151951) ((-1040 . -145) 151865) ((-1040 . -117) 151844) ((-1040 . -115) 151823) ((-1040 . -589) 151733) ((-1040 . -101) T) ((-1040 . -22) T) ((-1040 . -69) T) ((-1040 . -12) T) ((-1040 . -1130) T) ((-1040 . -553) 151715) ((-1040 . -1014) T) ((-1040 . -20) T) ((-1040 . -18) T) ((-1040 . -962) T) ((-1040 . -664) T) ((-1040 . -1062) T) ((-1040 . -1026) T) ((-1040 . -971) T) ((-1040 . -354) 151699) ((-1040 . -276) 151671) ((-1040 . -259) 151658) ((-1040 . -554) 151406) ((-1034 . -484) T) ((-1034 . -1135) T) ((-1034 . -1067) T) ((-1034 . -951) 151388) ((-1034 . -554) 151303) ((-1034 . -934) T) ((-1034 . -797) 151285) ((-1034 . -756) T) ((-1034 . -722) T) ((-1034 . -719) T) ((-1034 . -760) T) ((-1034 . -757) T) ((-1034 . -717) T) ((-1034 . -715) T) ((-1034 . -741) T) ((-1034 . -591) 151257) ((-1034 . -581) 151239) ((-1034 . -833) T) ((-1034 . -496) T) ((-1034 . -245) T) ((-1034 . -145) T) ((-1034 . -556) 151211) ((-1034 . -655) 151198) ((-1034 . -583) 151185) ((-1034 . -969) 151172) ((-1034 . -964) 151159) ((-1034 . -79) 151144) ((-1034 . -35) 151131) ((-1034 . -392) T) ((-1034 . -257) T) ((-1034 . -188) T) ((-1034 . -185) 151118) ((-1034 . -189) T) ((-1034 . -113) T) ((-1034 . -962) T) ((-1034 . -664) T) ((-1034 . -1062) T) ((-1034 . -1026) T) ((-1034 . -971) T) ((-1034 . -18) T) ((-1034 . -589) 151090) ((-1034 . -20) T) ((-1034 . -1014) T) ((-1034 . -553) 151072) ((-1034 . -1130) T) ((-1034 . -12) T) ((-1034 . -69) T) ((-1034 . -22) T) ((-1034 . -101) T) ((-1034 . -117) T) ((-1034 . -753) T) ((-1034 . -319) T) ((-1034 . -81) T) ((-1034 . -605) T) ((-1030 . -996) T) ((-1030 . -430) 151053) ((-1030 . -553) 151019) ((-1030 . -556) 151000) ((-1030 . -1014) T) ((-1030 . -1130) T) ((-1030 . -12) T) ((-1030 . -69) T) ((-1030 . -61) T) ((-1029 . -1014) T) ((-1029 . -553) 150982) ((-1029 . -1130) T) ((-1029 . -12) T) ((-1029 . -69) T) ((-1027 . -195) 150961) ((-1027 . -1188) 150931) ((-1027 . -722) 150910) ((-1027 . -719) 150889) ((-1027 . -760) 150843) ((-1027 . -757) 150797) ((-1027 . -717) 150776) ((-1027 . -718) 150755) ((-1027 . -655) 150700) ((-1027 . -583) 150625) ((-1027 . -242) 150602) ((-1027 . -240) 150579) ((-1027 . -539) 150556) ((-1027 . -951) 150385) ((-1027 . -556) 150189) ((-1027 . -354) 150158) ((-1027 . -581) 150066) ((-1027 . -591) 149905) ((-1027 . -328) 149875) ((-1027 . -429) 149859) ((-1027 . -380) 149843) ((-1027 . -456) 149776) ((-1027 . -259) 149714) ((-1027 . -31) T) ((-1027 . -317) 149698) ((-1027 . -319) 149677) ((-1027 . -189) 149630) ((-1027 . -589) 149418) ((-1027 . -971) 149397) ((-1027 . -1026) 149376) ((-1027 . -1062) 149355) ((-1027 . -664) 149334) ((-1027 . -962) 149313) ((-1027 . -185) 149209) ((-1027 . -188) 149111) ((-1027 . -224) 149081) ((-1027 . -807) 148953) ((-1027 . -812) 148827) ((-1027 . -810) 148760) ((-1027 . -183) 148730) ((-1027 . -553) 148427) ((-1027 . -969) 148352) ((-1027 . -964) 148257) ((-1027 . -79) 148177) ((-1027 . -101) 148052) ((-1027 . -22) 147889) ((-1027 . -69) 147626) ((-1027 . -12) T) ((-1027 . -1130) T) ((-1027 . -1014) 147382) ((-1027 . -20) 147238) ((-1027 . -18) 147153) ((-1023 . -1024) 147137) ((-1023 . |MappingCategory|) 147111) ((-1023 . -1130) T) ((-1023 . -77) 147095) ((-1023 . -1014) T) ((-1023 . -553) 147077) ((-1023 . -12) T) ((-1023 . -69) T) ((-1018 . -1017) 147041) ((-1018 . -69) T) ((-1018 . -553) 147023) ((-1018 . -1014) T) ((-1018 . -240) 146979) ((-1018 . -1130) T) ((-1018 . -12) T) ((-1018 . -558) 146894) ((-1016 . -1017) 146846) ((-1016 . -69) T) ((-1016 . -553) 146828) ((-1016 . -1014) T) ((-1016 . -240) 146784) ((-1016 . -1130) T) ((-1016 . -12) T) ((-1016 . -558) 146687) ((-1015 . -319) T) ((-1015 . -69) T) ((-1015 . -12) T) ((-1015 . -1130) T) ((-1015 . -553) 146669) ((-1015 . -1014) T) ((-1010 . -368) 146653) ((-1010 . -1012) 146637) ((-1010 . -317) 146621) ((-1010 . -319) 146600) ((-1010 . -192) 146584) ((-1010 . -554) 146545) ((-1010 . -121) 146529) ((-1010 . -429) 146513) ((-1010 . -1014) T) ((-1010 . -380) 146497) ((-1010 . -456) 146430) ((-1010 . -259) 146368) ((-1010 . -553) 146350) ((-1010 . -69) T) ((-1010 . -1130) T) ((-1010 . -12) T) ((-1010 . -31) T) ((-1010 . -1036) 146334) ((-1010 . -73) 146318) ((-1010 . -182) 146302) ((-1009 . -996) T) ((-1009 . -430) 146283) ((-1009 . -553) 146249) ((-1009 . -556) 146230) ((-1009 . -1014) T) ((-1009 . -1130) T) ((-1009 . -12) T) ((-1009 . -69) T) ((-1009 . -61) T) ((-1005 . -1130) T) ((-1005 . -12) T) ((-1005 . -1014) 146200) ((-1005 . -553) 146159) ((-1005 . -69) 146129) ((-1004 . -996) T) ((-1004 . -430) 146110) ((-1004 . -553) 146076) ((-1004 . -556) 146057) ((-1004 . -1014) T) ((-1004 . -1130) T) ((-1004 . -12) T) ((-1004 . -69) T) ((-1004 . -61) T) ((-1002 . -1007) 146041) ((-1002 . -558) 146025) ((-1002 . -1014) 146003) ((-1002 . -553) 145970) ((-1002 . -1130) 145948) ((-1002 . -12) 145926) ((-1002 . -69) 145904) ((-1002 . -1008) 145862) ((-1001 . -227) 145846) ((-1001 . -556) 145830) ((-1001 . -951) 145814) ((-1001 . -760) T) ((-1001 . -69) T) ((-1001 . -1014) T) ((-1001 . -553) 145796) ((-1001 . -757) T) ((-1001 . -185) 145783) ((-1001 . -12) T) ((-1001 . -1130) T) ((-1001 . -188) T) ((-1000 . -212) 145720) ((-1000 . -556) 145463) ((-1000 . -951) 145292) ((-1000 . -554) NIL) ((-1000 . -276) 145253) ((-1000 . -354) 145237) ((-1000 . -35) 145089) ((-1000 . -79) 144914) ((-1000 . -964) 144760) ((-1000 . -969) 144606) ((-1000 . -589) 144516) ((-1000 . -591) 144405) ((-1000 . -583) 144257) ((-1000 . -655) 144109) ((-1000 . -115) 144088) ((-1000 . -117) 144067) ((-1000 . -145) 143981) ((-1000 . -380) 143965) ((-1000 . -496) 143899) ((-1000 . -245) 143833) ((-1000 . -44) 143794) ((-1000 . -328) 143778) ((-1000 . -581) 143726) ((-1000 . -392) 143680) ((-1000 . -456) 143543) ((-1000 . -810) 143478) ((-1000 . -807) 143376) ((-1000 . -812) 143278) ((-1000 . -797) NIL) ((-1000 . -822) 143257) ((-1000 . -1135) 143236) ((-1000 . -862) 143181) ((-1000 . -259) 143168) ((-1000 . -189) 143147) ((-1000 . -101) T) ((-1000 . -22) T) ((-1000 . -69) T) ((-1000 . -553) 143129) ((-1000 . -1014) T) ((-1000 . -20) T) ((-1000 . -18) T) ((-1000 . -971) T) ((-1000 . -1026) T) ((-1000 . -1062) T) ((-1000 . -664) T) ((-1000 . -962) T) ((-1000 . -185) 143077) ((-1000 . -12) T) ((-1000 . -1130) T) ((-1000 . -188) 143031) ((-1000 . -224) 143015) ((-1000 . -183) 142999) ((-998 . -553) 142981) ((-995 . -757) T) ((-995 . -553) 142963) ((-995 . -1014) T) ((-995 . -69) T) ((-995 . -12) T) ((-995 . -1130) T) ((-995 . -760) T) ((-995 . -554) 142944) ((-992 . -662) 142923) ((-992 . -951) 142821) ((-992 . -354) 142805) ((-992 . -581) 142753) ((-992 . -591) 142630) ((-992 . -328) 142614) ((-992 . -321) 142593) ((-992 . -117) 142572) ((-992 . -556) 142397) ((-992 . -655) 142271) ((-992 . -583) 142145) ((-992 . -589) 142043) ((-992 . -969) 141956) ((-992 . -964) 141869) ((-992 . -79) 141761) ((-992 . -35) 141635) ((-992 . -352) 141614) ((-992 . -344) 141593) ((-992 . -115) 141547) ((-992 . -1067) 141526) ((-992 . -298) 141505) ((-992 . -319) 141459) ((-992 . -200) 141413) ((-992 . -245) 141367) ((-992 . -257) 141321) ((-992 . -392) 141275) ((-992 . -496) 141229) ((-992 . -833) 141183) ((-992 . -1135) 141137) ((-992 . -311) 141091) ((-992 . -189) 141019) ((-992 . -185) 140895) ((-992 . -188) 140777) ((-992 . -224) 140747) ((-992 . -807) 140619) ((-992 . -812) 140493) ((-992 . -810) 140426) ((-992 . -183) 140396) ((-992 . -554) 140380) ((-992 . -18) T) ((-992 . -20) T) ((-992 . -1014) T) ((-992 . -553) 140362) ((-992 . -1130) T) ((-992 . -12) T) ((-992 . -69) T) ((-992 . -22) T) ((-992 . -101) T) ((-992 . -962) T) ((-992 . -664) T) ((-992 . -1062) T) ((-992 . -1026) T) ((-992 . -971) T) ((-992 . -145) T) ((-990 . -1014) T) ((-990 . -553) 140344) ((-990 . -1130) T) ((-990 . -12) T) ((-990 . -69) T) ((-990 . -240) 140323) ((-989 . -1014) T) ((-989 . -553) 140305) ((-989 . -1130) T) ((-989 . -12) T) ((-989 . -69) T) ((-988 . -1014) T) ((-988 . -553) 140287) ((-988 . -1130) T) ((-988 . -12) T) ((-988 . -69) T) ((-988 . -240) 140266) ((-988 . -951) 140243) ((-988 . -556) 140220) ((-987 . -1130) T) ((-987 . -12) T) ((-986 . -996) T) ((-986 . -430) 140201) ((-986 . -553) 140167) ((-986 . -556) 140148) ((-986 . -1014) T) ((-986 . -1130) T) ((-986 . -12) T) ((-986 . -69) T) ((-986 . -61) T) ((-979 . -996) T) ((-979 . -430) 140129) ((-979 . -553) 140095) ((-979 . -556) 140076) ((-979 . -1014) T) ((-979 . -1130) T) ((-979 . -12) T) ((-979 . -69) T) ((-979 . -61) T) ((-976 . -484) T) ((-976 . -1135) T) ((-976 . -1067) T) ((-976 . -951) 140058) ((-976 . -554) 139973) ((-976 . -934) T) ((-976 . -797) 139955) ((-976 . -756) T) ((-976 . -722) T) ((-976 . -719) T) ((-976 . -760) T) ((-976 . -757) T) ((-976 . -717) T) ((-976 . -715) T) ((-976 . -741) T) ((-976 . -591) 139927) ((-976 . -581) 139909) ((-976 . -833) T) ((-976 . -496) T) ((-976 . -245) T) ((-976 . -145) T) ((-976 . -556) 139881) ((-976 . -655) 139868) ((-976 . -583) 139855) ((-976 . -969) 139842) ((-976 . -964) 139829) ((-976 . -79) 139814) ((-976 . -35) 139801) ((-976 . -392) T) ((-976 . -257) T) ((-976 . -188) T) ((-976 . -185) 139788) ((-976 . -189) T) ((-976 . -113) T) ((-976 . -962) T) ((-976 . -664) T) ((-976 . -1062) T) ((-976 . -1026) T) ((-976 . -971) T) ((-976 . -18) T) ((-976 . -589) 139760) ((-976 . -20) T) ((-976 . -1014) T) ((-976 . -553) 139742) ((-976 . -1130) T) ((-976 . -12) T) ((-976 . -69) T) ((-976 . -22) T) ((-976 . -101) T) ((-976 . -117) T) ((-976 . -558) 139723) ((-975 . -981) 139702) ((-975 . -69) T) ((-975 . -12) T) ((-975 . -1130) T) ((-975 . -553) 139684) ((-975 . -1014) T) ((-972 . -1130) T) ((-972 . -12) T) ((-972 . -1014) 139662) ((-972 . -553) 139629) ((-972 . -69) 139607) ((-967 . -966) 139547) ((-967 . -583) 139492) ((-967 . -655) 139437) ((-967 . -429) 139421) ((-967 . -380) 139405) ((-967 . -456) 139338) ((-967 . -259) 139276) ((-967 . -31) T) ((-967 . -317) 139260) ((-967 . -591) 139244) ((-967 . -589) 139213) ((-967 . -101) T) ((-967 . -22) T) ((-967 . -69) T) ((-967 . -12) 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T) ((-918 . -715) T) ((-918 . -741) T) ((-918 . -797) 136572) ((-918 . -342) 136554) ((-918 . -581) 136536) ((-918 . -328) 136518) ((-918 . -240) NIL) ((-918 . -259) NIL) ((-918 . -456) NIL) ((-918 . -380) 136500) ((-918 . -287) 136482) ((-918 . -200) T) ((-918 . -79) 136409) ((-918 . -964) 136359) ((-918 . -969) 136309) ((-918 . -245) T) ((-918 . -655) 136259) ((-918 . -583) 136209) ((-918 . -591) 136159) ((-918 . -589) 136109) ((-918 . -35) 136059) ((-918 . -257) T) ((-918 . -392) T) ((-918 . -145) T) ((-918 . -496) T) ((-918 . -833) T) ((-918 . -1135) T) ((-918 . -311) T) ((-918 . -189) T) ((-918 . -185) 136046) ((-918 . -188) T) ((-918 . -224) 136028) ((-918 . -807) NIL) ((-918 . -812) NIL) ((-918 . -810) NIL) ((-918 . -183) 136010) ((-918 . -117) T) ((-918 . -115) NIL) ((-918 . -101) T) ((-918 . -22) T) ((-918 . -69) T) ((-918 . -12) T) ((-918 . -1130) T) ((-918 . -553) 135970) ((-918 . -1014) T) ((-918 . -20) T) ((-918 . -18) T) ((-918 . -962) T) ((-918 . -664) T) ((-918 . -1062) T) ((-918 . -1026) T) ((-918 . -971) T) ((-917 . -290) 135944) ((-917 . -145) T) ((-917 . -556) 135874) ((-917 . -971) T) ((-917 . -1026) T) ((-917 . -1062) T) ((-917 . -664) T) ((-917 . -962) T) ((-917 . -591) 135776) ((-917 . -589) 135706) ((-917 . -101) T) ((-917 . -22) T) ((-917 . -69) T) ((-917 . -12) T) ((-917 . -1130) T) ((-917 . -553) 135688) ((-917 . -1014) T) ((-917 . -20) T) ((-917 . -18) T) ((-917 . -969) 135633) ((-917 . -964) 135578) ((-917 . -79) 135495) ((-917 . -554) 135479) ((-917 . -183) 135456) ((-917 . -810) 135408) ((-917 . -812) 135320) ((-917 . -807) 135230) ((-917 . -224) 135207) ((-917 . -188) 135147) ((-917 . -185) 135081) ((-917 . -189) 135053) ((-917 . -311) T) ((-917 . -1135) T) ((-917 . -833) T) ((-917 . -496) T) ((-917 . -655) 134998) ((-917 . -583) 134943) ((-917 . -35) 134888) ((-917 . -392) T) ((-917 . -257) T) ((-917 . -245) T) ((-917 . -200) T) ((-917 . -319) NIL) ((-917 . -298) NIL) ((-917 . -1067) NIL) ((-917 . -115) 134860) ((-917 . -344) NIL) 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. -200) 132886) ((-910 . -189) 132865) ((-910 . -185) 132813) ((-910 . -188) 132767) ((-910 . -224) 132751) ((-910 . -807) 132675) ((-910 . -812) 132601) ((-910 . -810) 132560) ((-910 . -183) 132544) ((-910 . -554) 132505) ((-910 . -117) 132484) ((-910 . -115) 132463) ((-910 . -101) T) ((-910 . -22) T) ((-910 . -69) T) ((-910 . -12) T) ((-910 . -1130) T) ((-910 . -553) 132445) ((-910 . -1014) T) ((-910 . -20) T) ((-910 . -18) T) ((-910 . -962) T) ((-910 . -664) T) ((-910 . -1062) T) ((-910 . -1026) T) ((-910 . -971) T) ((-908 . -996) T) ((-908 . -430) 132426) ((-908 . -553) 132392) ((-908 . -556) 132373) ((-908 . -1014) T) ((-908 . -1130) T) ((-908 . -12) T) ((-908 . -69) T) ((-908 . -61) T) ((-907 . -18) T) ((-907 . -589) 132355) ((-907 . -20) T) ((-907 . -1014) T) ((-907 . -553) 132337) ((-907 . -1130) T) ((-907 . -12) T) ((-907 . -69) T) ((-907 . -22) T) ((-907 . -101) T) ((-907 . -240) 132304) ((-903 . -553) 132286) ((-900 . -1014) T) ((-900 . -553) 132268) ((-900 . -1130) T) 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-556) 125182) ((-818 . -655) 125147) ((-818 . -583) 125112) ((-818 . -35) 125077) ((-818 . -392) T) ((-818 . -257) T) ((-818 . -79) 125026) ((-818 . -964) 124991) ((-818 . -969) 124956) ((-818 . -589) 124906) ((-818 . -591) 124871) ((-818 . -245) T) ((-818 . -200) T) ((-818 . -344) T) ((-818 . -188) T) ((-818 . -1130) T) ((-818 . -12) T) ((-818 . -185) 124858) ((-818 . -962) T) ((-818 . -664) T) ((-818 . -1062) T) ((-818 . -1026) T) ((-818 . -971) T) ((-818 . -18) T) ((-818 . -20) T) ((-818 . -1014) T) ((-818 . -553) 124840) ((-818 . -69) T) ((-818 . -22) T) ((-818 . -101) T) ((-818 . -189) T) ((-818 . -279) 124827) ((-818 . -117) 124809) ((-818 . -951) 124796) ((-818 . -1188) 124783) ((-818 . -1199) 124770) ((-818 . -554) 124752) ((-817 . -1014) T) ((-817 . -553) 124734) ((-817 . -1130) T) ((-817 . -12) T) ((-817 . -69) T) ((-814 . -816) 124718) ((-814 . -760) 124672) ((-814 . -757) 124626) ((-814 . -664) T) ((-814 . -1014) T) ((-814 . -553) 124608) ((-814 . -69) T) ((-814 . -1026) T) ((-814 . -413) T) ((-814 . -1130) T) ((-814 . -12) T) ((-814 . -240) 124587) ((-813 . -89) 124571) ((-813 . -429) 124555) ((-813 . -1014) 124533) ((-813 . -380) 124517) ((-813 . -456) 124450) ((-813 . -259) 124388) ((-813 . -553) 124302) ((-813 . -69) 124256) ((-813 . -1130) T) ((-813 . -12) T) ((-813 . -31) T) ((-813 . -924) 124240) ((-804 . -757) T) ((-804 . -553) 124222) ((-804 . -1014) T) ((-804 . -69) T) ((-804 . -12) T) ((-804 . -1130) T) ((-804 . -760) T) ((-804 . -951) 124199) ((-804 . -556) 124176) ((-801 . -1014) T) ((-801 . -553) 124158) ((-801 . -1130) T) ((-801 . -12) T) ((-801 . -69) T) ((-801 . -951) 124126) ((-801 . -556) 124094) ((-799 . -1014) T) ((-799 . -553) 124076) ((-799 . -1130) T) ((-799 . -12) T) ((-799 . -69) T) ((-796 . -1014) T) ((-796 . -553) 124058) ((-796 . -1130) T) ((-796 . -12) T) ((-796 . -69) T) ((-786 . -996) T) ((-786 . -430) 124039) ((-786 . -553) 124005) ((-786 . -556) 123986) ((-786 . -1014) T) ((-786 . -1130) T) ((-786 . -12) T) ((-786 . -69) T) ((-786 . -61) T) ((-786 . -1176) T) ((-784 . -1014) T) ((-784 . -553) 123968) ((-784 . -1130) T) ((-784 . -12) T) ((-784 . -69) T) ((-784 . -556) 123950) ((-783 . -1130) T) ((-783 . -12) T) ((-783 . -553) 123825) ((-783 . -1014) 123776) ((-783 . -69) 123727) ((-782 . -905) 123711) ((-782 . -1067) 123689) ((-782 . -951) 123556) ((-782 . -556) 123455) ((-782 . -554) 123258) ((-782 . -934) 123237) ((-782 . -822) 123216) ((-782 . -795) 123200) ((-782 . -756) 123179) ((-782 . -722) 123158) ((-782 . -719) 123137) ((-782 . -760) 123091) ((-782 . -757) 123045) ((-782 . -717) 123024) ((-782 . -715) 123003) ((-782 . -741) 122982) ((-782 . -797) 122907) ((-782 . -342) 122891) ((-782 . -581) 122839) ((-782 . -591) 122755) ((-782 . -328) 122739) ((-782 . -240) 122697) ((-782 . -259) 122662) ((-782 . -456) 122574) ((-782 . -380) 122558) ((-782 . -287) 122542) ((-782 . -200) T) ((-782 . -79) 122473) ((-782 . -964) 122425) ((-782 . -969) 122377) ((-782 . -245) T) ((-782 . -655) 122329) ((-782 . -583) 122281) ((-782 . -589) 122218) ((-782 . -35) 122170) ((-782 . -257) T) ((-782 . -392) T) ((-782 . -145) T) ((-782 . -496) T) ((-782 . -833) T) ((-782 . -1135) T) ((-782 . -311) T) ((-782 . -189) 122149) ((-782 . -185) 122097) ((-782 . -188) 122051) ((-782 . -224) 122035) ((-782 . -807) 121959) ((-782 . -812) 121885) ((-782 . -810) 121844) ((-782 . -183) 121828) ((-782 . -117) 121782) ((-782 . -115) 121761) ((-782 . -101) T) ((-782 . -22) T) ((-782 . -69) T) ((-782 . -12) T) ((-782 . -1130) T) ((-782 . -553) 121743) ((-782 . -1014) T) ((-782 . -20) T) ((-782 . -18) T) ((-782 . -962) T) ((-782 . -664) T) ((-782 . -1062) T) ((-782 . -1026) T) ((-782 . -971) T) ((-781 . -905) 121720) ((-781 . -1067) NIL) ((-781 . -951) 121697) ((-781 . -556) 121627) ((-781 . -554) NIL) ((-781 . -934) NIL) ((-781 . -822) NIL) ((-781 . -795) 121604) ((-781 . -756) NIL) ((-781 . -722) NIL) ((-781 . -719) NIL) ((-781 . -760) NIL) ((-781 . -757) NIL) ((-781 . -717) NIL) ((-781 . -715) NIL) ((-781 . -741) NIL) ((-781 . -797) NIL) ((-781 . -342) 121581) ((-781 . -581) 121558) ((-781 . -591) 121503) ((-781 . -328) 121480) ((-781 . -240) 121410) ((-781 . -259) 121354) ((-781 . -456) 121217) ((-781 . -380) 121194) ((-781 . -287) 121171) ((-781 . -200) T) ((-781 . -79) 121088) ((-781 . -964) 121033) ((-781 . -969) 120978) ((-781 . -245) T) ((-781 . -655) 120923) ((-781 . -583) 120868) ((-781 . -589) 120798) ((-781 . -35) 120743) ((-781 . -257) T) ((-781 . -392) T) ((-781 . -145) T) ((-781 . -496) T) ((-781 . -833) T) ((-781 . -1135) T) ((-781 . -311) T) ((-781 . -189) NIL) ((-781 . -185) NIL) ((-781 . -188) NIL) ((-781 . -224) 120720) ((-781 . -807) NIL) ((-781 . -812) NIL) ((-781 . -810) NIL) ((-781 . -183) 120697) ((-781 . -117) T) ((-781 . -115) NIL) ((-781 . -101) T) ((-781 . -22) T) ((-781 . -69) T) ((-781 . -12) T) ((-781 . -1130) T) ((-781 . -553) 120679) ((-781 . -1014) T) ((-781 . -20) T) ((-781 . -18) T) ((-781 . -962) T) ((-781 . -664) T) ((-781 . -1062) T) ((-781 . -1026) T) ((-781 . -971) T) ((-779 . -780) 120663) ((-779 . -833) T) ((-779 . -496) T) ((-779 . -245) T) ((-779 . -145) T) ((-779 . -556) 120635) ((-779 . -655) 120622) ((-779 . -583) 120609) ((-779 . -969) 120596) ((-779 . -964) 120583) ((-779 . -79) 120568) ((-779 . -35) 120555) ((-779 . -392) T) ((-779 . -257) T) ((-779 . -962) T) ((-779 . -664) T) ((-779 . -1062) T) ((-779 . -1026) T) ((-779 . -971) T) ((-779 . -18) T) ((-779 . -589) 120527) ((-779 . -20) T) ((-779 . -1014) T) ((-779 . -553) 120509) ((-779 . -1130) T) ((-779 . -12) T) ((-779 . -69) T) ((-779 . -22) T) ((-779 . -101) T) ((-779 . -591) 120496) ((-779 . -117) T) ((-776 . -962) T) ((-776 . -664) T) ((-776 . -1062) T) ((-776 . -1026) T) ((-776 . -971) T) ((-776 . -18) T) ((-776 . -589) 120441) ((-776 . -20) T) ((-776 . -1014) T) ((-776 . -553) 120403) ((-776 . -1130) T) ((-776 . -12) T) ((-776 . -69) T) ((-776 . -22) T) ((-776 . -101) T) ((-776 . -591) 120363) ((-776 . -556) 120298) ((-776 . -430) 120275) ((-776 . -35) 120245) ((-776 . -79) 120210) ((-776 . -964) 120180) ((-776 . -969) 120150) ((-776 . -583) 120120) ((-776 . -655) 120090) ((-775 . -1014) T) ((-775 . -553) 120072) ((-775 . -1130) T) ((-775 . -12) T) ((-775 . -69) T) ((-774 . -753) T) ((-774 . -760) T) ((-774 . -757) T) ((-774 . -1014) T) ((-774 . -553) 120054) ((-774 . -1130) T) ((-774 . -12) T) ((-774 . -69) T) ((-774 . -319) T) ((-774 . -554) 119976) ((-773 . -1014) T) ((-773 . -553) 119958) ((-773 . -1130) T) ((-773 . -12) T) ((-773 . -69) T) ((-772 . -771) T) ((-772 . -146) T) ((-772 . -553) 119940) ((-768 . -757) T) ((-768 . -553) 119922) ((-768 . -1014) T) ((-768 . -69) T) ((-768 . -12) T) ((-768 . -1130) T) ((-768 . -760) T) ((-765 . -762) 119906) ((-765 . -951) 119804) ((-765 . -556) 119702) ((-765 . -354) 119686) ((-765 . -655) 119656) ((-765 . -583) 119626) ((-765 . -591) 119600) ((-765 . -589) 119559) ((-765 . -101) T) ((-765 . -22) T) ((-765 . -69) T) ((-765 . -12) T) ((-765 . -1130) T) ((-765 . -553) 119541) ((-765 . -1014) T) ((-765 . -20) T) ((-765 . -18) T) ((-765 . -969) 119525) ((-765 . -964) 119509) ((-765 . -79) 119488) ((-765 . -962) T) ((-765 . -664) T) ((-765 . -1062) T) ((-765 . -1026) T) ((-765 . -971) T) ((-765 . -35) 119458) ((-764 . -762) 119442) ((-764 . -951) 119340) ((-764 . -556) 119259) ((-764 . -354) 119243) ((-764 . -655) 119213) ((-764 . -583) 119183) ((-764 . -591) 119157) ((-764 . -589) 119116) ((-764 . -101) T) ((-764 . -22) T) ((-764 . -69) T) ((-764 . -12) T) ((-764 . -1130) T) ((-764 . -553) 119098) ((-764 . -1014) T) ((-764 . -20) T) ((-764 . -18) T) ((-764 . -969) 119082) ((-764 . -964) 119066) ((-764 . -79) 119045) ((-764 . -962) T) ((-764 . -664) T) ((-764 . -1062) T) ((-764 . -1026) T) ((-764 . -971) T) ((-764 . -35) 119015) ((-758 . -760) T) ((-758 . -1130) T) ((-758 . -12) T) ((-758 . -69) T) ((-758 . -430) 118999) ((-758 . -553) 118947) ((-758 . -556) 118931) ((-751 . -1014) T) ((-751 . -553) 118913) ((-751 . -1130) T) ((-751 . -12) T) ((-751 . -69) T) ((-751 . -354) 118897) ((-751 . -556) 118770) ((-751 . -951) 118668) ((-751 . -18) 118623) ((-751 . -589) 118543) ((-751 . -20) 118498) ((-751 . -22) 118453) ((-751 . -101) 118408) ((-751 . -756) 118387) ((-751 . -722) 118366) ((-751 . -719) 118345) ((-751 . -760) 118324) ((-751 . -757) 118303) ((-751 . -717) 118282) ((-751 . -715) 118261) ((-751 . -962) 118240) ((-751 . -664) 118219) ((-751 . -1062) 118198) ((-751 . -1026) 118177) ((-751 . -971) 118156) ((-751 . -591) 118129) ((-751 . -117) 118108) ((-750 . -748) 118090) ((-750 . -69) T) ((-750 . -12) T) ((-750 . -1130) T) ((-750 . -553) 118072) ((-750 . -1014) T) ((-746 . -962) T) ((-746 . -664) T) ((-746 . -1062) T) ((-746 . -1026) T) ((-746 . -971) T) ((-746 . -18) T) ((-746 . -589) 118017) ((-746 . -20) T) ((-746 . -1014) T) ((-746 . -553) 117999) ((-746 . -1130) T) ((-746 . -12) T) ((-746 . -69) T) ((-746 . -22) T) ((-746 . -101) T) ((-746 . -591) 117959) ((-746 . -556) 117914) ((-746 . -951) 117884) ((-746 . -240) 117863) ((-746 . -117) 117842) ((-746 . -115) 117821) ((-746 . -35) 117791) ((-746 . -79) 117756) ((-746 . -964) 117726) ((-746 . -969) 117696) ((-746 . -583) 117666) ((-746 . -655) 117636) ((-744 . -1014) T) ((-744 . -553) 117618) ((-744 . -1130) T) ((-744 . -12) T) ((-744 . -69) T) ((-744 . -354) 117602) ((-744 . -556) 117475) ((-744 . -951) 117373) ((-744 . -18) 117328) ((-744 . -589) 117248) ((-744 . -20) 117203) ((-744 . -22) 117158) ((-744 . -101) 117113) ((-744 . -756) 117092) ((-744 . -722) 117071) ((-744 . -719) 117050) ((-744 . -760) 117029) ((-744 . -757) 117008) ((-744 . -717) 116987) ((-744 . -715) 116966) ((-744 . -962) 116945) ((-744 . -664) 116924) ((-744 . -1062) 116903) ((-744 . -1026) 116882) ((-744 . -971) 116861) ((-744 . -591) 116834) ((-744 . -117) 116813) ((-742 . -646) 116797) ((-742 . -556) 116752) ((-742 . -655) 116722) ((-742 . -583) 116692) ((-742 . -591) 116666) ((-742 . -589) 116625) ((-742 . -101) T) ((-742 . -22) T) ((-742 . -69) T) ((-742 . -12) T) ((-742 . -1130) T) ((-742 . -553) 116607) ((-742 . -1014) T) ((-742 . -20) T) ((-742 . -18) T) ((-742 . -969) 116591) ((-742 . -964) 116575) ((-742 . -79) 116554) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1062) T) ((-742 . -1026) T) ((-742 . -971) T) ((-742 . -35) 116524) ((-742 . -189) 116503) ((-742 . -185) 116476) ((-742 . -188) 116455) ((-740 . -335) 116439) ((-740 . -556) 116423) ((-740 . -951) 116407) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1026) T) ((-740 . -69) T) ((-740 . -12) T) ((-740 . -1130) T) ((-740 . -553) 116389) ((-740 . -1014) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -227) 116373) ((-739 . -556) 116357) ((-739 . -951) 116341) ((-739 . -760) T) ((-739 . -69) T) ((-739 . -1014) T) ((-739 . -553) 116323) ((-739 . -757) T) ((-739 . -185) 116310) ((-739 . -12) T) ((-739 . -1130) T) ((-739 . -188) T) ((-738 . -79) 116245) ((-738 . -964) 116196) ((-738 . -969) 116147) ((-738 . -18) T) ((-738 . -589) 116083) ((-738 . -20) T) ((-738 . -1014) T) ((-738 . -553) 116052) ((-738 . -1130) T) ((-738 . -12) T) ((-738 . -69) T) ((-738 . -22) T) ((-738 . -101) T) ((-738 . -591) 116003) ((-738 . -189) T) ((-738 . -556) 115912) ((-738 . -971) T) ((-738 . -1026) T) ((-738 . -1062) T) ((-738 . -664) T) ((-738 . -962) T) ((-738 . -185) 115899) ((-738 . -188) T) ((-738 . -430) 115883) ((-738 . -311) 115862) ((-738 . -1135) 115841) ((-738 . -833) 115820) ((-738 . -496) 115799) ((-738 . -145) 115778) ((-738 . -655) 115715) ((-738 . -583) 115652) ((-738 . -35) 115589) ((-738 . -392) 115568) ((-738 . -257) 115547) ((-738 . -245) 115526) ((-738 . -200) 115505) ((-737 . -212) 115444) ((-737 . -556) 115188) ((-737 . -951) 115018) ((-737 . -554) NIL) ((-737 . -276) 114980) ((-737 . -354) 114964) ((-737 . -35) 114816) ((-737 . -79) 114641) ((-737 . -964) 114487) ((-737 . -969) 114333) ((-737 . -589) 114243) ((-737 . -591) 114132) ((-737 . -583) 113984) ((-737 . -655) 113836) ((-737 . -115) 113815) ((-737 . -117) 113794) ((-737 . -145) 113708) ((-737 . -380) 113692) ((-737 . -496) 113626) ((-737 . -245) 113560) ((-737 . -44) 113522) ((-737 . -328) 113506) ((-737 . -581) 113454) ((-737 . -392) 113408) ((-737 . -456) 113273) ((-737 . -810) 113209) ((-737 . -807) 113108) ((-737 . -812) 113011) ((-737 . -797) NIL) ((-737 . -822) 112990) ((-737 . -1135) 112969) ((-737 . -862) 112916) ((-737 . -259) 112903) ((-737 . -189) 112882) ((-737 . -101) T) ((-737 . -22) T) ((-737 . -69) T) ((-737 . -553) 112864) ((-737 . -1014) T) ((-737 . -20) T) ((-737 . -18) T) ((-737 . -971) T) ((-737 . -1026) T) ((-737 . -1062) T) ((-737 . -664) T) ((-737 . -962) T) ((-737 . -185) 112812) ((-737 . -12) T) ((-737 . -1130) T) ((-737 . -188) 112766) ((-737 . -224) 112750) ((-737 . -183) 112734) ((-736 . -195) 112713) ((-736 . -1188) 112683) ((-736 . -722) 112662) ((-736 . -719) 112641) ((-736 . -760) 112595) ((-736 . -757) 112549) ((-736 . -717) 112528) ((-736 . -718) 112507) ((-736 . -655) 112452) ((-736 . -583) 112377) ((-736 . -242) 112354) ((-736 . -240) 112331) ((-736 . -539) 112308) ((-736 . -951) 112137) ((-736 . -556) 111941) ((-736 . -354) 111910) ((-736 . -581) 111818) ((-736 . -591) 111657) ((-736 . -328) 111627) ((-736 . -429) 111611) ((-736 . -380) 111595) ((-736 . -456) 111528) ((-736 . -259) 111466) ((-736 . -31) T) ((-736 . -317) 111450) ((-736 . -319) 111429) ((-736 . -189) 111382) ((-736 . -589) 111170) ((-736 . -971) 111149) ((-736 . -1026) 111128) ((-736 . -1062) 111107) ((-736 . -664) 111086) ((-736 . -962) 111065) ((-736 . -185) 110961) ((-736 . -188) 110863) ((-736 . -224) 110833) ((-736 . -807) 110705) ((-736 . -812) 110579) ((-736 . -810) 110512) ((-736 . -183) 110482) ((-736 . -553) 110179) ((-736 . -969) 110104) ((-736 . -964) 110009) ((-736 . -79) 109929) ((-736 . -101) 109804) ((-736 . -22) 109641) ((-736 . -69) 109378) ((-736 . -12) T) ((-736 . -1130) T) ((-736 . -1014) 109134) ((-736 . -20) 108990) ((-736 . -18) 108905) ((-723 . -721) 108889) ((-723 . -760) 108868) ((-723 . -757) 108847) ((-723 . -951) 108640) ((-723 . -556) 108493) ((-723 . -354) 108457) ((-723 . -240) 108415) ((-723 . -259) 108380) ((-723 . -456) 108292) ((-723 . -380) 108276) ((-723 . -287) 108260) ((-723 . -319) 108239) ((-723 . -554) 108200) ((-723 . -117) 108179) ((-723 . -115) 108158) ((-723 . -655) 108142) ((-723 . -583) 108126) ((-723 . -591) 108100) ((-723 . -589) 108059) ((-723 . -101) T) ((-723 . -22) T) ((-723 . -69) T) ((-723 . -12) T) ((-723 . -1130) T) ((-723 . -553) 108041) ((-723 . -1014) T) ((-723 . -20) T) ((-723 . -18) T) ((-723 . -969) 108025) ((-723 . -964) 108009) ((-723 . -79) 107988) ((-723 . -962) T) ((-723 . -664) T) ((-723 . -1062) T) ((-723 . -1026) T) ((-723 . -971) T) ((-723 . -35) 107972) ((-705 . -1156) 107956) ((-705 . -1067) 107934) ((-705 . -554) NIL) ((-705 . -259) 107921) ((-705 . -456) 107869) ((-705 . -276) 107846) ((-705 . -951) 107708) ((-705 . -354) 107692) ((-705 . -35) 107524) ((-705 . -79) 107329) ((-705 . -964) 107155) ((-705 . -969) 106981) ((-705 . -589) 106891) ((-705 . -591) 106780) ((-705 . -583) 106612) ((-705 . -655) 106444) ((-705 . -556) 106200) ((-705 . -115) 106179) ((-705 . -117) 106158) ((-705 . -380) 106142) ((-705 . -44) 106119) ((-705 . -328) 106103) ((-705 . -581) 106051) ((-705 . -810) 105995) ((-705 . -807) 105902) ((-705 . -812) 105813) ((-705 . -797) NIL) ((-705 . -822) 105792) ((-705 . -1135) 105771) ((-705 . -862) 105741) ((-705 . -833) 105720) ((-705 . -496) 105634) ((-705 . -245) 105548) ((-705 . -145) 105442) ((-705 . -392) 105376) ((-705 . -257) 105355) ((-705 . -240) 105282) ((-705 . -189) T) ((-705 . -101) T) ((-705 . -22) T) ((-705 . -69) T) ((-705 . -553) 105243) ((-705 . -1014) T) ((-705 . -20) T) ((-705 . -18) T) ((-705 . -971) T) ((-705 . -1026) T) ((-705 . -1062) T) ((-705 . -664) T) ((-705 . -962) T) ((-705 . -185) 105230) ((-705 . -12) T) ((-705 . -1130) T) ((-705 . -188) T) ((-705 . -224) 105214) ((-705 . -183) 105198) ((-704 . -978) 105165) ((-704 . -554) 104800) ((-704 . -259) 104787) ((-704 . -456) 104739) ((-704 . -276) 104711) ((-704 . -951) 104570) ((-704 . -354) 104554) ((-704 . -35) 104406) ((-704 . -556) 104179) ((-704 . -591) 104068) ((-704 . -589) 103978) ((-704 . -971) T) ((-704 . -1026) T) ((-704 . -1062) T) ((-704 . -664) T) ((-704 . -962) T) ((-704 . -79) 103803) ((-704 . -964) 103649) ((-704 . -969) 103495) ((-704 . -18) T) ((-704 . -20) T) ((-704 . -1014) T) ((-704 . -553) 103409) ((-704 . -1130) T) ((-704 . -12) T) ((-704 . -69) T) ((-704 . -22) T) ((-704 . -101) T) ((-704 . -583) 103261) ((-704 . -655) 103113) ((-704 . -115) 103092) ((-704 . -117) 103071) ((-704 . -145) 102985) ((-704 . -380) 102969) ((-704 . -496) 102903) ((-704 . -245) 102837) ((-704 . -44) 102809) ((-704 . -328) 102793) ((-704 . -581) 102741) ((-704 . -392) 102695) ((-704 . -810) 102679) ((-704 . -807) 102661) ((-704 . -812) 102645) ((-704 . -797) 102504) ((-704 . -822) 102483) ((-704 . -1135) 102462) ((-704 . -862) 102429) ((-697 . -1014) T) ((-697 . -553) 102411) ((-697 . -1130) T) ((-697 . -12) T) ((-697 . -69) T) 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T) ((-559 . -553) 86991) ((-559 . -1130) T) ((-559 . -12) T) ((-559 . -69) T) ((-559 . -22) T) ((-559 . -101) T) ((-559 . -583) 86975) ((-559 . -655) 86959) ((-559 . -756) 86938) ((-559 . -722) 86917) ((-559 . -719) 86896) ((-559 . -760) 86875) ((-559 . -757) 86854) ((-559 . -717) 86833) ((-559 . -715) 86812) ((-559 . -117) 86791) ((-557 . -881) T) ((-557 . -69) T) ((-557 . -553) 86773) ((-557 . -1014) T) ((-557 . -605) T) ((-557 . -12) T) ((-557 . -1130) T) ((-557 . -81) T) ((-557 . -319) T) ((-551 . -102) T) ((-551 . -69) T) ((-551 . -12) T) ((-551 . -1130) T) ((-551 . -553) 86755) ((-551 . -1014) T) ((-551 . -757) T) ((-551 . -760) T) ((-551 . -795) 86739) ((-551 . -554) 86600) ((-548 . -313) 86538) ((-548 . -69) T) ((-548 . -12) T) ((-548 . -1130) T) ((-548 . -553) 86520) ((-548 . -1014) T) ((-548 . -1108) 86496) ((-548 . -182) 86441) ((-548 . -73) 86386) ((-548 . -1036) 86318) ((-548 . -121) 86263) ((-548 . -554) NIL) ((-548 . -192) 86208) ((-548 . -539) 86184) ((-548 . -259) 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85118) ((-541 . -18) T) ((-541 . -589) 85087) ((-541 . -20) T) ((-541 . -1014) T) ((-541 . -553) 85056) ((-541 . -1130) T) ((-541 . -12) T) ((-541 . -69) T) ((-541 . -22) T) ((-541 . -101) T) ((-541 . -591) 85040) ((-541 . -583) 85024) ((-541 . -655) 85008) ((-541 . -360) 84973) ((-541 . -315) 84908) ((-541 . -240) 84866) ((-540 . -996) T) ((-540 . -430) 84847) ((-540 . -553) 84797) ((-540 . -556) 84778) ((-540 . -1014) T) ((-540 . -1130) T) ((-540 . -12) T) ((-540 . -69) T) ((-540 . -61) T) ((-537 . -380) 84762) ((-537 . -12) T) ((-537 . -1130) T) ((-537 . -553) 84744) ((-533 . -1014) T) ((-533 . -553) 84710) ((-533 . -1130) T) ((-533 . -12) T) ((-533 . -69) T) ((-533 . -430) 84691) ((-533 . -556) 84672) ((-532 . -962) T) ((-532 . -664) T) ((-532 . -1062) T) ((-532 . -1026) T) ((-532 . -971) T) ((-532 . -18) T) ((-532 . -589) 84631) ((-532 . -20) T) ((-532 . -1014) T) ((-532 . -553) 84613) ((-532 . -1130) T) ((-532 . -12) T) ((-532 . -69) T) ((-532 . -22) T) ((-532 . -101) T) ((-532 . 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. -101) T) ((-531 . -189) 82652) ((-529 . -996) T) ((-529 . -430) 82633) ((-529 . -553) 82599) ((-529 . -556) 82580) ((-529 . -1014) T) ((-529 . -1130) T) ((-529 . -12) T) ((-529 . -69) T) ((-529 . -61) T) ((-523 . -1014) T) ((-523 . -553) 82546) ((-523 . -1130) T) ((-523 . -12) T) ((-523 . -69) T) ((-523 . -430) 82527) ((-523 . -556) 82508) ((-520 . -655) 82483) ((-520 . -583) 82458) ((-520 . -591) 82433) ((-520 . -589) 82393) ((-520 . -101) T) ((-520 . -22) T) ((-520 . -69) T) ((-520 . -12) T) ((-520 . -1130) T) ((-520 . -553) 82375) ((-520 . -1014) T) ((-520 . -20) T) ((-520 . -18) T) ((-520 . -969) 82350) ((-520 . -964) 82325) ((-520 . -79) 82286) ((-520 . -951) 82270) ((-520 . -556) 82254) ((-518 . -298) T) ((-518 . -1067) T) ((-518 . -319) T) ((-518 . -115) T) ((-518 . -311) T) ((-518 . -1135) T) ((-518 . -833) T) ((-518 . -496) T) ((-518 . -145) T) ((-518 . -556) 82204) ((-518 . -655) 82169) ((-518 . -583) 82134) ((-518 . -35) 82099) ((-518 . -392) T) ((-518 . -257) T) ((-518 . 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-589) 81622) ((-517 . -20) T) ((-517 . -1014) T) ((-517 . -553) 81604) ((-517 . -1130) T) ((-517 . -12) T) ((-517 . -69) T) ((-517 . -22) T) ((-517 . -101) T) ((-517 . -591) 81591) ((-517 . -117) T) ((-516 . -1014) T) ((-516 . -553) 81573) ((-516 . -1130) T) ((-516 . -12) T) ((-516 . -69) T) ((-515 . -1014) T) ((-515 . -553) 81555) ((-515 . -1130) T) ((-515 . -12) T) ((-515 . -69) T) ((-514 . -513) T) ((-514 . -771) T) ((-514 . -146) T) ((-514 . -466) T) ((-514 . -553) 81537) ((-508 . -494) 81521) ((-508 . -32) T) ((-508 . -63) T) ((-508 . -238) T) ((-508 . -433) T) ((-508 . -1119) T) ((-508 . -1116) T) ((-508 . -951) 81503) ((-508 . -916) T) ((-508 . -760) T) ((-508 . -757) T) ((-508 . -496) T) ((-508 . -245) T) ((-508 . -145) T) ((-508 . -556) 81475) ((-508 . -655) 81462) ((-508 . -583) 81449) ((-508 . -591) 81436) ((-508 . -589) 81408) ((-508 . -101) T) ((-508 . -22) T) ((-508 . -69) T) ((-508 . -12) T) ((-508 . -1130) T) ((-508 . -553) 81390) ((-508 . -1014) T) ((-508 . -20) T) ((-508 . -18) T) ((-508 . -969) 81377) ((-508 . -964) 81364) ((-508 . -79) 81349) ((-508 . -962) T) ((-508 . -664) T) ((-508 . -1062) T) ((-508 . -1026) T) ((-508 . -971) T) ((-508 . -35) 81336) ((-508 . -392) T) ((-490 . -1108) 81315) ((-490 . -182) 81263) ((-490 . -73) 81211) ((-490 . -1036) 81146) ((-490 . -121) 81094) ((-490 . -554) NIL) ((-490 . -192) 81042) ((-490 . -539) 81021) ((-490 . -259) 80819) ((-490 . -456) 80571) ((-490 . -380) 80506) ((-490 . -429) 80441) ((-490 . -240) 80420) ((-490 . -242) 80399) ((-490 . -550) 80378) ((-490 . -1014) T) ((-490 . -553) 80360) ((-490 . -69) T) ((-490 . -1130) T) ((-490 . -12) T) ((-490 . -31) T) ((-490 . -317) 80308) ((-489 . -753) T) ((-489 . -760) T) ((-489 . -757) T) ((-489 . -1014) T) ((-489 . -553) 80290) ((-489 . -1130) T) ((-489 . -12) T) ((-489 . -69) T) ((-489 . -319) T) ((-488 . -753) T) ((-488 . -760) T) ((-488 . -757) T) ((-488 . -1014) T) ((-488 . -553) 80272) ((-488 . -1130) T) ((-488 . -12) T) ((-488 . -69) T) ((-488 . -319) T) ((-487 . -753) T) ((-487 . -760) T) ((-487 . -757) T) ((-487 . -1014) T) ((-487 . -553) 80254) ((-487 . -1130) T) ((-487 . -12) T) ((-487 . -69) T) ((-487 . -319) T) ((-486 . -753) T) ((-486 . -760) T) ((-486 . -757) T) ((-486 . -1014) T) ((-486 . -553) 80236) ((-486 . -1130) T) ((-486 . -12) T) ((-486 . -69) T) ((-486 . -319) T) ((-485 . -484) T) ((-485 . -1135) T) ((-485 . -1067) T) ((-485 . -951) 80218) ((-485 . -554) 80133) ((-485 . -934) T) ((-485 . -797) 80115) ((-485 . -756) T) ((-485 . -722) T) ((-485 . -719) T) ((-485 . -760) T) ((-485 . -757) T) ((-485 . -717) T) ((-485 . -715) T) ((-485 . -741) T) ((-485 . -591) 80087) ((-485 . -581) 80069) ((-485 . -833) T) ((-485 . -496) T) ((-485 . -245) T) ((-485 . -145) T) ((-485 . -556) 80041) ((-485 . -655) 80028) ((-485 . -583) 80015) ((-485 . -969) 80002) ((-485 . -964) 79989) ((-485 . -79) 79974) ((-485 . -35) 79961) ((-485 . -392) T) ((-485 . -257) T) ((-485 . -188) T) ((-485 . -185) 79948) ((-485 . -189) T) ((-485 . -113) T) ((-485 . -962) T) ((-485 . -664) T) ((-485 . -1062) T) ((-485 . -1026) T) ((-485 . -971) T) ((-485 . -18) T) ((-485 . -589) 79920) ((-485 . -20) T) ((-485 . -1014) T) ((-485 . -553) 79902) ((-485 . -1130) T) ((-485 . -12) T) ((-485 . -69) T) ((-485 . -22) T) ((-485 . -101) T) ((-485 . -117) T) ((-474 . -1017) 79854) ((-474 . -69) T) ((-474 . -553) 79836) ((-474 . -1014) T) ((-474 . -240) 79792) ((-474 . -1130) T) ((-474 . -12) T) ((-474 . -558) 79695) ((-474 . -554) 79676) ((-472 . -692) 79658) ((-472 . -466) T) ((-472 . -146) T) ((-472 . -771) T) ((-472 . -513) T) ((-472 . -553) 79640) ((-470 . -718) T) ((-470 . -101) T) ((-470 . -22) T) ((-470 . -69) T) ((-470 . -12) T) ((-470 . -1130) T) ((-470 . -553) 79622) ((-470 . -1014) T) ((-470 . -20) T) ((-470 . -717) T) ((-470 . -757) T) ((-470 . -760) T) ((-470 . -719) T) ((-470 . -722) T) ((-470 . -450) 79599) ((-470 . -380) 79581) ((-470 . -558) 79544) ((-468 . -466) T) ((-468 . -146) T) ((-468 . -553) 79526) ((-464 . -996) T) ((-464 . -430) 79507) ((-464 . -553) 79473) ((-464 . -556) 79454) ((-464 . -1014) T) ((-464 . -1130) T) ((-464 . -12) T) ((-464 . -69) T) ((-464 . -61) T) ((-463 . -996) T) ((-463 . -430) 79435) ((-463 . -553) 79401) ((-463 . -556) 79382) ((-463 . -1014) T) ((-463 . -1130) T) ((-463 . -12) T) ((-463 . -69) T) ((-463 . -61) T) ((-460 . -279) 79359) ((-460 . -189) T) ((-460 . -185) 79346) ((-460 . -188) T) ((-460 . -319) T) ((-460 . -1067) T) ((-460 . -298) T) ((-460 . -117) 79328) ((-460 . -556) 79258) ((-460 . -591) 79203) ((-460 . -589) 79133) ((-460 . -101) T) ((-460 . -22) T) ((-460 . -69) T) ((-460 . -12) T) ((-460 . -1130) T) ((-460 . -553) 79115) ((-460 . -1014) T) ((-460 . -20) T) ((-460 . -18) T) ((-460 . -971) T) ((-460 . -1026) T) ((-460 . -1062) T) ((-460 . -664) T) ((-460 . -962) T) ((-460 . -311) T) ((-460 . -1135) T) ((-460 . -833) T) ((-460 . -496) T) ((-460 . -145) T) ((-460 . -655) 79060) ((-460 . -583) 79005) ((-460 . -35) 78970) ((-460 . -392) T) ((-460 . -257) T) ((-460 . -79) 78887) ((-460 . -964) 78832) ((-460 . -969) 78777) ((-460 . -245) T) ((-460 . -200) T) ((-460 . -344) T) ((-460 . -115) T) ((-460 . -951) 78754) ((-460 . -1188) 78731) ((-460 . -1199) 78708) ((-459 . -996) T) ((-459 . -430) 78689) ((-459 . -553) 78655) ((-459 . -556) 78636) ((-459 . -1014) T) ((-459 . -1130) T) ((-459 . -12) T) ((-459 . -69) T) ((-459 . -61) T) ((-458 . -16) 78620) ((-458 . -1036) 78604) ((-458 . -317) 78588) ((-458 . -31) T) ((-458 . -12) T) ((-458 . -1130) T) ((-458 . -69) 78522) ((-458 . -553) 78437) ((-458 . -259) 78375) ((-458 . -456) 78308) ((-458 . -380) 78292) ((-458 . -1014) 78245) ((-458 . -429) 78229) ((-458 . -594) 78213) ((-458 . -242) 78190) ((-458 . -240) 78142) ((-458 . -539) 78119) ((-458 . -554) 78080) ((-458 . -121) 78064) ((-458 . -757) 78043) ((-458 . -760) 78022) ((-458 . -323) 78006) ((-458 . -236) 77990) ((-457 . -273) 77969) ((-457 . -556) 77953) ((-457 . -951) 77937) ((-457 . -20) T) ((-457 . -1014) T) ((-457 . -553) 77919) ((-457 . -1130) T) ((-457 . -12) T) ((-457 . -69) T) ((-457 . -22) T) ((-457 . -101) T) ((-454 . -69) T) ((-454 . -12) T) ((-454 . -1130) T) ((-454 . -553) 77891) ((-453 . -718) T) ((-453 . -101) T) ((-453 . -22) T) ((-453 . -69) T) ((-453 . -12) T) ((-453 . -1130) T) ((-453 . -553) 77873) ((-453 . -1014) T) ((-453 . -20) T) ((-453 . -717) T) ((-453 . -757) T) ((-453 . -760) T) ((-453 . -719) T) ((-453 . -722) T) ((-453 . -450) 77852) ((-453 . -380) 77836) ((-453 . -558) 77801) ((-452 . -717) T) ((-452 . -757) T) ((-452 . -760) T) ((-452 . -719) T) ((-452 . -22) T) ((-452 . -69) T) ((-452 . -12) T) ((-452 . -1130) T) ((-452 . -553) 77783) ((-452 . -1014) T) ((-452 . -20) T) ((-452 . -450) 77762) ((-452 . -380) 77746) ((-452 . -558) 77711) ((-451 . -450) 77690) ((-451 . -553) 77630) ((-451 . -1014) 77581) ((-451 . -380) 77565) ((-451 . -558) 77530) ((-451 . -1130) T) ((-451 . -12) T) ((-451 . -69) T) ((-449 . -20) T) ((-449 . -1014) T) ((-449 . -553) 77512) ((-449 . -1130) T) ((-449 . -12) T) ((-449 . -69) T) ((-449 . -22) T) ((-449 . -450) 77491) ((-449 . -380) 77475) ((-449 . -558) 77440) ((-448 . -18) T) ((-448 . -589) 77422) ((-448 . -20) T) ((-448 . -1014) T) ((-448 . -553) 77404) ((-448 . -1130) T) ((-448 . -12) T) ((-448 . -69) T) ((-448 . -22) T) ((-448 . -101) T) ((-448 . -450) 77383) ((-448 . -380) 77367) ((-448 . -558) 77332) ((-447 . -1014) T) ((-447 . -553) 77314) ((-447 . -1130) T) ((-447 . -12) T) ((-447 . -69) T) ((-444 . -1014) T) ((-444 . -553) 77296) ((-444 . -1130) T) ((-444 . -12) T) ((-444 . -69) T) ((-442 . -757) T) ((-442 . -553) 77278) ((-442 . -1014) T) ((-442 . -69) T) ((-442 . -12) T) ((-442 . -1130) T) ((-442 . -760) T) ((-442 . -556) 77259) ((-440 . -93) T) ((-440 . -323) 77242) ((-440 . -760) T) ((-440 . -757) T) ((-440 . -121) 77225) ((-440 . -554) 77207) ((-440 . -240) 77158) ((-440 . -539) 77134) ((-440 . -242) 77110) ((-440 . -594) 77093) ((-440 . -429) 77076) ((-440 . -1014) T) ((-440 . -380) 77059) ((-440 . -456) NIL) ((-440 . -259) NIL) ((-440 . -553) 77041) ((-440 . -69) T) ((-440 . -31) T) ((-440 . -317) 77024) ((-440 . -1036) 77007) ((-440 . -16) 76990) ((-440 . -605) T) ((-440 . -12) T) ((-440 . -1130) T) ((-440 . -81) T) ((-437 . -54) 76964) ((-437 . -1036) 76948) ((-437 . -429) 76932) ((-437 . -1014) 76910) ((-437 . -380) 76894) ((-437 . -456) 76827) ((-437 . -259) 76765) ((-437 . -553) 76700) ((-437 . -69) 76654) ((-437 . -1130) T) ((-437 . -12) T) ((-437 . -31) T) ((-437 . -317) 76638) ((-436 . -16) 76622) ((-436 . -1036) 76606) ((-436 . -317) 76590) ((-436 . -31) T) ((-436 . -12) T) ((-436 . -1130) T) ((-436 . -69) 76524) ((-436 . -553) 76439) ((-436 . -259) 76377) ((-436 . -456) 76310) ((-436 . -380) 76294) ((-436 . -1014) 76247) ((-436 . -429) 76231) ((-436 . -594) 76215) ((-436 . -242) 76192) ((-436 . -240) 76144) ((-436 . -539) 76121) ((-436 . -554) 76082) ((-436 . -121) 76066) ((-436 . -757) 76045) ((-436 . -760) 76024) ((-436 . -323) 76008) ((-435 . -253) T) ((-435 . -69) T) ((-435 . -12) T) ((-435 . -1130) T) ((-435 . -553) 75990) ((-435 . -1014) T) ((-435 . -556) 75891) ((-435 . -951) 75834) ((-435 . -456) 75800) ((-435 . -259) 75787) ((-435 . -24) T) ((-435 . -916) T) ((-435 . -200) T) ((-435 . -79) 75736) ((-435 . -964) 75701) ((-435 . -969) 75666) ((-435 . -245) T) ((-435 . -655) 75631) ((-435 . -583) 75596) ((-435 . -591) 75546) ((-435 . -589) 75496) ((-435 . -101) T) ((-435 . -22) T) ((-435 . -20) T) ((-435 . -18) T) ((-435 . -962) T) ((-435 . -664) T) ((-435 . -1062) T) ((-435 . -1026) T) ((-435 . -971) T) ((-435 . -35) 75461) ((-435 . -257) T) ((-435 . -392) T) ((-435 . -145) T) ((-435 . -496) T) ((-435 . -833) T) ((-435 . -1135) T) ((-435 . -311) T) ((-435 . -581) 75421) ((-435 . -934) T) ((-435 . -554) 75366) ((-435 . -117) T) ((-435 . -189) T) ((-435 . -185) 75353) ((-435 . -188) T) ((-431 . -1014) T) ((-431 . -553) 75319) ((-431 . -1130) T) ((-431 . -12) T) ((-431 . -69) T) ((-427 . -905) 75301) ((-427 . -1067) T) ((-427 . -556) 75251) ((-427 . -951) 75211) ((-427 . -554) 75141) ((-427 . -934) T) ((-427 . -822) NIL) ((-427 . -795) 75123) ((-427 . -756) T) ((-427 . -722) T) ((-427 . -719) T) ((-427 . -760) T) ((-427 . -757) T) ((-427 . -717) T) ((-427 . -715) T) ((-427 . -741) T) ((-427 . -797) 75105) ((-427 . -342) 75087) ((-427 . -581) 75069) ((-427 . -328) 75051) ((-427 . -240) NIL) ((-427 . -259) NIL) ((-427 . -456) NIL) ((-427 . -380) 75033) ((-427 . -287) 75015) ((-427 . -200) T) ((-427 . -79) 74942) ((-427 . -964) 74892) ((-427 . -969) 74842) ((-427 . -245) T) ((-427 . -655) 74792) ((-427 . -583) 74742) ((-427 . -591) 74692) ((-427 . -589) 74642) ((-427 . -35) 74592) ((-427 . -257) T) ((-427 . -392) T) ((-427 . -145) T) ((-427 . -496) T) ((-427 . -833) T) ((-427 . -1135) T) ((-427 . -311) T) ((-427 . -189) T) ((-427 . -185) 74579) ((-427 . -188) T) ((-427 . -224) 74561) ((-427 . -807) NIL) ((-427 . -812) NIL) ((-427 . -810) NIL) ((-427 . -183) 74543) ((-427 . -117) T) ((-427 . -115) NIL) ((-427 . -101) T) ((-427 . -22) T) ((-427 . -69) T) ((-427 . -12) T) ((-427 . -1130) T) ((-427 . -553) 74485) ((-427 . -1014) T) ((-427 . -20) T) ((-427 . -18) T) ((-427 . -962) T) ((-427 . -664) T) ((-427 . -1062) T) ((-427 . -1026) T) ((-427 . -971) T) ((-425 . -285) 74454) ((-425 . -101) T) ((-425 . -22) T) ((-425 . -69) T) ((-425 . -12) T) ((-425 . -1130) T) ((-425 . -553) 74436) ((-425 . -1014) T) ((-425 . -20) T) ((-425 . -589) 74418) ((-425 . -18) T) ((-424 . -882) 74402) ((-424 . -317) 74386) ((-424 . -429) 74370) ((-424 . -1014) 74348) ((-424 . -380) 74332) ((-424 . -456) 74265) ((-424 . -259) 74203) ((-424 . -553) 74138) ((-424 . -69) 74092) ((-424 . -1130) T) ((-424 . -12) T) ((-424 . -31) T) ((-424 . -1036) 74076) ((-424 . -73) 74060) ((-423 . -996) T) ((-423 . -430) 74041) ((-423 . -553) 74007) ((-423 . -556) 73988) ((-423 . -1014) T) ((-423 . -1130) T) ((-423 . -12) T) ((-423 . -69) T) ((-423 . -61) T) ((-422 . -195) 73967) ((-422 . -1188) 73937) ((-422 . -722) 73916) ((-422 . -719) 73895) ((-422 . -760) 73849) ((-422 . -757) 73803) ((-422 . -717) 73782) ((-422 . -718) 73761) ((-422 . -655) 73706) ((-422 . -583) 73631) ((-422 . -242) 73608) ((-422 . -240) 73585) ((-422 . -539) 73562) ((-422 . -951) 73391) ((-422 . -556) 73195) ((-422 . -354) 73164) ((-422 . -581) 73072) ((-422 . -591) 72911) ((-422 . -328) 72881) ((-422 . -429) 72865) ((-422 . -380) 72849) ((-422 . -456) 72782) ((-422 . -259) 72720) ((-422 . -31) T) ((-422 . -317) 72704) ((-422 . -319) 72683) ((-422 . -189) 72636) ((-422 . -589) 72424) ((-422 . -971) 72403) ((-422 . -1026) 72382) ((-422 . -1062) 72361) ((-422 . -664) 72340) ((-422 . -962) 72319) ((-422 . -185) 72215) ((-422 . -188) 72117) ((-422 . -224) 72087) ((-422 . -807) 71959) ((-422 . -812) 71833) ((-422 . -810) 71766) ((-422 . -183) 71736) ((-422 . -553) 71433) ((-422 . -969) 71358) ((-422 . -964) 71263) ((-422 . -79) 71183) ((-422 . -101) 71058) ((-422 . -22) 70895) ((-422 . -69) 70632) ((-422 . -12) T) ((-422 . -1130) T) ((-422 . -1014) 70388) ((-422 . -20) 70244) 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66383) ((-417 . -969) 66348) ((-417 . -18) T) ((-417 . -20) T) ((-417 . -1014) T) ((-417 . -553) 66300) ((-417 . -1130) T) ((-417 . -12) T) ((-417 . -69) T) ((-417 . -22) T) ((-417 . -101) T) ((-417 . -245) T) ((-417 . -200) T) ((-417 . -117) T) ((-417 . -951) 66260) ((-417 . -934) T) ((-417 . -554) 66182) ((-416 . -1125) 66151) ((-416 . -1036) 66135) ((-416 . -553) 66097) ((-416 . -121) 66081) ((-416 . -31) T) ((-416 . -12) T) ((-416 . -1130) T) ((-416 . -69) T) ((-416 . -259) 66019) ((-416 . -456) 65952) ((-416 . -380) 65936) ((-416 . -1014) T) ((-416 . -429) 65920) ((-416 . -554) 65881) ((-416 . -317) 65865) ((-416 . -890) 65834) ((-415 . -1108) 65813) ((-415 . -182) 65761) ((-415 . -73) 65709) ((-415 . -1036) 65644) ((-415 . -121) 65592) ((-415 . -554) NIL) ((-415 . -192) 65540) ((-415 . -539) 65519) ((-415 . -259) 65317) ((-415 . -456) 65069) ((-415 . -380) 65004) ((-415 . -429) 64939) ((-415 . -240) 64918) ((-415 . -242) 64897) ((-415 . -550) 64876) ((-415 . -1014) T) ((-415 . 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-664) T) ((-414 . -1062) T) ((-414 . -1026) T) ((-414 . -971) T) ((-414 . -257) 62452) ((-414 . -392) 62431) ((-414 . -145) 62365) ((-414 . -496) 62319) ((-414 . -833) 62298) ((-414 . -1135) 62277) ((-414 . -311) 62256) ((-408 . -1014) T) ((-408 . -553) 62238) ((-408 . -1130) T) ((-408 . -12) T) ((-408 . -69) T) ((-403 . -890) 62207) ((-403 . -317) 62191) ((-403 . -554) 62152) ((-403 . -429) 62136) ((-403 . -1014) T) ((-403 . -380) 62120) ((-403 . -456) 62053) ((-403 . -259) 61991) ((-403 . -553) 61953) ((-403 . -69) T) ((-403 . -1130) T) ((-403 . -12) T) ((-403 . -31) T) ((-403 . -121) 61937) ((-403 . -1036) 61921) ((-401 . -655) 61892) ((-401 . -583) 61863) ((-401 . -591) 61834) ((-401 . -589) 61790) ((-401 . -101) T) ((-401 . -22) T) ((-401 . -69) T) ((-401 . -12) T) ((-401 . -1130) T) ((-401 . -553) 61772) ((-401 . -1014) T) ((-401 . -20) T) ((-401 . -18) T) ((-401 . -969) 61743) ((-401 . -964) 61714) ((-401 . -79) 61675) ((-394 . -862) 61642) ((-394 . -556) 61434) ((-394 . -951) 61312) ((-394 . -1135) 61291) ((-394 . -822) 61270) ((-394 . -797) NIL) ((-394 . -812) 61247) ((-394 . -807) 61222) ((-394 . -810) 61199) ((-394 . -456) 61137) ((-394 . -392) 61091) ((-394 . -581) 61039) ((-394 . -591) 60928) ((-394 . -328) 60912) ((-394 . -44) 60891) ((-394 . -35) 60743) ((-394 . -583) 60595) ((-394 . -655) 60447) ((-394 . -245) 60381) ((-394 . -496) 60315) ((-394 . -380) 60299) ((-394 . -79) 60124) ((-394 . -964) 59970) ((-394 . -969) 59816) ((-394 . -145) 59730) ((-394 . -117) 59709) ((-394 . -115) 59688) ((-394 . -589) 59598) ((-394 . -101) T) ((-394 . -22) T) ((-394 . -69) T) ((-394 . -12) T) ((-394 . -1130) T) ((-394 . -553) 59580) ((-394 . -1014) T) ((-394 . -20) T) ((-394 . -18) T) ((-394 . -962) T) ((-394 . -664) T) ((-394 . -1062) T) ((-394 . -1026) T) ((-394 . -971) T) ((-394 . -354) 59564) ((-394 . -276) 59543) ((-394 . -259) 59530) ((-394 . -554) 59391) ((-393 . -360) 59361) ((-393 . -684) 59331) ((-393 . -658) T) ((-393 . -686) T) ((-393 . -79) 59282) 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((-371 . -69) T) ((-371 . -22) T) ((-371 . -101) T) ((-371 . -583) 58649) ((-371 . -655) 58633) ((-357 . -664) T) ((-357 . -1014) T) ((-357 . -553) 58615) ((-357 . -1130) T) ((-357 . -12) T) ((-357 . -69) T) ((-357 . -1026) T) ((-355 . -413) T) ((-355 . -1026) T) ((-355 . -69) T) ((-355 . -12) T) ((-355 . -1130) T) ((-355 . -553) 58597) ((-355 . -1014) T) ((-355 . -664) T) ((-349 . -905) 58581) ((-349 . -1067) 58559) ((-349 . -951) 58426) ((-349 . -556) 58325) ((-349 . -554) 58128) ((-349 . -934) 58107) ((-349 . -822) 58086) ((-349 . -795) 58070) ((-349 . -756) 58049) ((-349 . -722) 58028) ((-349 . -719) 58007) ((-349 . -760) 57961) ((-349 . -757) 57915) ((-349 . -717) 57894) ((-349 . -715) 57873) ((-349 . -741) 57852) ((-349 . -797) 57777) ((-349 . -342) 57761) ((-349 . -581) 57709) ((-349 . -591) 57625) ((-349 . -328) 57609) ((-349 . -240) 57567) ((-349 . -259) 57532) ((-349 . -456) 57444) ((-349 . -380) 57428) ((-349 . -287) 57412) ((-349 . -200) T) ((-349 . -79) 57343) ((-349 . -964) 57295) ((-349 . -969) 57247) ((-349 . -245) T) ((-349 . -655) 57199) ((-349 . -583) 57151) ((-349 . -589) 57088) ((-349 . -35) 57040) ((-349 . -257) T) ((-349 . -392) T) ((-349 . -145) T) ((-349 . -496) T) ((-349 . -833) T) ((-349 . -1135) T) ((-349 . -311) T) ((-349 . -189) 57019) ((-349 . -185) 56967) ((-349 . -188) 56921) ((-349 . -224) 56905) ((-349 . -807) 56829) ((-349 . -812) 56755) ((-349 . -810) 56714) ((-349 . -183) 56698) ((-349 . -117) 56652) ((-349 . -115) 56631) ((-349 . -101) T) ((-349 . -22) T) ((-349 . -69) T) ((-349 . -12) T) ((-349 . -1130) T) ((-349 . -553) 56613) ((-349 . -1014) T) ((-349 . -20) T) ((-349 . -18) T) ((-349 . -962) T) ((-349 . -664) T) ((-349 . -1062) T) ((-349 . -1026) T) ((-349 . -971) T) ((-347 . -496) T) ((-347 . -245) T) ((-347 . -145) T) ((-347 . -556) 56522) ((-347 . -655) 56496) ((-347 . -583) 56470) ((-347 . -591) 56444) ((-347 . -589) 56403) ((-347 . -101) T) ((-347 . -22) T) ((-347 . -69) T) ((-347 . -12) T) ((-347 . -1130) T) ((-347 . -553) 56385) ((-347 . -1014) T) ((-347 . -20) T) ((-347 . -18) T) ((-347 . -969) 56359) ((-347 . -964) 56333) ((-347 . -79) 56300) ((-347 . -962) T) ((-347 . -664) T) ((-347 . -1062) T) ((-347 . -1026) T) ((-347 . -971) T) ((-347 . -35) 56274) ((-347 . -183) 56258) ((-347 . -810) 56217) ((-347 . -812) 56143) ((-347 . -807) 56067) ((-347 . -224) 56051) ((-347 . -188) 56005) ((-347 . -185) 55953) ((-347 . -189) 55932) ((-347 . -287) 55916) ((-347 . -456) 55758) ((-347 . -380) 55742) ((-347 . -259) 55681) ((-347 . -240) 55609) ((-347 . -354) 55593) ((-347 . -951) 55491) ((-347 . -392) 55444) ((-347 . -934) 55423) ((-347 . -554) 55326) ((-347 . -1135) 55304) ((-341 . -1014) T) ((-341 . -553) 55286) ((-341 . -1130) T) ((-341 . -12) T) ((-341 . -69) T) ((-341 . -188) T) ((-341 . -185) 55273) ((-341 . -554) 55250) ((-339 . -684) 55234) ((-339 . -658) T) ((-339 . -686) T) ((-339 . -79) 55213) ((-339 . -964) 55197) ((-339 . -969) 55181) ((-339 . -18) T) ((-339 . -589) 55150) ((-339 . -20) T) ((-339 . -1014) T) ((-339 . -553) 55132) ((-339 . -1130) T) ((-339 . -12) T) ((-339 . -69) T) ((-339 . -22) T) ((-339 . -101) T) ((-339 . -591) 55116) ((-339 . -583) 55100) ((-339 . -655) 55084) ((-337 . -338) T) ((-337 . -69) T) ((-337 . -12) T) ((-337 . -1130) T) ((-337 . -553) 55050) ((-337 . -1014) T) ((-337 . -556) 55031) ((-337 . -430) 55012) ((-336 . -335) 54996) ((-336 . -556) 54980) ((-336 . -951) 54964) ((-336 . -760) 54943) ((-336 . -757) 54922) ((-336 . -1026) T) ((-336 . -69) T) ((-336 . -12) T) ((-336 . -1130) T) ((-336 . -553) 54904) ((-336 . -1014) T) ((-336 . -664) T) ((-333 . -334) 54883) ((-333 . -556) 54867) ((-333 . -951) 54851) ((-333 . -583) 54821) ((-333 . -655) 54791) ((-333 . -380) 54775) ((-333 . -591) 54759) ((-333 . -589) 54728) ((-333 . -101) T) ((-333 . -22) T) ((-333 . -69) T) ((-333 . -12) T) ((-333 . -1130) T) ((-333 . -553) 54710) ((-333 . -1014) T) ((-333 . -20) T) ((-333 . -18) T) ((-333 . -969) 54694) ((-333 . -964) 54678) ((-333 . -79) 54657) ((-332 . -79) 54636) ((-332 . -964) 54620) ((-332 . -969) 54604) ((-332 . -18) T) ((-332 . -589) 54573) ((-332 . -20) T) ((-332 . -1014) T) ((-332 . -553) 54555) ((-332 . -1130) T) ((-332 . -12) T) ((-332 . -69) T) ((-332 . -22) T) ((-332 . -101) T) ((-332 . -591) 54539) ((-332 . -450) 54518) ((-332 . -380) 54502) ((-332 . -558) 54467) ((-332 . -655) 54437) ((-332 . -583) 54407) ((-329 . -346) T) ((-329 . -117) T) ((-329 . -556) 54357) ((-329 . -591) 54322) ((-329 . -589) 54272) ((-329 . -101) T) ((-329 . -22) T) ((-329 . -69) T) ((-329 . -12) T) ((-329 . -1130) T) ((-329 . -553) 54239) ((-329 . -1014) T) ((-329 . -20) T) ((-329 . -18) T) ((-329 . -971) T) ((-329 . -1026) T) ((-329 . -1062) T) ((-329 . -664) T) ((-329 . -962) T) ((-329 . -554) 54153) ((-329 . -311) T) ((-329 . -1135) T) ((-329 . -833) T) ((-329 . -496) T) ((-329 . -145) T) ((-329 . -655) 54118) ((-329 . -583) 54083) ((-329 . -35) 54048) ((-329 . -392) T) ((-329 . -257) T) ((-329 . -79) 53997) ((-329 . -964) 53962) 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((-105 . -951) 10398) ((-105 . -1014) T) ((-105 . -553) 10380) ((-105 . -1130) T) ((-105 . -12) T) ((-105 . -69) T) ((-105 . -410) 10335) ((-105 . -240) 10312) ((-104 . -757) T) ((-104 . -553) 10294) ((-104 . -1014) T) ((-104 . -69) T) ((-104 . -12) T) ((-104 . -1130) T) ((-104 . -760) T) ((-104 . -20) T) ((-104 . -22) T) ((-104 . -664) T) ((-104 . -1026) T) ((-104 . -951) 10276) ((-104 . -556) 10258) ((-103 . -996) T) ((-103 . -430) 10239) ((-103 . -553) 10205) ((-103 . -556) 10186) ((-103 . -1014) T) ((-103 . -1130) T) ((-103 . -12) T) ((-103 . -69) T) ((-103 . -61) T) ((-100 . -1014) T) ((-100 . -553) 10168) ((-100 . -1130) T) ((-100 . -12) T) ((-100 . -69) T) ((-99 . -16) 10151) ((-99 . -1036) 10134) ((-99 . -317) 10117) ((-99 . -31) T) ((-99 . -12) T) ((-99 . -1130) T) ((-99 . -69) T) ((-99 . -553) 10062) ((-99 . -259) NIL) ((-99 . -456) NIL) ((-99 . -380) 10045) ((-99 . -1014) T) ((-99 . -429) 10028) ((-99 . -594) 10011) ((-99 . -242) 9987) ((-99 . -240) 9938) ((-99 . -539) 9914) ((-99 . -554) NIL) ((-99 . -121) 9897) ((-99 . -757) T) ((-99 . -760) T) ((-99 . -323) 9880) ((-98 . -753) T) ((-98 . -760) T) ((-98 . -757) T) ((-98 . -1014) T) ((-98 . -553) 9862) ((-98 . -1130) T) ((-98 . -12) T) ((-98 . -69) T) ((-98 . -319) T) ((-98 . -605) T) ((-97 . -95) 9846) ((-97 . -1036) 9830) ((-97 . -317) 9814) ((-97 . -924) 9798) ((-97 . -31) T) ((-97 . -12) T) ((-97 . -1130) T) ((-97 . -69) 9752) ((-97 . -553) 9687) ((-97 . -259) 9625) ((-97 . -456) 9558) ((-97 . -380) 9542) ((-97 . -1014) 9520) ((-97 . -429) 9504) ((-97 . -89) 9488) ((-96 . -95) 9472) ((-96 . -1036) 9456) ((-96 . -317) 9440) ((-96 . -924) 9424) ((-96 . -31) T) ((-96 . -12) T) ((-96 . -1130) T) ((-96 . -69) 9378) ((-96 . -553) 9313) ((-96 . -259) 9251) ((-96 . -456) 9184) ((-96 . -380) 9168) ((-96 . -1014) 9146) ((-96 . -429) 9130) ((-96 . -89) 9114) ((-91 . -95) 9098) ((-91 . -1036) 9082) ((-91 . -317) 9066) ((-91 . -924) 9050) ((-91 . -31) T) ((-91 . -12) T) ((-91 . -1130) T) ((-91 . -69) 9004) ((-91 . -553) 8939) ((-91 . -259) 8877) ((-91 . -456) 8810) ((-91 . -380) 8794) ((-91 . -1014) 8772) ((-91 . -429) 8756) ((-91 . -89) 8740) ((-87 . -905) 8718) ((-87 . -1067) NIL) ((-87 . -951) 8696) ((-87 . -556) 8627) ((-87 . -554) NIL) ((-87 . -934) NIL) ((-87 . -822) NIL) ((-87 . -795) 8605) ((-87 . -756) NIL) ((-87 . -722) NIL) ((-87 . -719) NIL) ((-87 . -760) NIL) ((-87 . -757) NIL) ((-87 . -717) NIL) ((-87 . -715) NIL) ((-87 . -741) NIL) ((-87 . -797) NIL) ((-87 . -342) 8583) ((-87 . -581) 8561) ((-87 . -591) 8507) ((-87 . -328) 8485) ((-87 . -240) 8419) ((-87 . -259) 8366) ((-87 . -456) 8236) ((-87 . -380) 8214) ((-87 . -287) 8192) ((-87 . -200) T) ((-87 . -79) 8111) ((-87 . -964) 8057) ((-87 . -969) 8003) ((-87 . -245) T) ((-87 . -655) 7949) ((-87 . -583) 7895) ((-87 . -589) 7826) ((-87 . -35) 7772) ((-87 . -257) T) ((-87 . -392) T) ((-87 . -145) T) ((-87 . -496) T) ((-87 . -833) T) ((-87 . -1135) T) ((-87 . -311) T) ((-87 . -189) NIL) ((-87 . -185) NIL) ((-87 . -188) NIL) ((-87 . -224) 7750) ((-87 . -807) NIL) ((-87 . -812) NIL) ((-87 . -810) NIL) ((-87 . -183) 7728) ((-87 . -117) T) ((-87 . -115) NIL) ((-87 . -101) T) ((-87 . -22) T) ((-87 . -69) T) ((-87 . -12) T) ((-87 . -1130) T) ((-87 . -553) 7710) ((-87 . -1014) T) ((-87 . -20) T) ((-87 . -18) T) ((-87 . -962) T) ((-87 . -664) T) ((-87 . -1062) T) ((-87 . -1026) T) ((-87 . -971) T) ((-86 . -780) 7694) ((-86 . -833) T) ((-86 . -496) T) ((-86 . -245) T) ((-86 . -145) T) ((-86 . -556) 7666) ((-86 . -655) 7653) ((-86 . -583) 7640) ((-86 . -969) 7627) ((-86 . -964) 7614) ((-86 . -79) 7599) ((-86 . -35) 7586) ((-86 . -392) T) ((-86 . -257) T) ((-86 . -962) T) ((-86 . -664) T) ((-86 . -1062) T) ((-86 . -1026) T) ((-86 . -971) T) ((-86 . -18) T) ((-86 . -589) 7558) ((-86 . -20) T) ((-86 . -1014) T) ((-86 . -553) 7540) ((-86 . -1130) T) ((-86 . -12) T) ((-86 . -69) T) ((-86 . -22) T) ((-86 . -101) T) ((-86 . -591) 7527) ((-86 . -117) T) ((-83 . -757) T) ((-83 . -553) 7509) ((-83 . -1014) T) ((-83 . -69) T) ((-83 . -12) T) ((-83 . -1130) T) ((-83 . -760) T) ((-83 . -748) 7490) ((-82 . -753) T) ((-82 . -760) T) ((-82 . -757) T) ((-82 . -1014) T) ((-82 . -553) 7472) ((-82 . -1130) T) ((-82 . -12) T) ((-82 . -69) T) ((-82 . -319) T) ((-82 . -881) T) ((-82 . -605) T) ((-82 . -81) T) ((-82 . -554) 7454) ((-78 . -93) T) ((-78 . -323) 7437) ((-78 . -760) T) ((-78 . -757) T) ((-78 . -121) 7420) ((-78 . -554) 7402) ((-78 . -240) 7353) ((-78 . -539) 7329) ((-78 . -242) 7305) ((-78 . -594) 7288) ((-78 . -429) 7271) ((-78 . -1014) T) ((-78 . -380) 7254) ((-78 . -456) NIL) ((-78 . -259) NIL) ((-78 . -553) 7236) ((-78 . -69) T) ((-78 . -31) T) ((-78 . -317) 7219) ((-78 . -1036) 7202) ((-78 . -16) 7185) ((-78 . -605) T) ((-78 . -12) T) ((-78 . -1130) T) ((-78 . -81) T) ((-76 . -77) 7169) ((-76 . -1130) T) ((-76 . |MappingCategory|) 7143) ((-76 . -1014) T) ((-76 . -553) 7125) ((-76 . -12) T) ((-76 . -69) T) ((-75 . -553) 7107) ((-74 . -905) 7089) ((-74 . -1067) T) ((-74 . -556) 7039) ((-74 . -951) 6999) ((-74 . -554) 6929) ((-74 . -934) T) ((-74 . -822) NIL) ((-74 . -795) 6911) ((-74 . -756) T) ((-74 . -722) T) ((-74 . -719) T) ((-74 . -760) T) ((-74 . -757) T) ((-74 . -717) T) ((-74 . -715) T) ((-74 . -741) T) ((-74 . -797) 6893) ((-74 . -342) 6875) ((-74 . -581) 6857) ((-74 . -328) 6839) ((-74 . -240) NIL) ((-74 . -259) NIL) ((-74 . -456) NIL) ((-74 . -380) 6821) ((-74 . -287) 6803) ((-74 . -200) T) ((-74 . -79) 6730) ((-74 . -964) 6680) ((-74 . -969) 6630) ((-74 . -245) T) ((-74 . -655) 6580) ((-74 . -583) 6530) ((-74 . -591) 6480) ((-74 . -589) 6430) ((-74 . -35) 6380) ((-74 . -257) T) ((-74 . -392) T) ((-74 . -145) T) ((-74 . -496) T) ((-74 . -833) T) ((-74 . -1135) T) ((-74 . -311) T) ((-74 . -189) T) ((-74 . -185) 6367) ((-74 . -188) T) ((-74 . -224) 6349) ((-74 . -807) NIL) ((-74 . -812) NIL) ((-74 . -810) NIL) ((-74 . -183) 6331) ((-74 . -117) T) ((-74 . -115) NIL) ((-74 . -101) T) ((-74 . -22) T) ((-74 . -69) T) ((-74 . -12) T) ((-74 . -1130) T) ((-74 . -553) 6274) ((-74 . -1014) T) ((-74 . -20) T) ((-74 . -18) T) ((-74 . -962) T) ((-74 . -664) T) ((-74 . -1062) T) ((-74 . -1026) T) ((-74 . -971) T) ((-70 . -95) 6258) ((-70 . -1036) 6242) ((-70 . -317) 6226) ((-70 . -924) 6210) ((-70 . -31) T) ((-70 . -12) T) ((-70 . -1130) T) ((-70 . -69) 6164) ((-70 . -553) 6099) ((-70 . -259) 6037) ((-70 . -456) 5970) ((-70 . -380) 5954) ((-70 . -1014) 5932) ((-70 . -429) 5916) ((-70 . -89) 5900) ((-66 . -413) T) ((-66 . -1026) T) ((-66 . -69) T) ((-66 . -12) T) ((-66 . -1130) T) ((-66 . -553) 5882) ((-66 . -1014) T) ((-66 . -664) T) ((-66 . -240) 5861) ((-64 . -996) T) ((-64 . -430) 5842) ((-64 . -553) 5808) ((-64 . -556) 5789) ((-64 . -1014) T) ((-64 . -1130) T) ((-64 . -12) T) ((-64 . -69) T) ((-64 . -61) T) ((-59 . -1035) 5773) ((-59 . -317) 5757) ((-59 . -429) 5741) ((-59 . -1014) 5719) ((-59 . -380) 5703) ((-59 . -456) 5636) ((-59 . -259) 5574) ((-59 . -553) 5509) ((-59 . -69) 5463) ((-59 . -1130) T) ((-59 . -12) T) ((-59 . -31) T) ((-59 . -1036) 5447) ((-59 . -73) 5431) ((-57 . -54) 5393) ((-57 . -1036) 5377) ((-57 . -429) 5361) ((-57 . -1014) 5339) ((-57 . -380) 5323) ((-57 . -456) 5256) ((-57 . -259) 5194) ((-57 . -553) 5129) ((-57 . -69) 5083) ((-57 . -1130) T) ((-57 . -12) T) ((-57 . -31) T) ((-57 . -317) 5067) ((-55 . -16) 5051) ((-55 . -1036) 5035) ((-55 . -317) 5019) ((-55 . -31) T) ((-55 . -12) T) ((-55 . -1130) T) ((-55 . -69) 4953) ((-55 . -553) 4868) ((-55 . -259) 4806) ((-55 . -456) 4739) ((-55 . -380) 4723) ((-55 . -1014) 4676) ((-55 . -429) 4660) ((-55 . -594) 4644) ((-55 . -242) 4621) ((-55 . -240) 4573) ((-55 . -539) 4550) ((-55 . -554) 4511) ((-55 . -121) 4495) ((-55 . -757) 4474) ((-55 . -760) 4453) ((-55 . -323) 4437) ((-52 . -1014) T) ((-52 . -553) 4419) ((-52 . -1130) T) ((-52 . -12) T) ((-52 . -69) T) ((-52 . -951) 4401) ((-52 . -556) 4383) ((-48 . -1014) T) ((-48 . -553) 4365) ((-48 . -1130) T) ((-48 . -12) T) ((-48 . -69) T) ((-47 . -561) 4349) ((-47 . -556) 4318) ((-47 . -591) 4292) ((-47 . -589) 4251) ((-47 . -971) T) ((-47 . -1026) T) ((-47 . -1062) T) ((-47 . -664) T) ((-47 . -962) T) ((-47 . -18) T) ((-47 . -20) T) ((-47 . -1014) T) ((-47 . -553) 4233) ((-47 . -1130) T) ((-47 . -12) T) ((-47 . -69) T) ((-47 . -22) T) ((-47 . -101) T) ((-47 . -951) 4217) ((-47 . -380) 4201) ((-46 . -1014) T) ((-46 . -553) 4183) ((-46 . -1130) T) ((-46 . -12) T) ((-46 . -69) T) ((-45 . -253) T) ((-45 . -69) T) ((-45 . -12) T) ((-45 . -1130) T) ((-45 . -553) 4165) ((-45 . -1014) T) ((-45 . -556) 4066) ((-45 . -951) 4009) ((-45 . -456) 3975) ((-45 . -259) 3962) ((-45 . -24) T) ((-45 . -916) T) ((-45 . -200) T) ((-45 . -79) 3911) ((-45 . -964) 3876) ((-45 . -969) 3841) ((-45 . -245) T) ((-45 . -655) 3806) ((-45 . -583) 3771) ((-45 . -591) 3721) ((-45 . -589) 3671) ((-45 . -101) T) ((-45 . -22) T) ((-45 . -20) T) ((-45 . -18) T) ((-45 . -962) T) ((-45 . -664) T) ((-45 . -1062) T) ((-45 . -1026) T) ((-45 . -971) T) ((-45 . -35) 3636) ((-45 . -257) T) ((-45 . -392) T) ((-45 . -145) T) ((-45 . -496) T) ((-45 . -833) T) ((-45 . -1135) T) ((-45 . -311) T) ((-45 . -581) 3596) ((-45 . -934) T) ((-45 . -554) 3541) ((-45 . -117) T) ((-45 . -189) T) ((-45 . -185) 3528) ((-45 . -188) T) ((-42 . -33) 3507) ((-42 . -550) 3486) ((-42 . -242) 3409) ((-42 . -240) 3307) ((-42 . -429) 3242) ((-42 . -380) 3177) ((-42 . -456) 2929) ((-42 . -259) 2727) ((-42 . -539) 2650) ((-42 . -192) 2598) ((-42 . -73) 2546) ((-42 . -182) 2494) ((-42 . -1108) 2473) ((-42 . -1036) 2408) ((-42 . -236) 2356) ((-42 . -121) 2304) ((-42 . -31) T) ((-42 . -12) T) ((-42 . -1130) T) ((-42 . -69) T) ((-42 . -553) 2286) ((-42 . -1014) T) ((-42 . -554) NIL) ((-42 . -594) 2234) ((-42 . -323) 2182) ((-42 . -760) NIL) ((-42 . -757) NIL) ((-42 . -317) 2130) ((-42 . -1065) 2078) ((-42 . -924) 2026) ((-42 . -1169) 1974) ((-42 . -609) 1922) ((-41 . -360) 1906) ((-41 . -684) 1890) ((-41 . -658) T) ((-41 . -686) T) ((-41 . -79) 1869) ((-41 . -964) 1853) ((-41 . -969) 1837) ((-41 . -18) T) ((-41 . -589) 1780) ((-41 . -20) T) ((-41 . -1014) T) ((-41 . -553) 1762) ((-41 . -69) T) ((-41 . -22) T) ((-41 . -101) T) ((-41 . -591) 1720) ((-41 . -583) 1704) ((-41 . -655) 1688) ((-41 . -315) 1672) ((-41 . -1130) T) ((-41 . -12) T) ((-41 . -240) 1649) ((-37 . -290) 1623) ((-37 . -145) T) ((-37 . -556) 1553) ((-37 . -971) T) ((-37 . -1026) T) ((-37 . -1062) T) ((-37 . -664) T) ((-37 . -962) T) ((-37 . -591) 1455) ((-37 . -589) 1385) ((-37 . -101) T) ((-37 . -22) T) ((-37 . -69) T) ((-37 . -12) T) ((-37 . -1130) T) ((-37 . -553) 1367) ((-37 . -1014) T) ((-37 . -20) T) ((-37 . -18) T) ((-37 . -969) 1312) ((-37 . -964) 1257) ((-37 . -79) 1174) ((-37 . -554) 1158) ((-37 . -183) 1135) ((-37 . -810) 1087) ((-37 . -812) 999) ((-37 . -807) 909) ((-37 . -224) 886) ((-37 . -188) 826) ((-37 . -185) 760) ((-37 . -189) 732) ((-37 . -311) T) ((-37 . -1135) T) ((-37 . -833) T) ((-37 . -496) T) ((-37 . -655) 677) ((-37 . -583) 622) ((-37 . -35) 567) ((-37 . -392) T) ((-37 . -257) T) ((-37 . -245) T) ((-37 . -200) T) ((-37 . -319) NIL) ((-37 . -298) NIL) ((-37 . -1067) NIL) ((-37 . -115) 539) ((-37 . -344) NIL) ((-37 . -352) 511) ((-37 . -117) 483) ((-37 . -321) 455) ((-37 . -328) 432) ((-37 . -581) 366) ((-37 . -354) 343) ((-37 . -951) 220) ((-37 . -662) 192) ((-28 . -996) T) ((-28 . -430) 173) ((-28 . -553) 139) ((-28 . -556) 120) ((-28 . -1014) T) ((-28 . -1130) T) ((-28 . -12) T) ((-28 . -69) T) ((-28 . -61) T) ((-27 . -867) T) ((-27 . -553) 102) ((0 . |EnumerationCategory|) T) ((0 . -553) 84) ((0 . -1014) T) ((0 . -69) T) ((0 . -1130) T) ((-2 . |RecordCategory|) T) ((-2 . -553) 66) ((-2 . -1014) T) ((-2 . -69) T) ((-2 . -1130) T) ((-3 . |UnionCategory|) T) ((-3 . -553) 48) ((-3 . -1014) T) ((-3 . -69) T) ((-3 . -1130) T) ((-1 . -1014) T) ((-1 . -553) 30) ((-1 . -1130) T) ((-1 . -12) T) ((-1 . -69) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 1d141e01..9505169d 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,11 +1,10 @@
 
-(30 . 3580478883)            
-(4004 |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|
+(30 . 3581069278)            
+(3998 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+ ATTRIBUTE |package| |domain| |category| CATEGORY AND |Join| |ofType| SIGNATURE
+ |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&|
+ |AbelianGroup| |AbelianMonoid&| |AbelianMonoid| |AbelianSemiGroup&|
+ |AbelianSemiGroup| |AlgebraicallyClosedField&| |AlgebraicallyClosedField|
  |AlgebraicallyClosedFunctionSpace&| |AlgebraicallyClosedFunctionSpace|
  |PlaneAlgebraicCurvePlot| |AddAst| |AlgebraicFunction| |Aggregate&|
  |Aggregate| |ArcHyperbolicFunctionCategory| |AssociationListAggregate|
@@ -925,8 +924,8 @@
  |RemainderList| |unexpand| |expand| |shape| |youngDiagram| Y |triangSolve|
  |univariateSolve| |realSolve| |positiveSolve| |squareFree| |convert|
  |linearlyDependentOverZ?| |linearDependenceOverZ| |solveLinearlyOverQ| |nil|
- |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable|
- |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision|
+ |infinite| |arbitraryExponent| |approximate| |complex| |canonical|
+ |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision|
  |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary|
  |additiveValuation| |unitsKnown| |canonicalUnitNormal|
- |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| |commutative|) 
\ No newline at end of file
+ |multiplicativeValuation| |commutative|) 
\ No newline at end of file
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 57156d5f..399145ca 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4065 +1,4065 @@
 
-(2793740 . 3580478893)       
-((-1740 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1738 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3794 ((|#2| $ (-488) |#2|) NIL T ELT) ((|#2| $ (-1150 (-488)) |#2|) 44 T ELT)) (-2302 (($ $) 80 T ELT)) (-3848 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3425 (((-488) (-1 (-85) |#2|) $) 27 T ELT) (((-488) |#2| $) NIL T ELT) (((-488) |#2| $ (-488)) 96 T ELT)) (-3524 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2614 (((-587 |#2|) $) 13 T ELT)) (-3332 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3849 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2309 (($ |#2| $ (-488)) NIL T ELT) (($ $ $ (-488)) 67 T ELT)) (-1734 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1736 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3806 ((|#2| $ (-488) |#2|) NIL T ELT) ((|#2| $ (-488)) NIL T ELT) (($ $ (-1150 (-488))) 66 T ELT)) (-2310 (($ $ (-488)) 76 T ELT) (($ $ (-1150 (-488))) 75 T ELT)) (-1735 (((-698) |#2| $) NIL T ELT) (((-698) (-1 (-85) |#2|) $) 34 T ELT)) (-1739 (($ $ $ (-488)) 69 T ELT)) (-3406 (($ $) 68 T ELT)) (-3536 (($ (-587 |#2|)) 73 T ELT)) (-3808 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-587 $)) 85 T ELT)) (-3953 (((-776) $) 92 T ELT)) (-1737 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3062 (((-85) $ $) 95 T ELT)) (-2691 (((-85) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -7 (-15 -3062 ((-85) |#1| |#1|)) (-15 -3953 ((-776) |#1|)) (-15 -3332 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2691 ((-85) |#1| |#1|)) (-15 -1738 (|#1| |#1|)) (-15 -1738 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2302 (|#1| |#1|)) (-15 -1739 (|#1| |#1| |#1| (-488))) (-15 -1740 ((-85) |#1|)) (-15 -3524 (|#1| |#1| |#1|)) (-15 -3425 ((-488) |#2| |#1| (-488))) (-15 -3425 ((-488) |#2| |#1|)) (-15 -3425 ((-488) (-1 (-85) |#2|) |#1|)) (-15 -1740 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3524 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -1737 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1736 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1735 ((-698) (-1 (-85) |#2|) |#1|)) (-15 -2614 ((-587 |#2|) |#1|)) (-15 -3848 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3848 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1734 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -1735 ((-698) |#2| |#1|)) (-15 -3848 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3794 (|#2| |#1| (-1150 (-488)) |#2|)) (-15 -2309 (|#1| |#1| |#1| (-488))) (-15 -2309 (|#1| |#2| |#1| (-488))) (-15 -2310 (|#1| |#1| (-1150 (-488)))) (-15 -2310 (|#1| |#1| (-488))) (-15 -3849 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3808 (|#1| (-587 |#1|))) (-15 -3808 (|#1| |#1| |#1|)) (-15 -3808 (|#1| |#2| |#1|)) (-15 -3808 (|#1| |#1| |#2|)) (-15 -3806 (|#1| |#1| (-1150 (-488)))) (-15 -3536 (|#1| (-587 |#2|))) (-15 -3806 (|#2| |#1| (-488))) (-15 -3806 (|#2| |#1| (-488) |#2|)) (-15 -3794 (|#2| |#1| (-488) |#2|)) (-15 -3849 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3406 (|#1| |#1|))) (-19 |#2|) (-1133)) (T -18)) 
-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(-13 (-1017) (-10 -8 (-15 -3845 ($ $ $)) (-15 * ($ (-834) $)))) 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-352 (-488))) . T) ((-38 $) . T) ((-72) . T) ((-82 (-352 (-488)) (-352 (-488))) . T) ((-82 $ $) . T) ((-104) . T) ((-559 (-352 (-488))) . T) ((-559 (-488)) . T) ((-559 $) . T) ((-556 (-776)) . T) ((-148) . T) ((-203) . T) ((-248) . T) ((-260) . T) ((-314) . T) ((-395) . T) ((-499) . T) ((-13) . T) ((-592 (-352 (-488))) . T) ((-592 (-488)) . T) ((-592 $) . T) ((-594 (-352 (-488))) . T) ((-594 $) . T) ((-586 (-352 (-488))) . T) ((-586 $) . T) ((-658 (-352 (-488))) . T) ((-658 $) . T) ((-667) . T) ((-836) . T) ((-919) . T) ((-967 (-352 (-488))) . T) ((-967 $) . T) ((-972 (-352 (-488))) . T) ((-972 $) . T) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1133) . T) ((-1138) . T)) 
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-NIL 
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-NIL 
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-NIL 
-(-13 (-965) (-658 |t#1|) (-559 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-559 (-488)) . T) ((-559 |#1|) . T) ((-556 (-776)) . T) ((-13) . T) ((-592 (-488)) . T) ((-592 |#1|) . T) ((-592 $) . T) ((-594 |#1|) . T) ((-594 $) . T) ((-586 |#1|) . T) ((-658 |#1|) . T) ((-667) . T) ((-967 |#1|) . T) ((-972 |#1|) . T) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1133) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+(2793524 . 3581069288)       
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+NIL 
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+(((-16 |#1|) (-110) (-1130)) (T -16)) 
+NIL 
+(-12 (-323 |t#1|) (-1036 |t#1|)) 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+(((-18) . T) ((-20) . T) ((-22) . T) ((-35 (-349 (-485))) . T) ((-35 |#1|) |has| |#1| (-145)) ((-35 $) . T) ((-24) . T) ((-69) . T) ((-79 (-349 (-485)) (-349 (-485))) . T) ((-79 |#1| |#1|) |has| |#1| (-145)) ((-79 $ $) . T) ((-101) . T) ((-115) |has| |#1| (-115)) ((-117) |has| |#1| (-117)) ((-556 (-349 (-485))) . T) ((-556 (-349 (-858 |#1|))) |has| |#1| (-496)) ((-556 (-485)) . T) ((-556 (-551 $)) . T) ((-556 (-858 |#1|)) |has| |#1| (-962)) ((-556 (-1091)) . T) ((-556 |#1|) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-145) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-554 (-801 (-329))) |has| |#1| (-554 (-801 (-329)))) ((-554 (-801 (-485))) |has| |#1| (-554 (-801 (-485)))) ((-200) . T) ((-245) . T) ((-257) . T) ((-259 $) . T) ((-253) . T) ((-311) . T) ((-328 |#1|) |has| |#1| (-962)) ((-342 |#1|) . T) ((-354 |#1|) . T) ((-363 |#1|) . T) ((-392) . T) ((-413) |has| |#1| (-413)) ((-456 (-551 $) $) . T) ((-456 $ $) . T) ((-496) . T) ((-12) . T) ((-589 (-349 (-485))) . T) ((-589 (-485)) . T) ((-589 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-145))) ((-589 $) . T) ((-591 (-349 (-485))) . T) ((-591 (-485)) -11 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-591 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-145))) ((-591 $) . T) ((-583 (-349 (-485))) . T) ((-583 |#1|) |has| |#1| (-145)) ((-583 $) . T) ((-581 (-485)) -11 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-581 |#1|) |has| |#1| (-962)) ((-655 (-349 (-485))) . T) ((-655 |#1|) |has| |#1| (-145)) ((-655 $) . T) ((-664) . T) ((-807 $ (-1091)) |has| |#1| (-962)) ((-810 (-1091)) |has| |#1| (-962)) ((-812 (-1091)) |has| |#1| (-962)) ((-797 (-329)) |has| |#1| (-797 (-329))) ((-797 (-485)) |has| |#1| (-797 (-485))) ((-795 |#1|) . T) ((-833) . T) ((-916) . T) ((-951 (-349 (-485))) OR (|has| |#1| (-951 (-349 (-485)))) (-11 (|has| |#1| (-496)) (|has| |#1| (-951 (-485))))) ((-951 (-349 (-858 |#1|))) |has| |#1| (-496)) ((-951 (-485)) |has| |#1| (-951 (-485))) ((-951 (-551 $)) . T) ((-951 (-858 |#1|)) |has| |#1| (-962)) ((-951 (-1091)) . T) ((-951 |#1|) . T) ((-964 (-349 (-485))) . T) ((-964 |#1|) |has| |#1| (-145)) ((-964 $) . T) ((-969 (-349 (-485))) . T) ((-969 |#1|) |has| |#1| (-145)) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T) ((-1135) . T)) 
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+(((-31) . T) ((-73 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-69) OR (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-69)) (|has| |#2| (-1014)) (|has| |#2| (-69))) ((-553 (-773)) OR (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-1014)) (|has| |#2| (-553 (-773)))) ((-121 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-554 (-474)) |has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-554 (-474))) ((-182 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-192 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-240 (-485) (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-240 (-1147 (-485)) $) . T) ((-240 |#1| |#2|) . T) ((-242 (-485) (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-242 |#1| |#2|) . T) ((-259 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) -11 (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-1014))) ((-259 |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-236 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-317 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-323 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-380 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-380 |#2|) . T) ((-429 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-429 |#2|) . T) ((-539 (-485) (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-539 |#1| |#2|) . T) ((-456 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) -11 (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-1014))) ((-456 |#2| |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-12) . T) ((-550 |#1| |#2|) . T) ((-594 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-609 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-757) |has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-757)) ((-760) |has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-757)) ((-924 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-1014) OR (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3864 |#1|) (|:| |entry| |#2|)) (-757)) (|has| |#2| (-1014))) ((-1036 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-1036 |#2|) . T) ((-1065 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T) ((-1108 |#1| |#2|) . T) ((-1130) . T) ((-1169 (-2 (|:| -3864 |#1|) (|:| |entry| |#2|))) . T)) 
+((-3950 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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+NIL 
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+(((-18) . T) ((-20) . T) ((-22) . T) ((-69) . T) ((-79 |#1| |#1|) . T) ((-101) . T) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-12) . T) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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ELT) (($ $ (-584 (-1091))) NIL (OR (-11 (|has| (-349 |#2|) (-311)) (|has| (-349 |#2|) (-810 (-1091)))) (-11 (|has| (-349 |#2|) (-311)) (|has| (-349 |#2|) (-812 (-1091))))) ELT) (($ $ (-1091)) NIL (OR (-11 (|has| (-349 |#2|) (-311)) (|has| (-349 |#2|) (-810 (-1091)))) (-11 (|has| (-349 |#2|) (-311)) (|has| (-349 |#2|) (-812 (-1091))))) ELT) (($ $ (-695)) NIL (OR (-11 (|has| (-349 |#2|) (-189)) (|has| (-349 |#2|) (-311))) (-11 (|has| (-349 |#2|) (-188)) (|has| (-349 |#2|) (-311))) (|has| (-349 |#2|) (-298))) ELT) (($ $) NIL (OR (-11 (|has| (-349 |#2|) (-189)) (|has| (-349 |#2|) (-311))) (-11 (|has| (-349 |#2|) (-188)) (|has| (-349 |#2|) (-311))) (|has| (-349 |#2|) (-298))) ELT)) (-3059 (((-82) $ $) NIL T ELT)) (-3953 (($ $ $) NIL (|has| (-349 |#2|) (-311)) ELT)) (-3840 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3842 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) NIL (|has| (-349 |#2|) (-311)) ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T 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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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(|has| (-86 |#1|) (-951 (-485))) ELT) (((-485) $) NIL (|has| (-86 |#1|) (-951 (-485))) ELT)) (-3733 (($ $) NIL T ELT) (($ (-485) $) NIL T ELT)) (-2567 (($ $ $) NIL T ELT)) (-2281 (((-631 (-485)) (-631 $)) NIL (|has| (-86 |#1|) (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 (-485))) (|:| |vec| (-1180 (-485)))) (-631 $) (-1180 $)) NIL (|has| (-86 |#1|) (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 (-86 |#1|))) (|:| |vec| (-1180 (-86 |#1|)))) (-631 $) (-1180 $)) NIL T ELT) (((-631 (-86 |#1|)) (-631 $)) NIL T ELT)) (-3470 (((-3 $ #1#) $) NIL T ELT)) (-2997 (($) NIL (|has| (-86 |#1|) (-484)) ELT)) (-2566 (($ $ $) NIL T ELT)) (-2744 (((-2 (|:| -3958 (-584 $)) (|:| -2411 $)) (-584 $)) NIL T ELT)) (-3726 (((-82) $) NIL T ELT)) (-3189 (((-82) $) NIL (|has| (-86 |#1|) (-741)) ELT)) (-2799 (((-799 (-485) $) $ (-801 (-485)) (-799 (-485) $)) NIL (|has| (-86 |#1|) (-797 (-485))) ELT) (((-799 (-329) $) $ (-801 (-329)) (-799 (-329) $)) NIL (|has| (-86 |#1|) (-797 (-329))) ELT)) (-1215 (((-82) $ $) NIL T ELT)) (-2412 (((-82) $) NIL T ELT)) (-2999 (($ $) NIL T ELT)) (-3001 (((-86 |#1|) $) NIL T ELT)) (-3448 (((-633 $) $) NIL (|has| (-86 |#1|) (-1067)) ELT)) (-3190 (((-82) $) NIL (|has| (-86 |#1|) (-741)) ELT)) (-1606 (((-3 (-584 $) #1#) (-584 $) $) NIL T ELT)) (-2534 (($ $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-2860 (($ $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-3846 (($ (-1 (-86 |#1|) (-86 |#1|)) $) NIL T ELT)) (-2282 (((-631 (-485)) (-1180 $)) NIL (|has| (-86 |#1|) (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 (-485))) (|:| |vec| (-1180 (-485)))) (-1180 $) $) NIL (|has| (-86 |#1|) (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 (-86 |#1|))) (|:| |vec| (-1180 (-86 |#1|)))) (-1180 $) $) NIL T ELT) (((-631 (-86 |#1|)) (-1180 $)) NIL T ELT)) (-1896 (($ $ $) NIL T ELT) (($ (-584 $)) NIL T ELT)) (-3245 (((-1074) $) NIL T ELT)) (-2487 (($ $) NIL T ELT)) (-3449 (($) NIL (|has| (-86 |#1|) (-1067)) CONST)) (-3246 (((-1034) $) NIL T ELT)) (-2711 (((-1086 $) (-1086 $) (-1086 $)) NIL T ELT)) (-3147 (($ $ $) NIL T ELT) (($ (-584 $)) NIL T ELT)) (-3131 (($ $) NIL (|has| (-86 |#1|) (-257)) ELT)) (-3133 (((-86 |#1|) $) NIL (|has| (-86 |#1|) (-484)) ELT)) (-2708 (((-347 (-1086 $)) (-1086 $)) NIL (|has| (-86 |#1|) (-822)) ELT)) (-2709 (((-347 (-1086 $)) (-1086 $)) NIL (|has| (-86 |#1|) (-822)) ELT)) (-3735 (((-347 $) $) NIL T ELT)) (-1607 (((-2 (|:| |coef1| $) (|:| |coef2| $) (|:| -2411 $)) $ $) NIL T ELT) (((-3 (-2 (|:| |coef1| $) (|:| |coef2| $)) #1#) $ $ $) NIL T ELT)) (-3469 (((-3 $ #1#) $ $) NIL T ELT)) (-2743 (((-633 (-584 $)) (-584 $) $) NIL T ELT)) (-3771 (($ $ (-584 (-86 |#1|)) (-584 (-86 |#1|))) NIL (|has| (-86 |#1|) (-259 (-86 |#1|))) ELT) (($ $ (-86 |#1|) (-86 |#1|)) NIL (|has| (-86 |#1|) (-259 (-86 |#1|))) ELT) (($ $ (-248 (-86 |#1|))) NIL (|has| (-86 |#1|) (-259 (-86 |#1|))) ELT) (($ $ (-584 (-248 (-86 |#1|)))) NIL (|has| (-86 |#1|) (-259 (-86 |#1|))) ELT) (($ $ (-584 (-1091)) (-584 (-86 |#1|))) NIL (|has| (-86 |#1|) (-456 (-1091) (-86 |#1|))) ELT) (($ $ (-1091) (-86 |#1|)) NIL (|has| (-86 |#1|) (-456 (-1091) (-86 |#1|))) ELT)) (-1608 (((-695) $) NIL T ELT)) (-3803 (($ $ (-86 |#1|)) NIL (|has| (-86 |#1|) (-240 (-86 |#1|) (-86 |#1|))) ELT)) (-2882 (((-2 (|:| -1974 $) (|:| -2905 $)) $ $) NIL T ELT)) (-3761 (($ $ (-1 (-86 |#1|) (-86 |#1|))) NIL T ELT) (($ $ (-1 (-86 |#1|) (-86 |#1|)) (-695)) NIL T ELT) (($ $ (-1091)) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-584 (-1091))) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-1091) (-695)) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $) NIL (|has| (-86 |#1|) (-188)) ELT) (($ $ (-695)) NIL (|has| (-86 |#1|) (-188)) ELT)) (-2998 (($ $) NIL T ELT)) (-3000 (((-86 |#1|) $) NIL T ELT)) (-3975 (((-801 (-485)) $) NIL (|has| (-86 |#1|) (-554 (-801 (-485)))) ELT) (((-801 (-329)) $) NIL (|has| (-86 |#1|) (-554 (-801 (-329)))) ELT) (((-474) $) NIL (|has| (-86 |#1|) (-554 (-474))) ELT) (((-329) $) NIL (|has| (-86 |#1|) (-934)) ELT) (((-178) $) NIL (|has| (-86 |#1|) (-934)) ELT)) (-2619 (((-147 (-349 (-485))) $) NIL T ELT)) (-2706 (((-3 (-1180 $) #1#) (-631 $)) NIL (-11 (|has| $ (-115)) (|has| (-86 |#1|) (-822))) ELT)) (-3950 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ $) NIL T ELT) (($ (-349 (-485))) NIL T ELT) (($ (-86 |#1|)) NIL T ELT) (($ (-1091)) NIL (|has| (-86 |#1|) (-951 (-1091))) ELT)) (-2705 (((-633 $) $) NIL (OR (-11 (|has| $ (-115)) (|has| (-86 |#1|) (-822))) (|has| (-86 |#1|) (-115))) ELT)) (-3129 (((-695)) NIL T CONST)) (-3134 (((-86 |#1|) $) NIL (|has| (-86 |#1|) (-484)) ELT)) (-1266 (((-82) $ $) NIL T ELT)) (-2064 (((-82) $ $) NIL T ELT)) (-3773 (((-349 (-485)) $ (-485)) NIL T ELT)) (-3128 (((-82) $ $) NIL T ELT)) (-3386 (($ $) NIL (|has| (-86 |#1|) (-741)) ELT)) (-2663 (($) NIL T CONST)) (-2669 (($) NIL T CONST)) (-2672 (($ $ (-1 (-86 |#1|) (-86 |#1|))) NIL T ELT) (($ $ (-1 (-86 |#1|) (-86 |#1|)) (-695)) NIL T ELT) (($ $ (-1091)) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-584 (-1091))) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-1091) (-695)) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| (-86 |#1|) (-812 (-1091))) ELT) (($ $) NIL (|has| (-86 |#1|) (-188)) ELT) (($ $ (-695)) NIL (|has| (-86 |#1|) (-188)) ELT)) (-2569 (((-82) $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-2570 (((-82) $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-3059 (((-82) $ $) NIL T ELT)) (-2687 (((-82) $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-2688 (((-82) $ $) NIL (|has| (-86 |#1|) (-757)) ELT)) (-3953 (($ $ $) NIL T ELT) (($ (-86 |#1|) (-86 |#1|)) NIL T ELT)) (-3840 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3842 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-349 (-485))) NIL T ELT) (($ (-349 (-485)) $) NIL T ELT) (($ (-86 |#1|) $) NIL T ELT) (($ $ (-86 |#1|)) NIL T ELT))) 
+(((-87 |#1|) (-12 (-905 (-86 |#1|)) (-10 -8 (-14 -3773 ((-349 (-485)) $ (-485))) (-14 -2619 ((-147 (-349 (-485))) $)) (-14 -3733 ($ $)) (-14 -3733 ($ (-485) $)))) (-485)) (T -87)) 
+((-3773 (*1 *2 *1 *3) (-11 (-5 *2 (-349 (-485))) (-5 *1 (-87 *4)) (-13 *4 *3) (-5 *3 (-485)))) (-2619 (*1 *2 *1) (-11 (-5 *2 (-147 (-349 (-485)))) (-5 *1 (-87 *3)) (-13 *3 (-485)))) (-3733 (*1 *1 *1) (-11 (-5 *1 (-87 *2)) (-13 *2 (-485)))) (-3733 (*1 *1 *2 *1) (-11 (-5 *2 (-485)) (-5 *1 (-87 *3)) (-13 *3 *2)))) 
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+NIL 
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+(((-89 |#1|) (-110) (-1130)) (T -89)) 
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+(-12 (-924 |t#1|) (-10 -8 (-14 -3141 ($ $)) (-14 -3803 ($ $ "left")) (-14 -3140 ($ $)) (-14 -3803 ($ $ "right")) (IF (|has| $ (-1036 |t#1|)) (PROGN (-14 -3791 ($ $ "left" $)) (-14 -1295 ($ $ $)) (-14 -3791 ($ $ "right" $)) (-14 -1294 ($ $ $))) |%noBranch|))) 
+(((-31) . T) ((-69) OR (|has| |#1| (-1014)) (|has| |#1| (-69))) ((-553 (-773)) OR (|has| |#1| (-1014)) (|has| |#1| (-553 (-773)))) ((-259 |#1|) -11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ((-380 |#1|) . T) ((-429 |#1|) . T) ((-456 |#1| |#1|) -11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ((-12) . T) ((-924 |#1|) . T) ((-1014) |has| |#1| (-1014)) ((-1130) . T)) 
+((-1298 (((-82) |#1|) 29 T ELT)) (-1297 (((-695) (-695)) 28 T ELT) (((-695)) 27 T ELT)) (-1296 (((-82) |#1| (-82)) 30 T ELT) (((-82) |#1|) 31 T ELT))) 
+(((-90 |#1|) (-10 -7 (-14 -1296 ((-82) |#1|)) (-14 -1296 ((-82) |#1| (-82))) (-14 -1297 ((-695))) (-14 -1297 ((-695) (-695))) (-14 -1298 ((-82) |#1|))) (-1156 (-485))) (T -90)) 
+((-1298 (*1 *2 *3) (-11 (-5 *2 (-82)) (-5 *1 (-90 *3)) (-4 *3 (-1156 (-485))))) (-1297 (*1 *2 *2) (-11 (-5 *2 (-695)) (-5 *1 (-90 *3)) (-4 *3 (-1156 (-485))))) (-1297 (*1 *2) (-11 (-5 *2 (-695)) (-5 *1 (-90 *3)) (-4 *3 (-1156 (-485))))) (-1296 (*1 *2 *3 *2) (-11 (-5 *2 (-82)) (-5 *1 (-90 *3)) (-4 *3 (-1156 (-485))))) (-1296 (*1 *2 *3) (-11 (-5 *2 (-82)) (-5 *1 (-90 *3)) (-4 *3 (-1156 (-485)))))) 
+((-2571 (((-82) $ $) NIL (|has| |#1| (-69)) ELT)) (-3405 ((|#1| $) 18 T ELT)) (-3421 (((-2 (|:| |less| $) (|:| |greater| $)) |#1| $) 26 T ELT)) (-3028 ((|#1| $ |#1|) NIL (|has| $ (-1036 |#1|)) ELT)) (-1294 (($ $ $) 21 (|has| $ (-1036 |#1|)) ELT)) (-1295 (($ $ $) 23 (|has| $ (-1036 |#1|)) ELT)) (-3791 ((|#1| $ #1="value" |#1|) NIL (|has| $ (-1036 |#1|)) ELT) (($ $ #2="left" $) NIL (|has| $ (-1036 |#1|)) ELT) (($ $ #3="right" $) NIL (|has| $ (-1036 |#1|)) ELT)) (-3029 (($ $ (-584 $)) NIL (|has| $ (-1036 |#1|)) ELT)) (-3727 (($) NIL T CONST)) (-3140 (($ $) 20 T ELT)) (-3845 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (|has| |#1| (-69)) ELT) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL T ELT) ((|#1| (-1 |#1| |#1| |#1|) $) NIL T ELT)) (-3034 (((-584 $) $) NIL T ELT)) (-3030 (((-82) $ $) NIL (|has| |#1| (-69)) ELT)) (-1303 (($ $ |#1| $) 27 T ELT)) (-2611 (((-584 |#1|) $) NIL T ELT)) (-3248 (((-82) |#1| $) NIL (|has| |#1| (-69)) ELT)) (-3329 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-3846 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-3141 (($ $) 22 T ELT)) (-3033 (((-584 |#1|) $) NIL T ELT)) (-3530 (((-82) $) NIL T ELT)) (-3245 (((-1074) $) NIL (|has| |#1| (-1014)) ELT)) (-1299 (($ |#1| $) 28 T ELT)) (-3612 (($ |#1| $) 15 T ELT)) (-3246 (((-1034) $) NIL (|has| |#1| (-1014)) ELT)) (-1731 (((-3 |#1| "failed") (-1 (-82) |#1|) $) NIL T ELT)) (-1733 (((-82) (-1 (-82) |#1|) $) NIL T ELT)) (-3771 (($ $ (-584 (-248 |#1|))) NIL (-11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ELT) (($ $ (-248 |#1|)) NIL (-11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ELT) (($ $ |#1| |#1|) NIL (-11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ELT) (($ $ (-584 |#1|) (-584 |#1|)) NIL (-11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ELT)) (-1223 (((-82) $ $) NIL T ELT)) (-3406 (((-82) $) 17 T ELT)) (-3568 (($) 11 T ELT)) (-3803 ((|#1| $ #1#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $ #3#) NIL T ELT)) (-3032 (((-485) $ $) NIL T ELT)) (-3636 (((-82) $) NIL T ELT)) (-1732 (((-695) |#1| $) NIL (|has| |#1| (-69)) ELT) (((-695) (-1 (-82) |#1|) $) NIL T ELT)) (-3403 (($ $) NIL T ELT)) (-3950 (((-773) $) NIL (|has| |#1| (-553 (-773))) ELT)) (-3525 (((-584 $) $) NIL T ELT)) (-3031 (((-82) $ $) NIL (|has| |#1| (-69)) ELT)) (-1300 (($ (-584 |#1|)) 16 T ELT)) (-1266 (((-82) $ $) NIL (|has| |#1| (-69)) ELT)) (-1734 (((-82) (-1 (-82) |#1|) $) NIL T ELT)) (-3059 (((-82) $ $) NIL (|has| |#1| (-69)) ELT)) (-3961 (((-695) $) NIL T ELT))) 
+(((-91 |#1|) (-12 (-95 |#1|) (-10 -8 (-14 -1300 ($ (-584 |#1|))) (-14 -3612 ($ |#1| $)) (-14 -1299 ($ |#1| $)) (-14 -3421 ((-2 (|:| |less| $) (|:| |greater| $)) |#1| $)))) (-757)) (T -91)) 
+((-1300 (*1 *1 *2) (-11 (-5 *2 (-584 *3)) (-4 *3 (-757)) (-5 *1 (-91 *3)))) (-3612 (*1 *1 *2 *1) (-11 (-5 *1 (-91 *2)) (-4 *2 (-757)))) (-1299 (*1 *1 *2 *1) (-11 (-5 *1 (-91 *2)) (-4 *2 (-757)))) (-3421 (*1 *2 *3 *1) (-11 (-5 *2 (-2 (|:| |less| (-91 *3)) (|:| |greater| (-91 *3)))) (-5 *1 (-91 *3)) (-4 *3 (-757))))) 
+((-2315 (($ $) 13 T ELT)) (-2563 (($ $) 11 T ELT)) (-1301 (($ $ $) 23 T ELT)) (-1302 (($ $ $) 21 T ELT)) (-2313 (($ $ $) 19 T ELT)) (-2314 (($ $ $) 17 T ELT))) 
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+NIL 
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+NIL 
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(-822))) ELT)) (-3950 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ (-1040 |#1| |#2|)) 32 T ELT) (($ (-349 (-485))) NIL (OR (|has| |#1| (-35 (-349 (-485)))) (|has| |#1| (-951 (-349 (-485))))) ELT) (($ $) NIL (|has| |#1| (-496)) ELT)) (-3820 (((-584 |#1|) $) NIL T ELT)) (-3680 ((|#1| $ (-470 |#3|)) NIL T ELT) (($ $ |#3| (-695)) NIL T ELT) (($ $ (-584 |#3|) (-584 (-695))) NIL T ELT)) (-2705 (((-633 $) $) NIL (OR (-11 (|has| $ (-115)) (|has| |#1| (-822))) (|has| |#1| (-115))) ELT)) (-3129 (((-695)) NIL T CONST)) (-1624 (($ $ $ (-695)) NIL (|has| |#1| (-145)) ELT)) (-1266 (((-82) $ $) NIL T ELT)) (-2064 (((-82) $ $) NIL (|has| |#1| (-496)) ELT)) (-3128 (((-82) $ $) NIL T ELT)) (-2663 (($) NIL T CONST)) (-2669 (($) NIL T CONST)) (-2672 (($ $ (-584 |#3|) (-584 (-695))) NIL T ELT) (($ $ |#3| (-695)) NIL T ELT) (($ $ (-584 |#3|)) NIL T ELT) (($ $ |#3|) NIL T ELT) (($ $ (-1 |#1| |#1|)) NIL T ELT) (($ $ (-1 |#1| |#1|) (-695)) NIL T ELT) (($ $ (-1091)) NIL (|has| |#1| (-812 (-1091))) ELT) (($ $ (-584 (-1091))) NIL (|has| |#1| (-812 (-1091))) ELT) (($ $ (-1091) (-695)) NIL (|has| |#1| (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| |#1| (-812 (-1091))) ELT) (($ $) NIL (|has| |#1| (-188)) ELT) (($ $ (-695)) NIL (|has| |#1| (-188)) ELT)) (-3059 (((-82) $ $) NIL T ELT)) (-3953 (($ $ |#1|) NIL (|has| |#1| (-311)) ELT)) (-3840 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3842 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-349 (-485))) NIL (|has| |#1| (-35 (-349 (-485)))) ELT) (($ (-349 (-485)) $) NIL (|has| |#1| (-35 (-349 (-485)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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+NIL 
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+NIL 
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+(((-69) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-185 $) . T) ((-188) . T) ((-12) . T) ((-757) . T) ((-760) . T) ((-951 |#1|) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-((-1899 (($ $ $) 14 T ELT) (($ (-587 $)) 21 T ELT)) (-2714 (((-1089 $) (-1089 $) (-1089 $)) 45 T ELT)) (-3150 (($ $ $) NIL T ELT) (($ (-587 $)) 22 T ELT))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-149) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
-(-13 (-718) (-120) (-667)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-559 (-488)) . T) ((-556 (-776)) . T) ((-13) . T) ((-592 (-488)) . T) ((-592 $) . T) ((-594 $) . T) ((-667) . T) ((-718) . T) ((-720) . T) ((-722) . T) ((-725) . T) ((-760) . T) ((-763) . T) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1133) . T)) 
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-(((-760) (-113)) (T -760)) 
-NIL 
-(-13 (-1017) (-763)) 
-(((-72) . T) ((-556 (-776)) . T) ((-13) . T) ((-763) . T) ((-1017) . T) ((-1133) . T)) 
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-NIL 
-((-2537 (($ $ $) 16 T ELT)) (-2863 (($ $ $) 15 T ELT)) (-1269 (((-85) $ $) 17 T ELT)) (-2572 (((-85) $ $) 12 T ELT)) (-2573 (((-85) $ $) 9 T ELT)) (-3062 (((-85) $ $) 14 T ELT)) (-2690 (((-85) $ $) 11 T ELT))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-72) . T) ((-556 (-776)) . T) ((-13) . T) ((-1133) . T)) 
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-NIL 
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-(((-72) . T) ((-556 (-776)) . T) ((-561 (-587 $)) . T) ((-561 |#1|) . T) ((-561 |#2|) . T) ((-561 |#3|) . T) ((-561 |#4|) . T) ((-561 |#5|) . T) ((-243 (-488) $) . T) ((-243 (-587 (-488)) $) . T) ((-13) . T) ((-1017) . T) ((-1133) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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T) ((-148) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-557 (-181)) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-557 (-332)) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-557 (-477)) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-477)))) ((-557 (-804 (-332))) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-804 (-332))))) ((-557 (-804 (-488))) -12 (|has| |#1| (-314)) (|has| |#2| (-557 (-804 (-488))))) ((-188 $) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-191))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-186 |#2|) |has| |#1| (-314)) ((-192) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-191) OR (|has| |#1| (-15 * (|#1| (-488) |#1|))) (-12 (|has| |#1| (-314)) (|has| |#2| (-191))) (-12 (|has| |#1| (-314)) (|has| |#2| (-192)))) ((-227 |#2|) |has| |#1| (-314)) ((-203) |has| |#1| (-314)) ((-241) |has| |#1| (-38 (-352 (-488)))) ((-243 (-488) |#1|) . T) ((-243 |#2| $) -12 (|has| |#1| (-314)) (|has| |#2| (-243 |#2| |#2|))) ((-243 $ $) |has| (-488) (-1029)) ((-248) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-260) |has| |#1| (-314)) ((-262 |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-262 |#2|))) ((-314) |has| |#1| (-314)) ((-290 |#2|) |has| |#1| (-314)) ((-331 |#2|) |has| |#1| (-314)) ((-345 |#2|) |has| |#1| (-314)) ((-383 |#1|) . T) ((-383 |#2|) |has| |#1| (-314)) ((-395) |has| |#1| (-314)) ((-436) |has| |#1| (-38 (-352 (-488)))) ((-459 (-1094) |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-459 (-1094) |#2|))) ((-459 |#2| |#2|) -12 (|has| |#1| (-314)) (|has| |#2| (-262 |#2|))) ((-499) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-13) . T) ((-592 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-592 (-488)) . T) ((-592 |#1|) . T) ((-592 |#2|) |has| |#1| (-314)) ((-592 $) . T) ((-594 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-594 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-584 (-488)))) ((-594 |#1|) . T) ((-594 |#2|) |has| |#1| (-314)) ((-594 $) . T) ((-586 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-586 |#1|) |has| |#1| (-148)) ((-586 |#2|) |has| |#1| (-314)) ((-586 $) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-584 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-584 (-488)))) ((-584 |#2|) |has| |#1| (-314)) ((-658 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-658 |#1|) |has| |#1| (-148)) ((-658 |#2|) |has| |#1| (-314)) ((-658 $) OR (|has| |#1| (-499)) (|has| |#1| (-314))) ((-667) . T) ((-718) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-720) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-722) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-725) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-744) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-759) -12 (|has| |#1| (-314)) (|has| |#2| (-744))) ((-760) OR (-12 (|has| |#1| (-314)) (|has| |#2| (-760))) (-12 (|has| |#1| (-314)) (|has| |#2| (-744)))) ((-763) OR (-12 (|has| |#1| (-314)) (|has| |#2| (-760))) (-12 (|has| |#1| (-314)) (|has| |#2| (-744)))) ((-810 $ (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-815 (-1094)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-813 (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-815 (-1094)) OR (-12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-488) |#1|)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-815 (-1094)))) (-12 (|has| |#1| (-314)) (|has| |#2| (-813 (-1094))))) ((-800 (-332)) -12 (|has| |#1| (-314)) (|has| |#2| (-800 (-332)))) ((-800 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-800 (-488)))) ((-798 |#2|) |has| |#1| (-314)) ((-825) -12 (|has| |#1| (-314)) (|has| |#2| (-825))) ((-890 |#1| (-488) (-998)) . T) ((-836) |has| |#1| (-314)) ((-908 |#2|) |has| |#1| (-314)) ((-919) |has| |#1| (-38 (-352 (-488)))) ((-937) -12 (|has| |#1| (-314)) (|has| |#2| (-937))) ((-954 (-352 (-488))) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-488)))) ((-954 (-488)) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-488)))) ((-954 (-1094)) -12 (|has| |#1| (-314)) (|has| |#2| (-954 (-1094)))) ((-954 |#2|) . T) ((-967 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-967 |#1|) . T) ((-967 |#2|) |has| |#1| (-314)) ((-967 $) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-972 (-352 (-488))) OR (|has| |#1| (-314)) (|has| |#1| (-38 (-352 (-488))))) ((-972 |#1|) . T) ((-972 |#2|) |has| |#1| (-314)) ((-972 $) OR (|has| |#1| (-499)) (|has| |#1| (-314)) (|has| |#1| (-148))) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1070) -12 (|has| |#1| (-314)) (|has| |#2| (-1070))) ((-1119) |has| |#1| (-38 (-352 (-488)))) ((-1122) |has| |#1| (-38 (-352 (-488)))) ((-1133) . T) ((-1138) |has| |#1| (-314)) ((-1145 |#1|) . T) ((-1162 |#1| (-488)) . T)) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-698)) . T) ((-25) . T) ((-38 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-38 |#1|) |has| |#1| (-148)) ((-38 $) |has| |#1| (-499)) ((-35) |has| |#1| (-38 (-352 (-488)))) ((-66) |has| |#1| (-38 (-352 (-488)))) ((-72) . T) ((-82 (-352 (-488)) (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-499)) (|has| |#1| (-148))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-559 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-559 (-488)) . T) ((-559 |#1|) |has| |#1| (-148)) ((-559 $) |has| |#1| (-499)) ((-556 (-776)) . T) ((-148) OR (|has| |#1| (-499)) (|has| |#1| (-148))) ((-188 $) |has| |#1| (-15 * (|#1| (-698) |#1|))) ((-192) |has| |#1| (-15 * (|#1| (-698) |#1|))) ((-191) |has| |#1| (-15 * (|#1| (-698) |#1|))) ((-241) |has| |#1| (-38 (-352 (-488)))) ((-243 (-698) |#1|) . T) ((-243 $ $) |has| (-698) (-1029)) ((-248) |has| |#1| (-499)) ((-383 |#1|) . T) ((-436) |has| |#1| (-38 (-352 (-488)))) ((-499) |has| |#1| (-499)) ((-13) . T) ((-592 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-592 (-488)) . T) ((-592 |#1|) . T) ((-592 $) . T) ((-594 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-594 |#1|) . T) ((-594 $) . T) ((-586 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-586 |#1|) |has| |#1| (-148)) ((-586 $) |has| |#1| (-499)) ((-658 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-658 |#1|) |has| |#1| (-148)) ((-658 $) |has| |#1| (-499)) ((-667) . T) ((-810 $ (-1094)) -12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-698) |#1|)))) ((-813 (-1094)) -12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-698) |#1|)))) ((-815 (-1094)) -12 (|has| |#1| (-813 (-1094))) (|has| |#1| (-15 * (|#1| (-698) |#1|)))) ((-890 |#1| (-698) (-998)) . T) ((-919) |has| |#1| (-38 (-352 (-488)))) ((-967 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-967 |#1|) . T) ((-967 $) OR (|has| |#1| (-499)) (|has| |#1| (-148))) ((-972 (-352 (-488))) |has| |#1| (-38 (-352 (-488)))) ((-972 |#1|) . T) ((-972 $) OR (|has| |#1| (-499)) (|has| |#1| (-148))) ((-965) . T) ((-974) . T) ((-1029) . T) ((-1065) . T) ((-1017) . T) ((-1119) |has| |#1| (-38 (-352 (-488)))) ((-1122) |has| |#1| (-38 (-352 (-488)))) ((-1133) . T) ((-1162 |#1| (-698)) . T)) 
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-NIL 
-(((-1179) (-113)) (T -1179)) 
-NIL 
-(-13 (-10 -7 (-6 -2292))) 
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-NIL 
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*6 (-587 (-1094))) (-14 *7 (-587 (-1094)))))) 
-((-3981 (((-3 (-1183 (-352 (-488))) #1="failed") (-1183 |#1|) |#1|) 21 T ELT)) (-3979 (((-85) (-1183 |#1|)) 12 T ELT)) (-3980 (((-3 (-1183 (-488)) #1#) (-1183 |#1|)) 16 T ELT))) 
-(((-1212 |#1|) (-10 -7 (-15 -3979 ((-85) (-1183 |#1|))) (-15 -3980 ((-3 (-1183 (-488)) #1="failed") (-1183 |#1|))) (-15 -3981 ((-3 (-1183 (-352 (-488))) #1#) (-1183 |#1|) |#1|))) (-13 (-965) (-584 (-488)))) (T -1212)) 
-((-3981 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) (-5 *2 (-1183 (-352 (-488)))) (-5 *1 (-1212 *4)))) (-3980 (*1 *2 *3) (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) (-5 *2 (-1183 (-488))) (-5 *1 (-1212 *4)))) (-3979 (*1 *2 *3) (-12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) (-5 *2 (-85)) (-5 *1 (-1212 *4))))) 
-((-2574 (((-85) $ $) NIL T ELT)) (-3194 (((-85) $) 12 T ELT)) (-1316 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3142 (((-698)) 9 T ELT)) (-3730 (($) NIL T CONST)) (-3473 (((-3 $ #1#) $) 57 T ELT)) (-3000 (($) 46 T ELT)) (-1218 (((-85) $ $) NIL T ELT)) (-2415 (((-85) $) 38 T ELT)) (-3451 (((-636 $) $) 36 T ELT)) (-2015 (((-834) $) 14 T ELT)) (-3248 (((-1077) $) NIL T ELT)) (-3452 (($) 26 T CONST)) (-2405 (($ (-834)) 47 T ELT)) (-3249 (((-1037) $) NIL T ELT)) (-3978 (((-488) $) 16 T ELT)) (-3953 (((-776) $) 21 T ELT) (($ (-488)) 18 T ELT)) (-3132 (((-698)) 10 T CONST)) (-1269 (((-85) $ $) 59 T ELT)) (-3131 (((-85) $ $) NIL T ELT)) (-2666 (($) 23 T CONST)) (-2672 (($) 25 T CONST)) (-3062 (((-85) $ $) 31 T ELT)) (-3843 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3845 (($ $ $) 29 T ELT)) (** (($ $ (-834)) NIL T ELT) (($ $ (-698)) 52 T ELT)) (* (($ (-834) $) NIL T ELT) (($ (-698) $) NIL T ELT) (($ (-488) $) 41 T ELT) (($ $ $) 40 T ELT))) 
-(((-1213 |#1|) (-13 (-148) (-322) (-557 (-488)) (-1070)) (-834)) (T -1213)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-((-3 2793725 2793730 2793735 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2793710 2793715 2793720 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2793695 2793700 2793705 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2793680 2793685 2793690 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1213 2792659 2793598 2793675 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1212 2791874 2792053 2792272 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1211 2783033 2784902 2786836 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1210 2782421 2782574 2782763 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1209 2781883 2782186 2782299 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1208 2779443 2781345 2781548 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1207 2776327 2777980 2778530 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1206 2773566 2775296 2775350 "XPOLYC" 2775635 XPOLYC (NIL T T) -9 NIL 2775748 NIL) (-1205 2771085 2773070 2773273 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1204 2767333 2769944 2770332 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1203 2762283 2763916 2763970 "XFALG" 2766016 XFALG (NIL T T) -9 NIL 2766778 NIL) (-1202 2757439 2760172 2760214 "XF" 2760832 XF (NIL T) -9 NIL 2761228 NIL) (-1201 2757157 2757267 2757434 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1200 2756384 2756506 2756710 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1199 2754126 2756284 2756379 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1198 2752707 2753502 2753544 "XALG" 2753549 XALG (NIL T) -9 NIL 2753658 NIL) (-1197 2746558 2751117 2751595 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1196 2744801 2745803 2746124 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1195 2744400 2744672 2744741 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1194 2743887 2744190 2744283 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1193 2742964 2743174 2743469 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1192 2741260 2741723 2742185 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1191 2740149 2740734 2740776 "VSPACE" 2740912 VSPACE (NIL T) -9 NIL 2740986 NIL) (-1190 2740020 2740053 2740144 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1189 2739863 2739917 2739985 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1188 2736846 2737641 2738378 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1187 2727944 2730545 2732718 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1186 2721521 2723412 2724991 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1185 2720005 2720400 2720806 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1184 2718832 2719113 2719429 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1183 2714229 2718659 2718751 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1182 2707555 2711884 2711927 "VECTCAT" 2712915 VECTCAT (NIL T) -9 NIL 2713499 NIL) (-1181 2706834 2707160 2707550 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1180 2706328 2706570 2706690 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1179 2706261 2706266 2706296 "UTYPE" 2706301 UTYPE (NIL) -9 NIL NIL NIL) (-1178 2705248 2705424 2705685 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1177 2703099 2703607 2704131 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1176 2692963 2698933 2698975 "UTSCAT" 2700073 UTSCAT (NIL T) -9 NIL 2700830 NIL) (-1175 2691028 2691971 2692958 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1174 2690702 2690751 2690882 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1173 2682413 2688898 2689377 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2676957 2679230 2679273 "URAGG" 2681313 URAGG (NIL T) -9 NIL 2682038 NIL) (-1171 2675028 2675960 2676952 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1170 2670735 2674004 2674466 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1169 2663164 2670659 2670730 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1168 2651797 2659284 2659345 "UPXSCCA" 2659913 UPXSCCA (NIL T T) -9 NIL 2660145 NIL) (-1167 2651518 2651620 2651792 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1166 2640052 2647264 2647306 "UPXSCAT" 2647946 UPXSCAT (NIL T) -9 NIL 2648554 NIL) (-1165 2639565 2639650 2639827 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1164 2631251 2639156 2639418 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1163 2630146 2630416 2630766 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1162 2622831 2626316 2626370 "UPSCAT" 2627439 UPSCAT (NIL T T) -9 NIL 2628203 NIL) (-1161 2622251 2622503 2622826 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1160 2621925 2621974 2622105 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1159 2606036 2614991 2615033 "UPOLYC" 2617111 UPOLYC (NIL T) -9 NIL 2618331 NIL) (-1158 2600091 2602939 2606031 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1157 2599527 2599652 2599815 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1156 2599161 2599248 2599387 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1155 2597974 2598241 2598545 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1154 2597307 2597437 2597622 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1153 2596899 2596974 2597121 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1152 2587663 2596665 2596793 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1151 2587025 2587162 2587367 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1150 2585626 2586473 2586749 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1149 2584855 2585052 2585277 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1148 2571665 2584779 2584850 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1147 2551421 2564656 2564717 "ULSCCAT" 2565348 ULSCCAT (NIL T T) -9 NIL 2565635 NIL) (-1146 2550756 2551042 2551416 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1145 2539110 2546244 2546286 "ULSCAT" 2547139 ULSCAT (NIL T) -9 NIL 2547869 NIL) (-1144 2538623 2538708 2538885 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1143 2520740 2538122 2538363 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1142 2519774 2520467 2520581 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2520692) (-1141 2518807 2519500 2519614 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2519725) (-1140 2517840 2518533 2518647 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2518758) (-1139 2516873 2517566 2517680 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2517791) (-1138 2514880 2516101 2516131 "UFD" 2516342 UFD (NIL) -9 NIL 2516455 NIL) (-1137 2514724 2514781 2514875 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1136 2513976 2514183 2514399 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1135 2512196 2512649 2513114 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1134 2511921 2512161 2512191 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1133 2511859 2511864 2511894 "TYPE" 2511899 TYPE (NIL) -9 NIL 2511906 NIL) (-1132 2511018 2511238 2511478 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1131 2510196 2510627 2510862 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1130 2508350 2508923 2509462 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1129 2507384 2507620 2507856 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1128 2495982 2500159 2500255 "TSETCAT" 2505470 TSETCAT (NIL T T T T) -9 NIL 2506974 NIL) (-1127 2492319 2494135 2495977 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1126 2486711 2491545 2491827 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1125 2482048 2483061 2483990 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1124 2481545 2481620 2481783 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1123 2479621 2479911 2480266 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1122 2479105 2479254 2479284 "TRIGCAT" 2479497 TRIGCAT (NIL) -9 NIL NIL NIL) (-1121 2478856 2478959 2479100 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1120 2475852 2477962 2478243 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1119 2474958 2475654 2475684 "TRANFUN" 2475719 TRANFUN (NIL) -9 NIL 2475785 NIL) (-1118 2474422 2474673 2474953 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1117 2474259 2474297 2474358 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1116 2473716 2473847 2473998 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1115 2472457 2473114 2473350 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1114 2472269 2472306 2472378 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1113 2470483 2471129 2471558 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1112 2468863 2469200 2469522 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1111 2458848 2466552 2466608 "TBAGG" 2466925 TBAGG (NIL T T) -9 NIL 2467135 NIL) (-1110 2456253 2457508 2458843 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1109 2455730 2455855 2456000 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1108 2455240 2455560 2455650 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1107 2454737 2454854 2454992 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1106 2447241 2454665 2454732 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1105 2442994 2444289 2445534 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1104 2442363 2442522 2442703 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1103 2439517 2440270 2441053 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1102 2439291 2439481 2439512 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1101 2438245 2438930 2439056 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2439242) (-1100 2437509 2438057 2438136 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2438196) (-1099 2434332 2435491 2436191 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1098 2432015 2432698 2433332 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1097 2428093 2429139 2430116 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1096 2425192 2427748 2427977 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1095 2424788 2424875 2424997 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1094 2421412 2422886 2423705 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1093 2414372 2420609 2420902 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1092 2406058 2413963 2414225 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1091 2405337 2405476 2405693 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1090 2405021 2405086 2405197 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1089 2395744 2404733 2404858 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1088 2394474 2394772 2395127 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1087 2393879 2393957 2394148 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1086 2376031 2393378 2393619 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1085 2375630 2375902 2375971 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1084 2374966 2375247 2375387 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1083 2369568 2370827 2371780 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1082 2369100 2369200 2369364 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1081 2364211 2365493 2366640 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1080 2358669 2360140 2361451 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1079 2351584 2353648 2355439 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1078 2343753 2351522 2351579 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1077 2338702 2343467 2343582 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1076 2338289 2338372 2338516 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1075 2337440 2337641 2337876 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1074 2337180 2337238 2337331 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1073 2330706 2335383 2335991 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1072 2329882 2330087 2330318 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1071 2329127 2329498 2329645 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1070 2328615 2328857 2328887 "STEP" 2328981 STEP (NIL) -9 NIL 2329052 NIL) (-1069 2321109 2328533 2328610 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1068 2316134 2319889 2319932 "STAGG" 2320359 STAGG (NIL T) -9 NIL 2320533 NIL) (-1067 2314592 2315300 2316129 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1066 2312754 2314419 2314511 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1065 2312034 2312573 2312603 "SRING" 2312608 SRING (NIL) -9 NIL 2312628 NIL) (-1064 2304949 2310572 2311011 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1063 2298723 2300162 2301666 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2291340 2295998 2296028 "SRAGG" 2297327 SRAGG (NIL) -9 NIL 2297931 NIL) (-1061 2290637 2290957 2291335 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1060 2284743 2289959 2290382 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1059 2278672 2282096 2282847 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1058 2275101 2275920 2276557 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1057 2274076 2274381 2274411 "SPFCAT" 2274855 SPFCAT (NIL) -9 NIL NIL NIL) (-1056 2273013 2273265 2273529 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1055 2263771 2266045 2266075 "SPADXPT" 2270712 SPADXPT (NIL) -9 NIL 2272836 NIL) (-1054 2263573 2263619 2263688 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1053 2261229 2263537 2263568 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1052 2252903 2254992 2255034 "SPACEC" 2259349 SPACEC (NIL T) -9 NIL 2261154 NIL) (-1051 2250732 2252850 2252898 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1050 2249711 2249900 2250183 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1049 2248115 2248448 2248859 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1048 2247380 2247614 2247875 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1047 2243560 2244520 2245515 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1046 2239918 2240617 2241346 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1045 2233940 2239203 2239299 "SNTSCAT" 2239304 SNTSCAT (NIL T T T T) -9 NIL 2239374 NIL) (-1044 2227761 2232581 2232971 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1043 2221533 2227680 2227756 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1042 2219965 2220296 2220694 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1041 2211579 2216513 2216615 "SMATCAT" 2217958 SMATCAT (NIL NIL T T T) -9 NIL 2218506 NIL) (-1040 2209420 2210404 2211574 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1039 2209022 2209194 2209237 "SMAGG" 2209322 SMAGG (NIL T) -9 NIL 2209379 NIL) (-1038 2206565 2208171 2208214 "SKAGG" 2208475 SKAGG (NIL T) -9 NIL 2208611 NIL) (-1037 2202611 2206385 2206496 "SINT" NIL SINT (NIL) -8 NIL NIL 2206537) (-1036 2202421 2202465 2202531 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1035 2201496 2201728 2201996 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1034 2200500 2200662 2200938 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1033 2199846 2200186 2200309 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1032 2199192 2199499 2199639 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1031 2197303 2197795 2198301 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1030 2190787 2197222 2197298 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1029 2190290 2190527 2190557 "SGROUP" 2190650 SGROUP (NIL) -9 NIL 2190712 NIL) (-1028 2190180 2190212 2190285 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1027 2189818 2189858 2189899 "SGPOPC" 2189904 SGPOPC (NIL T) -9 NIL 2190105 NIL) (-1026 2189352 2189629 2189735 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1025 2186775 2187544 2188266 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1024 2180896 2186159 2186255 "SFRTCAT" 2186260 SFRTCAT (NIL T T T T) -9 NIL 2186298 NIL) (-1023 2175288 2176401 2177528 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1022 2169464 2170625 2171789 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1021 2168436 2169338 2169459 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1020 2164044 2164939 2165034 "SEXCAT" 2167647 SEXCAT (NIL T T T T T) -9 NIL 2168198 NIL) (-1019 2163017 2163971 2164039 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1018 2161408 2161993 2162295 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1017 2160931 2161116 2161146 "SETCAT" 2161263 SETCAT (NIL) -9 NIL 2161347 NIL) (-1016 2160763 2160827 2160926 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1015 2157815 2159199 2159242 "SETAGG" 2160110 SETAGG (NIL T) -9 NIL 2160448 NIL) (-1014 2157421 2157573 2157810 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1013 2154666 2157368 2157416 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1012 2154132 2154442 2154542 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1011 2153259 2153625 2153686 "SEGXCAT" 2153972 SEGXCAT (NIL T T) -9 NIL 2154092 NIL) (-1010 2152184 2152452 2152495 "SEGCAT" 2153017 SEGCAT (NIL T) -9 NIL 2153238 NIL) (-1009 2151864 2151929 2152042 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1008 2150930 2151400 2151608 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1007 2150508 2150787 2150863 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1006 2149873 2150009 2150213 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1005 2148939 2149686 2149868 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1004 2148192 2148887 2148934 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1003 2139677 2148059 2148187 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1002 2138531 2138821 2139140 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1001 2137829 2138041 2138231 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-1000 2137173 2137330 2137508 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-999 2136746 2136977 2137005 "SASTCAT" 2137010 SASTCAT (NIL) -9 NIL 2137023 NIL) (-998 2136213 2136638 2136712 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-997 2135816 2135857 2136028 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-996 2135447 2135488 2135645 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-995 2128528 2135364 2135442 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-994 2127178 2127507 2127903 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-993 2125939 2126300 2126600 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-992 2125563 2125784 2125865 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-991 2123023 2123657 2124110 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-990 2122862 2122895 2122963 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-989 2122353 2122656 2122747 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-988 2117981 2118849 2119760 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-987 2107036 2112299 2112393 "RSETCAT" 2116449 RSETCAT (NIL T T T T) -9 NIL 2117537 NIL) (-986 2105574 2106216 2107031 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-985 2099348 2100793 2102300 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-984 2097230 2097787 2097859 "RRCC" 2098932 RRCC (NIL T T) -9 NIL 2099273 NIL) (-983 2096755 2096954 2097225 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-982 2096225 2096535 2096633 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-981 2068758 2079472 2079536 "RPOLCAT" 2090010 RPOLCAT (NIL T T T) -9 NIL 2093155 NIL) (-980 2062857 2065680 2068753 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-979 2059024 2062605 2062743 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-978 2057352 2058091 2058347 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-977 2052995 2055807 2055835 "RNS" 2056097 RNS (NIL) -9 NIL 2056349 NIL) (-976 2051898 2052385 2052922 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-975 2051016 2051417 2051617 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-974 2050154 2050716 2050744 "RNG" 2050804 RNG (NIL) -9 NIL 2050858 NIL) (-973 2050043 2050077 2050149 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-972 2049305 2049810 2049850 "RMODULE" 2049855 RMODULE (NIL T) -9 NIL 2049881 NIL) (-971 2048244 2048350 2048680 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-970 2045141 2047834 2048127 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-969 2037982 2040426 2040538 "RMATCAT" 2043709 RMATCAT (NIL NIL NIL T T T) -9 NIL 2044640 NIL) (-968 2037499 2037678 2037977 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-967 2037067 2037278 2037319 "RLINSET" 2037380 RLINSET (NIL T) -9 NIL 2037424 NIL) (-966 2036712 2036793 2036919 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-965 2035558 2036289 2036317 "RING" 2036372 RING (NIL) -9 NIL 2036464 NIL) (-964 2035403 2035459 2035553 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-963 2034457 2034724 2034980 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-962 2025681 2034085 2034286 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-961 2024906 2025417 2025456 "RGBCSPC" 2025513 RGBCSPC (NIL T) -9 NIL 2025564 NIL) (-960 2023940 2024426 2024465 "RGBCMDL" 2024693 RGBCMDL (NIL T) -9 NIL 2024807 NIL) (-959 2023652 2023721 2023822 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-958 2023415 2023456 2023551 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-957 2021839 2022269 2022649 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-956 2019426 2020094 2020762 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-955 2018976 2019074 2019234 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-954 2018598 2018696 2018737 "RETRACT" 2018868 RETRACT (NIL T) -9 NIL 2018955 NIL) (-953 2018478 2018509 2018593 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-952 2018080 2018352 2018419 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-951 2016560 2017451 2017648 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-950 2016251 2016312 2016408 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-949 2015994 2016035 2016140 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-948 2015729 2015770 2015879 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-947 2010800 2012251 2013466 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-946 2007896 2008654 2009462 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-945 2005865 2006487 2007087 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-944 1998793 2004416 2004852 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-943 1998105 1998385 1998534 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-942 1997590 1997705 1997870 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-941 1993183 1996993 1997214 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-940 1992415 1992614 1992827 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-939 1989705 1990543 1991425 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-938 1986287 1987323 1988382 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-937 1986123 1986176 1986204 "REAL" 1986209 REAL (NIL) -9 NIL 1986244 NIL) (-936 1985613 1985917 1986008 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-935 1985093 1985171 1985376 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-934 1984326 1984518 1984729 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-933 1983214 1983511 1983878 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-932 1981481 1981951 1982484 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-931 1980405 1980682 1981069 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-930 1979234 1979543 1979962 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-929 1972582 1976094 1976122 "RCFIELD" 1977399 RCFIELD (NIL) -9 NIL 1978129 NIL) (-928 1971200 1971812 1972509 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-927 1967954 1969286 1969327 "RCAGG" 1970381 RCAGG (NIL T) -9 NIL 1970843 NIL) (-926 1967681 1967791 1967949 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-925 1967126 1967255 1967416 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-924 1966743 1966822 1966941 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-923 1966158 1966308 1966458 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-922 1965940 1965990 1966061 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-921 1958382 1965058 1965366 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-920 1948084 1958249 1958377 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-919 1947718 1947811 1947839 "RADCAT" 1947996 RADCAT (NIL) -9 NIL NIL NIL) (-918 1947556 1947616 1947713 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-917 1945661 1947387 1947476 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-916 1945342 1945391 1945518 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-915 1937611 1941695 1941735 "QUATCAT" 1942513 QUATCAT (NIL T) -9 NIL 1943277 NIL) (-914 1934861 1936141 1937517 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-913 1930701 1934811 1934856 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-912 1928039 1929698 1929739 "QUAGG" 1930114 QUAGG (NIL T) -9 NIL 1930290 NIL) (-911 1927641 1927913 1927980 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-910 1926647 1927277 1927440 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-909 1926328 1926377 1926504 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-908 1915910 1922079 1922119 "QFCAT" 1922777 QFCAT (NIL T) -9 NIL 1923770 NIL) (-907 1912794 1914233 1915816 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-906 1912340 1912474 1912604 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-905 1906536 1907697 1908859 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-904 1905955 1906135 1906367 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-903 1903777 1904305 1904728 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-902 1902676 1902918 1903235 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-901 1901037 1901235 1901588 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-900 1896793 1898009 1898050 "PTRANFN" 1899934 PTRANFN (NIL T) -9 NIL NIL NIL) (-899 1895440 1895785 1896106 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-898 1895133 1895196 1895303 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-897 1889430 1893874 1893914 "PTCAT" 1894206 PTCAT (NIL T) -9 NIL 1894359 NIL) (-896 1889123 1889164 1889288 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-895 1888002 1888318 1888652 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-894 1876881 1879442 1881751 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-893 1870083 1872646 1872740 "PSETCAT" 1875714 PSETCAT (NIL T T T T) -9 NIL 1876523 NIL) (-892 1868533 1869267 1870078 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-891 1867852 1868047 1868075 "PSCURVE" 1868343 PSCURVE (NIL) -9 NIL 1868510 NIL) (-890 1863436 1865256 1865320 "PSCAT" 1866155 PSCAT (NIL T T T) -9 NIL 1866394 NIL) (-889 1862750 1863032 1863431 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-888 1861147 1862062 1862325 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-887 1860638 1860941 1861032 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-886 1851658 1854080 1856268 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-885 1849352 1850921 1850961 "PRQAGG" 1851144 PRQAGG (NIL T) -9 NIL 1851247 NIL) (-884 1848525 1848971 1848999 "PROPLOG" 1849138 PROPLOG (NIL) -9 NIL 1849252 NIL) (-883 1848200 1848263 1848386 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-882 1847636 1847775 1847947 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-881 1845884 1846647 1846944 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-880 1845436 1845568 1845696 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-879 1839877 1844376 1845196 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-878 1839706 1839744 1839803 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-877 1839145 1839285 1839436 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-876 1837613 1838032 1838498 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-875 1837330 1837391 1837419 "PRIMCAT" 1837543 PRIMCAT (NIL) -9 NIL NIL NIL) (-874 1836501 1836697 1836925 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-873 1832662 1836451 1836496 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-872 1832361 1832423 1832534 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-871 1829497 1832010 1832243 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-870 1828948 1829105 1829133 "PPCURVE" 1829338 PPCURVE (NIL) -9 NIL 1829474 NIL) (-869 1828561 1828806 1828889 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-868 1826317 1826738 1827330 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-867 1825760 1825824 1826057 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-866 1822480 1822966 1823577 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-865 1808052 1814182 1814246 "POLYCAT" 1817731 POLYCAT (NIL T T T) -9 NIL 1819608 NIL) (-864 1803562 1805709 1808047 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-863 1803219 1803293 1803412 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-862 1802912 1802975 1803082 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-861 1796275 1802645 1802804 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-860 1795162 1795425 1795701 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-859 1793766 1794079 1794409 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-858 1789209 1793716 1793761 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-857 1787697 1788108 1788483 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-856 1786454 1786763 1787159 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-855 1786125 1786209 1786326 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-854 1785704 1785779 1785953 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-853 1785190 1785286 1785446 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-852 1784662 1784782 1784936 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-851 1783557 1783775 1784152 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-850 1783168 1783253 1783405 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-849 1782719 1782801 1782982 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-848 1782411 1782492 1782605 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-847 1781924 1781999 1782207 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-846 1781272 1781400 1781602 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-845 1780634 1780768 1780931 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-844 1779938 1780120 1780301 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-843 1779661 1779735 1779829 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-842 1776229 1777418 1778334 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-841 1775313 1775514 1775749 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-840 1770878 1772262 1773404 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-839 1750799 1755686 1760533 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-838 1750539 1750592 1750695 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-837 1749980 1750114 1750294 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-836 1747989 1749210 1749238 "PID" 1749435 PID (NIL) -9 NIL 1749562 NIL) (-835 1747777 1747820 1747895 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-834 1746964 1747624 1747711 "PI" NIL PI (NIL) -8 NIL NIL 1747751) (-833 1746416 1746567 1746743 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-832 1742744 1743702 1744607 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-831 1741108 1741397 1741763 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-830 1740550 1740665 1740826 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-829 1737091 1739419 1739772 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-828 1735697 1735977 1736302 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-827 1734462 1734716 1735064 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-826 1733172 1733399 1733751 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-825 1730182 1731742 1731770 "PFECAT" 1732363 PFECAT (NIL) -9 NIL 1732740 NIL) (-824 1729805 1729970 1730177 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-823 1728629 1728911 1729212 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-822 1726811 1727198 1727628 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-821 1722781 1726737 1726806 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-820 1718684 1719831 1720698 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-819 1716616 1717705 1717746 "PERMCAT" 1718145 PERMCAT (NIL T) -9 NIL 1718442 NIL) (-818 1716312 1716359 1716482 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-817 1712761 1714442 1715087 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-816 1710787 1712516 1712637 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-815 1709670 1709933 1709972 "PDSPC" 1710493 PDSPC (NIL T) -9 NIL 1710738 NIL) (-814 1709039 1709305 1709665 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-813 1707676 1708669 1708708 "PDRING" 1708713 PDRING (NIL T) -9 NIL 1708740 NIL) (-812 1706388 1707177 1707228 "PDMOD" 1707233 PDMOD (NIL T T) -9 NIL 1707336 NIL) (-811 1705481 1705693 1705942 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-810 1705086 1705153 1705207 "PDDOM" 1705372 PDDOM (NIL T T) -9 NIL 1705452 NIL) (-809 1704938 1704974 1705081 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-808 1704724 1704763 1704852 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-807 1703041 1703795 1704094 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-806 1702730 1702793 1702902 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-805 1700868 1701298 1701749 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-804 1694488 1696317 1697609 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-803 1694119 1694192 1694324 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-802 1691821 1692501 1692982 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-801 1690025 1690453 1690856 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-800 1689471 1689719 1689760 "PATMAB" 1689867 PATMAB (NIL T) -9 NIL 1689950 NIL) (-799 1688118 1688522 1688779 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-798 1687656 1687787 1687828 "PATAB" 1687833 PATAB (NIL T) -9 NIL 1688005 NIL) (-797 1686199 1686636 1687059 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-796 1685877 1685952 1686054 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-795 1685566 1685629 1685738 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-794 1685371 1685417 1685484 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-793 1685049 1685124 1685226 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-792 1684738 1684801 1684910 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-791 1684429 1684499 1684596 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-790 1684118 1684181 1684290 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-789 1683279 1683658 1683837 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-788 1682886 1682984 1683103 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-787 1681854 1682279 1682498 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-786 1680519 1681173 1681533 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-785 1673609 1679923 1680117 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-784 1666030 1673107 1673291 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-783 1662755 1664670 1664710 "PADICCT" 1665291 PADICCT (NIL NIL) -9 NIL 1665573 NIL) (-782 1660745 1662705 1662750 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-781 1659907 1660117 1660383 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-780 1659249 1659392 1659596 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-779 1657630 1658657 1658935 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-778 1657154 1657413 1657510 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-777 1656213 1656891 1657063 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-776 1646635 1649504 1651703 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-775 1646027 1646341 1646467 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-774 1645304 1645499 1645527 "OUTBCON" 1645845 OUTBCON (NIL) -9 NIL 1646011 NIL) (-773 1645012 1645142 1645299 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-772 1644393 1644538 1644699 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-771 1643764 1644191 1644280 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-770 1643179 1643594 1643622 "OSGROUP" 1643627 OSGROUP (NIL) -9 NIL 1643649 NIL) (-769 1642143 1642404 1642689 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-768 1639412 1642018 1642138 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-767 1636553 1639163 1639289 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-766 1634571 1635099 1635659 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-765 1627913 1630453 1630493 "OREPCAT" 1632814 OREPCAT (NIL T) -9 NIL 1633916 NIL) (-764 1625939 1626873 1627908 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-763 1625136 1625407 1625435 "ORDTYPE" 1625740 ORDTYPE (NIL) -9 NIL 1625898 NIL) (-762 1624670 1624881 1625131 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-761 1624132 1624508 1624665 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-760 1623626 1623989 1624017 "ORDSET" 1624022 ORDSET (NIL) -9 NIL 1624044 NIL) (-759 1622191 1623213 1623241 "ORDRING" 1623246 ORDRING (NIL) -9 NIL 1623274 NIL) (-758 1621439 1621996 1622024 "ORDMON" 1622029 ORDMON (NIL) -9 NIL 1622050 NIL) (-757 1620743 1620905 1621097 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-756 1619954 1620462 1620490 "ORDFIN" 1620555 ORDFIN (NIL) -9 NIL 1620629 NIL) (-755 1619348 1619487 1619673 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-754 1616023 1618316 1618722 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-753 1615430 1615785 1615890 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-752 1615238 1615283 1615349 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-751 1614539 1614815 1614856 "OPERCAT" 1615067 OPERCAT (NIL T) -9 NIL 1615163 NIL) (-750 1614351 1614418 1614534 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-749 1611717 1613153 1613649 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-748 1611138 1611265 1611439 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-747 1608039 1610277 1610643 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-746 1604905 1607414 1607454 "OMSAGG" 1607515 OMSAGG (NIL T) -9 NIL 1607579 NIL) (-745 1603317 1604576 1604744 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-744 1601513 1602754 1602782 "OINTDOM" 1602787 OINTDOM (NIL) -9 NIL 1602808 NIL) (-743 1598943 1600515 1600844 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-742 1598197 1598893 1598938 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-741 1595399 1598038 1598192 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-740 1586936 1595270 1595394 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-739 1580391 1586827 1586931 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-738 1579363 1579600 1579873 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-737 1577004 1577674 1578378 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-736 1572781 1573741 1574764 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-735 1572289 1572377 1572571 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-734 1569738 1570320 1570993 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-733 1567133 1567641 1568237 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-732 1564130 1564669 1565315 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-731 1563485 1563593 1563851 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-730 1562643 1562768 1562989 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-729 1558927 1559723 1560636 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-728 1558367 1558462 1558684 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-727 1558048 1558097 1558224 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-726 1554651 1557847 1557966 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-725 1553811 1554433 1554461 "OCAMON" 1554466 OCAMON (NIL) -9 NIL 1554487 NIL) (-724 1548005 1550819 1550859 "OC" 1551954 OC (NIL T) -9 NIL 1552810 NIL) (-723 1546005 1546931 1547911 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-722 1545421 1545839 1545867 "OASGP" 1545872 OASGP (NIL) -9 NIL 1545892 NIL) (-721 1544484 1545133 1545161 "OAMONS" 1545201 OAMONS (NIL) -9 NIL 1545244 NIL) (-720 1543629 1544210 1544238 "OAMON" 1544295 OAMON (NIL) -9 NIL 1544346 NIL) (-719 1543525 1543557 1543624 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-718 1542276 1543050 1543078 "OAGROUP" 1543224 OAGROUP (NIL) -9 NIL 1543316 NIL) (-717 1542067 1542154 1542271 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-716 1541807 1541863 1541951 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-715 1536869 1538432 1539959 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-714 1533564 1534598 1535633 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-713 1532674 1532907 1533125 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-712 1521535 1524563 1527011 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-711 1515658 1520921 1521015 "NTSCAT" 1521020 NTSCAT (NIL T T T T) -9 NIL 1521058 NIL) (-710 1514999 1515178 1515371 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-709 1514692 1514755 1514862 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-708 1502359 1512312 1513122 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-707 1491368 1502224 1502354 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-706 1490088 1490413 1490770 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-705 1488924 1489188 1489546 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-704 1488091 1488224 1488440 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-703 1486409 1486728 1487134 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-702 1486122 1486156 1486280 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-701 1485941 1485976 1486045 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-700 1485717 1485907 1485936 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-699 1485281 1485348 1485525 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-698 1483567 1484644 1484899 "NNI" NIL NNI (NIL) -8 NIL NIL 1485246) (-697 1482295 1482632 1482996 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-696 1481272 1481524 1481826 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-695 1480359 1480924 1480965 "NETCLT" 1481136 NETCLT (NIL T) -9 NIL 1481217 NIL) (-694 1479263 1479530 1479811 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-693 1479062 1479105 1479180 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-692 1477593 1477981 1478401 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-691 1476226 1477192 1477220 "NASRING" 1477330 NASRING (NIL) -9 NIL 1477410 NIL) (-690 1476071 1476127 1476221 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-689 1475000 1475678 1475706 "NARNG" 1475823 NARNG (NIL) -9 NIL 1475914 NIL) (-688 1474776 1474861 1474995 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-687 1473542 1474296 1474336 "NAALG" 1474415 NAALG (NIL T) -9 NIL 1474476 NIL) (-686 1473412 1473447 1473537 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-685 1468391 1469576 1470762 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-684 1467786 1467873 1468057 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-683 1459777 1464272 1464324 "MTSCAT" 1465384 MTSCAT (NIL T T) -9 NIL 1465898 NIL) (-682 1459543 1459603 1459695 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-681 1459369 1459408 1459468 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-680 1456998 1458883 1458924 "MSETAGG" 1458929 MSETAGG (NIL T) -9 NIL 1458963 NIL) (-679 1453368 1456041 1456362 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-678 1449761 1451584 1452303 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-677 1449398 1449471 1449600 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-676 1449051 1449092 1449236 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-675 1446916 1447253 1447684 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-674 1440314 1446815 1446911 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-673 1439839 1439880 1440088 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-672 1439398 1439447 1439630 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-671 1438672 1438765 1438984 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-670 1437289 1437650 1438040 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-669 1436810 1436877 1436916 "MONOPC" 1436976 MONOPC (NIL T) -9 NIL 1437195 NIL) (-668 1436261 1436597 1436725 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-667 1435403 1435782 1435810 "MONOID" 1436028 MONOID (NIL) -9 NIL 1436172 NIL) (-666 1435062 1435212 1435398 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-665 1424000 1430870 1430929 "MONOGEN" 1431603 MONOGEN (NIL T T) -9 NIL 1432059 NIL) (-664 1422012 1422898 1423881 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-663 1420726 1421270 1421298 "MONADWU" 1421689 MONADWU (NIL) -9 NIL 1421924 NIL) (-662 1420274 1420474 1420721 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-661 1419551 1419852 1419880 "MONAD" 1420087 MONAD (NIL) -9 NIL 1420199 NIL) (-660 1419318 1419414 1419546 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-659 1417708 1418478 1418757 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-658 1416842 1417369 1417409 "MODULE" 1417414 MODULE (NIL T) -9 NIL 1417452 NIL) (-657 1416521 1416647 1416837 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-656 1414240 1415126 1415440 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-655 1411419 1412836 1413349 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-654 1410053 1410627 1410903 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-653 1399272 1408718 1409131 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-652 1396236 1398280 1398549 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1395320 1395687 1395877 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-650 1394889 1394938 1395117 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-649 1392714 1393710 1393750 "MLO" 1394167 MLO (NIL T) -9 NIL 1394407 NIL) (-648 1390595 1391122 1391717 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-647 1390063 1390159 1390313 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-646 1389733 1389809 1389932 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-645 1388945 1389131 1389359 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-644 1388438 1388554 1388710 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-643 1387810 1387924 1388109 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-642 1386837 1387110 1387387 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-641 1386270 1386358 1386529 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-640 1383428 1384307 1385186 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-639 1382095 1382443 1382796 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-638 1379519 1381182 1381223 "MDAGG" 1381480 MDAGG (NIL T) -9 NIL 1381625 NIL) (-637 1378793 1378957 1379157 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-636 1377871 1378157 1378387 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-635 1375968 1376545 1377106 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-634 1371712 1375558 1375805 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-633 1368061 1368830 1369564 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-632 1366814 1366983 1367312 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-631 1356259 1359883 1359959 "MATCAT" 1364947 MATCAT (NIL T T T) -9 NIL 1366393 NIL) (-630 1353540 1354846 1356254 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-629 1351941 1352301 1352685 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-628 1351074 1351271 1351493 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-627 1349825 1350151 1350478 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-626 1348987 1349389 1349565 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-625 1348656 1348720 1348843 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-624 1348304 1348377 1348491 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-623 1347839 1347954 1348096 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-622 1346048 1346816 1347117 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-621 1345542 1345844 1345934 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-620 1339863 1343839 1343880 "LZSTAGG" 1344657 LZSTAGG (NIL T) -9 NIL 1344947 NIL) (-619 1337212 1338524 1339858 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-618 1334599 1335565 1336048 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-617 1334180 1334459 1334533 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-616 1326395 1334041 1334175 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-615 1325758 1325903 1326131 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-614 1323242 1323940 1324652 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-613 1321458 1321781 1322215 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-612 1314838 1320490 1320531 "LSAGG" 1320593 LSAGG (NIL T) -9 NIL 1320671 NIL) (-611 1312532 1313631 1314833 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-610 1310012 1311881 1312130 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-609 1309679 1309770 1309893 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-608 1309350 1309429 1309457 "LOGIC" 1309568 LOGIC (NIL) -9 NIL 1309650 NIL) (-607 1309245 1309274 1309345 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-606 1308564 1308722 1308915 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-605 1307349 1307598 1307949 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-604 1303171 1305970 1306010 "LODOCAT" 1306442 LODOCAT (NIL T) -9 NIL 1306653 NIL) (-603 1302964 1303040 1303166 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-602 1299964 1302841 1302959 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-601 1297062 1299914 1299959 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-600 1294149 1296992 1297057 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-599 1293202 1293377 1293679 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-598 1291334 1292464 1292717 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-597 1287249 1289475 1289516 "LNAGG" 1290375 LNAGG (NIL T) -9 NIL 1290813 NIL) (-596 1286636 1286903 1287244 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-595 1283208 1284149 1284786 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-594 1282470 1282975 1283015 "LMODULE" 1283020 LMODULE (NIL T) -9 NIL 1283046 NIL) (-593 1279939 1282206 1282329 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-592 1279507 1279718 1279759 "LLINSET" 1279820 LLINSET (NIL T) -9 NIL 1279864 NIL) (-591 1279183 1279443 1279502 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-590 1278782 1278862 1279001 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-589 1277233 1277581 1277980 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-588 1276404 1276600 1276828 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-587 1269718 1275660 1275914 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-586 1269295 1269528 1269569 "LINSET" 1269574 LINSET (NIL T) -9 NIL 1269607 NIL) (-585 1268196 1268918 1269085 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-584 1266462 1267217 1267257 "LINEXP" 1267743 LINEXP (NIL T) -9 NIL 1268016 NIL) (-583 1265084 1266071 1266252 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-582 1263911 1264183 1264485 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-581 1263124 1263713 1263823 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-580 1260682 1261404 1262154 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-579 1259317 1259614 1260005 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-578 1258110 1258712 1258752 "LIECAT" 1258892 LIECAT (NIL T) -9 NIL 1259043 NIL) (-577 1257984 1258017 1258105 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-576 1252240 1257674 1257902 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-575 1243880 1251916 1252072 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-574 1240332 1241281 1242216 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-573 1238956 1239864 1239892 "LFCAT" 1240099 LFCAT (NIL) -9 NIL 1240238 NIL) (-572 1237195 1237525 1237870 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-571 1234712 1235377 1236058 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-570 1231724 1232702 1233205 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-569 1231215 1231518 1231609 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-568 1229922 1230246 1230646 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-567 1229188 1229273 1229499 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-566 1224191 1227756 1228292 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-565 1223816 1223866 1224026 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-564 1222587 1223360 1223400 "LALG" 1223461 LALG (NIL T) -9 NIL 1223519 NIL) (-563 1222370 1222447 1222582 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-562 1220223 1221638 1221889 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-561 1220052 1220082 1220123 "KVTFROM" 1220185 KVTFROM (NIL T) -9 NIL NIL NIL) (-560 1218868 1219583 1219772 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-559 1218697 1218727 1218768 "KRCFROM" 1218830 KRCFROM (NIL T) -9 NIL NIL NIL) (-558 1217799 1217996 1218291 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-557 1217628 1217658 1217699 "KONVERT" 1217761 KONVERT (NIL T) -9 NIL NIL NIL) (-556 1217457 1217487 1217528 "KOERCE" 1217590 KOERCE (NIL T) -9 NIL NIL NIL) (-555 1217027 1217120 1217252 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-554 1215080 1215974 1216346 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-553 1208067 1212759 1212813 "KDAGG" 1213189 KDAGG (NIL T T) -9 NIL 1213429 NIL) (-552 1207725 1207860 1208062 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-551 1201029 1207517 1207663 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-550 1200679 1200961 1201024 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-549 1199649 1200148 1200397 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-548 1198775 1199224 1199429 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-547 1197639 1198131 1198431 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-546 1196921 1197320 1197481 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-545 1196631 1196867 1196916 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-544 1190886 1196321 1196549 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-543 1190304 1190637 1190757 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-542 1187032 1188492 1188544 "IXAGG" 1189441 IXAGG (NIL T T) -9 NIL 1189901 NIL) (-541 1186319 1186650 1187027 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-540 1185388 1185663 1185905 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-539 1184050 1184257 1184550 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-538 1183001 1183223 1183506 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-537 1182676 1182739 1182862 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-536 1181938 1182310 1182484 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-535 1179914 1181214 1181488 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-534 1169462 1175231 1176388 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-533 1168707 1168859 1169095 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-532 1168198 1168501 1168592 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-531 1167491 1167582 1167795 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-530 1166623 1166848 1167088 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-529 1165036 1165417 1165845 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-528 1164821 1164865 1164941 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-527 1163671 1163968 1164263 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-526 1162944 1163295 1163446 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-525 1162147 1162278 1162491 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-524 1160309 1160806 1161350 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-523 1157390 1158658 1159347 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-522 1157215 1157255 1157315 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-521 1153213 1157141 1157210 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-520 1151216 1153152 1153208 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-519 1150587 1150886 1151016 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-518 1150040 1150328 1150460 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-517 1149121 1149746 1149872 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-516 1148531 1149025 1149053 "IOBCON" 1149058 IOBCON (NIL) -9 NIL 1149079 NIL) (-515 1148102 1148166 1148348 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-514 1140161 1142532 1144857 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-513 1137272 1138055 1138919 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-512 1136949 1137046 1137163 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-511 1134391 1136885 1136944 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-510 1132503 1133032 1133599 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-509 1132005 1132119 1132259 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-508 1130389 1130795 1131257 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-507 1128168 1128762 1129373 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-506 1125541 1126151 1126871 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-505 1124945 1125103 1125311 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-504 1124464 1124550 1124738 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-503 1122669 1123190 1123647 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-502 1115759 1117412 1119141 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-501 1115125 1115287 1115460 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-500 1112998 1113462 1114006 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-499 1111124 1112074 1112102 "INTDOM" 1112401 INTDOM (NIL) -9 NIL 1112606 NIL) (-498 1110677 1110879 1111119 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-497 1106484 1108956 1109010 "INTCAT" 1109806 INTCAT (NIL T) -9 NIL 1110122 NIL) (-496 1106049 1106169 1106296 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-495 1104889 1105061 1105367 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-494 1104462 1104558 1104715 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-493 1096945 1104369 1104457 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-492 1096243 1096798 1096863 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096897) (-491 1095540 1096095 1096160 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096194) (-490 1094837 1095392 1095457 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095491) (-489 1094134 1094689 1094754 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094788) (-488 1090597 1094053 1094129 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-487 1084654 1088137 1088165 "INS" 1089095 INS (NIL) -9 NIL 1089754 NIL) (-486 1082716 1083634 1084581 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-485 1081775 1081998 1082273 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-484 1080989 1081130 1081327 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-483 1079979 1080120 1080357 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-482 1079131 1079295 1079555 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-481 1078411 1078526 1078714 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-480 1077150 1077419 1077743 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-479 1076430 1076571 1076754 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-478 1076093 1076165 1076263 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-477 1073171 1074657 1075180 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-476 1072770 1072877 1072991 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-475 1071926 1072571 1072672 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-474 1070776 1071044 1071365 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-473 1069766 1070706 1070771 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-472 1069391 1069471 1069588 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-471 1068305 1068850 1069054 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-470 1064400 1065455 1066398 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-469 1063254 1063577 1063605 "INBCON" 1064118 INBCON (NIL) -9 NIL 1064384 NIL) (-468 1062708 1062973 1063249 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-467 1062202 1062504 1062594 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-466 1061659 1061968 1062073 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-465 1060498 1060639 1060956 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-464 1058921 1059190 1059529 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-463 1053764 1058852 1058916 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-462 1053144 1053478 1053593 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-461 1048236 1052582 1052768 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-460 1047266 1048158 1048231 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-459 1046838 1046915 1046969 "IEVALAB" 1047176 IEVALAB (NIL T T) -9 NIL NIL NIL) (-458 1046593 1046673 1046833 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-457 1045978 1046205 1046362 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-456 1044971 1045898 1045973 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-455 1044034 1044891 1044966 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-454 1043117 1043763 1043900 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-453 1041581 1042152 1042203 "IDPC" 1042612 IDPC (NIL T T) -9 NIL 1042903 NIL) (-452 1040869 1041503 1041576 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-451 1040039 1040791 1040864 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-450 1039732 1039945 1040005 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-449 1039436 1039476 1039515 "IDEMOPC" 1039520 IDEMOPC (NIL T) -9 NIL 1039657 NIL) (-448 1036507 1037388 1038280 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-447 1030133 1031410 1032449 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-446 1029395 1029525 1029724 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-445 1028568 1029067 1029205 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-444 1026959 1027290 1027681 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-443 1022996 1026915 1026954 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-442 1020254 1020878 1021573 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-441 1018480 1018960 1019493 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-440 1016295 1018386 1018475 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-439 1012437 1016233 1016290 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-438 1006016 1011401 1011869 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-437 1005584 1005647 1005820 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-436 1005076 1005225 1005253 "HYPCAT" 1005460 HYPCAT (NIL) -9 NIL NIL NIL) (-435 1004732 1004885 1005071 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-434 1004345 1004590 1004673 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-433 1004178 1004227 1004268 "HOMOTOP" 1004273 HOMOTOP (NIL T) -9 NIL 1004306 NIL) (-432 1002681 1003493 1003534 "HOAGG" 1003539 HOAGG (NIL T) -9 NIL 1003839 NIL) (-431 1002308 1002455 1002676 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-430 995508 1002033 1002181 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-429 994443 994701 994964 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-428 993378 994308 994438 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-427 991577 993211 993299 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-426 990892 991244 991377 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-425 984390 990825 990887 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-424 977529 984126 984277 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-423 976982 977139 977302 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-422 969482 976899 976977 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-421 968973 969276 969367 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-420 966523 968760 968939 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-419 962209 966406 966518 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-418 954686 962106 962204 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-417 946623 954055 954310 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-416 945647 946156 946184 "GROUP" 946387 GROUP (NIL) -9 NIL 946521 NIL) (-415 945190 945391 945642 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-414 943862 944201 944588 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-413 942684 943041 943092 "GRMOD" 943621 GRMOD (NIL T T) -9 NIL 943787 NIL) (-412 942503 942551 942679 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-411 938626 939837 940837 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-410 937348 937672 937987 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-409 936901 937029 937170 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-408 935974 936473 936524 "GRALG" 936677 GRALG (NIL T T) -9 NIL 936767 NIL) (-407 935693 935794 935969 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-406 932712 935384 935551 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-405 932125 932188 932445 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-404 927979 928875 929400 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-403 927154 927356 927594 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-402 922157 923084 924103 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-401 921905 921962 922051 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-400 921387 921476 921641 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-399 920896 920937 921150 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-398 919697 919980 920284 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-397 912972 919387 919548 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-396 902755 907762 908866 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-395 900807 901910 901938 "GCDDOM" 902193 GCDDOM (NIL) -9 NIL 902350 NIL) (-394 900430 900587 900802 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-393 891223 893693 896081 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-392 889358 889683 890101 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-391 888299 888488 888755 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-390 887170 887377 887681 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-389 886633 886775 886923 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-388 885245 885593 885906 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-387 883790 884111 884433 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-386 881416 881772 882177 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-385 874668 876329 877907 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-384 874320 874541 874609 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-383 874065 874107 874148 "FUNCTOR" 874232 FUNCTOR (NIL T) -9 NIL 874291 NIL) (-382 873689 873910 873991 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-381 871786 872469 872929 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-380 870379 870686 871078 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-379 869034 869393 869717 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-378 868337 868461 868648 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-377 867311 867577 867924 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-376 864969 865499 865981 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-375 864552 864612 864781 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-374 862852 863766 864069 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-373 862000 862134 862357 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-372 861171 861332 861559 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-371 857387 860048 860089 "FSAGG" 860459 FSAGG (NIL T) -9 NIL 860720 NIL) (-370 855741 856500 857292 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-369 853697 853993 854537 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-368 852744 852926 853226 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-367 852425 852474 852601 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-366 832581 842082 842123 "FS" 845993 FS (NIL T) -9 NIL 848271 NIL) (-365 824812 828305 832284 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-364 824346 824473 824625 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-363 818869 822027 822067 "FRNAALG" 823387 FRNAALG (NIL T) -9 NIL 823985 NIL) (-362 815610 816861 818119 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-361 815291 815340 815467 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-360 813778 814335 814629 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-359 813064 813157 813444 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-358 810898 811664 811980 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-357 810007 810450 810491 "FRETRCT" 810496 FRETRCT (NIL T) -9 NIL 810667 NIL) (-356 809380 809658 810002 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-355 806124 807644 807703 "FRAMALG" 808585 FRAMALG (NIL T T) -9 NIL 808877 NIL) (-354 804720 805271 805901 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-353 804413 804476 804583 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-352 798054 804218 804408 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-351 797747 797810 797917 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-350 790156 794727 796034 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-349 783934 787437 787465 "FPS" 788584 FPS (NIL) -9 NIL 789140 NIL) (-348 783491 783624 783788 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-347 780301 782344 782372 "FPC" 782597 FPC (NIL) -9 NIL 782739 NIL) (-346 780147 780199 780296 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-345 778924 779633 779674 "FPATMAB" 779679 FPATMAB (NIL T) -9 NIL 779831 NIL) (-344 777354 777950 778297 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-343 776929 776987 777160 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-342 775432 776327 776501 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-341 774047 774552 774580 "FNCAT" 775037 FNCAT (NIL) -9 NIL 775294 NIL) (-340 773504 774014 774042 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-339 772091 773453 773499 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-338 768679 770037 770078 "FMONCAT" 771295 FMONCAT (NIL T) -9 NIL 771899 NIL) (-337 765638 766718 766771 "FMCAT" 767853 FMCAT (NIL T T) -9 NIL 768323 NIL) (-336 764338 765461 765560 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-335 763386 764186 764333 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-334 761573 762025 762519 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-333 759508 760044 760622 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-332 752894 757845 758459 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-331 751375 752476 752516 "FLINEXP" 752521 FLINEXP (NIL T) -9 NIL 752614 NIL) (-330 750784 751043 751370 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-329 750033 750192 750406 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-328 746916 747995 748047 "FLALG" 749274 FLALG (NIL T T) -9 NIL 749741 NIL) (-327 746087 746248 746475 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-326 739793 743483 743524 "FLAGG" 744763 FLAGG (NIL T) -9 NIL 745411 NIL) (-325 738901 739305 739788 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-324 735462 736726 736785 "FINRALG" 737913 FINRALG (NIL T T) -9 NIL 738421 NIL) (-323 734853 735118 735457 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-322 734151 734447 734475 "FINITE" 734671 FINITE (NIL) -9 NIL 734778 NIL) (-321 734059 734085 734146 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-320 730829 732155 732196 "FINAGG" 733195 FINAGG (NIL T) -9 NIL 733702 NIL) (-319 729748 730271 730824 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-318 721709 724300 724340 "FINAALG" 727992 FINAALG (NIL T) -9 NIL 729430 NIL) (-317 717976 719221 720344 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-316 716528 716947 717001 "FILECAT" 717685 FILECAT (NIL T T) -9 NIL 717901 NIL) (-315 715879 716353 716456 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-314 713127 715005 715033 "FIELD" 715073 FIELD (NIL) -9 NIL 715153 NIL) (-313 712152 712613 713122 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-312 710156 711102 711448 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-311 709399 709580 709799 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-310 704669 709337 709394 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-309 704331 704398 704533 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-308 703871 703913 704122 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-307 700551 701428 702205 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-306 695835 700483 700546 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-305 690514 695324 695514 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-304 684995 689795 690053 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-303 679202 684446 684657 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-302 678225 678435 678750 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-301 673665 676370 676398 "FFIELDC" 677017 FFIELDC (NIL) -9 NIL 677392 NIL) (-300 672734 673174 673660 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-299 672349 672407 672531 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-298 670493 671016 671533 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-297 665587 670292 670393 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-296 660687 665376 665483 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-295 655353 660478 660586 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-294 654807 654856 655091 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-293 633382 644416 644502 "FFCAT" 649652 FFCAT (NIL T T T) -9 NIL 651088 NIL) (-292 629622 630848 632154 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-291 624465 629553 629617 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-290 623488 623957 623998 "FEVALAB" 624003 FEVALAB (NIL T) -9 NIL 624242 NIL) (-289 622893 623145 623483 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-288 619720 620631 620746 "FDIVCAT" 622313 FDIVCAT (NIL T T T T) -9 NIL 622749 NIL) (-287 619514 619546 619715 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-286 618821 618914 619191 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-285 617307 618305 618508 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-284 616400 616784 616986 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-283 615522 616011 616151 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-282 607109 611752 611792 "FAXF" 613593 FAXF (NIL T) -9 NIL 614283 NIL) (-281 605025 605829 606644 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-280 600174 604547 604721 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-279 594613 597037 597089 "FAMR" 598100 FAMR (NIL T T) -9 NIL 598559 NIL) (-278 593812 594177 594608 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-277 592833 593754 593807 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-276 590427 591306 591359 "FAMONC" 592300 FAMONC (NIL T T) -9 NIL 592685 NIL) (-275 588983 590285 590422 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-274 587063 587424 587826 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-273 586340 586537 586759 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-272 578200 585787 585986 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-271 576219 576789 577375 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-270 573121 573763 574483 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-269 568278 568985 569790 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-268 567967 568030 568139 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-267 552760 567016 567442 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-266 543287 552080 552368 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-265 542781 543083 543173 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-264 542557 542747 542776 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-263 542246 542314 542427 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-262 541763 541905 541946 "EVALAB" 542116 EVALAB (NIL T) -9 NIL 542220 NIL) (-261 541391 541537 541758 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-260 538434 540029 540057 "EUCDOM" 540611 EUCDOM (NIL) -9 NIL 540960 NIL) (-259 537361 537854 538429 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-258 537086 537142 537242 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-257 536774 536838 536947 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-256 530545 532445 532473 "ES" 535215 ES (NIL) -9 NIL 536599 NIL) (-255 527060 528592 530384 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-254 526408 526561 526737 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-253 518914 526338 526403 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-252 518603 518666 518775 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-251 512340 515465 516869 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-250 508643 509739 510832 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-249 507469 507820 508126 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-248 506354 507085 507113 "ENTIRER" 507118 ENTIRER (NIL) -9 NIL 507162 NIL) (-247 506243 506277 506349 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-246 502884 504681 505030 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-245 501985 502200 502252 "ELTAGG" 502618 ELTAGG (NIL T T) -9 NIL 502832 NIL) (-244 501767 501841 501980 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-243 501513 501548 501602 "ELTAB" 501686 ELTAB (NIL T T) -9 NIL 501738 NIL) (-242 500764 500934 501133 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-241 500488 500562 500590 "ELEMFUN" 500695 ELEMFUN (NIL) -9 NIL NIL NIL) (-240 500388 500415 500483 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-239 495705 498395 498436 "ELAGG" 499369 ELAGG (NIL T) -9 NIL 499830 NIL) (-238 494503 495041 495700 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-237 493921 494088 494244 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-236 492834 493153 493432 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-235 486227 488225 489052 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-234 480206 482202 483012 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-233 478020 478426 478897 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-232 469020 470933 472474 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-231 468133 468634 468783 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-230 466831 467505 467545 "DVARCAT" 467828 DVARCAT (NIL T) -9 NIL 467968 NIL) (-229 466250 466514 466826 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-228 458317 466118 466245 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-227 456655 457446 457487 "DSEXT" 457850 DSEXT (NIL T) -9 NIL 458144 NIL) (-226 455460 455984 456650 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-225 455184 455249 455347 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-224 451335 452551 453682 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-223 446981 448336 449400 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-222 445656 446017 446403 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-221 445342 445401 445519 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-220 444317 444615 444905 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-219 443902 443977 444127 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-218 436315 438427 440542 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-217 431832 432851 433930 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-216 428380 430441 430482 "DQAGG" 431111 DQAGG (NIL T) -9 NIL 431384 NIL) (-215 414904 422545 422627 "DPOLCAT" 424464 DPOLCAT (NIL T T T T) -9 NIL 425007 NIL) (-214 411312 412960 414899 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-213 404361 411210 411307 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-212 397319 404190 404356 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-211 396912 397172 397261 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-210 396326 396774 396854 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-209 395612 395937 396088 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-208 388751 395348 395499 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-207 386500 387817 387857 "DMEXT" 387862 DMEXT (NIL T) -9 NIL 388037 NIL) (-206 386156 386218 386362 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-205 379748 385641 385831 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-204 376956 378559 378600 "DLAGG" 379141 DLAGG (NIL T) -9 NIL 379373 NIL) (-203 375307 376178 376206 "DIVRING" 376298 DIVRING (NIL) -9 NIL 376381 NIL) (-202 374758 375002 375302 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-201 373186 373603 374009 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-200 372223 372444 372709 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-199 365741 372155 372218 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-198 354061 360483 360536 "DIRPCAT" 360792 DIRPCAT (NIL NIL T) -9 NIL 361667 NIL) (-197 352067 352837 353724 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-196 351514 351680 351866 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-195 348837 350373 350414 "DIOPS" 350834 DIOPS (NIL T) -9 NIL 351062 NIL) (-194 348497 348641 348832 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-193 347504 348250 348278 "DIOID" 348283 DIOID (NIL) -9 NIL 348305 NIL) (-192 346332 347161 347189 "DIFRING" 347194 DIFRING (NIL) -9 NIL 347215 NIL) (-191 345968 346066 346094 "DIFFSPC" 346213 DIFFSPC (NIL) -9 NIL 346288 NIL) (-190 345709 345811 345963 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-189 344612 345237 345277 "DIFFMOD" 345282 DIFFMOD (NIL T) -9 NIL 345379 NIL) (-188 344296 344353 344394 "DIFFDOM" 344515 DIFFDOM (NIL T) -9 NIL 344583 NIL) (-187 344177 344207 344291 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-186 341850 343371 343411 "DIFEXT" 343416 DIFEXT (NIL T) -9 NIL 343568 NIL) (-185 339778 341314 341355 "DIAGG" 341360 DIAGG (NIL T) -9 NIL 341380 NIL) (-184 339334 339524 339773 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-183 334518 338524 338801 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-182 330976 332029 333039 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-181 325526 330130 330457 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-180 324092 324384 324759 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-179 321374 322626 322994 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-178 319099 321205 321294 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-177 318482 318627 318809 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-176 315800 316524 317324 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-175 313909 314367 314929 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-174 313292 313625 313739 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-173 306492 313017 313165 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-172 304412 304922 305426 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-171 304051 304100 304251 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-170 303310 303872 303963 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-169 301334 301776 302136 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-168 300626 300915 301061 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-167 300077 300223 300375 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-166 297439 298232 298959 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-165 296878 297024 297195 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-164 294950 295261 295628 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-163 294507 294762 294863 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-162 293708 294091 294119 "CTORCAT" 294300 CTORCAT (NIL) -9 NIL 294412 NIL) (-161 293411 293545 293703 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-160 292904 293161 293269 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-159 292320 292751 292824 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-158 291779 291896 292049 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-157 288173 288929 289684 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-156 287664 287967 288058 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-155 286883 287092 287320 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-154 286387 286492 286696 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-153 286140 286174 286280 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-152 283079 283841 284559 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-151 282598 282740 282879 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-150 278491 281061 281553 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-149 278365 278392 278420 "CONDUIT" 278457 CONDUIT (NIL) -9 NIL NIL NIL) (-148 277244 277975 278003 "COMRING" 278008 COMRING (NIL) -9 NIL 278058 NIL) (-147 276409 276776 276954 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-146 276105 276146 276274 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-145 275798 275861 275968 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-144 264640 275748 275793 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-143 264101 264240 264400 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-142 263854 263895 263993 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-141 245267 257517 257557 "COMPCAT" 258558 COMPCAT (NIL T) -9 NIL 259900 NIL) (-140 237805 241318 244911 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-139 237481 237521 237560 "COMOPC" 237565 COMOPC (NIL T) -9 NIL 237730 NIL) (-138 237168 237286 237399 "COMOP" NIL COMOP (NIL T) -8 NIL NIL NIL) (-137 236927 236961 237063 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236757 236796 236854 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236338 236617 236691 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 235915 236156 236243 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235110 235358 235386 "COMBOPC" 235724 COMBOPC (NIL) -9 NIL 235899 NIL) (-132 234174 234426 234668 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231106 231790 232413 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 229986 230437 230672 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229477 229780 229871 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229164 229217 229342 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228634 228944 229042 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225154 226224 227304 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223449 224434 224672 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221053 222214 222255 "CLAGG" 222724 CLAGG (NIL T) -9 NIL 223051 NIL) (-123 220723 220855 221048 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220352 220443 220583 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218289 218796 219344 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217250 217981 218009 "CHARZ" 218014 CHARZ (NIL) -9 NIL 218028 NIL) (-119 217044 217090 217168 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215883 216646 216674 "CHARNZ" 216735 CHARNZ (NIL) -9 NIL 216783 NIL) (-117 213361 214458 214981 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213069 213148 213176 "CFCAT" 213287 CFCAT (NIL) -9 NIL NIL NIL) (-115 212412 212541 212723 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208680 211825 212105 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208058 208245 208422 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207586 208005 208053 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207059 207368 207465 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206550 206853 206944 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205799 205959 206180 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201899 203156 203864 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200265 201296 201547 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199846 200125 200199 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199280 199533 199561 "CACHSET" 199693 CACHSET (NIL) -9 NIL 199771 NIL) (-104 198632 199047 199075 "CABMON" 199125 CABMON (NIL) -9 NIL 199181 NIL) (-103 198162 198426 198536 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193651 197830 197991 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192621 193325 193460 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193623) (-100 190087 192388 192494 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187524 189841 189949 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184702 186908 186947 "BTCAT" 187014 BTCAT (NIL T) -9 NIL 187095 NIL) (-97 184453 184551 184697 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179770 183626 183652 "BTAGG" 183763 BTAGG (NIL) -9 NIL 183871 NIL) (-95 179401 179562 179765 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176480 178893 179083 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175750 175902 176080 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172826 174447 174486 "BRAGG" 175115 BRAGG (NIL T) -9 NIL 175375 NIL) (-91 171901 172332 172821 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164435 171406 171587 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162427 164387 164430 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162160 162196 162307 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160399 160832 161280 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156365 157781 158671 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155241 156132 156254 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154827 154984 155010 "BOOLE" 155118 BOOLE (NIL) -9 NIL 155199 NIL) (-83 154620 154701 154822 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153758 154285 154335 "BMODULE" 154340 BMODULE (NIL T T) -9 NIL 154404 NIL) (-81 149643 153615 153684 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149456 149496 149535 "BINOPC" 149540 BINOPC (NIL T) -9 NIL 149585 NIL) (-79 148998 149271 149373 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148519 148663 148801 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141725 148249 148394 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 139941 140914 140953 "BGAGG" 141209 BGAGG (NIL T) -9 NIL 141349 NIL) (-75 139810 139848 139936 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138661 138862 139147 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135316 137841 138146 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 134901 134994 135020 "BASTYPE" 135191 BASTYPE (NIL) -9 NIL 135287 NIL) (-71 134671 134767 134896 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134186 134274 134424 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133085 133760 133945 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 132833 132838 132864 "ATTREG" 132869 ATTREG (NIL) -9 NIL NIL NIL) (-67 132438 132710 132775 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 131938 132087 132113 "ATRIG" 132314 ATRIG (NIL) -9 NIL NIL NIL) (-65 131793 131846 131933 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131363 131594 131620 "ASTCAT" 131625 ASTCAT (NIL) -9 NIL 131655 NIL) (-63 131162 131239 131358 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129326 130995 131083 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128133 128446 128811 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 125926 128063 128128 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125117 125308 125529 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 120985 124848 124962 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115535 117597 117672 "ARR2CAT" 119940 ARR2CAT (NIL T T T) -9 NIL 120591 NIL) (-56 114496 114978 115530 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 113864 114235 114357 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 112796 112964 113260 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112497 112551 112669 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 111880 112026 112182 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111285 111575 111695 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 108980 110141 110443 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108505 108765 108861 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102200 107567 108009 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97835 99498 99548 "AMR" 100189 AMR (NIL T T) -9 NIL 100764 NIL) (-46 97189 97469 97830 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79174 97123 97184 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75577 78850 79019 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72587 73247 73854 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71966 72079 72263 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68378 69003 69595 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57867 68071 68221 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57184 57338 57516 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55897 56692 56730 "ALGEBRA" 56735 ALGEBRA (NIL T) -9 NIL 56775 NIL) (-37 55683 55760 55892 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33898 52685 52737 "ALAGG" 52872 ALAGG (NIL T T) -9 NIL 53044 NIL) (-35 33398 33547 33573 "AHYP" 33774 AHYP (NIL) -9 NIL NIL NIL) (-34 32880 33012 33038 "AGG" 33243 AGG (NIL) -9 NIL 33369 NIL) (-33 32723 32781 32875 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30862 31322 31722 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30357 30660 30749 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29727 30022 30178 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17285 26564 26602 "ACFS" 27209 ACFS (NIL T) -9 NIL 27448 NIL) (-28 15908 16518 17280 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11460 13839 13865 "ACF" 14744 ACF (NIL) -9 NIL 15156 NIL) (-26 10556 10962 11455 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10058 10298 10324 "ABELSG" 10416 ABELSG (NIL) -9 NIL 10481 NIL) (-24 9956 9987 10053 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9111 9485 9511 "ABELMON" 9736 ABELMON (NIL) -9 NIL 9869 NIL) (-22 8793 8933 9106 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8005 8488 8514 "ABELGRP" 8586 ABELGRP (NIL) -9 NIL 8661 NIL) (-20 7558 7754 8000 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6767 6806 "A1AGG" 6811 A1AGG (NIL T) -9 NIL 6845 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
+(((-237 |#1|) (-10 -7 (-14 ** (|#1| |#1| |#1|))) (-238)) (T -237)) 
+NIL 
+((-3946 (($ $) 6 T ELT)) (-3947 (($ $) 7 T ELT)) (** (($ $ $) 8 T ELT))) 
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+NIL 
+((-3791 ((|#2| $ |#1| |#2|) 10 (|has| $ (-1036 |#2|)) ELT)) (-1577 ((|#2| $ |#1| |#2|) 9 (|has| $ (-1036 |#2|)) ELT)) (-3115 ((|#2| $ |#1|) 11 T ELT)) (-3803 ((|#2| $ |#1|) 6 T ELT) ((|#2| $ |#1| |#2|) 12 T ELT))) 
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+((-3128 (((-82) $ $) 10 T ELT))) 
+(((-244 |#1|) (-10 -7 (-14 -3128 ((-82) |#1| |#1|))) (-245)) (T -244)) 
+NIL 
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+(((-245) (-110)) (T -245)) 
+NIL 
+(-12 (-962) (-79 $ $) (-10 -7 (-6 -3990))) 
+(((-18) . T) ((-20) . T) ((-22) . T) ((-69) . T) ((-79 $ $) . T) ((-101) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-12) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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+(((-31) . T) ((-69) OR (|has| |#1| (-1014)) (|has| |#1| (-69))) ((-553 (-773)) OR (|has| |#1| (-1014)) (|has| |#1| (-553 (-773)))) ((-259 |#1|) -11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ((-380 |#1|) . T) ((-429 |#1|) . T) ((-456 |#1| |#1|) -11 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1014))) ((-12) . T) ((-1014) |has| |#1| (-1014)) ((-1130) . T)) 
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+(((-318 |#1|) (-10 -7 (-14 -2997 (|#1|))) (-319)) (T -318)) 
+NIL 
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+NIL 
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+(((-18) . T) ((-20) . T) ((-22) . T) ((-35 |#1|) . T) ((-69) . T) ((-79 |#1| |#1|) . T) ((-101) . T) ((-115) |has| |#1| (-115)) ((-117) |has| |#1| (-117)) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-12) . T) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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+NIL 
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+((-1896 (($ $ $) 14 T ELT) (($ (-584 $)) 21 T ELT)) (-2711 (((-1086 $) (-1086 $) (-1086 $)) 45 T ELT)) (-3147 (($ $ $) NIL T ELT) (($ (-584 $)) 22 T ELT))) 
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+NIL 
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+NIL 
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(($ (-349 (-485)) $) NIL T ELT) (($ $ (-518 |#1|)) NIL T ELT) (($ (-518 |#1|) $) NIL T ELT))) 
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+NIL 
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+(((-469 |#1|) (-10 -7 (-14 -2020 ((-1 |#1| |#1|))) (-14 -2021 ((-1 |#1| |#1|) |#1|))) (-12 (-664) (-22))) (T -469)) 
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+(((-470 |#1|) (-12 (-718) (-450 (-695) |#1|)) (-757)) (T -470)) 
+NIL 
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ELT)) (-1710 (((-82)) NIL T ELT)) (-1712 (((-82)) NIL T ELT)) (-1714 (((-82)) NIL T ELT)) (-3593 (((-3 $ #1#) $) NIL (|has| |#2| (-311)) ELT)) (-3246 (((-1034) $) NIL T ELT)) (-1717 (((-82)) NIL T ELT)) (-1731 (((-3 |#2| #1#) (-1 (-82) |#2|) $) NIL T ELT)) (-3469 (((-3 $ #1#) $ |#2|) NIL (|has| |#2| (-496)) ELT)) (-1733 (((-82) (-1 (-82) |#2|) $) NIL T ELT)) (-3771 (($ $ (-584 (-248 |#2|))) NIL (-11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-248 |#2|)) NIL (-11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ |#2| |#2|) NIL (-11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ELT)) (-1223 (((-82) $ $) NIL T ELT)) (-3406 (((-82) $) NIL T ELT)) (-3568 (($) NIL T ELT)) (-3803 ((|#2| $ (-485) (-485) |#2|) NIL T ELT) ((|#2| $ (-485) (-485)) 27 T ELT) ((|#2| $ (-485)) NIL T ELT)) (-3761 (($ $ (-1 |#2| |#2|) (-695)) NIL T ELT) (($ $ (-1 |#2| |#2|)) NIL T ELT) (($ $) NIL (|has| 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(-695)) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| |#2| (-812 (-1091))) ELT)) (-3059 (((-82) $ $) NIL T ELT)) (-3953 (($ $ |#2|) NIL (|has| |#2| (-311)) ELT)) (-3840 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3842 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) NIL (|has| |#2| (-311)) ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-196 |#1| |#2|) $ (-196 |#1| |#2|)) NIL T ELT) (((-196 |#1| |#2|) (-196 |#1| |#2|) $) NIL T ELT)) (-3961 (((-695) $) NIL T ELT))) 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+(((-18) . T) ((-20) . T) ((-22) . T) ((-35 $) . T) ((-69) . T) ((-79 $ $) . T) ((-101) . T) ((-117) . T) ((-556 (-485)) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-145) . T) ((-245) . T) ((-496) . T) ((-12) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-583 $) . T) ((-655 $) . T) ((-664) . T) ((-715) . T) ((-717) . T) ((-719) . T) ((-722) . T) ((-756) . T) ((-757) . T) ((-760) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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+NIL 
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$) NIL (|has| (-704 |#1| (-774 |#2|)) (-554 (-474))) ELT)) (-3533 (($ (-584 (-704 |#1| (-774 |#2|)))) NIL T ELT)) (-2913 (($ $ (-774 |#2|)) NIL T ELT)) (-2915 (($ $ (-774 |#2|)) NIL T ELT)) (-3687 (($ $) NIL T ELT)) (-2914 (($ $ (-774 |#2|)) NIL T ELT)) (-3950 (((-773) $) NIL T ELT) (((-584 (-704 |#1| (-774 |#2|))) $) NIL T ELT)) (-3681 (((-695) $) NIL (|has| (-774 |#2|) (-319)) ELT)) (-1266 (((-82) $ $) NIL T ELT)) (-3701 (((-3 (-2 (|:| |bas| $) (|:| -3326 (-584 (-704 |#1| (-774 |#2|))))) #1#) (-584 (-704 |#1| (-774 |#2|))) (-1 (-82) (-704 |#1| (-774 |#2|)) (-704 |#1| (-774 |#2|)))) NIL T ELT) (((-3 (-2 (|:| |bas| $) (|:| -3326 (-584 (-704 |#1| (-774 |#2|))))) #1#) (-584 (-704 |#1| (-774 |#2|))) (-1 (-82) (-704 |#1| (-774 |#2|))) (-1 (-82) (-704 |#1| (-774 |#2|)) (-704 |#1| (-774 |#2|)))) NIL T ELT)) (-3693 (((-82) $ (-1 (-82) (-704 |#1| (-774 |#2|)) (-584 (-704 |#1| (-774 |#2|))))) NIL T ELT)) (-3192 (((-584 $) (-704 |#1| (-774 |#2|)) $) NIL T ELT) (((-584 $) (-704 |#1| (-774 |#2|)) 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+(((-1010 |#1|) (-368 |#1|) (-1014)) (T -1010)) 
+NIL 
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+NIL 
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+(((-1012 |#1|) (-110) (-1014)) (T -1012)) 
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+(((-1013 |#1|) (-10 -7 (-14 -3245 ((-1074) |#1|)) (-14 -3246 ((-1034) |#1|))) (-1014)) (T -1013)) 
+NIL 
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+(((-1014) (-110)) (T -1014)) 
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+(-12 (-69) (-553 (-773)) (-10 -8 (-14 -3246 ((-1034) $)) (-14 -3245 ((-1074) $)))) 
+(((-69) . T) ((-553 (-773)) . T) ((-12) . T) ((-1130) . T)) 
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+(((-1016) (-1017 (-1074) (-1091) (-485) (-178) (-773))) (T -1016)) 
+NIL 
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+(((-1017 |#1| |#2| |#3| |#4| |#5|) (-110) (-1014) (-1014) (-1014) (-1014) (-1014)) (T -1017)) 
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+(-12 (-1014) (-558 |t#1|) (-558 |t#2|) (-558 |t#3|) (-558 |t#4|) (-558 |t#4|) (-558 |t#5|) (-558 (-584 $)) (-240 (-485) $) (-240 (-584 (-485)) $) (-10 -8 (-14 -3269 ((-82) $ $)) (-14 -3268 ((-82) $)) (-14 -3267 ((-82) $)) (-14 -3266 ((-82) $)) (-14 -3265 ((-82) $)) (-14 -3264 ((-82) $)) (-14 -3263 ((-82) $)) (-14 -3262 ((-82) $)) (-14 -3261 ((-82) $)) (-14 -3260 ((-584 $) $)) (-14 -3538 (|t#1| $)) (-14 -3259 (|t#2| $)) (-14 -3258 (|t#3| $)) (-14 -3257 (|t#4| $)) (-14 -3256 (|t#5| $)) (-14 -3255 ($ $)) (-14 -3254 ($ $)) (-14 -3961 ((-485) $)))) 
+(((-69) . T) ((-553 (-773)) . T) ((-558 (-584 $)) . T) ((-558 |#1|) . T) ((-558 |#2|) . T) ((-558 |#3|) . T) ((-558 |#4|) . T) ((-558 |#5|) . T) ((-240 (-485) $) . T) ((-240 (-584 (-485)) $) . T) ((-12) . T) ((-1014) . T) ((-1130) . T)) 
+((-2571 (((-82) $ $) NIL T ELT)) (-3263 (((-82) $) 45 T ELT)) (-3259 ((|#2| $) 48 T ELT)) (-3264 (((-82) $) 20 T ELT)) (-3538 ((|#1| $) 21 T ELT)) (-3266 (((-82) $) 42 T ELT)) (-3268 (((-82) $) 14 T ELT)) (-3265 (((-82) $) 44 T ELT)) (-3245 (((-1074) $) NIL T ELT)) (-3262 (((-82) $) 46 T ELT)) (-3258 ((|#3| $) 50 T ELT)) (-3246 (((-1034) $) NIL T ELT)) (-3261 (((-82) $) 47 T ELT)) (-3257 ((|#4| $) 49 T ELT)) (-3256 ((|#5| $) 51 T ELT)) (-3269 (((-82) $ $) 41 T ELT)) (-3803 (($ $ (-485)) 62 T ELT) (($ $ (-584 (-485))) 64 T ELT)) (-3260 (((-584 $) $) 27 T ELT)) (-3975 (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ (-584 $)) 52 T ELT)) (-3950 (((-773) $) 28 T ELT)) (-3254 (($ $) 26 T ELT)) (-3255 (($ $) 58 T ELT)) (-1266 (((-82) $ $) NIL T ELT)) (-3267 (((-82) $) 23 T ELT)) (-3059 (((-82) $ $) 40 T ELT)) (-3961 (((-485) $) 60 T ELT))) 
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+NIL 
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+((-3312 (*1 *1 *2) (-11 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-69)) (-5 *1 (-1023 *3))))) 
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+NIL 
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+NIL 
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ELT) (((-2 (|:| |mat| (-631 (-485))) (|:| |vec| (-1180 (-485)))) (-631 $) (-1180 $)) NIL (-11 (|has| |#3| (-581 (-485))) (|has| |#3| (-962))) ELT) (((-2 (|:| |mat| (-631 |#3|)) (|:| |vec| (-1180 |#3|))) (-631 $) (-1180 $)) NIL (|has| |#3| (-962)) ELT) (((-631 |#3|) (-631 $)) NIL (|has| |#3| (-962)) ELT)) (-3845 ((|#3| (-1 |#3| |#3| |#3|) $ |#3| |#3|) NIL (|has| |#3| (-69)) ELT) ((|#3| (-1 |#3| |#3| |#3|) $ |#3|) NIL T ELT) ((|#3| (-1 |#3| |#3| |#3|) $) NIL T ELT)) (-3470 (((-3 $ #1#) $) NIL (|has| |#3| (-962)) ELT)) (-2997 (($) NIL (|has| |#3| (-319)) ELT)) (-1577 ((|#3| $ (-485) |#3|) NIL (|has| $ (-1036 |#3|)) ELT)) (-3115 ((|#3| $ (-485)) 12 T ELT)) (-3189 (((-82) $) NIL (|has| |#3| (-718)) ELT)) (-1215 (((-82) $ $) NIL (|has| |#3| (-20)) ELT)) (-2412 (((-82) $) NIL (|has| |#3| (-962)) ELT)) (-2202 (((-485) $) NIL (|has| (-485) (-757)) ELT)) (-2534 (($ $ $) NIL (|has| |#3| (-757)) ELT)) (-2611 (((-584 |#3|) $) NIL T ELT)) (-3248 (((-82) |#3| $) NIL (|has| |#3| (-69)) ELT)) (-2203 (((-485) $) NIL (|has| (-485) (-757)) ELT)) (-2860 (($ $ $) NIL (|has| |#3| (-757)) ELT)) (-3846 (($ (-1 |#3| |#3|) $) NIL T ELT)) (-2012 (((-831) $) NIL (|has| |#3| (-319)) ELT)) (-2282 (((-631 (-485)) (-1180 $)) NIL (-11 (|has| |#3| (-581 (-485))) (|has| |#3| (-962))) ELT) (((-2 (|:| |mat| (-631 (-485))) (|:| |vec| (-1180 (-485)))) (-1180 $) $) NIL (-11 (|has| |#3| (-581 (-485))) (|has| |#3| (-962))) ELT) (((-2 (|:| |mat| (-631 |#3|)) (|:| |vec| (-1180 |#3|))) (-1180 $) $) NIL (|has| |#3| (-962)) ELT) (((-631 |#3|) (-1180 $)) NIL (|has| |#3| (-962)) ELT)) (-3245 (((-1074) $) NIL (|has| |#3| (-1014)) ELT)) (-2205 (((-584 (-485)) $) NIL T ELT)) (-2206 (((-82) (-485) $) NIL T ELT)) (-2402 (($ (-831)) NIL (|has| |#3| (-319)) ELT)) (-3246 (((-1034) $) NIL (|has| |#3| (-1014)) ELT)) (-3804 ((|#3| $) NIL (|has| (-485) (-757)) ELT)) (-1731 (((-3 |#3| #1#) (-1 (-82) |#3|) $) NIL T ELT)) (-2201 (($ $ |#3|) NIL (|has| $ (-1036 |#3|)) ELT)) (-1733 (((-82) (-1 (-82) |#3|) $) NIL T ELT)) (-3771 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+NIL 
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+NIL 
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+(((-1038 |#1| |#2| |#3| |#4|) (-110) (-695) (-962) (-195 |t#1| |t#2|) (-195 |t#1| |t#2|)) (T -1038)) 
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+(((-18) . T) ((-20) . T) ((-22) . T) ((-31) . T) ((-35 |#2|) |has| |#2| (-6 (-3997 #1="*"))) ((-69) . T) ((-79 |#2| |#2|) . T) ((-101) . T) ((-556 (-349 (-485))) |has| |#2| (-951 (-349 (-485)))) ((-556 (-485)) . T) ((-556 |#2|) . T) ((-553 (-773)) . T) ((-185 $) OR (|has| |#2| (-188)) (|has| |#2| (-189))) ((-183 |#2|) . T) ((-189) |has| |#2| (-189)) ((-188) OR (|has| |#2| (-188)) (|has| |#2| (-189))) ((-224 |#2|) . T) ((-259 |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-317 |#2|) . T) ((-328 |#2|) . T) ((-354 |#2|) . T) ((-380 |#2|) . T) ((-429 |#2|) . T) ((-456 |#2| |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-12) . T) ((-589 (-485)) . T) ((-589 |#2|) . T) ((-589 $) . T) ((-591 (-485)) |has| |#2| (-581 (-485))) ((-591 |#2|) . T) ((-591 $) . T) ((-583 |#2|) OR (|has| |#2| (-145)) (|has| |#2| (-6 (-3997 #1#)))) ((-581 (-485)) |has| |#2| (-581 (-485))) ((-581 |#2|) . T) ((-655 |#2|) OR (|has| |#2| (-145)) (|has| |#2| (-6 (-3997 #1#)))) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-810 (-1091)) |has| |#2| (-810 (-1091))) ((-812 (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-966 |#1| |#1| |#2| |#3| |#4|) . T) ((-951 (-349 (-485))) |has| |#2| (-951 (-349 (-485)))) ((-951 (-485)) |has| |#2| (-951 (-485))) ((-951 |#2|) . T) ((-964 |#2|) . T) ((-969 |#2|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+(((-1042 |#1| |#2| |#3| |#4|) (-110) (-392) (-718) (-757) (-978 |t#1| |t#2| |t#3|)) (T -1042)) 
+NIL 
+(-12 (-1021 |t#1| |t#2| |t#3| |t#4|) (-708 |t#1| |t#2| |t#3| |t#4|)) 
+(((-31) . T) ((-69) . T) ((-553 (-584 |#4|)) . T) ((-553 (-773)) . T) ((-121 |#4|) . T) ((-554 (-474)) |has| |#4| (-554 (-474))) ((-259 |#4|) -11 (|has| |#4| (-259 |#4|)) (|has| |#4| (-1014))) ((-317 |#4|) . T) ((-380 |#4|) . T) ((-429 |#4|) . T) ((-456 |#4| |#4|) -11 (|has| |#4| (-259 |#4|)) (|has| |#4| (-1014))) ((-12) . T) ((-708 |#1| |#2| |#3| |#4|) . T) ((-890 |#1| |#2| |#3| |#4|) . T) ((-984 |#1| |#2| |#3| |#4|) . T) ((-1014) . T) ((-1036 |#4|) . T) ((-1021 |#1| |#2| |#3| |#4|) . T) ((-1125 |#1| |#2| |#3| |#4|) . T) ((-1130) . T)) 
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$)) NIL T ELT)) (-3845 ((|#2| (-1 |#2| |#2| |#2|) $) NIL T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) NIL T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) NIL (|has| |#2| (-69)) ELT)) (-3470 (((-3 $ #1#) $) 80 T ELT)) (-3111 (((-695) $) 68 (|has| |#2| (-496)) ELT)) (-3115 ((|#2| $ (-485) (-485)) NIL T ELT)) (-1215 (((-82) $ $) NIL T ELT)) (-2412 (((-82) $) NIL T ELT)) (-3110 (((-695) $) 70 (|has| |#2| (-496)) ELT)) (-3109 (((-584 (-196 |#1| |#2|)) $) 74 (|has| |#2| (-496)) ELT)) (-3117 (((-695) $) NIL T ELT)) (-3617 (($ |#2|) 23 T ELT)) (-3116 (((-695) $) NIL T ELT)) (-3330 ((|#2| $) 64 (|has| |#2| (-6 (-3997 #2="*"))) ELT)) (-3121 (((-485) $) NIL T ELT)) (-3119 (((-485) $) NIL T ELT)) (-2611 (((-584 |#2|) $) NIL T ELT)) (-3248 (((-82) |#2| $) NIL (|has| |#2| (-69)) ELT)) (-3120 (((-485) $) NIL T ELT)) (-3118 (((-485) $) NIL T ELT)) (-3126 (($ (-584 (-584 |#2|))) 35 T ELT)) (-3846 (($ (-1 |#2| |#2| |#2|) $ $) NIL T ELT) (($ (-1 |#2| |#2|) $) NIL T ELT)) (-3597 (((-584 (-584 |#2|)) $) NIL T 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(-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-196 |#1| |#2|) $ (-196 |#1| |#2|)) 56 T ELT) (((-196 |#1| |#2|) (-196 |#1| |#2|) $) 58 T ELT)) (-3961 (((-695) $) NIL T ELT))) 
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+(((-18) . T) ((-20) . T) ((-44 |#1| (-485)) . T) ((-22) . T) ((-35 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-35 |#1|) |has| |#1| (-145)) ((-35 |#2|) |has| |#1| (-311)) ((-35 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-32) |has| |#1| (-35 (-349 (-485)))) ((-63) |has| |#1| (-35 (-349 (-485)))) ((-69) . T) ((-79 (-349 (-485)) (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-79 |#1| |#1|) . T) ((-79 |#2| |#2|) |has| |#1| (-311)) ((-79 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-101) . T) ((-115) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-115))) (|has| |#1| (-115))) ((-117) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-741))) (-11 (|has| |#1| (-311)) (|has| |#2| (-117))) (|has| |#1| (-117))) ((-556 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-556 (-485)) . T) ((-556 (-1091)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-1091)))) ((-556 |#1|) |has| |#1| (-145)) ((-556 |#2|) . T) ((-556 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-553 (-773)) . T) ((-145) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-554 (-178)) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-329)) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-474)) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-474)))) ((-554 (-801 (-329))) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-329))))) ((-554 (-801 (-485))) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-485))))) ((-185 $) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-188))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-183 |#2|) |has| |#1| (-311)) ((-189) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-188) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-188))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-224 |#2|) |has| |#1| (-311)) ((-200) |has| |#1| (-311)) ((-238) |has| |#1| (-35 (-349 (-485)))) ((-240 (-485) |#1|) . T) ((-240 |#2| $) -11 (|has| |#1| (-311)) (|has| |#2| (-240 |#2| |#2|))) ((-240 $ $) |has| (-485) (-1026)) ((-245) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-257) |has| |#1| (-311)) ((-259 |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-311) |has| |#1| (-311)) ((-287 |#2|) |has| |#1| (-311)) ((-328 |#2|) |has| |#1| (-311)) ((-342 |#2|) |has| |#1| (-311)) ((-380 |#1|) . T) ((-380 |#2|) |has| |#1| (-311)) ((-392) |has| |#1| (-311)) ((-433) |has| |#1| (-35 (-349 (-485)))) ((-456 (-1091) |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-12) . T) ((-589 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-311)) ((-589 $) . T) ((-591 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-591 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-311)) ((-591 $) . T) ((-583 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-583 |#1|) |has| |#1| (-145)) ((-583 |#2|) |has| |#1| (-311)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-581 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-311)) ((-655 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-655 |#1|) |has| |#1| (-145)) ((-655 |#2|) |has| |#1| (-311)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-664) . T) ((-715) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-717) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-719) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-722) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-741) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-756) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-757) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-757))) (-11 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-760) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-757))) (-11 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-807 $ (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-812 (-1091)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-810 (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-812 (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-812 (-1091)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-797 (-329)) -11 (|has| |#1| (-311)) (|has| |#2| (-797 (-329)))) ((-797 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-797 (-485)))) ((-795 |#2|) |has| |#1| (-311)) ((-822) -11 (|has| |#1| (-311)) (|has| |#2| (-822))) ((-887 |#1| (-485) (-995)) . T) ((-833) |has| |#1| (-311)) ((-905 |#2|) |has| |#1| (-311)) ((-916) |has| |#1| (-35 (-349 (-485)))) ((-934) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-951 (-349 (-485))) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-485)))) ((-951 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-485)))) ((-951 (-1091)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-1091)))) ((-951 |#2|) . T) ((-964 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-311)) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-969 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-311)) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1067) -11 (|has| |#1| (-311)) (|has| |#2| (-1067))) ((-1116) |has| |#1| (-35 (-349 (-485)))) ((-1119) |has| |#1| (-35 (-349 (-485)))) ((-1130) . T) ((-1135) |has| |#1| (-311)) ((-1142 |#1|) . T) ((-1159 |#1| (-485)) . T)) 
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+NIL 
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|#1|)))) ELT) (($ $ (-1091) (-695)) 114 (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-695) |#1|)))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) 113 (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-695) |#1|)))) ELT) (($ $) 111 (|has| |#1| (-14 * (|#1| (-695) |#1|))) ELT) (($ $ (-695)) 109 (|has| |#1| (-14 * (|#1| (-695) |#1|))) ELT)) (-3059 (((-82) $ $) 8 T ELT)) (-3953 (($ $ |#1|) 79 (|has| |#1| (-311)) ELT)) (-3840 (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (-3842 (($ $ $) 18 T ELT)) (** (($ $ (-831)) 35 T ELT) (($ $ (-695)) 43 T ELT) (($ $ |#1|) 177 (|has| |#1| (-311)) ELT) (($ $ $) 173 (|has| |#1| (-35 (-349 (-485)))) ELT) (($ $ (-349 (-485))) 144 (|has| |#1| (-35 (-349 (-485)))) ELT)) (* (($ (-831) $) 17 T ELT) (($ (-695) $) 21 T ELT) (($ (-485) $) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| $) 88 T ELT) (($ (-349 (-485)) $) 77 (|has| |#1| (-35 (-349 (-485)))) ELT) (($ $ (-349 (-485))) 76 (|has| |#1| (-35 (-349 (-485)))) ELT))) 
+(((-1173 |#1|) (-110) (-962)) (T -1173)) 
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+(-12 (-1159 |t#1| (-695)) (-10 -8 (-14 -3821 ($ (-1070 (-2 (|:| |k| (-695)) (|:| |c| |t#1|))))) (-14 -3820 ((-1070 |t#1|) $)) (-14 -3821 ($ (-1070 |t#1|))) (-14 -3819 ($ $)) (-14 -3818 ($ (-1 |t#1| (-485)) $)) (-14 -3817 ((-858 |t#1|) $ (-695))) (-14 -3817 ((-858 |t#1|) $ (-695) (-695))) (IF (|has| |t#1| (-311)) (-14 ** ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (-35 (-349 (-485)))) (PROGN (-14 -3815 ($ $)) (IF (|has| |t#1| (-14 -3815 (|t#1| |t#1| (-1091)))) (IF (|has| |t#1| (-14 -3084 ((-584 (-1091)) |t#1|))) (-14 -3815 ($ $ (-1091))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (-1116)) (IF (|has| |t#1| (-872)) (IF (|has| |t#1| (-26 (-485))) (-14 -3815 ($ $ (-1091))) |%noBranch|) |%noBranch|) |%noBranch|) (-6 (-916)) (-6 (-1116))) |%noBranch|))) 
+(((-18) . T) ((-20) . T) ((-44 |#1| (-695)) . T) ((-22) . T) ((-35 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-35 |#1|) |has| |#1| (-145)) ((-35 $) |has| |#1| (-496)) ((-32) |has| |#1| (-35 (-349 (-485)))) ((-63) |has| |#1| (-35 (-349 (-485)))) ((-69) . T) ((-79 (-349 (-485)) (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-79 |#1| |#1|) . T) ((-79 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-145))) ((-101) . T) ((-115) |has| |#1| (-115)) ((-117) |has| |#1| (-117)) ((-556 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-556 (-485)) . T) ((-556 |#1|) |has| |#1| (-145)) ((-556 $) |has| |#1| (-496)) ((-553 (-773)) . T) ((-145) OR (|has| |#1| (-496)) (|has| |#1| (-145))) ((-185 $) |has| |#1| (-14 * (|#1| (-695) |#1|))) ((-189) |has| |#1| (-14 * (|#1| (-695) |#1|))) ((-188) |has| |#1| (-14 * (|#1| (-695) |#1|))) ((-238) |has| |#1| (-35 (-349 (-485)))) ((-240 (-695) |#1|) . T) ((-240 $ $) |has| (-695) (-1026)) ((-245) |has| |#1| (-496)) ((-380 |#1|) . T) ((-433) |has| |#1| (-35 (-349 (-485)))) ((-496) |has| |#1| (-496)) ((-12) . T) ((-589 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-583 |#1|) |has| |#1| (-145)) ((-583 $) |has| |#1| (-496)) ((-655 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-655 |#1|) |has| |#1| (-145)) ((-655 $) |has| |#1| (-496)) ((-664) . T) ((-807 $ (-1091)) -11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-695) |#1|)))) ((-810 (-1091)) -11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-695) |#1|)))) ((-812 (-1091)) -11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-695) |#1|)))) ((-887 |#1| (-695) (-995)) . T) ((-916) |has| |#1| (-35 (-349 (-485)))) ((-964 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-145))) ((-969 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-145))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1116) |has| |#1| (-35 (-349 (-485)))) ((-1119) |has| |#1| (-35 (-349 (-485)))) ((-1130) . T) ((-1159 |#1| (-695)) . T)) 
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+((-3829 (*1 *2 *3 *4) (-11 (-5 *3 (-584 *5)) (-5 *4 (-584 (-1 *6 (-584 *6)))) (-4 *5 (-35 (-349 (-485)))) (-4 *6 (-1173 *5)) (-5 *2 (-584 *6)) (-5 *1 (-1174 *5 *6)))) (-3828 (*1 *2 *3 *4) (-11 (-5 *3 (-1 *2 (-584 *2))) (-5 *4 (-584 *5)) (-4 *5 (-35 (-349 (-485)))) (-4 *2 (-1173 *5)) (-5 *1 (-1174 *5 *2)))) (-3827 (*1 *2 *3 *4 *4) (-11 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1173 *4)) (-5 *1 (-1174 *4 *2)) (-4 *4 (-35 (-349 (-485)))))) (-3826 (*1 *2 *3 *4) (-11 (-5 *3 (-1 *2 *2)) (-4 *2 (-1173 *4)) (-5 *1 (-1174 *4 *2)) (-4 *4 (-35 (-349 (-485)))))) (-3825 (*1 *2 *2 *2) (-11 (-4 *3 (-35 (-349 (-485)))) (-5 *1 (-1174 *3 *2)) (-4 *2 (-1173 *3)))) (-3824 (*1 *2 *3) (-11 (-5 *3 (-1 *5 (-584 *5))) (-4 *5 (-1173 *4)) (-4 *4 (-35 (-349 (-485)))) (-5 *2 (-1 (-1070 *4) (-584 (-1070 *4)))) (-5 *1 (-1174 *4 *5)))) (-3823 (*1 *2 *3) (-11 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1173 *4)) (-4 *4 (-35 (-349 (-485)))) (-5 *2 (-1 (-1070 *4) (-1070 *4) (-1070 *4))) (-5 *1 (-1174 *4 *5)))) (-3822 (*1 *2 *3) (-11 (-5 *3 (-1 *5 *5)) (-4 *5 (-1173 *4)) (-4 *4 (-35 (-349 (-485)))) (-5 *2 (-1 (-1070 *4) (-1070 *4))) (-5 *1 (-1174 *4 *5))))) 
+((-3831 ((|#2| |#4| (-695)) 31 T ELT)) (-3830 ((|#4| |#2|) 26 T ELT)) (-3833 ((|#4| (-349 |#2|)) 49 (|has| |#1| (-496)) ELT)) (-3832 (((-1 |#4| (-584 |#4|)) |#3|) 43 T ELT))) 
+(((-1175 |#1| |#2| |#3| |#4|) (-10 -7 (-14 -3830 (|#4| |#2|)) (-14 -3831 (|#2| |#4| (-695))) (-14 -3832 ((-1 |#4| (-584 |#4|)) |#3|)) (IF (|has| |#1| (-496)) (-14 -3833 (|#4| (-349 |#2|))) |%noBranch|)) (-962) (-1156 |#1|) (-601 |#2|) (-1173 |#1|)) (T -1175)) 
+((-3833 (*1 *2 *3) (-11 (-5 *3 (-349 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-496)) (-4 *4 (-962)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *5 *6 *2)) (-4 *6 (-601 *5)))) (-3832 (*1 *2 *3) (-11 (-4 *4 (-962)) (-4 *5 (-1156 *4)) (-5 *2 (-1 *6 (-584 *6))) (-5 *1 (-1175 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-1173 *4)))) (-3831 (*1 *2 *3 *4) (-11 (-5 *4 (-695)) (-4 *5 (-962)) (-4 *2 (-1156 *5)) (-5 *1 (-1175 *5 *2 *6 *3)) (-4 *6 (-601 *2)) (-4 *3 (-1173 *5)))) (-3830 (*1 *2 *3) (-11 (-4 *4 (-962)) (-4 *3 (-1156 *4)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *3 *5 *2)) (-4 *5 (-601 *3))))) 
+NIL 
+(((-1176) (-110)) (T -1176)) 
+NIL 
+(-12 (-10 -7 (-6 -2289))) 
+((-2571 (((-82) $ $) NIL T ELT)) (-3834 (((-1091)) 12 T ELT)) (-3245 (((-1074) $) 18 T ELT)) (-3246 (((-1034) $) NIL T ELT)) (-3950 (((-773) $) 11 T ELT) (((-1091) $) 8 T ELT)) (-1266 (((-82) $ $) NIL T ELT)) (-3059 (((-82) $ $) 15 T ELT))) 
+(((-1177 |#1|) (-12 (-1014) (-553 (-1091)) (-10 -8 (-14 -3950 ((-1091) $)) (-14 -3834 ((-1091))))) (-1091)) (T -1177)) 
+((-3950 (*1 *2 *1) (-11 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-13 *3 *2))) (-3834 (*1 *2) (-11 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-13 *3 *2)))) 
+((-3841 (($ (-695)) 19 T ELT)) (-3838 (((-631 |#2|) $ $) 41 T ELT)) (-3835 ((|#2| $) 51 T ELT)) (-3836 ((|#2| $) 50 T ELT)) (-3839 ((|#2| $ $) 36 T ELT)) (-3837 (($ $ $) 47 T ELT)) (-3840 (($ $) 23 T ELT) (($ $ $) 29 T ELT)) (-3842 (($ $ $) 15 T ELT)) (* (($ (-485) $) 26 T ELT) (($ |#2| $) 32 T ELT) (($ $ |#2|) 31 T ELT))) 
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+NIL 
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(-257) (-117) (-934))) (-5 *2 (-584 (-2 (|:| -1752 (-1086 *5)) (|:| -3227 (-584 (-858 *5)))))) (-5 *1 (-1208 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-13 *6 (-584 (-1091))) (-13 *7 (-584 (-1091))))) (-3971 (*1 *2 *3) (-11 (-5 *3 (-959 *4 *5)) (-4 *4 (-12 (-756) (-257) (-117) (-934))) (-13 *5 (-584 (-1091))) (-5 *2 (-584 (-2 (|:| -1752 (-1086 *4)) (|:| -3227 (-584 (-858 *4)))))) (-5 *1 (-1208 *4 *5 *6)) (-13 *6 (-584 (-1091))))) (-3970 (*1 *2 *3) (-11 (-5 *3 (-584 (-858 *4))) (-4 *4 (-12 (-756) (-257) (-117) (-934))) (-5 *2 (-584 (-959 *4 *5))) (-5 *1 (-1208 *4 *5 *6)) (-13 *5 (-584 (-1091))) (-13 *6 (-584 (-1091))))) (-3970 (*1 *2 *3 *4) (-11 (-5 *3 (-584 (-858 *5))) (-5 *4 (-82)) (-4 *5 (-12 (-756) (-257) (-117) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1208 *5 *6 *7)) (-13 *6 (-584 (-1091))) (-13 *7 (-584 (-1091))))) (-3970 (*1 *2 *3 *4 *4) (-11 (-5 *3 (-584 (-858 *5))) (-5 *4 (-82)) (-4 *5 (-12 (-756) (-257) (-117) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1208 *5 *6 *7)) (-13 *6 (-584 (-1091))) (-13 *7 (-584 (-1091)))))) 
+((-3978 (((-3 (-1180 (-349 (-485))) #1="failed") (-1180 |#1|) |#1|) 21 T ELT)) (-3976 (((-82) (-1180 |#1|)) 12 T ELT)) (-3977 (((-3 (-1180 (-485)) #1#) (-1180 |#1|)) 16 T ELT))) 
+(((-1209 |#1|) (-10 -7 (-14 -3976 ((-82) (-1180 |#1|))) (-14 -3977 ((-3 (-1180 (-485)) #1="failed") (-1180 |#1|))) (-14 -3978 ((-3 (-1180 (-349 (-485))) #1#) (-1180 |#1|) |#1|))) (-12 (-962) (-581 (-485)))) (T -1209)) 
+((-3978 (*1 *2 *3 *4) (|partial| -11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485)))) (-5 *2 (-1180 (-349 (-485)))) (-5 *1 (-1209 *4)))) (-3977 (*1 *2 *3) (|partial| -11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485)))) (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4)))) (-3976 (*1 *2 *3) (-11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485)))) (-5 *2 (-82)) (-5 *1 (-1209 *4))))) 
+((-2571 (((-82) $ $) NIL T ELT)) (-3191 (((-82) $) 12 T ELT)) (-1313 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3139 (((-695)) 9 T ELT)) (-3727 (($) NIL T CONST)) (-3470 (((-3 $ #1#) $) 57 T ELT)) (-2997 (($) 46 T ELT)) (-1215 (((-82) $ $) NIL T ELT)) (-2412 (((-82) $) 38 T ELT)) (-3448 (((-633 $) $) 36 T ELT)) (-2012 (((-831) $) 14 T ELT)) (-3245 (((-1074) $) NIL T ELT)) (-3449 (($) 26 T CONST)) (-2402 (($ (-831)) 47 T ELT)) (-3246 (((-1034) $) NIL T ELT)) (-3975 (((-485) $) 16 T ELT)) (-3950 (((-773) $) 21 T ELT) (($ (-485)) 18 T ELT)) (-3129 (((-695)) 10 T CONST)) (-1266 (((-82) $ $) 59 T ELT)) (-3128 (((-82) $ $) NIL T ELT)) (-2663 (($) 23 T CONST)) (-2669 (($) 25 T CONST)) (-3059 (((-82) $ $) 31 T ELT)) (-3840 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3842 (($ $ $) 29 T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) 52 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) 41 T ELT) (($ $ $) 40 T ELT))) 
+(((-1210 |#1|) (-12 (-145) (-319) (-554 (-485)) (-1067)) (-831)) (T -1210)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2793509 2793514 2793519 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2793494 2793499 2793504 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2793479 2793484 2793489 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2793464 2793469 2793474 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1210 2792443 2793382 2793459 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1209 2791658 2791837 2792056 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1208 2782817 2784686 2786620 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2782205 2782358 2782547 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2781667 2781970 2782083 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2779227 2781129 2781332 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2776111 2777764 2778314 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2773350 2775080 2775134 "XPOLYC" 2775419 XPOLYC (NIL T T) -9 NIL 2775532 NIL) (-1202 2770869 2772854 2773057 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2767117 2769728 2770116 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2762067 2763700 2763754 "XFALG" 2765800 XFALG (NIL T T) -9 NIL 2766562 NIL) (-1199 2757223 2759956 2759998 "XF" 2760616 XF (NIL T) -9 NIL 2761012 NIL) (-1198 2756941 2757051 2757218 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2756168 2756290 2756494 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2753910 2756068 2756163 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2752491 2753286 2753328 "XALG" 2753333 XALG (NIL T) -9 NIL 2753442 NIL) (-1194 2746342 2750901 2751379 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2744585 2745587 2745908 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2744184 2744456 2744525 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2743671 2743974 2744067 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2742748 2742958 2743253 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2741044 2741507 2741969 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2739933 2740518 2740560 "VSPACE" 2740696 VSPACE (NIL T) -9 NIL 2740770 NIL) (-1187 2739804 2739837 2739928 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2739647 2739701 2739769 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2736630 2737425 2738162 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2727728 2730329 2732502 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2721305 2723196 2724775 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2719789 2720184 2720590 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2718616 2718897 2719213 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2714013 2718443 2718535 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2707339 2711668 2711711 "VECTCAT" 2712699 VECTCAT (NIL T) -9 NIL 2713283 NIL) (-1178 2706618 2706944 2707334 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2706112 2706354 2706474 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2706045 2706050 2706080 "UTYPE" 2706085 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2705032 2705208 2705469 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2702883 2703391 2703915 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2692747 2698717 2698759 "UTSCAT" 2699857 UTSCAT (NIL T) -9 NIL 2700614 NIL) (-1172 2690812 2691755 2692742 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2690486 2690535 2690666 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2682197 2688682 2689161 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2676741 2679014 2679057 "URAGG" 2681097 URAGG (NIL T) -9 NIL 2681822 NIL) (-1168 2674812 2675744 2676736 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2670519 2673788 2674250 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2662948 2670443 2670514 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2651581 2659068 2659129 "UPXSCCA" 2659697 UPXSCCA (NIL T T) -9 NIL 2659929 NIL) (-1164 2651302 2651404 2651576 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2639836 2647048 2647090 "UPXSCAT" 2647730 UPXSCAT (NIL T) -9 NIL 2648338 NIL) (-1162 2639349 2639434 2639611 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2631035 2638940 2639202 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2629930 2630200 2630550 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2622615 2626100 2626154 "UPSCAT" 2627223 UPSCAT (NIL T T) -9 NIL 2627987 NIL) (-1158 2622035 2622287 2622610 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2621709 2621758 2621889 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2605820 2614775 2614817 "UPOLYC" 2616895 UPOLYC (NIL T) -9 NIL 2618115 NIL) (-1155 2599875 2602723 2605815 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2599311 2599436 2599599 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2598945 2599032 2599171 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2597758 2598025 2598329 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2597091 2597221 2597406 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2596683 2596758 2596905 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2587447 2596449 2596577 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2586809 2586946 2587151 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2585410 2586257 2586533 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2584639 2584836 2585061 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2571449 2584563 2584634 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2551205 2564440 2564501 "ULSCCAT" 2565132 ULSCCAT (NIL T T) -9 NIL 2565419 NIL) (-1143 2550540 2550826 2551200 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2538894 2546028 2546070 "ULSCAT" 2546923 ULSCAT (NIL T) -9 NIL 2547653 NIL) (-1141 2538407 2538492 2538669 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2520524 2537906 2538147 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2519558 2520251 2520365 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2520476) (-1138 2518591 2519284 2519398 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2519509) (-1137 2517624 2518317 2518431 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2518542) (-1136 2516657 2517350 2517464 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2517575) (-1135 2514664 2515885 2515915 "UFD" 2516126 UFD (NIL) -9 NIL 2516239 NIL) (-1134 2514508 2514565 2514659 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2513760 2513967 2514183 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2511980 2512433 2512898 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2511705 2511945 2511975 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2511643 2511648 2511678 "TYPE" 2511683 TYPE (NIL) -9 NIL 2511690 NIL) (-1129 2510802 2511022 2511262 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2509980 2510411 2510646 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2508134 2508707 2509246 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2507168 2507404 2507640 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2495766 2499943 2500039 "TSETCAT" 2505254 TSETCAT (NIL T T T T) -9 NIL 2506758 NIL) (-1124 2492103 2493919 2495761 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2486495 2491329 2491611 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2481832 2482845 2483774 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2481329 2481404 2481567 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2479405 2479695 2480050 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2478889 2479038 2479068 "TRIGCAT" 2479281 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2478640 2478743 2478884 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2475636 2477746 2478027 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2474742 2475438 2475468 "TRANFUN" 2475503 TRANFUN (NIL) -9 NIL 2475569 NIL) (-1115 2474206 2474457 2474737 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2474043 2474081 2474142 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2473500 2473631 2473782 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2472241 2472898 2473134 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2472053 2472090 2472162 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2470267 2470913 2471342 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2468647 2468984 2469306 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2458632 2466336 2466392 "TBAGG" 2466709 TBAGG (NIL T T) -9 NIL 2466919 NIL) (-1107 2456037 2457292 2458627 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2455514 2455639 2455784 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2455024 2455344 2455434 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2454521 2454638 2454776 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2447025 2454449 2454516 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2442778 2444073 2445318 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2442147 2442306 2442487 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2439301 2440054 2440837 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2439075 2439265 2439296 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2438029 2438714 2438840 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2439026) (-1097 2437293 2437841 2437920 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2437980) (-1096 2434116 2435275 2435975 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2431799 2432482 2433116 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2427877 2428923 2429900 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2424976 2427532 2427761 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2424572 2424659 2424781 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2421196 2422670 2423489 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2414156 2420393 2420686 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2405842 2413747 2414009 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2405121 2405260 2405477 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2404805 2404870 2404981 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2395528 2404517 2404642 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2394258 2394556 2394911 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2393663 2393741 2393932 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2375815 2393162 2393403 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2375414 2375686 2375755 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2374750 2375031 2375171 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2369352 2370611 2371564 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2368884 2368984 2369148 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2363995 2365277 2366424 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2358453 2359924 2361235 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2351368 2353432 2355223 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2343537 2351306 2351363 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2338486 2343251 2343366 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2338073 2338156 2338300 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2337224 2337425 2337660 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2336964 2337022 2337115 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2330490 2335167 2335775 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2329666 2329871 2330102 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2328911 2329282 2329429 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2328399 2328641 2328671 "STEP" 2328765 STEP (NIL) -9 NIL 2328836 NIL) (-1066 2320893 2328317 2328394 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2315918 2319673 2319716 "STAGG" 2320143 STAGG (NIL T) -9 NIL 2320317 NIL) (-1064 2314376 2315084 2315913 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2312538 2314203 2314295 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2311818 2312357 2312387 "SRING" 2312392 SRING (NIL) -9 NIL 2312412 NIL) (-1061 2304733 2310356 2310795 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2298507 2299946 2301450 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2291124 2295782 2295812 "SRAGG" 2297111 SRAGG (NIL) -9 NIL 2297715 NIL) (-1058 2290421 2290741 2291119 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2284527 2289743 2290166 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2278456 2281880 2282631 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2274885 2275704 2276341 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2273860 2274165 2274195 "SPFCAT" 2274639 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2272797 2273049 2273313 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2263555 2265829 2265859 "SPADXPT" 2270496 SPADXPT (NIL) -9 NIL 2272620 NIL) (-1051 2263357 2263403 2263472 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2261013 2263321 2263352 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2252687 2254776 2254818 "SPACEC" 2259133 SPACEC (NIL T) -9 NIL 2260938 NIL) (-1048 2250516 2252634 2252682 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2249495 2249684 2249967 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2247899 2248232 2248643 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2247164 2247398 2247659 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2243344 2244304 2245299 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2239702 2240401 2241130 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2233724 2238987 2239083 "SNTSCAT" 2239088 SNTSCAT (NIL T T T T) -9 NIL 2239158 NIL) (-1041 2227545 2232365 2232755 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2221317 2227464 2227540 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2219749 2220080 2220478 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2211363 2216297 2216399 "SMATCAT" 2217742 SMATCAT (NIL NIL T T T) -9 NIL 2218290 NIL) (-1037 2209204 2210188 2211358 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2208806 2208978 2209021 "SMAGG" 2209106 SMAGG (NIL T) -9 NIL 2209163 NIL) (-1035 2206349 2207955 2207998 "SKAGG" 2208259 SKAGG (NIL T) -9 NIL 2208395 NIL) (-1034 2202395 2206169 2206280 "SINT" NIL SINT (NIL) -8 NIL NIL 2206321) (-1033 2202205 2202249 2202315 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2201280 2201512 2201780 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2200284 2200446 2200722 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2199630 2199970 2200093 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2198976 2199283 2199423 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2197087 2197579 2198085 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2190571 2197006 2197082 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2190074 2190311 2190341 "SGROUP" 2190434 SGROUP (NIL) -9 NIL 2190496 NIL) (-1025 2189964 2189996 2190069 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2189602 2189642 2189683 "SGPOPC" 2189688 SGPOPC (NIL T) -9 NIL 2189889 NIL) (-1023 2189136 2189413 2189519 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2186559 2187328 2188050 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2180680 2185943 2186039 "SFRTCAT" 2186044 SFRTCAT (NIL T T T T) -9 NIL 2186082 NIL) (-1020 2175072 2176185 2177312 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2169248 2170409 2171573 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2168220 2169122 2169243 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2163828 2164723 2164818 "SEXCAT" 2167431 SEXCAT (NIL T T T T T) -9 NIL 2167982 NIL) (-1016 2162801 2163755 2163823 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2161192 2161777 2162079 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2160715 2160900 2160930 "SETCAT" 2161047 SETCAT (NIL) -9 NIL 2161131 NIL) (-1013 2160547 2160611 2160710 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2157599 2158983 2159026 "SETAGG" 2159894 SETAGG (NIL T) -9 NIL 2160232 NIL) (-1011 2157205 2157357 2157594 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2154450 2157152 2157200 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2153916 2154226 2154326 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2153043 2153409 2153470 "SEGXCAT" 2153756 SEGXCAT (NIL T T) -9 NIL 2153876 NIL) (-1007 2151968 2152236 2152279 "SEGCAT" 2152801 SEGCAT (NIL T) -9 NIL 2153022 NIL) (-1006 2151648 2151713 2151826 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2150714 2151184 2151392 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2150292 2150571 2150647 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2149657 2149793 2149997 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2148723 2149470 2149652 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2147976 2148671 2148718 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2139461 2147843 2147971 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2138321 2138611 2138928 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2137627 2137839 2138027 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2136977 2137134 2137310 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2136550 2136781 2136809 "SASTCAT" 2136814 SASTCAT (NIL) -9 NIL 2136827 NIL) (-995 2136017 2136442 2136516 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2135620 2135661 2135832 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2135251 2135292 2135449 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2128332 2135168 2135246 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2126982 2127311 2127707 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2125743 2126104 2126404 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2125367 2125588 2125669 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2122827 2123461 2123914 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2122666 2122699 2122767 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2122157 2122460 2122551 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2117785 2118653 2119564 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2106840 2112103 2112197 "RSETCAT" 2116253 RSETCAT (NIL T T T T) -9 NIL 2117341 NIL) (-983 2105378 2106020 2106835 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2099152 2100597 2102104 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2097034 2097591 2097663 "RRCC" 2098736 RRCC (NIL T T) -9 NIL 2099077 NIL) (-980 2096559 2096758 2097029 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2096029 2096339 2096437 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2068562 2079276 2079340 "RPOLCAT" 2089814 RPOLCAT (NIL T T T) -9 NIL 2092959 NIL) (-977 2062661 2065484 2068557 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2058828 2062409 2062547 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2057156 2057895 2058151 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2052799 2055611 2055639 "RNS" 2055901 RNS (NIL) -9 NIL 2056153 NIL) (-973 2051702 2052189 2052726 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2050820 2051221 2051421 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2049958 2050520 2050548 "RNG" 2050608 RNG (NIL) -9 NIL 2050662 NIL) (-970 2049847 2049881 2049953 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2049109 2049614 2049654 "RMODULE" 2049659 RMODULE (NIL T) -9 NIL 2049685 NIL) (-968 2048048 2048154 2048484 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2044945 2047638 2047931 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2037786 2040230 2040342 "RMATCAT" 2043513 RMATCAT (NIL NIL NIL T T T) -9 NIL 2044444 NIL) (-965 2037303 2037482 2037781 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2036871 2037082 2037123 "RLINSET" 2037184 RLINSET (NIL T) -9 NIL 2037228 NIL) (-963 2036516 2036597 2036723 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2035362 2036093 2036121 "RING" 2036176 RING (NIL) -9 NIL 2036268 NIL) (-961 2035207 2035263 2035357 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2034261 2034528 2034784 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2025485 2033889 2034090 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2024710 2025221 2025260 "RGBCSPC" 2025317 RGBCSPC (NIL T) -9 NIL 2025368 NIL) (-957 2023744 2024230 2024269 "RGBCMDL" 2024497 RGBCMDL (NIL T) -9 NIL 2024611 NIL) (-956 2023456 2023525 2023626 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2023219 2023260 2023355 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2021643 2022073 2022453 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2019230 2019898 2020566 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2018780 2018878 2019038 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2018402 2018500 2018541 "RETRACT" 2018672 RETRACT (NIL T) -9 NIL 2018759 NIL) (-950 2018282 2018313 2018397 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2017884 2018156 2018223 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2016364 2017255 2017452 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2016055 2016116 2016212 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2015798 2015839 2015944 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2015533 2015574 2015683 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2010604 2012055 2013270 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2007700 2008458 2009266 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2005669 2006291 2006891 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 1998597 2004220 2004656 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 1997909 1998189 1998338 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 1997394 1997509 1997674 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 1992987 1996797 1997018 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 1992219 1992418 1992631 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 1989509 1990347 1991229 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1986091 1987127 1988186 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1985927 1985980 1986008 "REAL" 1986013 REAL (NIL) -9 NIL 1986048 NIL) (-933 1985417 1985721 1985812 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1984897 1984975 1985180 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1984130 1984322 1984533 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1983018 1983315 1983682 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1981285 1981755 1982288 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1980209 1980486 1980873 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1979038 1979347 1979766 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1972386 1975898 1975926 "RCFIELD" 1977203 RCFIELD (NIL) -9 NIL 1977933 NIL) (-925 1971004 1971616 1972313 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1967758 1969090 1969131 "RCAGG" 1970185 RCAGG (NIL T) -9 NIL 1970647 NIL) (-923 1967485 1967595 1967753 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1966930 1967059 1967220 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1966547 1966626 1966745 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1965962 1966112 1966262 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1965744 1965794 1965865 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1958186 1964862 1965170 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1947888 1958053 1958181 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1947522 1947615 1947643 "RADCAT" 1947800 RADCAT (NIL) -9 NIL NIL NIL) (-915 1947360 1947420 1947517 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1945465 1947191 1947280 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1945146 1945195 1945322 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1937415 1941499 1941539 "QUATCAT" 1942317 QUATCAT (NIL T) -9 NIL 1943081 NIL) (-911 1934665 1935945 1937321 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1930505 1934615 1934660 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1927843 1929502 1929543 "QUAGG" 1929918 QUAGG (NIL T) -9 NIL 1930094 NIL) (-908 1927445 1927717 1927784 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1926451 1927081 1927244 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1926132 1926181 1926308 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1915714 1921883 1921923 "QFCAT" 1922581 QFCAT (NIL T) -9 NIL 1923574 NIL) (-904 1912598 1914037 1915620 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1912144 1912278 1912408 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1906340 1907501 1908663 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1905759 1905939 1906171 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1903581 1904109 1904532 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1902480 1902722 1903039 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1900841 1901039 1901392 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1896597 1897813 1897854 "PTRANFN" 1899738 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1895244 1895589 1895910 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1894937 1895000 1895107 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1889234 1893678 1893718 "PTCAT" 1894010 PTCAT (NIL T) -9 NIL 1894163 NIL) (-893 1888927 1888968 1889092 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1887806 1888122 1888456 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1876685 1879246 1881555 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1869887 1872450 1872544 "PSETCAT" 1875518 PSETCAT (NIL T T T T) -9 NIL 1876327 NIL) (-889 1868337 1869071 1869882 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1867656 1867851 1867879 "PSCURVE" 1868147 PSCURVE (NIL) -9 NIL 1868314 NIL) (-887 1863240 1865060 1865124 "PSCAT" 1865959 PSCAT (NIL T T T) -9 NIL 1866198 NIL) (-886 1862554 1862836 1863235 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1860951 1861866 1862129 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1860442 1860745 1860836 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1851462 1853884 1856072 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1849156 1850725 1850765 "PRQAGG" 1850948 PRQAGG (NIL T) -9 NIL 1851051 NIL) (-881 1848329 1848775 1848803 "PROPLOG" 1848942 PROPLOG (NIL) -9 NIL 1849056 NIL) (-880 1848004 1848067 1848190 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1847440 1847579 1847751 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1845688 1846451 1846748 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1845240 1845372 1845500 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1839681 1844180 1845000 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1839510 1839548 1839607 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1838949 1839089 1839240 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1837417 1837836 1838302 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1837134 1837195 1837223 "PRIMCAT" 1837347 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1836305 1836501 1836729 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1832466 1836255 1836300 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1832165 1832227 1832338 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1829301 1831814 1832047 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1828752 1828909 1828937 "PPCURVE" 1829142 PPCURVE (NIL) -9 NIL 1829278 NIL) (-866 1828365 1828610 1828693 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1826121 1826542 1827134 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1825564 1825628 1825861 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1822284 1822770 1823381 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1807856 1813986 1814050 "POLYCAT" 1817535 POLYCAT (NIL T T T) -9 NIL 1819412 NIL) (-861 1803366 1805513 1807851 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1803023 1803097 1803216 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1802716 1802779 1802886 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1796079 1802449 1802608 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1794966 1795229 1795505 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1793570 1793883 1794213 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1789013 1793520 1793565 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1787501 1787912 1788287 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1786258 1786567 1786963 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1785929 1786013 1786130 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1785508 1785583 1785757 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1784994 1785090 1785250 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1784466 1784586 1784740 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1783361 1783579 1783956 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1782972 1783057 1783209 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1782523 1782605 1782786 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1782215 1782296 1782409 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1781728 1781803 1782011 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1781076 1781204 1781406 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1780438 1780572 1780735 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1779742 1779924 1780105 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1779465 1779539 1779633 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1776033 1777222 1778138 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1775117 1775318 1775553 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1770682 1772066 1773208 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1750603 1755490 1760337 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1750343 1750396 1750499 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1749784 1749918 1750098 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1747793 1749014 1749042 "PID" 1749239 PID (NIL) -9 NIL 1749366 NIL) (-832 1747581 1747624 1747699 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1746768 1747428 1747515 "PI" NIL PI (NIL) -8 NIL NIL 1747555) (-830 1746220 1746371 1746547 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1742548 1743506 1744411 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1740912 1741201 1741567 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1740354 1740469 1740630 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1736895 1739223 1739576 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1735501 1735781 1736106 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1734266 1734520 1734868 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1732976 1733203 1733555 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1729986 1731546 1731574 "PFECAT" 1732167 PFECAT (NIL) -9 NIL 1732544 NIL) (-821 1729609 1729774 1729981 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1728433 1728715 1729016 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1726615 1727002 1727432 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1722585 1726541 1726610 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1718488 1719635 1720502 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1716420 1717509 1717550 "PERMCAT" 1717949 PERMCAT (NIL T) -9 NIL 1718246 NIL) (-815 1716116 1716163 1716286 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1712565 1714246 1714891 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1710591 1712320 1712441 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1709474 1709737 1709776 "PDSPC" 1710297 PDSPC (NIL T) -9 NIL 1710542 NIL) (-811 1708843 1709109 1709469 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1707480 1708473 1708512 "PDRING" 1708517 PDRING (NIL T) -9 NIL 1708544 NIL) (-809 1706192 1706981 1707032 "PDMOD" 1707037 PDMOD (NIL T T) -9 NIL 1707140 NIL) (-808 1705285 1705497 1705746 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1704890 1704957 1705011 "PDDOM" 1705176 PDDOM (NIL T T) -9 NIL 1705256 NIL) (-806 1704742 1704778 1704885 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1704528 1704567 1704656 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1702845 1703599 1703898 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1702534 1702597 1702706 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1700672 1701102 1701553 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1694292 1696121 1697413 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1693923 1693996 1694128 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1691625 1692305 1692786 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1689829 1690257 1690660 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1689275 1689523 1689564 "PATMAB" 1689671 PATMAB (NIL T) -9 NIL 1689754 NIL) (-796 1687922 1688326 1688583 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1687460 1687591 1687632 "PATAB" 1687637 PATAB (NIL T) -9 NIL 1687809 NIL) (-794 1686003 1686440 1686863 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1685681 1685756 1685858 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1685370 1685433 1685542 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1685175 1685221 1685288 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1684853 1684928 1685030 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1684542 1684605 1684714 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1684233 1684303 1684400 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1683922 1683985 1684094 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1683083 1683462 1683641 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1682690 1682788 1682907 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1681658 1682083 1682302 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1680323 1680977 1681337 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1673413 1679727 1679921 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1665834 1672911 1673095 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1662559 1664474 1664514 "PADICCT" 1665095 PADICCT (NIL NIL) -9 NIL 1665377 NIL) (-779 1660549 1662509 1662554 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1659711 1659921 1660187 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1659053 1659196 1659400 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1657434 1658461 1658739 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1656958 1657217 1657314 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1656017 1656695 1656867 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1646439 1649308 1651507 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1645834 1646145 1646271 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1645120 1645312 1645340 "OUTBCON" 1645655 OUTBCON (NIL) -9 NIL 1645818 NIL) (-770 1644830 1644959 1645115 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1644211 1644356 1644517 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1643582 1644009 1644098 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1642997 1643412 1643440 "OSGROUP" 1643445 OSGROUP (NIL) -9 NIL 1643467 NIL) (-766 1641961 1642222 1642507 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1639230 1641836 1641956 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1636371 1638981 1639107 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1634389 1634917 1635477 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1627731 1630271 1630311 "OREPCAT" 1632632 OREPCAT (NIL T) -9 NIL 1633734 NIL) (-761 1625757 1626691 1627726 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1624954 1625225 1625253 "ORDTYPE" 1625558 ORDTYPE (NIL) -9 NIL 1625716 NIL) (-759 1624488 1624699 1624949 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1623950 1624326 1624483 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1623444 1623807 1623835 "ORDSET" 1623840 ORDSET (NIL) -9 NIL 1623862 NIL) (-756 1622009 1623031 1623059 "ORDRING" 1623064 ORDRING (NIL) -9 NIL 1623092 NIL) (-755 1621257 1621814 1621842 "ORDMON" 1621847 ORDMON (NIL) -9 NIL 1621868 NIL) (-754 1620561 1620723 1620915 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1619772 1620280 1620308 "ORDFIN" 1620373 ORDFIN (NIL) -9 NIL 1620447 NIL) (-752 1619166 1619305 1619491 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1615841 1618134 1618540 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1615248 1615603 1615708 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1615056 1615101 1615167 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1614357 1614633 1614674 "OPERCAT" 1614885 OPERCAT (NIL T) -9 NIL 1614981 NIL) (-747 1614169 1614236 1614352 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1611535 1612971 1613467 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1610956 1611083 1611257 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1607857 1610095 1610461 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1604723 1607232 1607272 "OMSAGG" 1607333 OMSAGG (NIL T) -9 NIL 1607397 NIL) (-742 1603135 1604394 1604562 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1601331 1602572 1602600 "OINTDOM" 1602605 OINTDOM (NIL) -9 NIL 1602626 NIL) (-740 1598761 1600333 1600662 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1598015 1598711 1598756 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1595217 1597856 1598010 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1586754 1595088 1595212 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1580209 1586645 1586749 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1579181 1579418 1579691 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1576822 1577492 1578196 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1572599 1573559 1574582 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1572107 1572195 1572389 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1569556 1570138 1570811 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1566951 1567459 1568055 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1563948 1564487 1565133 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1563303 1563411 1563669 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1562461 1562586 1562807 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1558745 1559541 1560454 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1558185 1558280 1558502 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1557866 1557915 1558042 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1554469 1557665 1557784 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1553629 1554251 1554279 "OCAMON" 1554284 OCAMON (NIL) -9 NIL 1554305 NIL) (-721 1547823 1550637 1550677 "OC" 1551772 OC (NIL T) -9 NIL 1552628 NIL) (-720 1545823 1546749 1547729 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1545239 1545657 1545685 "OASGP" 1545690 OASGP (NIL) -9 NIL 1545710 NIL) (-718 1544302 1544951 1544979 "OAMONS" 1545019 OAMONS (NIL) -9 NIL 1545062 NIL) (-717 1543447 1544028 1544056 "OAMON" 1544113 OAMON (NIL) -9 NIL 1544164 NIL) (-716 1543343 1543375 1543442 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1542094 1542868 1542896 "OAGROUP" 1543042 OAGROUP (NIL) -9 NIL 1543134 NIL) (-714 1541885 1541972 1542089 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1541625 1541681 1541769 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1536687 1538250 1539777 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1533382 1534416 1535451 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1532492 1532725 1532943 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1521353 1524381 1526829 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1515476 1520739 1520833 "NTSCAT" 1520838 NTSCAT (NIL T T T T) -9 NIL 1520876 NIL) (-707 1514817 1514996 1515189 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1514510 1514573 1514680 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1502177 1512130 1512940 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1491186 1502042 1502172 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1489906 1490231 1490588 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1488742 1489006 1489364 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1487909 1488042 1488258 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1486227 1486546 1486952 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1485940 1485974 1486098 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1485759 1485794 1485863 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1485535 1485725 1485754 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1485099 1485166 1485343 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1483385 1484462 1484717 "NNI" NIL NNI (NIL) -8 NIL NIL 1485064) (-694 1482113 1482450 1482814 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1481090 1481342 1481644 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1480182 1480742 1480783 "NETCLT" 1480954 NETCLT (NIL T) -9 NIL 1481035 NIL) (-691 1479086 1479353 1479634 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1478885 1478928 1479003 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1477416 1477804 1478224 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1476049 1477015 1477043 "NASRING" 1477153 NASRING (NIL) -9 NIL 1477233 NIL) (-687 1475894 1475950 1476044 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1474823 1475501 1475529 "NARNG" 1475646 NARNG (NIL) -9 NIL 1475737 NIL) (-685 1474599 1474684 1474818 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1473365 1474119 1474159 "NAALG" 1474238 NAALG (NIL T) -9 NIL 1474299 NIL) (-683 1473235 1473270 1473360 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1468214 1469399 1470585 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1467609 1467696 1467880 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1459600 1464095 1464147 "MTSCAT" 1465207 MTSCAT (NIL T T) -9 NIL 1465721 NIL) (-679 1459366 1459426 1459518 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1459192 1459231 1459291 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1456821 1458706 1458747 "MSETAGG" 1458752 MSETAGG (NIL T) -9 NIL 1458786 NIL) (-676 1453191 1455864 1456185 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1449584 1451407 1452126 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1449221 1449294 1449423 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1448874 1448915 1449059 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1446739 1447076 1447507 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1440137 1446638 1446734 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1439662 1439703 1439911 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1439221 1439270 1439453 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1438495 1438588 1438807 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1437112 1437473 1437863 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1436633 1436700 1436739 "MONOPC" 1436799 MONOPC (NIL T) -9 NIL 1437018 NIL) (-665 1436084 1436420 1436548 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1435226 1435605 1435633 "MONOID" 1435851 MONOID (NIL) -9 NIL 1435995 NIL) (-663 1434885 1435035 1435221 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1423823 1430693 1430752 "MONOGEN" 1431426 MONOGEN (NIL T T) -9 NIL 1431882 NIL) (-661 1421835 1422721 1423704 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1420549 1421093 1421121 "MONADWU" 1421512 MONADWU (NIL) -9 NIL 1421747 NIL) (-659 1420097 1420297 1420544 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1419374 1419675 1419703 "MONAD" 1419910 MONAD (NIL) -9 NIL 1420022 NIL) (-657 1419141 1419237 1419369 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1417531 1418301 1418580 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1416665 1417192 1417232 "MODULE" 1417237 MODULE (NIL T) -9 NIL 1417275 NIL) (-654 1416344 1416470 1416660 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1414063 1414949 1415263 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1411242 1412659 1413172 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1409876 1410450 1410726 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1399095 1408541 1408954 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1396059 1398103 1398372 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1395143 1395510 1395700 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1394712 1394761 1394940 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1392537 1393533 1393573 "MLO" 1393990 MLO (NIL T) -9 NIL 1394230 NIL) (-645 1390418 1390945 1391540 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1389886 1389982 1390136 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1389556 1389632 1389755 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1388768 1388954 1389182 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1388261 1388377 1388533 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1387633 1387747 1387932 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1386660 1386933 1387210 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1386093 1386181 1386352 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1383251 1384130 1385009 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1381918 1382266 1382619 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1379342 1381005 1381046 "MDAGG" 1381303 MDAGG (NIL T) -9 NIL 1381448 NIL) (-634 1378616 1378780 1378980 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1377694 1377980 1378210 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1375791 1376368 1376929 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1371535 1375381 1375628 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1367884 1368653 1369387 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1366637 1366806 1367135 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1356082 1359706 1359782 "MATCAT" 1364770 MATCAT (NIL T T T) -9 NIL 1366216 NIL) (-627 1353363 1354669 1356077 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1351764 1352124 1352508 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1350897 1351094 1351316 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1349648 1349974 1350301 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1348810 1349212 1349388 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1348479 1348543 1348666 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1348127 1348200 1348314 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1347662 1347777 1347919 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1345871 1346639 1346940 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1345365 1345667 1345757 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1339686 1343662 1343703 "LZSTAGG" 1344480 LZSTAGG (NIL T) -9 NIL 1344770 NIL) (-616 1337035 1338347 1339681 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1334422 1335388 1335871 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1334003 1334282 1334356 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1326218 1333864 1333998 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1325581 1325726 1325954 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1323065 1323763 1324475 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1321281 1321604 1322038 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1314661 1320313 1320354 "LSAGG" 1320416 LSAGG (NIL T) -9 NIL 1320494 NIL) (-608 1312355 1313454 1314656 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1309835 1311704 1311953 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1309502 1309593 1309716 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1309173 1309252 1309280 "LOGIC" 1309391 LOGIC (NIL) -9 NIL 1309473 NIL) (-604 1309068 1309097 1309168 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1308387 1308545 1308738 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1307172 1307421 1307772 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1302994 1305793 1305833 "LODOCAT" 1306265 LODOCAT (NIL T) -9 NIL 1306476 NIL) (-600 1302787 1302863 1302989 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1299787 1302664 1302782 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1296885 1299737 1299782 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1293972 1296815 1296880 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1293025 1293200 1293502 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1291157 1292287 1292540 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1287072 1289298 1289339 "LNAGG" 1290198 LNAGG (NIL T) -9 NIL 1290636 NIL) (-593 1286459 1286726 1287067 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1283031 1283972 1284609 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1282293 1282798 1282838 "LMODULE" 1282843 LMODULE (NIL T) -9 NIL 1282869 NIL) (-590 1279762 1282029 1282152 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1279330 1279541 1279582 "LLINSET" 1279643 LLINSET (NIL T) -9 NIL 1279687 NIL) (-588 1279006 1279266 1279325 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1278605 1278685 1278824 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1277056 1277404 1277803 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1276227 1276423 1276651 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1269541 1275483 1275737 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1269118 1269351 1269392 "LINSET" 1269397 LINSET (NIL T) -9 NIL 1269430 NIL) (-582 1268019 1268741 1268908 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1266285 1267040 1267080 "LINEXP" 1267566 LINEXP (NIL T) -9 NIL 1267839 NIL) (-580 1264907 1265894 1266075 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1263734 1264006 1264308 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1262947 1263536 1263646 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1260505 1261227 1261977 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1259140 1259437 1259828 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1257933 1258535 1258575 "LIECAT" 1258715 LIECAT (NIL T) -9 NIL 1258866 NIL) (-574 1257807 1257840 1257928 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1252063 1257497 1257725 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1243703 1251739 1251895 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1240155 1241104 1242039 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1238779 1239687 1239715 "LFCAT" 1239922 LFCAT (NIL) -9 NIL 1240061 NIL) (-569 1237018 1237348 1237693 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1234535 1235200 1235881 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1231547 1232525 1233028 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1231038 1231341 1231432 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1229745 1230069 1230469 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1229011 1229096 1229322 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1224014 1227579 1228115 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1223639 1223689 1223849 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1222410 1223183 1223223 "LALG" 1223284 LALG (NIL T) -9 NIL 1223342 NIL) (-560 1222193 1222270 1222405 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1220046 1221461 1221712 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1219875 1219905 1219946 "KVTFROM" 1220008 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1218691 1219406 1219595 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1218520 1218550 1218591 "KRCFROM" 1218653 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1217622 1217819 1218114 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1217451 1217481 1217522 "KONVERT" 1217584 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1217280 1217310 1217351 "KOERCE" 1217413 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1216850 1216943 1217075 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1214903 1215797 1216169 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1207890 1212582 1212636 "KDAGG" 1213012 KDAGG (NIL T T) -9 NIL 1213252 NIL) (-549 1207548 1207683 1207885 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1200852 1207340 1207486 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1200505 1200785 1200847 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1199475 1199974 1200223 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1198601 1199050 1199255 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1197467 1197958 1198257 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1196749 1197148 1197309 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1196462 1196696 1196744 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1190717 1196152 1196380 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1190135 1190468 1190588 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1186863 1188323 1188375 "IXAGG" 1189272 IXAGG (NIL T T) -9 NIL 1189732 NIL) (-538 1186150 1186481 1186858 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1185219 1185494 1185736 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1183881 1184088 1184381 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1182832 1183054 1183337 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1182507 1182570 1182693 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1181769 1182141 1182315 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1179745 1181045 1181319 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1169293 1175062 1176219 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1168538 1168690 1168926 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1168029 1168332 1168423 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1167322 1167413 1167626 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1166454 1166679 1166919 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1164867 1165248 1165676 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1164652 1164696 1164772 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1163502 1163799 1164094 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1162775 1163126 1163277 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1161978 1162109 1162322 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1160140 1160637 1161181 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1157221 1158489 1159178 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1157046 1157086 1157146 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1153044 1156972 1157041 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1151047 1152983 1153039 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1150421 1150719 1150848 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1149874 1150162 1150294 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1148960 1149580 1149706 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1148375 1148864 1148892 "IOBCON" 1148897 IOBCON (NIL) -9 NIL 1148918 NIL) (-512 1147946 1148010 1148192 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1140005 1142376 1144701 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1137116 1137899 1138763 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1136793 1136890 1137007 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1134235 1136729 1136788 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1132347 1132876 1133443 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1131849 1131963 1132103 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1130233 1130639 1131101 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1128012 1128606 1129217 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1125385 1125995 1126715 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1124789 1124947 1125155 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1124308 1124394 1124582 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1122513 1123034 1123491 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1115603 1117256 1118985 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1114969 1115131 1115304 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1112842 1113306 1113850 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1110968 1111918 1111946 "INTDOM" 1112245 INTDOM (NIL) -9 NIL 1112450 NIL) (-495 1110521 1110723 1110963 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1106328 1108800 1108854 "INTCAT" 1109650 INTCAT (NIL T) -9 NIL 1109966 NIL) (-493 1105893 1106013 1106140 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1104733 1104905 1105211 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1104306 1104402 1104559 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1096789 1104213 1104301 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1096087 1096642 1096707 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096741) (-488 1095384 1095939 1096004 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096038) (-487 1094681 1095236 1095301 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095335) (-486 1093978 1094533 1094598 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094632) (-485 1090441 1093897 1093973 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1084498 1087981 1088009 "INS" 1088939 INS (NIL) -9 NIL 1089598 NIL) (-483 1082560 1083478 1084425 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1081619 1081842 1082117 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1080833 1080974 1081171 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1079823 1079964 1080201 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1078975 1079139 1079399 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1078255 1078370 1078558 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1076994 1077263 1077587 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1076274 1076415 1076598 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1075937 1076009 1076107 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1073015 1074501 1075024 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1072614 1072721 1072835 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1071775 1072415 1072516 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1070625 1070893 1071214 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1069615 1070555 1070620 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1069240 1069320 1069437 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1068156 1068699 1068903 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1064251 1065306 1066249 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1063111 1063432 1063460 "INBCON" 1063971 INBCON (NIL) -9 NIL 1064235 NIL) (-465 1062567 1062831 1063106 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1062061 1062363 1062453 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1061518 1061827 1061932 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1060357 1060498 1060815 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1058780 1059049 1059388 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1053623 1058711 1058775 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1053003 1053337 1053452 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1048095 1052441 1052627 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1047125 1048017 1048090 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1046697 1046774 1046828 "IEVALAB" 1047035 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1046452 1046532 1046692 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1045837 1046064 1046221 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1044830 1045757 1045832 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1043893 1044750 1044825 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1042976 1043622 1043759 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1041440 1042011 1042062 "IDPC" 1042471 IDPC (NIL T T) -9 NIL 1042762 NIL) (-449 1040728 1041362 1041435 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1039898 1040650 1040723 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1039591 1039804 1039864 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1039295 1039335 1039374 "IDEMOPC" 1039379 IDEMOPC (NIL T) -9 NIL 1039516 NIL) (-445 1036366 1037247 1038139 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1029992 1031269 1032308 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1029254 1029384 1029583 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1028427 1028926 1029064 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1026818 1027149 1027540 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1022855 1026774 1026813 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1020113 1020737 1021432 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1018339 1018819 1019352 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1016154 1018245 1018334 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1012296 1016092 1016149 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1005875 1011260 1011728 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1005443 1005506 1005679 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1004935 1005084 1005112 "HYPCAT" 1005319 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1004591 1004744 1004930 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1004204 1004449 1004532 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1004037 1004086 1004127 "HOMOTOP" 1004132 HOMOTOP (NIL T) -9 NIL 1004165 NIL) (-429 1002540 1003352 1003393 "HOAGG" 1003398 HOAGG (NIL T) -9 NIL 1003698 NIL) (-428 1002167 1002314 1002535 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 995367 1001892 1002040 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 994302 994560 994823 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 993237 994167 994297 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 991436 993070 993158 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 990751 991103 991236 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 984249 990684 990746 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 977388 983985 984136 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 976841 976998 977161 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 969341 976758 976836 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968832 969135 969226 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 966382 968619 968798 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 962068 966265 966377 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 954545 961965 962063 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 946482 953914 954169 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 945506 946015 946043 "GROUP" 946246 GROUP (NIL) -9 NIL 946380 NIL) (-412 945049 945250 945501 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 943721 944060 944447 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 942543 942900 942951 "GRMOD" 943480 GRMOD (NIL T T) -9 NIL 943646 NIL) (-409 942362 942410 942538 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 938485 939696 940696 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 937207 937531 937846 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936760 936888 937029 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935833 936332 936383 "GRALG" 936536 GRALG (NIL T T) -9 NIL 936626 NIL) (-404 935552 935653 935828 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 932571 935243 935410 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931984 932047 932304 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927838 928734 929259 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 927013 927215 927453 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 922016 922943 923962 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921764 921821 921910 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 921246 921335 921500 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920755 920796 921009 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 919556 919839 920143 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912831 919246 919407 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 902614 907621 908725 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 900666 901769 901797 "GCDDOM" 902052 GCDDOM (NIL) -9 NIL 902209 NIL) (-391 900289 900446 900661 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 891082 893552 895940 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 889217 889542 889960 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 888158 888347 888614 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 887029 887236 887540 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 886492 886634 886782 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 885104 885452 885765 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 883649 883970 884292 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 881275 881631 882036 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 874527 876188 877766 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 874179 874400 874468 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873924 873966 874007 "FUNCTOR" 874091 FUNCTOR (NIL T) -9 NIL 874150 NIL) (-379 873548 873769 873850 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-378 871645 872328 872788 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-377 870238 870545 870937 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-376 868893 869252 869576 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-375 868196 868320 868507 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-374 867170 867436 867783 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-373 864828 865358 865840 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-372 864411 864471 864640 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-371 862711 863625 863928 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-370 861859 861993 862216 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-369 861030 861191 861418 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-368 857246 859907 859948 "FSAGG" 860318 FSAGG (NIL T) -9 NIL 860579 NIL) (-367 855600 856359 857151 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-366 853556 853852 854396 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-365 852603 852785 853085 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-364 852284 852333 852460 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-363 832440 841941 841982 "FS" 845852 FS (NIL T) -9 NIL 848130 NIL) (-362 824671 828164 832143 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-361 824205 824332 824484 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-360 818728 821886 821926 "FRNAALG" 823246 FRNAALG (NIL T) -9 NIL 823844 NIL) (-359 815469 816720 817978 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-358 815150 815199 815326 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-357 813637 814194 814488 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-356 812923 813016 813303 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 810757 811523 811839 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-354 809866 810309 810350 "FRETRCT" 810355 FRETRCT (NIL T) -9 NIL 810526 NIL) (-353 809239 809517 809861 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-352 805983 807503 807562 "FRAMALG" 808444 FRAMALG (NIL T T) -9 NIL 808736 NIL) (-351 804579 805130 805760 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-350 804272 804335 804442 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-349 797913 804077 804267 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-348 797606 797669 797776 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-347 790015 794586 795893 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-346 783793 787296 787324 "FPS" 788443 FPS (NIL) -9 NIL 788999 NIL) (-345 783350 783483 783647 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-344 780160 782203 782231 "FPC" 782456 FPC (NIL) -9 NIL 782598 NIL) (-343 780006 780058 780155 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-342 778783 779492 779533 "FPATMAB" 779538 FPATMAB (NIL T) -9 NIL 779690 NIL) (-341 777213 777809 778156 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-340 776788 776846 777019 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-339 775291 776186 776360 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-338 773906 774411 774439 "FNCAT" 774896 FNCAT (NIL) -9 NIL 775153 NIL) (-337 773363 773873 773901 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-336 771950 773312 773358 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-335 768538 769896 769937 "FMONCAT" 771154 FMONCAT (NIL T) -9 NIL 771758 NIL) (-334 765497 766577 766630 "FMCAT" 767712 FMCAT (NIL T T) -9 NIL 768182 NIL) (-333 764197 765320 765419 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-332 763245 764045 764192 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-331 761432 761884 762378 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-330 759367 759903 760481 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-329 752753 757704 758318 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-328 751234 752335 752375 "FLINEXP" 752380 FLINEXP (NIL T) -9 NIL 752473 NIL) (-327 750643 750902 751229 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-326 749892 750051 750265 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-325 746775 747854 747906 "FLALG" 749133 FLALG (NIL T T) -9 NIL 749600 NIL) (-324 745946 746107 746334 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-323 739652 743342 743383 "FLAGG" 744622 FLAGG (NIL T) -9 NIL 745270 NIL) (-322 738760 739164 739647 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-321 735321 736585 736644 "FINRALG" 737772 FINRALG (NIL T T) -9 NIL 738280 NIL) (-320 734712 734977 735316 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-319 734010 734306 734334 "FINITE" 734530 FINITE (NIL) -9 NIL 734637 NIL) (-318 733918 733944 734005 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-317 730688 732014 732055 "FINAGG" 733054 FINAGG (NIL T) -9 NIL 733561 NIL) (-316 729607 730130 730683 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-315 721568 724159 724199 "FINAALG" 727851 FINAALG (NIL T) -9 NIL 729289 NIL) (-314 717835 719080 720203 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-313 716387 716806 716860 "FILECAT" 717544 FILECAT (NIL T T) -9 NIL 717760 NIL) (-312 715738 716212 716315 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-311 712986 714864 714892 "FIELD" 714932 FIELD (NIL) -9 NIL 715012 NIL) (-310 712011 712472 712981 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-309 710015 710961 711307 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-308 709258 709439 709658 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-307 704528 709196 709253 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-306 704190 704257 704392 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-305 703730 703772 703981 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-304 700410 701287 702064 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-303 695694 700342 700405 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-302 690373 695183 695373 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-301 684854 689654 689912 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-300 679061 684305 684516 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-299 678084 678294 678609 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-298 673524 676229 676257 "FFIELDC" 676876 FFIELDC (NIL) -9 NIL 677251 NIL) (-297 672593 673033 673519 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-296 672208 672266 672390 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-295 670352 670875 671392 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-294 665446 670151 670252 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-293 660546 665235 665342 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-292 655212 660337 660445 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-291 654666 654715 654950 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-290 633241 644275 644361 "FFCAT" 649511 FFCAT (NIL T T T) -9 NIL 650947 NIL) (-289 629481 630707 632013 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-288 624324 629412 629476 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-287 623347 623816 623857 "FEVALAB" 623862 FEVALAB (NIL T) -9 NIL 624101 NIL) (-286 622752 623004 623342 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-285 619579 620490 620605 "FDIVCAT" 622172 FDIVCAT (NIL T T T T) -9 NIL 622608 NIL) (-284 619373 619405 619574 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-283 618680 618773 619050 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-282 617166 618164 618367 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-281 616259 616643 616845 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-280 615381 615870 616010 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-279 606968 611611 611651 "FAXF" 613452 FAXF (NIL T) -9 NIL 614142 NIL) (-278 604884 605688 606503 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-277 600033 604406 604580 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-276 594472 596896 596948 "FAMR" 597959 FAMR (NIL T T) -9 NIL 598418 NIL) (-275 593671 594036 594467 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-274 592692 593613 593666 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-273 590286 591165 591218 "FAMONC" 592159 FAMONC (NIL T T) -9 NIL 592544 NIL) (-272 588842 590144 590281 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-271 586922 587283 587685 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-270 586199 586396 586618 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-269 578059 585646 585845 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-268 576078 576648 577234 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-267 572980 573622 574342 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-266 568137 568844 569649 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-265 567826 567889 567998 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-264 552619 566875 567301 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-263 543146 551939 552227 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-262 542640 542942 543032 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-261 542416 542606 542635 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-260 542105 542173 542286 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-259 541622 541764 541805 "EVALAB" 541975 EVALAB (NIL T) -9 NIL 542079 NIL) (-258 541250 541396 541617 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-257 538293 539888 539916 "EUCDOM" 540470 EUCDOM (NIL) -9 NIL 540819 NIL) (-256 537220 537713 538288 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-255 536945 537001 537101 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-254 536633 536697 536806 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-253 530404 532304 532332 "ES" 535074 ES (NIL) -9 NIL 536458 NIL) (-252 526919 528451 530243 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-251 526267 526420 526596 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-250 518773 526197 526262 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-249 518462 518525 518634 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-248 512199 515324 516728 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-247 508502 509598 510691 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-246 507331 507681 507986 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-245 506216 506947 506975 "ENTIRER" 506980 ENTIRER (NIL) -9 NIL 507024 NIL) (-244 506105 506139 506211 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-243 502746 504543 504892 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-242 501847 502062 502114 "ELTAGG" 502480 ELTAGG (NIL T T) -9 NIL 502694 NIL) (-241 501629 501703 501842 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-240 501375 501410 501464 "ELTAB" 501548 ELTAB (NIL T T) -9 NIL 501600 NIL) (-239 500626 500796 500995 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-238 500350 500424 500452 "ELEMFUN" 500557 ELEMFUN (NIL) -9 NIL NIL NIL) (-237 500250 500277 500345 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-236 495567 498257 498298 "ELAGG" 499231 ELAGG (NIL T) -9 NIL 499692 NIL) (-235 494365 494903 495562 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-234 493783 493950 494106 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-233 492696 493015 493294 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-232 486089 488087 488914 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-231 480068 482064 482874 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-230 477882 478288 478759 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-229 468882 470795 472336 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-228 467995 468496 468645 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-227 466693 467367 467407 "DVARCAT" 467690 DVARCAT (NIL T) -9 NIL 467830 NIL) (-226 466112 466376 466688 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-225 458179 465980 466107 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-224 456517 457308 457349 "DSEXT" 457712 DSEXT (NIL T) -9 NIL 458006 NIL) (-223 455322 455846 456512 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-222 455046 455111 455209 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-221 451197 452413 453544 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-220 446843 448198 449262 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-219 445518 445879 446265 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-218 445204 445263 445381 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-217 444179 444477 444767 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-216 443764 443839 443989 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-215 436177 438289 440404 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-214 431694 432713 433792 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-213 428242 430303 430344 "DQAGG" 430973 DQAGG (NIL T) -9 NIL 431246 NIL) (-212 414766 422407 422489 "DPOLCAT" 424326 DPOLCAT (NIL T T T T) -9 NIL 424869 NIL) (-211 411174 412822 414761 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-210 404223 411072 411169 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-209 397181 404052 404218 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-208 396774 397034 397123 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-207 396188 396636 396716 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-206 395474 395799 395950 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-205 388613 395210 395361 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-204 386362 387679 387719 "DMEXT" 387724 DMEXT (NIL T) -9 NIL 387899 NIL) (-203 386018 386080 386224 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-202 379610 385503 385693 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-201 376818 378421 378462 "DLAGG" 379003 DLAGG (NIL T) -9 NIL 379235 NIL) (-200 375169 376040 376068 "DIVRING" 376160 DIVRING (NIL) -9 NIL 376243 NIL) (-199 374620 374864 375164 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-198 373048 373465 373871 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-197 372085 372306 372571 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-196 365603 372017 372080 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-195 353923 360345 360398 "DIRPCAT" 360654 DIRPCAT (NIL NIL T) -9 NIL 361529 NIL) (-194 351929 352699 353586 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-193 351376 351542 351728 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-192 348699 350235 350276 "DIOPS" 350696 DIOPS (NIL T) -9 NIL 350924 NIL) (-191 348359 348503 348694 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-190 347366 348112 348140 "DIOID" 348145 DIOID (NIL) -9 NIL 348167 NIL) (-189 346194 347023 347051 "DIFRING" 347056 DIFRING (NIL) -9 NIL 347077 NIL) (-188 345830 345928 345956 "DIFFSPC" 346075 DIFFSPC (NIL) -9 NIL 346150 NIL) (-187 345571 345673 345825 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-186 344474 345099 345139 "DIFFMOD" 345144 DIFFMOD (NIL T) -9 NIL 345241 NIL) (-185 344158 344215 344256 "DIFFDOM" 344377 DIFFDOM (NIL T) -9 NIL 344445 NIL) (-184 344039 344069 344153 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-183 341712 343233 343273 "DIFEXT" 343278 DIFEXT (NIL T) -9 NIL 343430 NIL) (-182 339640 341176 341217 "DIAGG" 341222 DIAGG (NIL T) -9 NIL 341242 NIL) (-181 339196 339386 339635 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-180 334380 338386 338663 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-179 330838 331891 332901 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-178 325388 329992 330319 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-177 323954 324246 324621 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-176 321236 322488 322856 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-175 318961 321067 321156 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-174 318344 318489 318671 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-173 315662 316386 317186 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-172 313771 314229 314791 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-171 313154 313487 313601 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-170 306354 312879 313027 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-169 304274 304784 305288 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-168 303913 303962 304113 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-167 303172 303734 303825 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-166 301196 301638 301998 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-165 300488 300777 300923 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-164 299939 300085 300237 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-163 297301 298094 298821 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-162 296740 296886 297057 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-161 294812 295123 295490 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-160 294369 294624 294725 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-159 293570 293953 293981 "CTORCAT" 294162 CTORCAT (NIL) -9 NIL 294274 NIL) (-158 293273 293407 293565 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-157 292766 293023 293131 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-156 292182 292613 292686 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-155 291641 291758 291911 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-154 288035 288791 289546 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-153 287526 287829 287920 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-152 286745 286954 287182 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-151 286249 286354 286558 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-150 286002 286036 286142 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-149 282941 283703 284421 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-148 282460 282602 282741 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-147 278353 280923 281415 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-146 278227 278254 278282 "CONDUIT" 278319 CONDUIT (NIL) -9 NIL NIL NIL) (-145 277106 277837 277865 "COMRING" 277870 COMRING (NIL) -9 NIL 277920 NIL) (-144 276271 276638 276816 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-143 275967 276008 276136 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-142 275660 275723 275830 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-141 264502 275610 275655 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-140 263963 264102 264262 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-139 263716 263757 263855 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-138 245129 257379 257419 "COMPCAT" 258420 COMPCAT (NIL T) -9 NIL 259762 NIL) (-137 237667 241180 244773 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-136 237343 237383 237422 "COMOPC" 237427 COMOPC (NIL T) -9 NIL 237592 NIL) (-135 237030 237148 237261 "COMOP" NIL COMOP (NIL T) -8 NIL NIL NIL) (-134 236789 236823 236925 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-133 236619 236658 236716 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-132 236200 236479 236553 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-131 235777 236018 236105 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-130 234972 235220 235248 "COMBOPC" 235586 COMBOPC (NIL) -9 NIL 235761 NIL) (-129 234036 234288 234530 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-128 230968 231652 232275 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-127 229848 230299 230534 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-126 229339 229642 229733 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-125 229026 229079 229204 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-124 228496 228806 228904 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-123 225016 226086 227166 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-122 223311 224296 224534 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-121 220915 222076 222117 "CLAGG" 222586 CLAGG (NIL T) -9 NIL 222913 NIL) (-120 220585 220717 220910 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-119 220214 220305 220445 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-118 218151 218658 219206 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-117 217112 217843 217871 "CHARZ" 217876 CHARZ (NIL) -9 NIL 217890 NIL) (-116 216906 216952 217030 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-115 215745 216508 216536 "CHARNZ" 216597 CHARNZ (NIL) -9 NIL 216645 NIL) (-114 213223 214320 214843 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-113 212931 213010 213038 "CFCAT" 213149 CFCAT (NIL) -9 NIL NIL NIL) (-112 212274 212403 212585 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-111 208542 211687 211967 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-110 207920 208107 208284 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-109 207448 207867 207915 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-108 206921 207230 207327 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-107 206412 206715 206806 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-106 205661 205821 206042 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-105 201761 203018 203726 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-104 200127 201158 201409 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-103 199708 199987 200061 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-102 199142 199395 199423 "CACHSET" 199555 CACHSET (NIL) -9 NIL 199633 NIL) (-101 198494 198909 198937 "CABMON" 198987 CABMON (NIL) -9 NIL 199043 NIL) (-100 198024 198288 198398 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-99 193641 197699 197856 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-98 192617 193321 193454 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193613) (-97 190087 192388 192492 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-96 187524 189841 189949 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-95 184702 186908 186947 "BTCAT" 187014 BTCAT (NIL T) -9 NIL 187095 NIL) (-94 184453 184551 184697 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-93 179770 183626 183652 "BTAGG" 183763 BTAGG (NIL) -9 NIL 183871 NIL) (-92 179401 179562 179765 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-91 176480 178893 179083 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-90 175750 175902 176080 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-89 172826 174447 174486 "BRAGG" 175115 BRAGG (NIL T) -9 NIL 175375 NIL) (-88 171901 172332 172821 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-87 164435 171406 171587 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-86 162427 164387 164430 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-85 162160 162196 162307 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-84 160399 160832 161280 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-83 156365 157781 158671 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-82 155241 156132 156254 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-81 154827 154984 155010 "BOOLE" 155118 BOOLE (NIL) -9 NIL 155199 NIL) (-80 154620 154701 154822 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-79 153758 154285 154335 "BMODULE" 154340 BMODULE (NIL T T) -9 NIL 154404 NIL) (-78 149643 153615 153684 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-77 149456 149496 149535 "BINOPC" 149540 BINOPC (NIL T) -9 NIL 149585 NIL) (-76 148998 149271 149373 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-75 148519 148663 148801 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-74 141725 148249 148394 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-73 139941 140914 140953 "BGAGG" 141209 BGAGG (NIL T) -9 NIL 141349 NIL) (-72 139810 139848 139936 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-71 138661 138862 139147 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-70 135316 137841 138146 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-69 134901 134994 135020 "BASTYPE" 135191 BASTYPE (NIL) -9 NIL 135287 NIL) (-68 134671 134767 134896 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-67 134186 134274 134424 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-66 133085 133760 133945 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-65 132833 132838 132864 "ATTREG" 132869 ATTREG (NIL) -9 NIL NIL NIL) (-64 132438 132710 132775 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-63 131938 132087 132113 "ATRIG" 132314 ATRIG (NIL) -9 NIL NIL NIL) (-62 131793 131846 131933 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-61 131363 131594 131620 "ASTCAT" 131625 ASTCAT (NIL) -9 NIL 131655 NIL) (-60 131162 131239 131358 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-59 129326 130995 131083 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-58 128133 128446 128811 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-57 125926 128063 128128 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-56 125117 125308 125529 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-55 120985 124848 124962 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-54 115535 117597 117672 "ARR2CAT" 119940 ARR2CAT (NIL T T T) -9 NIL 120591 NIL) (-53 114496 114978 115530 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-52 113864 114235 114357 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-51 112796 112964 113260 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-50 112497 112551 112669 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-49 111880 112026 112182 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-48 111285 111575 111695 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-47 108980 110141 110443 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-46 108505 108765 108861 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-45 102200 107567 108009 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-44 97835 99498 99548 "AMR" 100189 AMR (NIL T T) -9 NIL 100764 NIL) (-43 97189 97469 97830 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-42 79174 97123 97184 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-41 75577 78850 79019 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-40 72587 73247 73854 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-39 71966 72079 72263 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-38 68378 69003 69595 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-37 57867 68071 68221 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-36 57184 57338 57516 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-35 55897 56692 56730 "ALGEBRA" 56735 ALGEBRA (NIL T) -9 NIL 56775 NIL) (-34 55683 55760 55892 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-33 33898 52685 52737 "ALAGG" 52872 ALAGG (NIL T T) -9 NIL 53044 NIL) (-32 33398 33547 33573 "AHYP" 33774 AHYP (NIL) -9 NIL NIL NIL) (-31 32880 33012 33038 "AGG" 33243 AGG (NIL) -9 NIL 33369 NIL) (-30 32723 32781 32875 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-29 30862 31322 31722 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-28 30357 30660 30749 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-27 29727 30022 30178 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-26 17285 26564 26602 "ACFS" 27209 ACFS (NIL T) -9 NIL 27448 NIL) (-25 15908 16518 17280 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-24 11460 13839 13865 "ACF" 14744 ACF (NIL) -9 NIL 15156 NIL) (-23 10556 10962 11455 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-22 10058 10298 10324 "ABELSG" 10416 ABELSG (NIL) -9 NIL 10481 NIL) (-21 9956 9987 10053 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-20 9111 9485 9511 "ABELMON" 9736 ABELMON (NIL) -9 NIL 9869 NIL) (-19 8793 8933 9106 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-18 8005 8488 8514 "ABELGRP" 8586 ABELGRP (NIL) -9 NIL 8661 NIL) (-17 7558 7754 8000 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-16 3036 6767 6806 "A1AGG" 6811 A1AGG (NIL T) -9 NIL 6845 NIL) (-15 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 7ed631cd..404f34d9 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,14108 +1,14108 @@
 
-(628725 . 3580478884)        
+(628695 . 3581069280)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488))))
-   (-5 *2 (-1183 (-352 (-488)))) (-5 *1 (-1212 *4))))) 
+  (|partial| -11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485))))
+   (-5 *2 (-1180 (-349 (-485)))) (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488))))
-   (-5 *2 (-1183 (-488))) (-5 *1 (-1212 *4))))) 
+  (|partial| -11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485))))
+   (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1183 *4)) (-4 *4 (-13 (-965) (-584 (-488)))) (-5 *2 (-85))
-   (-5 *1 (-1212 *4))))) 
+  (-11 (-5 *3 (-1180 *4)) (-4 *4 (-12 (-962) (-581 (-485)))) (-5 *2 (-82))
+   (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-557 *2) (-148))) (-5 *2 (-804 *4)) (-5 *1 (-146 *4 *5 *3))
-   (-4 *4 (-1017)) (-4 *3 (-141 *5))))
+  (-11 (-4 *5 (-12 (-554 *2) (-145))) (-5 *2 (-801 *4)) (-5 *1 (-143 *4 *5 *3))
+   (-4 *4 (-1014)) (-4 *3 (-138 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1183 *3)) (-4 *3 (-148)) (-4 *1 (-355 *3 *4))
-   (-4 *4 (-1159 *3))))
+  (-11 (-5 *2 (-1180 *3)) (-4 *3 (-145)) (-4 *1 (-352 *3 *4))
+   (-4 *4 (-1156 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-355 *3 *4)) (-4 *3 (-148)) (-4 *4 (-1159 *3))
-   (-5 *2 (-1183 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1183 *3)) (-4 *3 (-148)) (-4 *1 (-363 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-363 *3)) (-4 *3 (-148)) (-5 *2 (-1183 *3))))
+  (-11 (-4 *1 (-352 *3 *4)) (-4 *3 (-145)) (-4 *4 (-1156 *3))
+   (-5 *2 (-1180 *3))))
+ ((*1 *1 *2) (-11 (-5 *2 (-1180 *3)) (-4 *3 (-145)) (-4 *1 (-360 *3))))
+ ((*1 *2 *1) (-11 (-4 *1 (-360 *3)) (-4 *3 (-145)) (-5 *2 (-1180 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-350 *1)) (-4 *1 (-366 *3)) (-4 *3 (-499)) (-4 *3 (-1017))))
+  (-11 (-5 *2 (-347 *1)) (-4 *1 (-363 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-587 *6)) (-4 *6 (-981 *3 *4 *5)) (-4 *3 (-965)) (-4 *4 (-721))
-   (-4 *5 (-760)) (-5 *1 (-406 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1019)) (-5 *1 (-477))))
- ((*1 *2 *1) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1133))))
- ((*1 *1 *2) (-12 (-4 *1 (-561 *2)) (-4 *2 (-1133))))
- ((*1 *1 *2) (-12 (-4 *3 (-148)) (-4 *1 (-665 *3 *2)) (-4 *2 (-1159 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-587 (-804 *3))) (-5 *1 (-804 *3)) (-4 *3 (-1017))))
+  (-11 (-5 *2 (-584 *6)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-403 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-11 (-5 *2 (-1016)) (-5 *1 (-474))))
+ ((*1 *2 *1) (-11 (-4 *1 (-554 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2) (-11 (-4 *1 (-558 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2) (-11 (-4 *3 (-145)) (-4 *1 (-662 *3 *2)) (-4 *2 (-1156 *3))))
+ ((*1 *1 *2) (-11 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-861 *3)) (-4 *3 (-965)) (-4 *1 (-981 *3 *4 *5))
-   (-4 *5 (-557 (-1094))) (-4 *4 (-721)) (-4 *5 (-760))))
+  (-11 (-5 *2 (-858 *3)) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5))
+   (-4 *5 (-554 (-1091))) (-4 *4 (-718)) (-4 *5 (-757))))
  ((*1 *1 *2)
   (OR
-   (-12 (-5 *2 (-861 (-488))) (-4 *1 (-981 *3 *4 *5))
-    (-12 (-2566 (-4 *3 (-38 (-352 (-488))))) (-4 *3 (-38 (-488)))
-     (-4 *5 (-557 (-1094))))
-    (-4 *3 (-965)) (-4 *4 (-721)) (-4 *5 (-760)))
-   (-12 (-5 *2 (-861 (-488))) (-4 *1 (-981 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-352 (-488)))) (-4 *5 (-557 (-1094)))) (-4 *3 (-965))
-    (-4 *4 (-721)) (-4 *5 (-760)))))
+   (-11 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
+    (-11 (-2563 (-4 *3 (-35 (-349 (-485))))) (-4 *3 (-35 (-485)))
+     (-4 *5 (-554 (-1091))))
+    (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
+   (-11 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
+    (-11 (-4 *3 (-35 (-349 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962))
+    (-4 *4 (-718)) (-4 *5 (-757)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-861 (-352 (-488)))) (-4 *1 (-981 *3 *4 *5))
-   (-4 *3 (-38 (-352 (-488)))) (-4 *5 (-557 (-1094))) (-4 *3 (-965))
-   (-4 *4 (-721)) (-4 *5 (-760))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-587 *7)) (|:| -1604 *8)))
-   (-4 *7 (-981 *4 *5 *6)) (-4 *8 (-987 *4 *5 *6 *7)) (-4 *4 (-395))
-   (-4 *5 (-721)) (-4 *6 (-760)) (-5 *2 (-1077))
-   (-5 *1 (-985 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
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-   (-4 *7 (-981 *4 *5 *6)) (-4 *8 (-1024 *4 *5 *6 *7)) (-4 *4 (-395))
-   (-4 *5 (-721)) (-4 *6 (-760)) (-5 *2 (-1077))
-   (-5 *1 (-1063 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1019)) (-5 *1 (-1099))))
- ((*1 *2 *1) (-12 (-5 *2 (-1019)) (-5 *1 (-1099))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-776)) (-5 *3 (-488)) (-5 *1 (-1113))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-776)) (-5 *3 (-488)) (-5 *1 (-1113))))
- ((*1 *2 *3)
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-   (-14 *5 (-587 (-1094))) (-5 *2 (-707 *4 (-777 *6))) (-5 *1 (-1211 *4 *5 *6))
-   (-14 *6 (-587 (-1094)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-861 *4)) (-4 *4 (-13 (-759) (-260) (-120) (-937)))
-   (-5 *2 (-861 (-941 (-352 *4)))) (-5 *1 (-1211 *4 *5 *6))
-   (-14 *5 (-587 (-1094))) (-14 *6 (-587 (-1094)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-707 *4 (-777 *6))) (-4 *4 (-13 (-759) (-260) (-120) (-937)))
-   (-14 *6 (-587 (-1094))) (-5 *2 (-861 (-941 (-352 *4))))
-   (-5 *1 (-1211 *4 *5 *6)) (-14 *5 (-587 (-1094)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1089 *4)) (-4 *4 (-13 (-759) (-260) (-120) (-937)))
-   (-5 *2 (-1089 (-941 (-352 *4)))) (-5 *1 (-1211 *4 *5 *6))
-   (-14 *5 (-587 (-1094))) (-14 *6 (-587 (-1094)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1064 *4 (-473 (-777 *6)) (-777 *6) (-707 *4 (-777 *6))))
-   (-4 *4 (-13 (-759) (-260) (-120) (-937))) (-14 *6 (-587 (-1094)))
-   (-5 *2 (-587 (-707 *4 (-777 *6)))) (-5 *1 (-1211 *4 *5 *6))
-   (-14 *5 (-587 (-1094)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-350 *3)) (-5 *1 (-501 *3)) (-4 *3 (-487))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-260)) (-5 *2 (-350 *3))
-   (-5 *1 (-685 *4 *5 *6 *3)) (-4 *3 (-865 *6 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-260)) (-4 *7 (-865 *6 *4 *5))
-   (-5 *2 (-350 (-1089 *7))) (-5 *1 (-685 *4 *5 *6 *7)) (-5 *3 (-1089 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-395)) (-4 *3 (-965)) (-4 *4 (-721)) (-4 *5 (-760))
-   (-5 *2 (-350 *1)) (-4 *1 (-865 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-760)) (-4 *5 (-721)) (-4 *6 (-395)) (-5 *2 (-350 *3))
-   (-5 *1 (-896 *4 *5 *6 *3)) (-4 *3 (-865 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-395)) (-4 *7 (-865 *6 *4 *5))
-   (-5 *2 (-350 (-1089 (-352 *7)))) (-5 *1 (-1091 *4 *5 *6 *7))
-   (-5 *3 (-1089 (-352 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-350 *1)) (-4 *1 (-1138))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-499)) (-5 *2 (-350 *3)) (-5 *1 (-1163 *4 *3))
-   (-4 *3 (-13 (-1159 *4) (-499) (-10 -8 (-15 -3150 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-962 *4 *5)) (-4 *4 (-13 (-759) (-260) (-120) (-937)))
-   (-14 *5 (-587 (-1094)))
-   (-5 *2 (-587 (-1064 *4 (-473 (-777 *6)) (-777 *6) (-707 *4 (-777 *6)))))
-   (-5 *1 (-1211 *4 *5 *6)) (-14 *6 (-587 (-1094)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-962 *4 *5)) (-4 *4 (-13 (-759) (-260) (-120) (-937)))
-   (-14 *5 (-587 (-1094))) (-5 *2 (-587 (-587 (-941 (-352 *4)))))
-   (-5 *1 (-1211 *4 *5 *6)) (-14 *6 (-587 (-1094)))))
+  (-11 (-5 *2 (-858 (-349 (-485)))) (-4 *1 (-978 *3 *4 *5))
+   (-4 *3 (-35 (-349 (-485)))) (-4 *5 (-554 (-1091))) (-4 *3 (-962))
+   (-4 *4 (-718)) (-4 *5 (-757))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1074))
+   (-5 *1 (-982 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-1021 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1074))
+   (-5 *1 (-1060 *4 *5 *6 *7 *8))))
+ ((*1 *1 *2) (-11 (-5 *2 (-1016)) (-5 *1 (-1096))))
+ ((*1 *2 *1) (-11 (-5 *2 (-1016)) (-5 *1 (-1096))))
+ ((*1 *1 *2 *3 *2) (-11 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
+ ((*1 *1 *2 *3) (-11 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-704 *4 (-774 *5))) (-4 *4 (-12 (-756) (-257) (-117) (-934)))
+   (-13 *5 (-584 (-1091))) (-5 *2 (-704 *4 (-774 *6))) (-5 *1 (-1208 *4 *5 *6))
+   (-13 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-858 *4)) (-4 *4 (-12 (-756) (-257) (-117) (-934)))
+   (-5 *2 (-858 (-938 (-349 *4)))) (-5 *1 (-1208 *4 *5 *6))
+   (-13 *5 (-584 (-1091))) (-13 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-704 *4 (-774 *6))) (-4 *4 (-12 (-756) (-257) (-117) (-934)))
+   (-13 *6 (-584 (-1091))) (-5 *2 (-858 (-938 (-349 *4))))
+   (-5 *1 (-1208 *4 *5 *6)) (-13 *5 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-1086 *4)) (-4 *4 (-12 (-756) (-257) (-117) (-934)))
+   (-5 *2 (-1086 (-938 (-349 *4)))) (-5 *1 (-1208 *4 *5 *6))
+   (-13 *5 (-584 (-1091))) (-13 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-1061 *4 (-470 (-774 *6)) (-774 *6) (-704 *4 (-774 *6))))
+   (-4 *4 (-12 (-756) (-257) (-117) (-934))) (-13 *6 (-584 (-1091)))
+   (-5 *2 (-584 (-704 *4 (-774 *6)))) (-5 *1 (-1208 *4 *5 *6))
+   (-13 *5 (-584 (-1091)))))) 
+(((*1 *2 *3) (-11 (-5 *2 (-347 *3)) (-5 *1 (-498 *3)) (-4 *3 (-484))))
+ ((*1 *2 *3)
+  (-11 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-257)) (-5 *2 (-347 *3))
+   (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-862 *6 *4 *5))))
+ ((*1 *2 *3)
+  (-11 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-257)) (-4 *7 (-862 *6 *4 *5))
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 (((*1 *1 *2)
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+     (|has| *3 (-14 -3815 (*3 *3 *2))) (-4 *3 (-35 (-349 (-485))))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1166 *2)) (-4 *2 (-965)) (-4 *2 (-38 (-352 (-488))))))
+  (-11 (-4 *1 (-1163 *2)) (-4 *2 (-962)) (-4 *2 (-35 (-349 (-485))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1180 *4)) (-14 *4 (-1094)) (-5 *1 (-1173 *3 *4 *5))
-   (-4 *3 (-38 (-352 (-488)))) (-4 *3 (-965)) (-14 *5 *3)))
+  (-11 (-5 *2 (-1177 *4)) (-13 *4 (-1091)) (-5 *1 (-1170 *3 *4 *5))
+   (-4 *3 (-35 (-349 (-485)))) (-4 *3 (-962)) (-13 *5 *3)))
  ((*1 *1 *1 *2)
   (OR
-   (-12 (-5 *2 (-1094)) (-4 *1 (-1176 *3)) (-4 *3 (-965))
-    (-12 (-4 *3 (-29 (-488))) (-4 *3 (-875)) (-4 *3 (-1119))
-     (-4 *3 (-38 (-352 (-488))))))
-   (-12 (-5 *2 (-1094)) (-4 *1 (-1176 *3)) (-4 *3 (-965))
-    (-12 (|has| *3 (-15 -3087 ((-587 *2) *3)))
-     (|has| *3 (-15 -3818 (*3 *3 *2))) (-4 *3 (-38 (-352 (-488))))))))
+   (-11 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-962))
+    (-11 (-4 *3 (-26 (-485))) (-4 *3 (-872)) (-4 *3 (-1116))
+     (-4 *3 (-35 (-349 (-485))))))
+   (-11 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-962))
+    (-11 (|has| *3 (-14 -3084 ((-584 *2) *3)))
+     (|has| *3 (-14 -3815 (*3 *3 *2))) (-4 *3 (-35 (-349 (-485))))))))
  ((*1 *1 *1)
-  (-12 (-4 *1 (-1176 *2)) (-4 *2 (-965)) (-4 *2 (-38 (-352 (-488))))))) 
+  (-11 (-4 *1 (-1173 *2)) (-4 *2 (-962)) (-4 *2 (-35 (-349 (-485))))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-698)) (-5 *2 (-1152 *5 *4)) (-5 *1 (-1093 *4 *5 *6))
-   (-4 *4 (-965)) (-14 *5 (-1094)) (-14 *6 *4)))
+  (-11 (-5 *3 (-695)) (-5 *2 (-1149 *5 *4)) (-5 *1 (-1090 *4 *5 *6))
+   (-4 *4 (-962)) (-13 *5 (-1091)) (-13 *6 *4)))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-698)) (-5 *2 (-1152 *5 *4)) (-5 *1 (-1173 *4 *5 *6))
-   (-4 *4 (-965)) (-14 *5 (-1094)) (-14 *6 *4)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-965)) (-5 *1 (-1079 *3))))
+  (-11 (-5 *3 (-695)) (-5 *2 (-1149 *5 *4)) (-5 *1 (-1170 *4 *5 *6))
+   (-4 *4 (-962)) (-13 *5 (-1091)) (-13 *6 *4)))) 
+(((*1 *2 *2) (-11 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-965)) (-14 *3 (-1094)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-965)) (-5 *1 (-1079 *3))))
+  (-11 (-5 *1 (-1170 *2 *3 *4)) (-4 *2 (-962)) (-13 *3 (-1091)) (-13 *4 *2)))) 
+(((*1 *2 *2) (-11 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-965)) (-14 *3 (-1094)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-965)) (-5 *1 (-1079 *3))))
+  (-11 (-5 *1 (-1170 *2 *3 *4)) (-4 *2 (-962)) (-13 *3 (-1091)) (-13 *4 *2)))) 
+(((*1 *2 *2) (-11 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-965)) (-14 *3 (-1094)) (-14 *4 *2)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-965)) (-5 *1 (-1079 *3))))
+  (-11 (-5 *1 (-1170 *2 *3 *4)) (-4 *2 (-962)) (-13 *3 (-1091)) (-13 *4 *2)))) 
+(((*1 *2 *2) (-11 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-965)) (-14 *3 (-1094)) (-14 *4 *2)))) 
+  (-11 (-5 *1 (-1170 *2 *3 *4)) (-4 *2 (-962)) (-13 *3 (-1091)) (-13 *4 *2)))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-1073 *4)) (-5 *3 (-488)) (-4 *4 (-965)) (-5 *1 (-1079 *4))))
+  (-11 (-5 *2 (-1070 *4)) (-5 *3 (-485)) (-4 *4 (-962)) (-5 *1 (-1076 *4))))
  ((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-488)) (-5 *1 (-1173 *3 *4 *5)) (-4 *3 (-965)) (-14 *4 (-1094))
-   (-14 *5 *3)))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1073 *3)) (-4 *3 (-965)) (-5 *1 (-1079 *3))))
+  (-11 (-5 *2 (-485)) (-5 *1 (-1170 *3 *4 *5)) (-4 *3 (-962)) (-13 *4 (-1091))
+   (-13 *5 *3)))) 
+(((*1 *2 *2) (-11 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-5 *1 (-1076 *3))))
  ((*1 *1 *1)
-  (-12 (-5 *1 (-1173 *2 *3 *4)) (-4 *2 (-965)) (-14 *3 (-1094)) (-14 *4 *2)))) 
+  (-11 (-5 *1 (-1170 *2 *3 *4)) (-4 *2 (-962)) (-13 *3 (-1091)) (-13 *4 *2)))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-1073 *4)) (-5 *3 (-488)) (-4 *4 (-965)) (-5 *1 (-1079 *4))))
+  (-11 (-5 *2 (-1070 *4)) (-5 *3 (-485)) (-4 *4 (-962)) (-5 *1 (-1076 *4))))
  ((*1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-488)) (-5 *1 (-1173 *3 *4 *5)) (-4 *3 (-965)) (-14 *4 (-1094))
-   (-14 *5 *3)))) 
+  (-11 (-5 *2 (-485)) (-5 *1 (-1170 *3 *4 *5)) (-4 *3 (-962)) (-13 *4 (-1091))
+   (-13 *5 *3)))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-1073 *4)) (-5 *3 (-488)) (-4 *4 (-965)) (-5 *1 (-1079 *4))))
+  (-11 (-5 *2 (-1070 *4)) (-5 *3 (-485)) (-4 *4 (-962)) (-5 *1 (-1076 *4))))
  ((*1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-488)) (-5 *1 (-1173 *3 *4 *5)) (-4 *3 (-965)) (-14 *4 (-1094))
-   (-14 *5 *3)))) 
-(((*1 *1 *2) (-12 (-5 *2 (-587 *1)) (-4 *1 (-597 *3)) (-4 *3 (-1133))))
- ((*1 *1 *1 *1) (-12 (-4 *1 (-597 *2)) (-4 *2 (-1133))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-597 *2)) (-4 *2 (-1133))))
- ((*1 *1 *1 *2) (-12 (-4 *1 (-597 *2)) (-4 *2 (-1133))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1073 (-1073 *4))) (-5 *2 (-1073 *4)) (-5 *1 (-1074 *4))
-   (-4 *4 (-1133))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-1133))))
- ((*1 *1 *1 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-1133))))) 
-(((*1 *2 *1)
-  (-12 (-4 *1 (-542 *3 *2)) (-4 *3 (-72)) (-4 *3 (-760)) (-4 *2 (-1133))))
- ((*1 *2 *1) (-12 (-5 *1 (-622 *2)) (-4 *2 (-760))))
- ((*1 *2 *1) (-12 (-5 *1 (-743 *2)) (-4 *2 (-760))))
- ((*1 *2 *1) (-12 (-4 *2 (-1133)) (-5 *1 (-786 *2 *3)) (-4 *3 (-1133))))
- ((*1 *2 *1) (-12 (-5 *2 (-618 *3)) (-5 *1 (-807 *3)) (-4 *3 (-760))))
- ((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-1128 *3 *4 *5 *2)) (-4 *3 (-499)) (-4 *4 (-721))
-   (-4 *5 (-760)) (-4 *2 (-981 *3 *4 *5))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-698)) (-4 *1 (-1172 *3)) (-4 *3 (-1133))))
- ((*1 *2 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-1133))))) 
+  (-11 (-5 *2 (-485)) (-5 *1 (-1170 *3 *4 *5)) (-4 *3 (-962)) (-13 *4 (-1091))
+   (-13 *5 *3)))) 
+(((*1 *1 *2) (-11 (-5 *2 (-584 *1)) (-4 *1 (-594 *3)) (-4 *3 (-1130))))
+ ((*1 *1 *1 *1) (-11 (-4 *1 (-594 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2 *1) (-11 (-4 *1 (-594 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *1 *2) (-11 (-4 *1 (-594 *2)) (-4 *2 (-1130))))
+ ((*1 *2 *3)
+  (-11 (-5 *3 (-1070 (-1070 *4))) (-5 *2 (-1070 *4)) (-5 *1 (-1071 *4))
+   (-4 *4 (-1130))))
+ ((*1 *1 *2 *1) (-11 (-4 *1 (-1169 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *1 *1) (-11 (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) 
+(((*1 *2 *1)
+  (-11 (-4 *1 (-539 *3 *2)) (-4 *3 (-69)) (-4 *3 (-757)) (-4 *2 (-1130))))
+ ((*1 *2 *1) (-11 (-5 *1 (-619 *2)) (-4 *2 (-757))))
+ ((*1 *2 *1) (-11 (-5 *1 (-740 *2)) (-4 *2 (-757))))
+ ((*1 *2 *1) (-11 (-4 *2 (-1130)) (-5 *1 (-783 *2 *3)) (-4 *3 (-1130))))
+ ((*1 *2 *1) (-11 (-5 *2 (-615 *3)) (-5 *1 (-804 *3)) (-4 *3 (-757))))
+ ((*1 *2 *1)
+  (|partial| -11 (-4 *1 (-1125 *3 *4 *5 *2)) (-4 *3 (-496)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-4 *2 (-978 *3 *4 *5))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 (-695)) (-4 *1 (-1169 *3)) (-4 *3 (-1130))))
+ ((*1 *2 *1) (-11 (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-488)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1133)) (-4 *4 (-326 *2))
-   (-4 *5 (-326 *2))))
+  (-11 (-5 *3 (-485)) (-4 *1 (-54 *2 *4 *5)) (-4 *2 (-1130)) (-4 *4 (-323 *2))
+   (-4 *5 (-323 *2))))
  ((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-488)) (-4 *1 (-57 *2 *4 *5)) (-4 *4 (-326 *2))
-   (-4 *5 (-326 *2)) (-4 *2 (-1133))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "right") (-4 *1 (-92 *3)) (-4 *3 (-1133))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "left") (-4 *1 (-92 *3)) (-4 *3 (-1133))))
+  (-11 (-5 *3 (-485)) (-4 *1 (-54 *2 *4 *5)) (-4 *4 (-323 *2))
+   (-4 *5 (-323 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 "right") (-4 *1 (-89 *3)) (-4 *3 (-1130))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 "left") (-4 *1 (-89 *3)) (-4 *3 (-1130))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-587 (-488))) (-4 *2 (-148)) (-5 *1 (-108 *4 *5 *2))
-   (-14 *4 (-488)) (-14 *5 (-698))))
+  (-11 (-5 *3 (-584 (-485))) (-4 *2 (-145)) (-5 *1 (-105 *4 *5 *2))
+   (-13 *4 (-485)) (-13 *5 (-695))))
  ((*1 *2 *1 *3 *3 *3 *3)
-  (-12 (-5 *3 (-488)) (-4 *2 (-148)) (-5 *1 (-108 *4 *5 *2)) (-14 *4 *3)
-   (-14 *5 (-698))))
+  (-11 (-5 *3 (-485)) (-4 *2 (-145)) (-5 *1 (-105 *4 *5 *2)) (-13 *4 *3)
+   (-13 *5 (-695))))
  ((*1 *2 *1 *3 *3 *3)
-  (-12 (-5 *3 (-488)) (-4 *2 (-148)) (-5 *1 (-108 *4 *5 *2)) (-14 *4 *3)
-   (-14 *5 (-698))))
+  (-11 (-5 *3 (-485)) (-4 *2 (-145)) (-5 *1 (-105 *4 *5 *2)) (-13 *4 *3)
+   (-13 *5 (-695))))
  ((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-488)) (-4 *2 (-148)) (-5 *1 (-108 *4 *5 *2)) (-14 *4 *3)
-   (-14 *5 (-698))))
+  (-11 (-5 *3 (-485)) (-4 *2 (-145)) (-5 *1 (-105 *4 *5 *2)) (-13 *4 *3)
+   (-13 *5 (-695))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-148)) (-5 *1 (-108 *3 *4 *2)) (-14 *3 (-488)) (-14 *4 (-698))))
+  (-11 (-4 *2 (-145)) (-5 *1 (-105 *3 *4 *2)) (-13 *3 (-485)) (-13 *4 (-695))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-1094)) (-5 *2 (-205 (-1077))) (-5 *1 (-169 *4))
+  (-11 (-5 *3 (-1091)) (-5 *2 (-202 (-1074))) (-5 *1 (-166 *4))
    (-4 *4
-    (-13 (-760)
-     (-10 -8 (-15 -3806 ((-1077) $ *3)) (-15 -3623 ((-1189) $))
-      (-15 -1968 ((-1189) $)))))))
+    (-12 (-757)
+     (-10 -8 (-14 -3803 ((-1074) $ *3)) (-14 -3620 ((-1186) $))
+      (-14 -1965 ((-1186) $)))))))
  ((*1 *1 *1 *2)
-  (-12 (-5 *2 (-906)) (-5 *1 (-169 *3))
+  (-11 (-5 *2 (-903)) (-5 *1 (-166 *3))
    (-4 *3
-    (-13 (-760)
-     (-10 -8 (-15 -3806 ((-1077) $ (-1094))) (-15 -3623 ((-1189) $))
-      (-15 -1968 ((-1189) $)))))))
+    (-12 (-757)
+     (-10 -8 (-14 -3803 ((-1074) $ (-1091))) (-14 -3620 ((-1186) $))
+      (-14 -1965 ((-1186) $)))))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 "count") (-5 *2 (-698)) (-5 *1 (-205 *4)) (-4 *4 (-760))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-205 *3)) (-4 *3 (-760))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "unique") (-5 *1 (-205 *3)) (-4 *3 (-760))))
- ((*1 *2 *1 *3) (-12 (-4 *1 (-243 *3 *2)) (-4 *3 (-1133)) (-4 *2 (-1133))))
- ((*1 *2 *1 *3 *2) (-12 (-4 *1 (-245 *3 *2)) (-4 *3 (-72)) (-4 *2 (-1133))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-86)) (-5 *3 (-587 *1)) (-4 *1 (-256))))
- ((*1 *1 *2 *1 *1 *1 *1) (-12 (-4 *1 (-256)) (-5 *2 (-86))))
- ((*1 *1 *2 *1 *1 *1) (-12 (-4 *1 (-256)) (-5 *2 (-86))))
- ((*1 *1 *2 *1 *1) (-12 (-4 *1 (-256)) (-5 *2 (-86))))
- ((*1 *1 *2 *1) (-12 (-4 *1 (-256)) (-5 *2 (-86))))
+  (-11 (-5 *3 "count") (-5 *2 (-695)) (-5 *1 (-202 *4)) (-4 *4 (-757))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 "sort") (-5 *1 (-202 *3)) (-4 *3 (-757))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 "unique") (-5 *1 (-202 *3)) (-4 *3 (-757))))
+ ((*1 *2 *1 *3) (-11 (-4 *1 (-240 *3 *2)) (-4 *3 (-1130)) (-4 *2 (-1130))))
+ ((*1 *2 *1 *3 *2) (-11 (-4 *1 (-242 *3 *2)) (-4 *3 (-69)) (-4 *2 (-1130))))
+ ((*1 *1 *2 *3) (-11 (-5 *2 (-83)) (-5 *3 (-584 *1)) (-4 *1 (-253))))
+ ((*1 *1 *2 *1 *1 *1 *1) (-11 (-4 *1 (-253)) (-5 *2 (-83))))
+ ((*1 *1 *2 *1 *1 *1) (-11 (-4 *1 (-253)) (-5 *2 (-83))))
+ ((*1 *1 *2 *1 *1) (-11 (-4 *1 (-253)) (-5 *2 (-83))))
+ ((*1 *1 *2 *1) (-11 (-4 *1 (-253)) (-5 *2 (-83))))
  ((*1 *2 *1 *2 *2)
-  (-12 (-4 *1 (-293 *2 *3 *4)) (-4 *2 (-1138)) (-4 *3 (-1159 *2))
-   (-4 *4 (-1159 (-352 *3)))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1094)) (-5 *2 (-1077)) (-5 *1 (-445))))
+  (-11 (-4 *1 (-290 *2 *3 *4)) (-4 *2 (-1135)) (-4 *3 (-1156 *2))
+   (-4 *4 (-1156 (-349 *3)))))
+ ((*1 *2 *1 *3) (-11 (-5 *3 (-1091)) (-5 *2 (-1074)) (-5 *1 (-442))))
  ((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-587 (-488))) (-4 *1 (-631 *3 *4 *5)) (-4 *3 (-965))
-   (-4 *4 (-326 *3)) (-4 *5 (-326 *3))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-587 (-776))) (-5 *1 (-776))))
+  (-11 (-5 *2 (-584 (-485))) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962))
+   (-4 *4 (-323 *3)) (-4 *5 (-323 *3))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 (-584 (-773))) (-5 *1 (-773))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-86)) (-5 *3 (-587 (-804 *4))) (-5 *1 (-804 *4))
-   (-4 *4 (-1017))))
+  (-11 (-5 *2 (-83)) (-5 *3 (-584 (-801 *4))) (-5 *1 (-801 *4))
+   (-4 *4 (-1014))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-698)) (-5 *2 (-817 *4)) (-5 *1 (-820 *4)) (-4 *4 (-1017))))
- ((*1 *2 *1 *3) (-12 (-5 *3 "value") (-4 *1 (-927 *2)) (-4 *2 (-1133))))
+  (-11 (-5 *3 (-695)) (-5 *2 (-814 *4)) (-5 *1 (-817 *4)) (-4 *4 (-1014))))
+ ((*1 *2 *1 *3) (-11 (-5 *3 "value") (-4 *1 (-924 *2)) (-4 *2 (-1130))))
  ((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-488)) (-4 *1 (-969 *4 *5 *2 *6 *7)) (-4 *2 (-965))
-   (-4 *6 (-198 *5 *2)) (-4 *7 (-198 *4 *2))))
+  (-11 (-5 *3 (-485)) (-4 *1 (-966 *4 *5 *2 *6 *7)) (-4 *2 (-962))
+   (-4 *6 (-195 *5 *2)) (-4 *7 (-195 *4 *2))))
  ((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-488)) (-4 *1 (-969 *4 *5 *2 *6 *7)) (-4 *6 (-198 *5 *2))
-   (-4 *7 (-198 *4 *2)) (-4 *2 (-965))))
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+   (-4 *7 (-195 *4 *2)) (-4 *2 (-962))))
  ((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-834)) (-4 *4 (-1017))
-   (-4 *5 (-13 (-965) (-800 *4) (-557 (-804 *4)))) (-5 *1 (-991 *4 *5 *2))
-   (-4 *2 (-13 (-366 *5) (-800 *4) (-557 (-804 *4))))))
+  (-11 (-5 *3 (-831)) (-4 *4 (-1014))
+   (-4 *5 (-12 (-962) (-797 *4) (-554 (-801 *4)))) (-5 *1 (-988 *4 *5 *2))
+   (-4 *2 (-12 (-363 *5) (-797 *4) (-554 (-801 *4))))))
  ((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-834)) (-4 *4 (-1017))
-   (-4 *5 (-13 (-965) (-800 *4) (-557 (-804 *4)))) (-5 *1 (-993 *4 *5 *2))
-   (-4 *2 (-13 (-366 *5) (-800 *4) (-557 (-804 *4))))))
- ((*1 *1 *1 *1) (-4 *1 (-1062)))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-587 (-776))) (-5 *1 (-1094))))
+  (-11 (-5 *3 (-831)) (-4 *4 (-1014))
+   (-4 *5 (-12 (-962) (-797 *4) (-554 (-801 *4)))) (-5 *1 (-990 *4 *5 *2))
+   (-4 *2 (-12 (-363 *5) (-797 *4) (-554 (-801 *4))))))
+ ((*1 *1 *1 *1) (-4 *1 (-1059)))
+ ((*1 *1 *1 *2) (-11 (-5 *2 (-584 (-773))) (-5 *1 (-1091))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *3 (-352 *1)) (-4 *1 (-1159 *2)) (-4 *2 (-965)) (-4 *2 (-314))))
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  ((*1 *2 *2 *2)
-  (-12 (-5 *2 (-352 *1)) (-4 *1 (-1159 *3)) (-4 *3 (-965)) (-4 *3 (-499))))
- ((*1 *2 *1 *3) (-12 (-5 *3 "last") (-4 *1 (-1172 *2)) (-4 *2 (-1133))))
- ((*1 *1 *1 *2) (-12 (-5 *2 "rest") (-4 *1 (-1172 *3)) (-4 *3 (-1133))))
- ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1172 *2)) (-4 *2 (-1133))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-622 *2)) (-4 *2 (-760))))
- ((*1 *1 *1) (-12 (-5 *1 (-743 *2)) (-4 *2 (-760))))
- ((*1 *1 *1) (-12 (-5 *1 (-807 *2)) (-4 *2 (-760))))
+  (-11 (-5 *2 (-349 *1)) (-4 *1 (-1156 *3)) (-4 *3 (-962)) (-4 *3 (-496))))
+ ((*1 *2 *1 *3) (-11 (-5 *3 "last") (-4 *1 (-1169 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *1 *2) (-11 (-5 *2 "rest") (-4 *1 (-1169 *3)) (-4 *3 (-1130))))
+ ((*1 *2 *1 *3) (-11 (-5 *3 "first") (-4 *1 (-1169 *2)) (-4 *2 (-1130))))) 
+(((*1 *1 *1) (-11 (-5 *1 (-619 *2)) (-4 *2 (-757))))
+ ((*1 *1 *1) (-11 (-5 *1 (-740 *2)) (-4 *2 (-757))))
+ ((*1 *1 *1) (-11 (-5 *1 (-804 *2)) (-4 *2 (-757))))
  ((*1 *1 *1)
-  (|partial| -12 (-4 *1 (-1128 *2 *3 *4 *5)) (-4 *2 (-499)) (-4 *3 (-721))
-   (-4 *4 (-760)) (-4 *5 (-981 *2 *3 *4))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-698)) (-4 *1 (-1172 *3)) (-4 *3 (-1133))))
- ((*1 *1 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-1133))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-204 *2)) (-4 *2 (-1133))))
- ((*1 *2 *1) (-12 (-5 *2 (-1053)) (-5 *1 (-1012))))
- ((*1 *2 *1)
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+   (-5 *2 (-82)) (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| (-85)) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-82)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 *4)) (-5 *1 (-1023 *5 *6 *7 *3 *4))
-   (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| (-85)) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-82)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 *4)) (-5 *1 (-1023 *5 *6 *7 *3 *4))
-   (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| (-85)) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-82)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| *3) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| *3) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4 *5 *5)
-  (-12 (-5 *5 (-85)) (-4 *6 (-395)) (-4 *7 (-721)) (-4 *8 (-760))
-   (-4 *3 (-981 *6 *7 *8)) (-5 *2 (-587 (-2 (|:| |val| *3) (|:| -1604 *4))))
-   (-5 *1 (-1023 *6 *7 *8 *3 *4)) (-4 *4 (-987 *6 *7 *8 *3))))
+  (-11 (-5 *5 (-82)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *3 (-978 *6 *7 *8)) (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *6 *7 *8 *3 *4)) (-4 *4 (-984 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-587 (-2 (|:| |val| (-587 *8)) (|:| -1604 *9)))) (-5 *5 (-85))
-   (-4 *8 (-981 *6 *7 *4)) (-4 *9 (-987 *6 *7 *4 *8)) (-4 *6 (-395))
-   (-4 *7 (-721)) (-4 *4 (-760))
-   (-5 *2 (-587 (-2 (|:| |val| *8) (|:| -1604 *9))))
-   (-5 *1 (-1023 *6 *7 *4 *8 *9))))) 
+  (-11 (-5 *3 (-584 (-2 (|:| |val| (-584 *8)) (|:| -1601 *9)))) (-5 *5 (-82))
+   (-4 *8 (-978 *6 *7 *4)) (-4 *9 (-984 *6 *7 *4 *8)) (-4 *6 (-392))
+   (-4 *7 (-718)) (-4 *4 (-757))
+   (-5 *2 (-584 (-2 (|:| |val| *8) (|:| -1601 *9))))
+   (-5 *1 (-1020 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-395)) (-4 *6 (-721)) (-4 *7 (-760)) (-4 *3 (-981 *5 *6 *7))
-   (-5 *2 (-587 (-2 (|:| |val| (-587 *3)) (|:| -1604 *4))))
-   (-5 *1 (-1023 *5 *6 *7 *3 *4)) (-4 *4 (-987 *5 *6 *7 *3))))) 
+  (-11 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-584 *3)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-395)) (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *2 (-1189)) (-5 *1 (-988 *3 *4 *5 *6 *7)) (-4 *7 (-987 *3 *4 *5 *6))))
+  (-11 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-395)) (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *2 (-1189)) (-5 *1 (-1023 *3 *4 *5 *6 *7)) (-4 *7 (-987 *3 *4 *5 *6))))) 
+  (-11 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1077)) (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-1189)) (-5 *1 (-988 *4 *5 *6 *7 *8))
-   (-4 *8 (-987 *4 *5 *6 *7))))
+  (-11 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1077)) (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-1189)) (-5 *1 (-1023 *4 *5 *6 *7 *8))
-   (-4 *8 (-987 *4 *5 *6 *7))))) 
+  (-11 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-395)) (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *2 (-1189)) (-5 *1 (-988 *3 *4 *5 *6 *7)) (-4 *7 (-987 *3 *4 *5 *6))))
+  (-11 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-395)) (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *2 (-1189)) (-5 *1 (-1023 *3 *4 *5 *6 *7)) (-4 *7 (-987 *3 *4 *5 *6))))) 
+  (-11 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1077)) (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-1189)) (-5 *1 (-988 *4 *5 *6 *7 *8))
-   (-4 *8 (-987 *4 *5 *6 *7))))
+  (-11 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1077)) (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-1189)) (-5 *1 (-1023 *4 *5 *6 *7 *8))
-   (-4 *8 (-987 *4 *5 *6 *7))))) 
+  (-11 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-395)) (-4 *7 (-721)) (-4 *8 (-760))
-   (-4 *9 (-981 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3272 (-587 *9)) (|:| -1604 *4) (|:| |ineq| (-587 *9))))
-   (-5 *1 (-905 *6 *7 *8 *9 *4)) (-5 *3 (-587 *9)) (-4 *4 (-987 *6 *7 *8 *9))))
+  (|partial| -11 (-5 *5 (-82)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3269 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9))))
  ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-395)) (-4 *7 (-721)) (-4 *8 (-760))
-   (-4 *9 (-981 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3272 (-587 *9)) (|:| -1604 *4) (|:| |ineq| (-587 *9))))
-   (-5 *1 (-1022 *6 *7 *8 *9 *4)) (-5 *3 (-587 *9))
-   (-4 *4 (-987 *6 *7 *8 *9))))) 
+  (|partial| -11 (-5 *5 (-82)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3269 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-1019 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9))
+   (-4 *4 (-984 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-587 *10)) (-5 *5 (-85)) (-4 *10 (-987 *6 *7 *8 *9))
-   (-4 *6 (-395)) (-4 *7 (-721)) (-4 *8 (-760)) (-4 *9 (-981 *6 *7 *8))
+  (-11 (-5 *4 (-584 *10)) (-5 *5 (-82)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-587 (-2 (|:| -3272 (-587 *9)) (|:| -1604 *10) (|:| |ineq| (-587 *9)))))
-   (-5 *1 (-905 *6 *7 *8 *9 *10)) (-5 *3 (-587 *9))))
+    (-584 (-2 (|:| -3269 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9)))))
+   (-5 *1 (-902 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))
  ((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-587 *10)) (-5 *5 (-85)) (-4 *10 (-987 *6 *7 *8 *9))
-   (-4 *6 (-395)) (-4 *7 (-721)) (-4 *8 (-760)) (-4 *9 (-981 *6 *7 *8))
+  (-11 (-5 *4 (-584 *10)) (-5 *5 (-82)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-587 (-2 (|:| -3272 (-587 *9)) (|:| -1604 *10) (|:| |ineq| (-587 *9)))))
-   (-5 *1 (-1022 *6 *7 *8 *9 *10)) (-5 *3 (-587 *9))))) 
+    (-584 (-2 (|:| -3269 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9)))))
+   (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-587 (-2 (|:| |val| (-587 *6)) (|:| -1604 *7))))
-   (-4 *6 (-981 *3 *4 *5)) (-4 *7 (-987 *3 *4 *5 *6)) (-4 *3 (-395))
-   (-4 *4 (-721)) (-4 *5 (-760)) (-5 *1 (-905 *3 *4 *5 *6 *7))))
+  (-11 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-587 (-2 (|:| |val| (-587 *6)) (|:| -1604 *7))))
-   (-4 *6 (-981 *3 *4 *5)) (-4 *7 (-987 *3 *4 *5 *6)) (-4 *3 (-395))
-   (-4 *4 (-721)) (-4 *5 (-760)) (-5 *1 (-1022 *3 *4 *5 *6 *7))))) 
+  (-11 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-587 *7)) (|:| -1604 *8)))
-   (-4 *7 (-981 *4 *5 *6)) (-4 *8 (-987 *4 *5 *6 *7)) (-4 *4 (-395))
-   (-4 *5 (-721)) (-4 *6 (-760)) (-5 *2 (-85)) (-5 *1 (-905 *4 *5 *6 *7 *8))))
+  (-11 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-82)) (-5 *1 (-902 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-587 *7)) (|:| -1604 *8)))
-   (-4 *7 (-981 *4 *5 *6)) (-4 *8 (-987 *4 *5 *6 *7)) (-4 *4 (-395))
-   (-4 *5 (-721)) (-4 *6 (-760)) (-5 *2 (-85)) (-5 *1 (-1022 *4 *5 *6 *7 *8))))) 
+  (-11 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-82)) (-5 *1 (-1019 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-587 *7)) (-4 *7 (-987 *3 *4 *5 *6)) (-4 *3 (-395))
-   (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *1 (-905 *3 *4 *5 *6 *7))))
+  (-11 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-587 *7)) (-4 *7 (-987 *3 *4 *5 *6)) (-4 *3 (-395))
-   (-4 *4 (-721)) (-4 *5 (-760)) (-4 *6 (-981 *3 *4 *5))
-   (-5 *1 (-1022 *3 *4 *5 *6 *7))))) 
+  (-11 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760)) (-4 *7 (-981 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-905 *4 *5 *6 *7 *3)) (-4 *3 (-987 *4 *5 *6 *7))))
+  (-11 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-82)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-587 *3)) (-4 *3 (-987 *5 *6 *7 *8)) (-4 *5 (-395))
-   (-4 *6 (-721)) (-4 *7 (-760)) (-4 *8 (-981 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-905 *5 *6 *7 *8 *3))))
+  (-11 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-82))
+   (-5 *1 (-902 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760)) (-4 *7 (-981 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1022 *4 *5 *6 *7 *3)) (-4 *3 (-987 *4 *5 *6 *7))))
+  (-11 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-82)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-587 *3)) (-4 *3 (-987 *5 *6 *7 *8)) (-4 *5 (-395))
-   (-4 *6 (-721)) (-4 *7 (-760)) (-4 *8 (-981 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1022 *5 *6 *7 *8 *3))))) 
+  (-11 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-82))
+   (-5 *1 (-1019 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-905 *4 *5 *6 *7 *3))
-   (-4 *3 (-987 *4 *5 *6 *7))))
+  (|partial| -11 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-82)) (-5 *1 (-902 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-395)) (-4 *5 (-721)) (-4 *6 (-760))
-   (-4 *7 (-981 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1022 *4 *5 *6 *7 *3))
-   (-4 *3 (-987 *4 *5 *6 *7))))) 
+  (|partial| -11 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-82)) (-5 *1 (-1019 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-587 *7)) (-4 *7 (-981 *4 *5 *6)) (-4 *4 (-395)) (-4 *5 (-721))
-   (-4 *6 (-760)) (-5 *2 (-85)) (-5 *1 (-905 *4 *5 *6 *7 *8))
-   (-4 *8 (-987 *4 *5 *6 *7))))
+  (-11 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-82)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
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-   (-4 *8 (-987 *4 *5 *6 *7))))) 
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-   (-4 *8 (-987 *4 *5 *6 *7))))
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-   (-4 *8 (-987 *4 *5 *6 *7))))) 
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-   (-4 *8 (-987 *4 *5 *6 *7))))
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-   (-4 *8 (-987 *4 *5 *6 *7))))) 
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    (-4 *2
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3 *4 *3 *3)
-  (-12 (-5 *3 (-251 *6)) (-5 *4 (-86)) (-4 *6 (-366 *5))
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  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-587 (-251 *7))) (-5 *4 (-587 (-86))) (-5 *5 (-251 *7))
-   (-4 *7 (-366 *6)) (-4 *6 (-13 (-499) (-557 (-477)))) (-5 *2 (-51))
-   (-5 *1 (-270 *6 *7))))
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  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-587 (-251 *8))) (-5 *4 (-587 (-86))) (-5 *5 (-251 *8))
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-   (-5 *2 (-51)) (-5 *1 (-270 *7 *8))))
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-  (-12 (-5 *3 (-587 *7)) (-5 *4 (-587 (-86))) (-5 *5 (-251 *7))
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+   (-4 *7 (-363 *6)) (-4 *6 (-12 (-496) (-554 (-474)))) (-5 *2 (-48))
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  ((*1 *2 *3 *4 *5 *6)
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  ((*1 *2 *3 *4 *3 *5)
-  (-12 (-5 *3 (-251 *5)) (-5 *4 (-86)) (-4 *5 (-366 *6))
-   (-4 *6 (-13 (-499) (-557 (-477)))) (-5 *2 (-51)) (-5 *1 (-270 *6 *5))))
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-  (-12 (-5 *4 (-86)) (-5 *5 (-251 *3)) (-4 *3 (-366 *6))
-   (-4 *6 (-13 (-499) (-557 (-477)))) (-5 *2 (-51)) (-5 *1 (-270 *6 *3))))
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  ((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-86)) (-5 *5 (-251 *3)) (-4 *3 (-366 *6))
-   (-4 *6 (-13 (-499) (-557 (-477)))) (-5 *2 (-51)) (-5 *1 (-270 *6 *3))))
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-  (-12 (-5 *4 (-86)) (-5 *5 (-251 *3)) (-5 *6 (-587 *3)) (-4 *3 (-366 *7))
-   (-4 *7 (-13 (-499) (-557 (-477)))) (-5 *2 (-51)) (-5 *1 (-270 *7 *3))))) 
+  (-11 (-5 *4 (-83)) (-5 *5 (-248 *3)) (-5 *6 (-584 *3)) (-4 *3 (-363 *7))
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 (((*1 *2 *1)
-  (-12 (-5 *2 (-85)) (-5 *1 (-267 *3)) (-4 *3 (-499)) (-4 *3 (-1017))))) 
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 (((*1 *1 *1 *2)
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 (((*1 *2 *1 *1 *1)
-  (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
-   (-4 *1 (-260))))
+  (|partial| -11 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
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 (((*1 *2 *3 *4 *5 *5)
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    (-5 *3
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\ No newline at end of file
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+ (-3808 . 90900) (-3809 . 90687) (-3810 . 90521) (-3811 . 90355)
+ (-3812 . 90189) (-3813 . 90023) (-3814 . 89753) (-3815 . 84339) (** . 81386)
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+ (-3821 . 77373) (-3822 . 77223) (-3823 . 77059) (-3824 . 76895)
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+ (-3853 . 52696) (-3854 . 52603) (-3855 . 52219) (-3856 . 52148)
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+ (-3865 . 50870) (-3866 . 50476) (-3867 . 50401) (-3868 . 50295)
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+ (-3957 . 17162) (-3958 . 16814) (-3959 . 16648) (-3960 . 16482)
+ (-3961 . 16071) (-3962 . 14964) (* . 10917) (-3964 . 10663) (-3965 . 10479)
+ (-3966 . 9522) (-3967 . 9469) (-3968 . 9409) (-3969 . 9140) (-3970 . 8513)
+ (-3971 . 7240) (-3972 . 5996) (-3973 . 5127) (-3974 . 3864) (-3975 . 420)
+ (-3976 . 306) (-3977 . 173) (-3978 . 30)) 
\ No newline at end of file