Fix up thinkos

7 files changed, 18081 insertions, 18063 deletions

diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet
index 26375731..3ff73675 100644
--- a/src/algebra/aggcat.spad.pamphlet
+++ b/src/algebra/aggcat.spad.pamphlet
@@ -189,7 +189,6 @@ FiniteAggregate(S: Type): Category == Exports where
 ++   shapes.
 ShallowlyMutableAggregate(S: Type): Category == Exports where
   Exports == HomogeneousAggregate S with
-      shallowlyMutable
       map!: (S->S,%) -> %
         ++ \spad{map!(f,u)} destructively replaces each element
         ++ \spad{x} of \spad{u} by \spad{f(x)}    
diff --git a/src/algebra/matfuns.spad.pamphlet b/src/algebra/matfuns.spad.pamphlet
index 21bfb0fe..6fe6db50 100644
--- a/src/algebra/matfuns.spad.pamphlet
+++ b/src/algebra/matfuns.spad.pamphlet
@@ -401,7 +401,7 @@ InnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2):_
         ++ 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.
-      if Col2 has ShallowlyMutableAggregate R then
+      if Col2 has ShallowlyMutableAggregate QF then
         nullSpace : M -> List Col
           ++ \spad{nullSpace(m)} returns a basis for the null space of the
           ++ matrix m.
@@ -415,7 +415,7 @@ InnerMatrixQuotientFieldFunctions(R,Row,Col,M,QF,Row2,Col2,M2):_
       (inv := inverse(qfMat m)$IMATLIN) case "failed" => "failed"
       inv :: M2
 
-    if Col2 has ShallowlyMutableAggregate R then
+    if Col2 has ShallowlyMutableAggregate QF then
       nullSpace m ==
         [clearDenominator(v)$CDEN for v in nullSpace(qfMat m)$IMATLIN]
 
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 86b9f8ba..8970f6c6 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(1968443 . 3578003924)       
+(1968360 . 3578007597)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the shallowly mutable property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
 NIL 
 (-19 S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the shallowly mutable property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-20 S) 
 ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) 
@@ -38,7 +38,7 @@ NIL
 NIL 
 (-27) 
 ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
@@ -46,7 +46,7 @@ NIL
 NIL 
 (-29 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T)) 
+((-3994 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T)) 
 NIL 
 (-30) 
 ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,10 +56,10 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3093) 
+(-32 R -3094) 
 ((|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 (-950 (-484))))) 
+((|HasCategory| |#1| (QUOTE (-951 (-485))))) 
 (-33 S) 
 ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\"")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) 
 NIL 
@@ -74,7 +74,7 @@ NIL
 NIL 
 (-36 |Key| |Entry|) 
 ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table.	It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-37 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
@@ -82,20 +82,20 @@ NIL
 NIL 
 (-38 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-39 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3093 UP UPUP -2615) 
+(-40 -3094 UP UPUP -2616) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) 
-(-41 R -3093) 
+((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) 
+(-41 R -3094) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-258)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
+((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
 (-45 |Key| |Entry|) 
 ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|))) (-12 (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|)))))) 
+NIL 
+((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|))) (-12 (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|)))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
+((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
 (-49) 
 ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-51) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3093) 
+(-54 |Base| R -3094) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,28 +158,28 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}"))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-58 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
 (-59 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-61 R L) 
 ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-312)))) 
 (-62 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-63 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -202,11 +202,11 @@ NIL
 NIL 
 (-68) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3998 "*") . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T)) 
+(((-3999 "*") . T) (-3994 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3993 . T) (-3996 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3984 . T)) 
 NIL 
 (-69 R) 
 ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-70 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -222,24 +222,24 @@ NIL
 NIL 
 (-73 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
 (-74 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE (-3998 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-3999 "*")))) 
 (-75 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) 
 NIL 
 NIL 
 (-76 S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-77) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
 (-78) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -254,11 +254,11 @@ NIL
 NIL 
 (-81) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-473)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-1013))) (-12 (|HasCategory| $ (QUOTE (-1035 (-85)))) (|HasCategory| (-85) (QUOTE (-756)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1035 (-85))))) 
+NIL 
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| (-85) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1036 (-85))))) 
 (-82 R S) 
 ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-83 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
@@ -280,22 +280,22 @@ NIL
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-88 -3093 UP) 
+(-88 -3094 UP) 
 ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) 
 NIL 
 NIL 
 (-89 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-90 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-473)))) (|HasCategory| (-89 |#1|) (QUOTE (-933))) (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756)))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-1066))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-89 |#1|) (QUOTE (-934))) (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757)))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
 (-91 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
 (-92 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -306,15 +306,15 @@ NIL
 NIL 
 (-94 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
 (-95 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-96) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-97 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
@@ -322,24 +322,24 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-99 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
 (-100 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
 (-101) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
 (-102) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-756)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (|HasCategory| (-101) (QUOTE (-552 (-772)))) (|HasCategory| (-101) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-101) (QUOTE (-756))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1013))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| $ (QUOTE (-1035 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1035 (-101)))) (|HasCategory| (-101) (QUOTE (-756))))) 
+NIL 
+((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1014))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| $ (QUOTE (-1036 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1036 (-101)))) (|HasCategory| (-101) (QUOTE (-757))))) 
 (-103) 
 ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) 
 NIL 
@@ -358,13 +358,13 @@ NIL
 NIL 
 (-107) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3998 "*") . T)) 
+(((-3999 "*") . T)) 
 NIL 
-(-108 |minix| -2622 R) 
+(-108 |minix| -2623 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2622 S T$) 
+(-109 |minix| -2623 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
@@ -386,8 +386,8 @@ NIL
 NIL 
 (-114) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
-((-3986 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-1013))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) 
+((-3987 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) 
 (-115 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
@@ -402,7 +402,7 @@ NIL
 NIL 
 (-118) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-119 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) 
@@ -410,9 +410,9 @@ NIL
 NIL 
 (-120) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-121 -3093 UP UPUP) 
+(-121 -3094 UP UPUP) 
 ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) 
 NIL 
 NIL 
@@ -423,14 +423,14 @@ NIL
 (-123 A S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
 (-124 S) 
 ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
 NIL 
 (-125 |n| K Q) 
 ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) 
-((-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
 (-126) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -452,7 +452,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-131 R -3093) 
+(-131 R -3094) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -483,10 +483,10 @@ NIL
 (-138 S R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495)))) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) 
 (-139 R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
-((-3989 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1376 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-140 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -498,8 +498,8 @@ NIL
 NIL 
 (-142 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-3989 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1376 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
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+((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|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 (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-974))) (-12 (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3996)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-143 R S) 
 ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) 
 NIL 
@@ -514,7 +514,7 @@ NIL
 NIL 
 (-146) 
 ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-147) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -522,7 +522,7 @@ NIL
 NIL 
 (-148 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) 
-(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-149) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -539,7 +539,7 @@ NIL
 (-152 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
+((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
 (-153 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -576,7 +576,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) 
 NIL 
 NIL 
-(-162 R -3093) 
+(-162 R -3094) 
 ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) 
 NIL 
 NIL 
@@ -604,23 +604,23 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) 
 NIL 
 NIL 
-(-169 -3093 UP UPUP R) 
+(-169 -3094 UP UPUP R) 
 ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) 
 NIL 
 NIL 
-(-170 -3093 FP) 
+(-170 -3094 FP) 
 ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
 (-171) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
 (-172) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-173 R -3093) 
+(-173 R -3094) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -634,19 +634,19 @@ NIL
 NIL 
 (-176 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-177 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-178 R -3093) 
+(-178 R -3094) 
 ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) 
 NIL 
 NIL 
 (-179) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-180) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -654,19 +654,19 @@ NIL
 NIL 
 (-181 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-182 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
 (-183 S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-184 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-185 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -678,7 +678,7 @@ NIL
 NIL 
 (-187 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-188 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
@@ -690,7 +690,7 @@ NIL
 NIL 
 (-190) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-191) 
 ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) 
@@ -702,25 +702,25 @@ NIL
 ((|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
 (-193 S) 
 ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-194) 
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-195 S -2622 R) 
+(-195 S -2623 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasAttribute| |#3| (QUOTE -3993)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) 
-(-196 -2622 R) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) 
+(-196 -2623 R) 
 ((|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."))) 
-((-3990 |has| |#2| (-961)) (-3991 |has| |#2| (-961)) (-3993 |has| |#2| (-6 -3993))) 
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
 NIL 
-(-197 -2622 R) 
+(-197 -2623 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."))) 
-((-3990 |has| |#2| (-961)) (-3991 |has| |#2| (-961)) (-3993 |has| |#2| (-6 -3993))) 
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|#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320))) (OR (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-961))))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-350 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(|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-961))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-961)))) 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(|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
-(-198 -2622 A B) 
+((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
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(|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-198 -2623 A B) 
 ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 
 NIL 
 NIL 
@@ -734,7 +734,7 @@ NIL
 NIL 
 (-201) 
 ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) 
-((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-202 S) 
 ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) 
@@ -742,20 +742,20 @@ NIL
 NIL 
 (-203 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-3997 . T)) 
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+NIL 
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 (-204 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-205 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-206 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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 (-207) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
@@ -770,23 +770,23 @@ NIL
 NIL 
 (-210 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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(-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#4|)))) 
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 (-211 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
-((-3993 OR (-2563 (|has| |#3| (-961)) (|has| |#3| (-190))) (|has| |#3| (-6 -3993)) (-2563 (|has| |#3| (-961)) (|has| |#3| (-809 (-1090))))) (-3990 |has| |#3| (-961)) (-3991 |has| |#3| (-961))) 
-((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (OR (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756)))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-809 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(-320))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasAttribute| |#3| (QUOTE -3993)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-552 (-772)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#3|)))) 
+((-3994 OR (-2564 (|has| |#3| (-962)) (|has| |#3| (-190))) (|has| |#3| (-6 -3994)) (-2564 (|has| |#3| (-962)) (|has| |#3| (-810 (-1091))))) (-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962))) 
+((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#3|)))) 
 (-212 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-190)))) 
 (-213 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
 (-214 S) 
 ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-215 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -827,15 +827,15 @@ NIL
 (-224 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-189)))) 
+((|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189)))) 
 (-225 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
 (-226 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#3| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#3| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#3| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#3| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#3| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#3| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-227 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -848,11 +848,11 @@ NIL
 ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) 
 NIL 
 NIL 
-(-230 R -3093) 
+(-230 R -3094) 
 ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the	inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) 
 NIL 
 NIL 
-(-231 R -3093) 
+(-231 R -3094) 
 ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) 
 NIL 
 NIL 
@@ -875,10 +875,10 @@ NIL
 (-236 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72)))) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72)))) 
 (-237 S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
-((-3997 . T)) 
+NIL 
 NIL 
 (-238 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
@@ -899,14 +899,14 @@ NIL
 (-242 S |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#3|)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#3|)))) 
 (-243 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-244 S R |Mod| -2037 -3519 |exactQuo|) 
+(-244 S R |Mod| -2038 -3520 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-245 S) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
@@ -914,7 +914,7 @@ NIL
 NIL 
 (-246) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-247) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
@@ -926,16 +926,16 @@ NIL
 NIL 
 (-249 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-3993 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3990 |has| |#1| (-961)) (-3991 |has| |#1| (-961))) 
-((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-663)))) 
+((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-962)) (-3992 |has| |#1| (-962))) 
+((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) 
 (-250 S R) 
 ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) 
 NIL 
 NIL 
 (-251 |Key| |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
 (-252) 
 ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) 
 NIL 
@@ -943,16 +943,16 @@ NIL
 (-253 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) 
+((|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) 
 (-254) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
 NIL 
-(-255 -3093 S) 
+(-255 -3094 S) 
 ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) 
 NIL 
 NIL 
-(-256 E -3093) 
+(-256 E -3094) 
 ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) 
 NIL 
 NIL 
@@ -962,7 +962,7 @@ NIL
 NIL 
 (-258) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-259 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
@@ -972,7 +972,7 @@ NIL
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-261 -3093) 
+(-261 -3094) 
 ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) 
 NIL 
 NIL 
@@ -986,12 +986,12 @@ NIL
 NIL 
 (-264 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-473)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-330)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-330)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
 (-265 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-3993 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-961)) (|has| |#1| (-413)))) (|has| |#1| (-961)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-495)) (-3988 |has| |#1| (-495))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
+((-3994 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
 (-266 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1000,7 +1000,7 @@ NIL
 ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) 
 NIL 
 NIL 
-(-268 R -3093) 
+(-268 R -3094) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
 NIL 
@@ -1010,8 +1010,8 @@ NIL
 NIL 
 (-270 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
 (-271 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1022,8 +1022,8 @@ NIL
 NIL 
 (-273 S) 
 ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-716)))) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-717)))) 
 (-274 S E) 
 ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'s.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1031,26 +1031,26 @@ NIL
 (-275 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-694) (QUOTE (-716)))) 
+((|HasCategory| (-695) (QUOTE (-717)))) 
 (-276 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
+((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
 (-277 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-278 S) 
 ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
-(-279 S -3093) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-279 S -3094) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-320)))) 
-(-280 -3093) 
+(-280 -3094) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-281 E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) 
@@ -1060,7 +1060,7 @@ NIL
 ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) 
 NIL 
 NIL 
-(-283 -3093 UP UPUP R) 
+(-283 -3094 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) 
 NIL 
 NIL 
@@ -1068,33 +1068,33 @@ NIL
 ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-285 S -3093 UP UPUP R) 
+(-285 S -3094 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
-(-286 -3093 UP UPUP R) 
+(-286 -3094 UP UPUP R) 
 ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-287 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-288 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-289 |p| |n|) 
 ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
-(-290 S -3093 UP UPUP) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
+(-290 S -3094 UP UPUP) 
 ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-291 -3093 UP UPUP) 
+(-291 -3094 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."))) 
-((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-292 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
@@ -1102,15 +1102,15 @@ NIL
 NIL 
 (-293 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
 (-294 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-295 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-296 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
@@ -1126,43 +1126,43 @@ NIL
 NIL 
 (-299) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-300 R UP -3093) 
+(-300 R UP -3094) 
 ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
 (-301 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
 (-302 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-303 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-304 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-305 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-306 -3093 GF) 
+(-306 -3094 GF) 
 ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-307 -3093 FP FPP) 
+(-307 -3094 FP FPP) 
 ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) 
 NIL 
 NIL 
 (-308 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-309 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
@@ -1170,7 +1170,7 @@ NIL
 NIL 
 (-310 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-311 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1178,7 +1178,7 @@ NIL
 NIL 
 (-312) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-313 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
@@ -1191,10 +1191,10 @@ NIL
 (-315 S R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-495)))) 
+((|HasCategory| |#2| (QUOTE (-496)))) 
 (-316 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
+((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
 NIL 
 (-317 A S) 
 ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,x)} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,u,0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. For collections,{}} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) holds for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\spad{p(x)} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) 
@@ -1218,12 +1218,12 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-322 R UP) 
 ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-323 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72)))) 
 (-324 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
@@ -1234,7 +1234,7 @@ NIL
 NIL 
 (-326 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) 
-((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
 NIL 
 (-327 S V) 
 ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) 
@@ -1243,14 +1243,14 @@ NIL
 (-328 S R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-580 (-484))))) 
+((|HasCategory| |#2| (QUOTE (-581 (-485))))) 
 (-329 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
 NIL 
 (-330) 
 ((|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3980 . T) (-3988 . T) (-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-331 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) 
@@ -1262,15 +1262,15 @@ NIL
 NIL 
 (-333 R S) 
 ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
 (-334 R S) 
 ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146)))) 
 (-335 R |Basis|) 
 ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-336 S) 
 ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1279,7 +1279,7 @@ NIL
 (-337 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
 (-338) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
@@ -1290,13 +1290,13 @@ NIL
 NIL 
 (-340 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-341 -3093 UP UPUP R) 
+(-341 -3094 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-342 -3093 UP) 
+(-342 -3094 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1310,28 +1310,28 @@ NIL
 NIL 
 (-345) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-346 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3987))) 
+((|HasAttribute| |#1| (QUOTE -3980)) (|HasAttribute| |#1| (QUOTE -3988))) 
 (-347) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-348 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| #1# #2# #3# #4#) $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-455 (-1090) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1134))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1134)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-392)))) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-456 (-1091) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-392)))) 
 (-349 R S) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) 
 NIL 
 NIL 
 (-350 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
-((-3983 -12 (|has| |#1| (-6 -3994)) (|has| |#1| (-392)) (|has| |#1| (-6 -3983))) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1090)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((-3984 -12 (|has| |#1| (-6 -3995)) (|has| |#1| (-392)) (|has| |#1| (-6 -3984))) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-351 A B) 
 ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) 
 NIL 
@@ -1342,28 +1342,28 @@ NIL
 NIL 
 (-353 R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-354 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) 
 (-355 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-356 R -3093 UP A) 
+(-356 R -3094 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-357 R1 F1 U1 A1 R2 F2 U2 A2) 
 ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-358 R -3093 UP A |ibasis|) 
+(-358 R -3094 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) 
 (-359 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1374,7 +1374,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-312)))) 
 (-361 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
+((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
 NIL 
 (-362 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
@@ -1383,10 +1383,10 @@ NIL
 (-363 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
 (-364 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-3993 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-495)) (-3988 |has| |#1| (-495))) 
+((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
 NIL 
 (-365 R A S B) 
 ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) 
@@ -1403,36 +1403,36 @@ NIL
 (-368 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) 
+((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) 
 (-369 S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3986 . T) (-3997 . T)) 
+((-3987 . T)) 
 NIL 
 (-370 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) 
 NIL 
 NIL 
-(-371 R -3093) 
+(-371 R -3094) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) 
 NIL 
 NIL 
 (-372 R E) 
 ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) 
-((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983)))) 
-(-373 R -3093) 
+((-3984 -12 (|has| |#1| (-6 -3984)) (|has| |#2| (-6 -3984))) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#2| (QUOTE -3984)))) 
+(-373 R -3094) 
 ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) 
 NIL 
 NIL 
-(-374 R -3093) 
+(-374 R -3094) 
 ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) 
 NIL 
 NIL 
-(-375 R -3093) 
+(-375 R -3094) 
 ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-27)))) 
-(-376 R -3093) 
+(-376 R -3094) 
 ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) 
 NIL 
 NIL 
@@ -1440,10 +1440,10 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-378 R -3093 UP) 
+(-378 R -3094 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 (-950 (-48))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-48))))) 
 (-379) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
@@ -1460,7 +1460,7 @@ NIL
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) 
 NIL 
 NIL 
-(-383 R UP -3093) 
+(-383 R UP -3094) 
 ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) 
 NIL 
 NIL 
@@ -1498,16 +1498,16 @@ NIL
 NIL 
 (-392) 
 ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-393 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,s2,..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,s2,..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,\\%x2,..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) 
-((-3993 |has| (-350 (-857 |#1|)) (-495)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| (-350 (-857 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-350 (-857 |#1|)) (QUOTE (-495)))) 
+((-3994 |has| (-350 (-858 |#1|)) (-496)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| (-350 (-858 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-350 (-858 |#1|)) (QUOTE (-496)))) 
 (-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"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
 (-395 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) 
 NIL 
@@ -1534,7 +1534,7 @@ NIL
 NIL 
 (-401 |vl| R IS E |ff| P) 
 ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-402 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1542,8 +1542,8 @@ NIL
 NIL 
 (-403 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+NIL 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
 (-404 S R E) 
 ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) 
 NIL 
@@ -1572,7 +1572,7 @@ NIL
 ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-411 |lv| -3093 R) 
+(-411 |lv| -3094 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1582,23 +1582,23 @@ NIL
 NIL 
 (-413) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
 (-414 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
 (-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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|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)}"))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+NIL 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
 (-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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 (-418) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) 
@@ -1606,29 +1606,29 @@ NIL
 NIL 
 (-419 |Key| |Entry| |hashfn|) 
 ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|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 
 (-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"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-422 -2622 S) 
+(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-422 -2623 S) 
 ((|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}."))) 
-((-3990 |has| |#2| (-961)) (-3991 |has| |#2| (-961)) (-3993 |has| |#2| (-6 -3993))) 
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(-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|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 
 (-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}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-425 -3093 UP UPUP R) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-425 -3094 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
 NIL 
@@ -1638,12 +1638,12 @@ NIL
 NIL 
 (-427) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
 (-428 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) 
+((|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) 
 (-429 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1664,3109 +1664,3113 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-434 -3093 UP |AlExt| |AlPol|) 
+(-434 -3094 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-435) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . 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."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
 (-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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-438 K R UP) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) 
 NIL 
 NIL 
-(-439 R UP -3093) 
+(-439 R UP -3094) 
 ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) 
 NIL 
 NIL 
-(-440 K R UP L) 
+(-440 |mn|) 
+((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
+NIL 
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| (-85) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1036 (-85))))) 
+(-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 
-(-441) 
+(-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 
-(-442 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 
-(-443 -3093 |Expon| |VarSet| |DPoly|) 
+(-444 -3094 |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 (-553 (-1090))))) 
-(-444 |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 
-(-445 T$) 
+(-446 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3057 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3058 (|f| |x| |x|) |x|))) . T)) 
 NIL 
-(-446) 
+(-447) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-447 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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-448 A S) 
+((-12 (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-449 A S) 
+((-12 (|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}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-450 A S) 
+(-451 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-451 A S) 
+((-12 (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-452 A S) 
+((-12 (|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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
-(-453 A S) 
+((-12 (|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 
-(-454 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 
-(-455 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 
-(-456 S E |un|) 
+(-457 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-716)))) 
-(-457 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}"))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
-(-458) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-459) 
 ((|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 
-(-459 |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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-320)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-320))) (|HasCategory| (-517 |#1|) (QUOTE (-118)))) 
-(-460 R |Row| |Col| M) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-320)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-320))) (|HasCategory| (-518 |#1|) (QUOTE (-118)))) 
+(-461 R |Row| |Col| M) 
 ((|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 -1035) (|devaluate| |#1|)))) 
-(-461 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 -1035) (|devaluate| |#1|)))) 
-(-462) 
+((|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 
-(-463) 
+(-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 
-(-464 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 
-(-465) 
+(-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 
-(-466 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 
-(-467) 
+(-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 
-(-468 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 
-(-469 |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 (-1013))) (|HasCategory| (-694) (QUOTE (-1013))))) 
-(-470 K -3093 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) 
+(-471 K -3094 |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 
-(-471) 
+(-472) 
 NIL 
 NIL 
 NIL 
-(-472) 
+(-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 
-(-473) 
+(-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|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-474 R) 
+(-475 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-475 |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 
-(-476 K -3093 |Par|) 
+(-477 K -3094 |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 
-(-477 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 
-(-478 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 
-(-479 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 
-(-480 |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 
-(-481 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 
-(-482 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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-483) 
+(-484) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-484) 
+(-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."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-485) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-486) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-487) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-488) 
+(-489) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-489 |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}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
-(-490 R -3093) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-491 R -3094) 
 ((|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 
-(-491 R0 -3093 UP UPUP R) 
+(-492 R0 -3094 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 
-(-492) 
+(-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 
-(-493 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."))) 
-((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-494 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 
-(-495) 
+(-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."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-496 R -3093) 
+(-497 R -3094) 
 ((|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 
-(-497 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 
-(-498 R -3093 L) 
+(-499 R -3094 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 -600) (|devaluate| |#2|)))) 
-(-499) 
+((|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 
-(-500 -3093 UP UPUP R) 
+(-501 -3094 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 
-(-501 -3093 UP) 
+(-502 -3094 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 
-(-502 R -3093 L) 
+(-503 R -3094 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 -600) (|devaluate| |#2|)))) 
-(-503 R -3093) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-504 R -3094) 
 ((|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 (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-569))))) 
-(-504 -3093 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-570))))) 
+(-505 -3094 UP) 
 ((|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 
-(-505 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 
-(-506 -3093) 
+(-507 -3094) 
 ((|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 
-(-507 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."))) 
-((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-508) 
+(-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 
-(-509 R -3093) 
+(-510 R -3094) 
 ((|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 (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495)))) 
-(-510 -3093 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496)))) 
+(-511 -3094 UP) 
 ((|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 
-(-511 R -3093) 
+(-512 R -3094) 
 ((|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 
-(-512) 
+(-513) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-513) 
+(-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 
-(-514) 
+(-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 
-(-515) 
+(-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 
-(-516 |p| |unBalanced?|) 
+(-517 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-517 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) 
-(-518) 
+(-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 
-(-519 -3093) 
+(-520 -3094) 
 ((|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}."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-950 (-1090))))) 
-(-520 E -3093) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-951 (-1091))))) 
+(-521 E -3094) 
 ((|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 
-(-521 R -3093) 
+(-522 R -3094) 
 ((|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 
-(-522) 
+(-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 
-(-523 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 
-(-524 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 
-(-525 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)))) 
-(-526) 
+(-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 
-(-527 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 
-(-528) 
+(-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|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-529 E V R P) 
+(-530 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-530 |Coef|) 
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (|HasCategory| (-484) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484)))))) 
 (-531 |Coef|) 
+((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) 
+(-532 |Coef|) 
 ((|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-495)))) 
-(-532) 
+(((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-496)))) 
+(-533) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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 
-(-533 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 
-(-534 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 
-(-535 R -3093 FG) 
+(-536 R -3094 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 
-(-536 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|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) 
 NIL 
 NIL 
-(-537 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 -1035) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) 
-(-538 |Index| |Entry|) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) 
+(-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 
-(-539) 
+(-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 
-(-540 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)."))) 
-((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3991 . T) (-3990 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-541) 
+((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-542) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
 NIL 
-(-542) 
+(-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| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-543) 
+(-544) 
 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "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 
-(-544) 
+(-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| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-545) 
+(-546) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "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 
-(-546) 
+(-547) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-547 |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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))))) 
-(-548 S |Key| |Entry|) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))))) 
+(-549 S |Key| |Entry|) 
 ((|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 
-(-549 |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}."))) 
-((-3997 . T)) 
 NIL 
-(-550 S) 
+NIL 
+(-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 (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484)))))) 
-(-551 R S) 
+((|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|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 
-(-552 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 
-(-553 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-554 -3093 UP) 
+(-555 -3094 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-555 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 
-(-556) 
+(-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| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-557 S) 
+(-558 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-558 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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-559 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 
-(-560 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."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-561 R -3093) 
+(-562 R -3094) 
 ((|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 
-(-562 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"))) 
-((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) 
-(-563 R E V P TS ST) 
+((-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+(-564 R E V P TS ST) 
 ((|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 
-(-564 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 
-(-565) 
+(-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 
-(-566 |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}}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-567 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 
-(-568 R -3093) 
+(-569 R -3094) 
 ((|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 
-(-569) 
+(-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 
-(-570 |lv| -3093) 
+(-571 |lv| -3094) 
 ((|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 
-(-571) 
+(-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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-553 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1035 (-51))))) 
-(-572 R A) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-1036 (-51))))) 
+(-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)."))) 
-((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3991 . T) (-3990 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-573 S R) 
+((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-574 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-574 R) 
+(-575 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
 NIL 
-(-575 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 
-(-576 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 
-(-577 |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 
-(-578 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 
-((-2561 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-579 K B) 
+((-2562 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-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}."))) 
-((-3991 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-577 |#2|) (QUOTE (-1013))))) 
-(-580 R) 
+((-3992 . T) (-3991 . T)) 
+((-12 (|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 
-(-581 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-582 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 
-(-583 S) 
+(-584 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
-(-584 A B) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-585 A B) 
 ((|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 
-(-585 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 
-(-586 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 
-(-587 T$) 
+(-588 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-588 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| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-589 S) 
+(-590 S) 
 ((|substitute| (($ |#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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-590 R) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+(-591 R) 
 ((|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 
-(-591 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 
-(-592 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 -1035) (|devaluate| |#2|)))) 
-(-593 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 
-(-594 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}."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-714)))) 
-(-595 R -3093 L) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-715)))) 
+(-596 R -3094 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 
-(-596 A -2493) 
+(-597 A -2494) 
 ((|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}}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-597 A) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-598 A) 
 ((|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}}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-598 A M) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-599 A M) 
 ((|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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-599 S A) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-600 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-600 A) 
+(-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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-601 -3093 UP) 
+(-602 -3094 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)))) 
-(-602 A L) 
+(-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 
-(-603 S) 
+(-604 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-604) 
+(-605) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-605 R) 
+(-606 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-606 |VarSet| R) 
+(-607 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3991 . T) (-3990 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3992 . T) (-3991 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-607 A S) 
+(-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 
-(-608 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}."))) 
-((-3997 . T)) 
 NIL 
-(-609 -3093 |Row| |Col| M) 
+NIL 
+(-610 -3094 |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 
-(-610 -3093) 
+(-611 -3094) 
 ((|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 
-(-611 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 
-(-612 |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."))) 
-((-3993 . T) (-3990 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-613) 
+((-3994 . T) (-3991 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-614) 
 ((|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 
-(-614 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-615 A S) 
+(-616 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-616 S) 
+(-617 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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 
-(-617) 
+(-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 
-(-618 |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 
-(-619 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 
-(-620 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 
-(-621 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 
-(-622) 
+(-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 
-(-623 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 
-(-624 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 
-(-625 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 
-(-626 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 (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495)))) 
-(-627 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3999 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|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."))) 
-((-3997 . T)) 
 NIL 
-(-628 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+NIL 
+(-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 
-(-629 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 (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495)))) 
-(-630 R) 
-((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|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 (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-632 R) 
 ((|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 
-(-632 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 
-(-633 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 
-(-634 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}."))) 
-((-3997 . T)) 
 NIL 
-(-635 U) 
+NIL 
+(-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 
-(-636) 
+(-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 
-(-637 OV E -3093 PG) 
+(-638 OV E -3094 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 
-(-638 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 
-(-639 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 
-(-640 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 
-(-641 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 
-(-642 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 
-(-643 S -2670 I) 
+(-644 S -2671 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 
-(-644 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 
-(-645 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)}.}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-646 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 
-(-647) 
+(-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 
-(-648 R |Mod| -2037 -3519 |exactQuo|) 
+(-649 R |Mod| -2038 -3520 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-649 R P) 
+(-650 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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-(-650 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| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-651 R M) 
+(-652 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-652 R |Mod| -2037 -3519 |exactQuo|) 
+(-653 R |Mod| -2038 -3520 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-653 S R) 
+(-654 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-654 R) 
+(-655 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-655 -3093) 
+(-656 -3094) 
 ((|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]]}."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-656 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-657) 
+(-658) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 
-(-658 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 
-(-659) 
+(-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 
-(-660 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 (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320)))) 
-(-661 R UP) 
+(-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."))) 
-((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-662 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 
-(-663) 
+(-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| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-664 T$) 
+(-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 (-3057 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-665 T$) 
+(-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 (-3057 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-666 -3093 UP) 
+(-667 -3094 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 
-(-667 |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 
-(-668 |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 
-(-669 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 
-(-670 |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."))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-671 E OV R PRF) 
+(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-672 E OV R PRF) 
 ((|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 
-(-672 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 
-(-673 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 
-(-674 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|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-756)))) 
-(-675 S) 
-((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
-((-3986 . T) (-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757)))) 
 (-676 S) 
+((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) 
+((-3987 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+(-677 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-3986 . T) (-3997 . T)) 
+((-3987 . T)) 
 NIL 
-(-677) 
+(-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 
-(-678 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 
-(-679 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-680 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 
-(-681 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 
-(-682 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 
-(-683 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-684 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-685) 
+(-686) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-686 S) 
+(-687 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 
-(-687) 
+(-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 
-(-688 |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 
-(-689 -3093) 
+(-690 -3094) 
 ((|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 
-(-690 P -3093) 
+(-691 P -3094) 
 ((|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 
-(-691 T$) 
+(-692 T$) 
 NIL 
 NIL 
 NIL 
-(-692 UP -3093) 
+(-693 UP -3094) 
 ((|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 
-(-693 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 
-(-694) 
+(-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."))) 
-(((-3998 "*") . T)) 
+(((-3999 "*") . T)) 
 NIL 
-(-695 R -3093) 
+(-696 R -3094) 
 ((|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 
-(-696) 
+(-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 
-(-697 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 
-(-698 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 
-(-699 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 
-(-700 -3093 |ExtF| |SUEx| |ExtP| |n|) 
+(-701 -3094 |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 
-(-701 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 
-(-702 |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 
-(-703 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."))) 
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-(-704 R) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
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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)}"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-705 R S) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-706 R S) 
 ((|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 
-(-706 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 (-350 (-484)))))) 
-(-707 R E V P) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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.}"))) 
-((-3997 . T)) 
 NIL 
-(-708 S) 
+NIL 
+(-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 (-495))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-709) 
+((-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-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 
-(-710) 
+(-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 
-(-711) 
+(-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 
-(-712 |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 
-(-713 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|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-714) 
+(-715) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\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 
-(-715 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 
-(-716) 
+(-717) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-717) 
+(-718) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-718) 
+(-719) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-719 S R) 
+(-720 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) 
-(-720 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) 
+(-721 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-721) 
+(-722) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-722 R) 
+(-723 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) 
-(-723 OR R OS S) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+(-724 OR R OS S) 
 ((|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 
-(-724 R -3093 L) 
+(-725 R -3094 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 
-(-725 R -3093) 
+(-726 R -3094) 
 ((|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 
-(-726 R -3093) 
+(-727 R -3094) 
 ((|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 
-(-727 -3093 UP UPUP R) 
+(-728 -3094 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 
-(-728 -3093 UP L LQ) 
+(-729 -3094 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 
-(-729 -3093 UP L LQ) 
+(-730 -3094 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 
-(-730 -3093 UP) 
+(-731 -3094 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 
-(-731 -3093 L UP A LO) 
+(-732 -3094 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 
-(-732 -3093 UP) 
+(-733 -3094 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)))) 
-(-733 -3093 LO) 
+(-734 -3094 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 
-(-734 -3093 LODO) 
+(-735 -3094 LODO) 
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(|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-1014)))) (|HasAttribute| |#2| (QUOTE -3994)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-738 (-1090)) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-738 (-1090)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-738 (-1090)) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-738 (-1090)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-738 (-1090)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-737 |Kernels| R |var|) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
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+(-738 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-3998 "*") |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 . T) (-3991 . T) (-3990 . T)) 
+(((-3999 "*") |has| |#2| (-312)) (-3990 |has| |#2| (-312)) (-3995 |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 . T) (-3992 . T) (-3991 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-738 S) 
+(-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 
-(-739 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| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-740) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-741) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-741 P R) 
+(-742 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) 
-(-742 S) 
+(-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}."))) 
-((-3986 . T) (-3997 . T)) 
+((-3987 . T)) 
 NIL 
-(-743 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."))) 
-((-3993 |has| |#1| (-755))) 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
-(-744 R S) 
+((-3994 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-745 R S) 
 ((|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 
-(-745 R) 
+(-746 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-746 A S) 
+(-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 
-(-747 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| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-748) 
+(-749) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-749) 
+(-750) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 
-(-750 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3993 |has| |#1| (-755))) 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
-(-751 R S) 
+((-3994 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-752 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-752) 
+(-753) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-753 -2622 S) 
+(-754 -2623 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-754) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-755) 
+(-756) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-756) 
+(-757) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-757 T$ |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 (-552 (-772))))) 
-(-758 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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-759) 
+(-760) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-760 S R) 
+(-761 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-761 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-762 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-762 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 (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
-(-763 R |sigma| -3245) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
+(-764 R |sigma| -3246) 
 ((|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."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-764 |x| R |sigma| -3245) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-765 |x| R |sigma| -3246) 
 ((|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}."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-765 R) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-766 R) 
 ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
-(-766) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) 
+(-767) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-767) 
+(-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 
-(-768) 
+(-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 
-(-769 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 
-(-770) 
+(-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 
-(-771) 
+(-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 
-(-772) 
+(-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 
-(-773 |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 
-(-774) 
+(-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 
-(-775 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)"))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-776 R PS UP) 
+(-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 
-(-777 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 
-(-778 |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)."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-779 |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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-780 |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)."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-473)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-1066))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) 
-(-781 |p| PADIC) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-1067))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-258))) (|HasCategory| (-779 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))))) 
+(-782 |p| PADIC) 
 ((|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)}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-483))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-782 S T$) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-783 S T$) 
 ((|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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))))) 
-(-783) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) 
+(-784) 
 ((|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 
-(-784) 
+(-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 
-(-785) 
+(-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 
-(-786 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 
-(-787 |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 
-(-788 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 
-(-789 |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 
-(-790) 
+(-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 
-(-791 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 
-(-792 |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 
-(-793) 
+(-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 
-(-794 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 
-(-795 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 
-(-796 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 
-(-797 |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 (-2561 (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-2561 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2561 (|HasCategory| |#2| (QUOTE (-950 (-1090)))))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) 
-(-798 R S) 
+((-12 (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2562 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) 
+(-799 R S) 
 ((|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 
-(-799 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 
-(-800 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 
-(-801 R -2670) 
+(-802 R -2671) 
 ((|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 
-(-802 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 
-(-803 |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 
-(-804 UP R) 
+(-805 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-805 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 
-(-806 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 
-(-807 UP -3093) 
+(-808 UP -3094) 
 ((|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 
-(-808 R S) 
+(-809 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-809 S) 
+(-810 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-810 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 
-(-811 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 
-(-812 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 (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
-(-813 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-814 S) 
 ((|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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3993 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) 
-(-814 |n| R) 
+((-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) 
+(-815 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 
-(-815 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."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-816 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 
-(-817 |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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) 
-(-818 R E |VarSet| S) 
+(-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 
-(-819 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 
-(-820 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)))) 
-(-821) 
+(-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}."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-822 R0 -3093 UP UPUP R) 
+(-823 R0 -3094 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 
-(-823 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 
-(-824 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 
-(-825 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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-826 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 
-(-827 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 
-(-828) 
+(-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 
-(-829 -3093) 
+(-830 -3094) 
 ((|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 
-(-830) 
+(-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}."))) 
-(((-3998 "*") . T)) 
+(((-3999 "*") . T)) 
 NIL 
-(-831 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 
-(-832) 
+(-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)}"))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-833 |xx| -3093) 
+(-834 |xx| -3094) 
 ((|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 
-(-834 -3093 P) 
+(-835 -3094 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-835 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 
-(-836) 
+(-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 
-(-837 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 
-(-838) 
+(-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 
-(-839) 
+(-840) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-840) 
+(-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 
-(-841 R -3093) 
+(-842 R -3094) 
 ((|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 
-(-842 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 
-(-843 S R -3093) 
+(-844 S R -3094) 
 ((|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 
-(-844 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 
-(-845 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 
-(-846 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 
-(-847 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 -796) (|devaluate| |#1|)))) 
-(-848 -2670) 
+((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+(-849 -2671) 
 ((|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 
-(-849 R -3093 -2670) 
+(-850 R -3094 -2671) 
 ((|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 
-(-850 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 
-(-851 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 
-(-852 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 
-(-853) 
+(-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 
-(-854 R) 
+(-855 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
-(-855 |lv| R) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-856 |lv| R) 
 ((|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 
-(-856 |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 (-755)))) 
-(-857 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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1090) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1090) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1090) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-858 R S) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1091) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-859 R S) 
 ((|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 
-(-859 |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 
-(-860 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 (-821))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#4| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) 
-(-861 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
+(-862 R E |VarSet|) 
 ((|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-862 E V R P -3093) 
+(-863 E V R P -3094) 
 ((|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 
-(-863 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 
-(-864 E V R P -3093) 
+(-865 E V R P -3094) 
 ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-392)))) 
-(-865) 
+(-866) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-866) 
+(-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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-867 R E) 
+(-868 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-868 R L) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) 
+(-869 R L) 
 ((|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 
-(-869 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"))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
-(-870 A B) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-871 A B) 
 ((|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 
-(-871) 
+(-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 
-(-872 -3093) 
+(-873 -3094) 
 ((|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 
-(-873 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 
-(-874) 
+(-875) 
 ((|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 
-(-875 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"))) 
-((-3993 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) 
-(-876) 
+((-3994 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) 
+(-877) 
 ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-877 T$) 
+(-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|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-878 T$) 
+(-879 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-879 S T$) 
+(-880 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-880) 
+(-881) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-881 S) 
+(-882 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-3997 . T)) 
 NIL 
-(-882 R |polR|) 
+NIL 
+(-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 (-392)))) 
-(-883) 
+(-884) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-884) 
+(-885) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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 
-(-885 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 
-(-886 |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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-887) 
+(-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 
-(-888 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 (-495)))) 
-(-889 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 
-(-890 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 (-258)))) (|HasCategory| |#1| (QUOTE (-392)))) 
-(-891 K) 
+(-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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-(-892 |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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-(-893 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}."))) 
-((-3997 . T)) 
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-(-894 R1 R2) 
+NIL 
+(-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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-(-895 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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-(-896 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 
-(-897 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 
-(-898 K R UP -3093) 
+(-899 K R UP -3094) 
 ((|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 
-(-899 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 (-258))))) 
-(-900 |vl| |nv|) 
+(-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 
-(-901 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 
-(-902) 
+(-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 
-(-903 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 (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1066)))) 
-(-904 S) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) 
+(-905 S) 
 ((|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-905 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 
-(-906 |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 
-(-907) 
+(-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 
-(-908 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."))) 
-((-3997 . T)) 
 NIL 
-(-909 R) 
+NIL 
+(-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.}"))) 
-((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483)))) 
-(-910 S R) 
+((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484)))) 
+(-911 S R) 
 ((|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 (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-246)))) 
-(-911 R) 
+((|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-246)))) 
+(-912 R) 
 ((|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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-912 QR R QS S) 
+(-913 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-913 S) 
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-914 S) 
+((|constructor| (NIL "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 (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-915 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-915) 
+(-916) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 
-(-916 -3093 UP UPUP |radicnd| |n|) 
+(-917 -3094 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) 
-(-917 |bb|) 
+((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) 
+(-918 |bb|) 
 ((|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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
-(-918) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+(-919) 
 ((|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 
-(-919) 
+(-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 
-(-920 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 
-(-921 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 
-(-922 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 -1035) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) 
-(-923 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) 
+(-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 
-(-924 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 
-(-925) 
+(-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}}"))) 
-((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
+((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) 
 NIL 
-(-926 R -3093) 
+(-927 R -3094) 
 ((|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 
-(-927 R -3093) 
+(-928 R -3094) 
 ((|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 
-(-928 -3093 UP) 
+(-929 -3094 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 
-(-929 -3093 UP) 
+(-930 -3094 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 
-(-930 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 
-(-931 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 
-(-932) 
+(-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 
-(-933) 
+(-934) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-934 |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 
-(-935 |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 
-(-936) 
+(-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 
-(-937 |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"))) 
-((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) 
-(-938 -3093 L) 
+((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) 
+(-939 -3094 L) 
 ((|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 
-(-939 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 
-(-940 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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-941) 
+NIL 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-942) 
 ((|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 
-(-942 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 (-3998 "*")))) 
-(-943 R) 
+((|HasAttribute| |#1| (QUOTE (-3999 "*")))) 
+(-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 (-312))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) 
-(-944 S) 
+(-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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-945 S) 
+(-946 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-946 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 
-(-947 -3093 |Expon| |VarSet| |FPol| |LFPol|) 
+(-948 -3094 |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"))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-948) 
+(-949) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-949 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 
-(-950 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 
-(-951 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 
-(-952 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 
-(-953) 
+(-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 
-(-954 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 
-(-955 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 
-(-956 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| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-957 T$) 
+(-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 
-(-958 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}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| (-703 |#1| (-773 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-553 (-473)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-773 |#2|) (QUOTE (-320))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) 
-(-959) 
+NIL 
+((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) 
+(-960) 
 ((|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 
-(-960 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 
-(-961) 
+(-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."))) 
-((-3993 . T)) 
+((-3994 . T)) 
 NIL 
-(-962 |xx| -3093) 
+(-963 |xx| -3094) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-963 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 
-(-964 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|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146)))) 
-(-965 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146)))) 
+(-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|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-966 |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}."))) 
-((-3991 . T) (-3990 . T)) 
-((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-552 (-772))))) 
-(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3992 . T) (-3991 . T)) 
+((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) 
+(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|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 
-(-968 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 
-(-969 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 
-(-970) 
+(-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|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-971 S T$) 
+(-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 (-1013)))) 
-(-972 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-973) 
+(-974) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-974 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-975) 
+(-976) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-976 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-904 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-1090))))) 
-(-977 R E V) 
+((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-905 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-1091))))) 
+(-978 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-978) 
+(-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 
-(-979 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 
-(-980 |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 
-(-981 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 
-(-982 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 
-(-983 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}."))) 
-((-3997 . T)) 
 NIL 
-(-984 R E V P TS) 
+NIL 
+(-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 
-(-985) 
+(-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 
-(-986) 
+(-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 
-(-987 |Base| R -3093) 
+(-988 |Base| R -3094) 
 ((|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 
-(-988 |f|) 
+(-989 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-989 |Base| R -3093) 
+(-990 |Base| R -3094) 
 ((|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 
-(-990 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 
-(-991 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."))) 
-((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) 
-(-992 UP SAE UPA) 
+((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) 
+(-993 UP SAE UPA) 
 ((|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 
-(-993 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 
-(-994) 
+(-995) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-995) 
+(-996) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-996 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 
-(-997) 
+(-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 
-(-998 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 
-(-999 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"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1000 S) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1001 S) 
 ((|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 
-(-1001 S) 
+(-1002 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) 
-(-1002 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 (-755)))) 
-(-1003) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1004) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1004 S) 
+(-1005 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) 
-(-1005 R S) 
+((|HasCategory| (-1002 |#1|) (QUOTE (-1014)))) 
+(-1006 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1006 S) 
+(-1007 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1007 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 
-(-1008) 
+(-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 
-(-1009 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)}}"))) 
-((-3986 . T) (-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-1010 A S) 
+((-3987 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+(-1011 A S) 
 ((|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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1011 S) 
+(-1012 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-3986 . T)) 
+((-3987 . T)) 
 NIL 
-(-1012 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 
-(-1013) 
+(-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 
-(-1014 |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 
-(-1015) 
+(-1016) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1016 |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 
-(-1017 |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 
-(-1018 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 
-(-1019 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 
-(-1020 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.}"))) 
-((-3997 . T)) 
 NIL 
-(-1021) 
+NIL 
+(-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 
-(-1022 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|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1023 T$) 
+(-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|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1024 S) 
+(-1025 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1025) 
+(-1026) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1026 |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}."))) 
-((-3990 |has| |#3| (-961)) (-3991 |has| |#3| (-961)) (-3993 |has| |#3| (-6 -3993))) 
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(-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|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 (-392)))) 
-(-1028) 
+(-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 
-(-1029) 
+(-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 
-(-1030 R -3093) 
+(-1031 R -3094) 
 ((|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 
-(-1031 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 
-(-1032) 
+(-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 
-(-1033) 
+(-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."))) 
-((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1034 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-3997 . T)) 
 NIL 
-(-1035 S) 
+NIL 
+(-1036 S) 
 ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) 
-((-3997 . T)) 
 NIL 
-(-1036 S |ndim| R |Row| |Col|) 
+NIL 
+(-1037 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
-(-1037 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3999 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
+(-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."))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1038 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 
-(-1039 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1040 |Coef| |Var| SMP) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1041 |Coef| |Var| SMP) 
 ((|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1041 R E V P) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-1042 R E V P) 
 ((|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}"))) 
-((-3997 . T)) 
 NIL 
-(-1042 UP -3093) 
+NIL 
+(-1043 UP -3094) 
 ((|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 
-(-1043 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 
-(-1044 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 
-(-1045 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 
-(-1046 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 (-756)))) 
-(-1047 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 
-(-1048 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 
-(-1049) 
+(-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 
-(-1050) 
+(-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 
-(-1051) 
+(-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 
-(-1052) 
+(-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 
-(-1053) 
+(-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 
-(-1054 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 
-(-1055 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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-1054 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-552 (-772)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|))))) 
-(-1056 |ndim| R) 
+NIL 
+((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|))))) 
+(-1057 |ndim| R) 
 ((|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}."))) 
-((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3990 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-1057 S) 
+((-3994 . T) (-3986 |has| |#2| (-6 (-3999 "*"))) (-3991 . T) (-3992 . T)) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-1058 S) 
 ((|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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1058) 
+(-1059) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-3997 . T)) 
 NIL 
-(-1059 R E V P TS) 
+NIL 
+(-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 
-(-1060 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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-1061) 
+NIL 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-1062) 
 ((|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 
-(-1062 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}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1063 A S) 
+NIL 
+((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-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 
-(-1064 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 
-(-1065 |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."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
-(-1066) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|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 
-(-1067) 
+(-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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1068 |Coef|) 
+(-1069 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1069 S) 
-((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-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 (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|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 
-(-1071 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 
-(-1072 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 
-(-1073) 
+(-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"))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-756)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-117) (QUOTE (-756))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1013))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| $ (QUOTE (-1035 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1035 (-117)))) (|HasCategory| (-117) (QUOTE (-756))))) 
-(-1074 |Entry|) 
+NIL 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| $ (QUOTE (-1036 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1036 (-117)))) (|HasCategory| (-117) (QUOTE (-757))))) 
+(-1075 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
-(-1075 A) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-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 (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
-(-1076 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-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 
-(-1077 |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 
-(-1078 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 (-258)))) 
-(-1079 |n| R) 
+(-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 
-(-1080 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 
-(-1081) 
+(-1082) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1082 |Coef| |var| |cen|) 
+(-1083 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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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-(-1083 R -3093) 
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(-1090 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasCategory| (-485) (QUOTE (-1026))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) 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|#3|) (QUOTE (-1067)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1090) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1090) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (|%list| (QUOTE -260) (|%list| (QUOTE -1090) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1090) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-797 (-330))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-757)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1084 R -3094) 
 ((|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 
-(-1084 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 
-(-1085 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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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-(-1086 R S) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-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 
-(-1087 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 
-(-1088 |Coef| |var| |cen|) 
-((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
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-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
 (-1089 |Coef| |var| |cen|) 
+((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1090 |Coef| |var| |cen|) 
 ((|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
-(-1090) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1091) 
 ((|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 
-(-1091 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 
-(-1092 R) 
+(-1093 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
-(-1093) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) 
+(-1094) 
 ((|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 
-(-1094) 
+(-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 
-(-1095) 
+(-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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1096 N) 
+(-1097 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1097 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 
-(-1098) 
+(-1099) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1099 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 
-(-1100) 
+(-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 
-(-1101 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 
-(-1102 |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}"))) 
-((-3997 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
-(-1103 S) 
+NIL 
+((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (|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 
-(-1104 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 
-(-1105 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 
-(-1106 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 
-(-1107 |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}."))) 
-((-3997 . T)) 
 NIL 
-(-1108 |Key| |Entry|) 
+NIL 
+(-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 
-(-1109) 
+(-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 
-(-1110 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 
-(-1111) 
+(-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 
-(-1112 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 
-(-1113) 
+(-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 
-(-1114 S) 
+(-1115 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1115) 
+(-1116) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1116 S) 
-((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-1117 S) 
+((|constructor| (NIL "\\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 (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+(-1118 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1118) 
+(-1119) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1119 R -3093) 
+(-1120 R -3094) 
 ((|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 
-(-1120 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 
-(-1121 R -3093) 
+(-1122 R -3094) 
 ((|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 -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -796) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -796) (|devaluate| |#1|))))) 
-(-1122 |Coef|) 
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) 
+(-1123 |Coef|) 
 ((|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1123 S R E V P) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-1124 S R E V P) 
 ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-320)))) 
-(-1124 R E V P) 
+(-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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-3997 . T)) 
 NIL 
-(-1125 |Curve|) 
+NIL 
+(-1126 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 
-(-1126) 
+(-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 
-(-1127 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 (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) 
-(-1128 -3093) 
+((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-1129 -3094) 
 ((|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 
-(-1129) 
+(-1130) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1130) 
+(-1131) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1131 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 (-756)))) 
-(-1132) 
+((|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 
-(-1133 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 
-(-1134) 
+(-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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1135) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1136) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1137) 
+(-1138) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1138) 
+(-1139) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1139 |Coef| |var| |cen|) 
+(-1140 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3998 "*") OR (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-740))) (|has| |#1| (-146)) (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-821)))) (-3989 OR (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-740))) (|has| |#1| (-495)) (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasCategory| (-484) (QUOTE (-1025))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-473))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-933)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-756))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -260) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-796 (-330))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-756)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1140 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
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(-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-757)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1141 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|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 
-(-1141 |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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+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1142 S |Coef| UTS) 
+(-1143 S |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-1143 |Coef| UTS) 
+(-1144 |Coef| UTS) 
 ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) 
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 NIL 
-(-1144 |Coef| UTS) 
+(-1145 |Coef| UTS) 
 ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) 
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(QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-821))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-118))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189)))) (OR (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-120))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118)))))) 
-(-1145 ZP) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
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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|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (|HasCategory| (-485) (QUOTE (-1026))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-741)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-822))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-118))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189)))) (OR (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-120))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118)))))) 
+(-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 
-(-1146 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 (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) 
-(-1147 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 (-755)))) 
-(-1148 |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}"))) 
-(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3992 |has| |#2| (-312)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1149 |x| R |y| S) 
+(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3993 |has| |#2| (-312)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-1150 |x| R |y| S) 
 ((|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 
-(-1150 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 
-(-1151 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 
-(-1152 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 
-(-1153 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 
-(-1154 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 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1066)))) 
-(-1155 R) 
+((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067)))) 
+(-1156 R) 
 ((|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1156 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 
-(-1157 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 (-809 (-1090)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1090)))))) 
-(-1158 |Coef| |Expon|) 
+((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) 
+(-1159 |Coef| |Expon|) 
 ((|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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1159 RC P) 
+(-1160 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1160 |Coef| |var| |cen|) 
+(-1161 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
-(-1161 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1162 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|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 
-(-1162 |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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1163 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 
-(-1164 |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)}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1165 |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)}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
-(-1166 R FE |var| |cen|) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) 
+(-1167 R FE |var| |cen|) 
 ((|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))}."))) 
-(((-3998 "*") |has| (-1160 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1160 |#2| |#3| |#4|) (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-495)))) 
-(-1167 A S) 
+(((-3999 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3990 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) 
+(-1168 A S) 
 ((|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
-(-1168 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+(-1169 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1169 |Coef| |var| |cen|) 
+(-1170 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
-(-1170 |Coef1| |Coef2| UTS1 UTS2) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(-1171 |Coef1| |Coef2| UTS1 UTS2) 
 ((|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 
-(-1171 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 (-484)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasSignature| |#2| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-1172 |Coef|) 
+((|HasCategory| |#2| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-1173 |Coef|) 
 ((|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."))) 
-(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1173 |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 
-(-1174 -3093 UP L UTS) 
+(-1175 -3094 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 (-495)))) 
-(-1175) 
+((|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 
-(-1176 |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 
-(-1177 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 (-915))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1178 R) 
+((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1179 R) 
 ((|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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-3997 . T)) 
 NIL 
-(-1179 R) 
+NIL 
+(-1180 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-3997 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
-(-1180 A B) 
+NIL 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+(-1181 A B) 
 ((|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 
-(-1181) 
+(-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 
-(-1182) 
+(-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 
-(-1183) 
+(-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 
-(-1184) 
+(-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 
-(-1185) 
+(-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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1186 A S) 
+(-1187 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1187 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}."))) 
-((-3991 . T) (-3990 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1188 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 
-(-1189 K R UP -3093) 
+(-1190 K R UP -3094) 
 ((|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 
-(-1190) 
+(-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 
-(-1191) 
+(-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 
-(-1192 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)"))) 
-((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1193 R E V P) 
+(-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}."))) 
-((-3997 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-1194 R) 
+NIL 
+((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-1195 R) 
 ((|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)"))) 
-((-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1195 |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."))) 
-((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1196 R |VarSet| XPOLY) 
+((-3994 . T) (-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|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 
-(-1197 S -3093) 
+(-1198 S -3094) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1198 -3093) 
+(-1199 -3094) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
-(-1199 |vl| R) 
+(-1200 |vl| R) 
 ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1200 |VarSet| R) 
+(-1201 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-350 (-484))))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1201 R) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-350 (-485))))) (|HasAttribute| |#2| (QUOTE -3990))) 
+(-1202 R) 
 ((|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."))) 
-((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989))) 
-(-1202 |vl| R) 
+((-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
 NIL 
-(-1203 R E) 
+(-1204 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) 
-((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989))) 
-(-1204 |VarSet| R) 
+((-3994 . T) (-3995 |has| |#1| (-6 -3995)) (-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3990))) 
+(-1205 |VarSet| R) 
 ((|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."))) 
-((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
-(-1205) 
+((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|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 
-(-1206 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 
-(-1207 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 
-(-1208 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 
-(-1209 |p|) 
+(-1210 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4784,4 +4788,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1968423 1968428 1968433 1968438) (-2 NIL 1968403 1968408 1968413 1968418) (-1 NIL 1968383 1968388 1968393 1968398) (0 NIL 1968363 1968368 1968373 1968378) (-1209 "ZMOD.spad" 1968172 1968185 1968301 1968358) (-1208 "ZLINDEP.spad" 1967270 1967281 1968162 1968167) (-1207 "ZDSOLVE.spad" 1957231 1957253 1967260 1967265) (-1206 "YSTREAM.spad" 1956726 1956737 1957221 1957226) (-1205 "YDIAGRAM.spad" 1956360 1956369 1956716 1956721) (-1204 "XRPOLY.spad" 1955580 1955600 1956216 1956285) (-1203 "XPR.spad" 1953375 1953388 1955298 1955397) (-1202 "XPOLYC.spad" 1952694 1952710 1953301 1953370) (-1201 "XPOLY.spad" 1952249 1952260 1952550 1952619) (-1200 "XPBWPOLY.spad" 1950720 1950740 1952055 1952124) (-1199 "XFALG.spad" 1947768 1947784 1950646 1950715) (-1198 "XF.spad" 1946231 1946246 1947670 1947763) (-1197 "XF.spad" 1944674 1944691 1946115 1946120) (-1196 "XEXPPKG.spad" 1943933 1943959 1944664 1944669) (-1195 "XDPOLY.spad" 1943547 1943563 1943789 1943858) (-1194 "XALG.spad" 1943215 1943226 1943503 1943542) (-1193 "WUTSET.spad" 1939069 1939086 1942700 1942715) (-1192 "WP.spad" 1938276 1938320 1938927 1938994) (-1191 "WHILEAST.spad" 1938074 1938083 1938266 1938271) (-1190 "WHEREAST.spad" 1937745 1937754 1938064 1938069) (-1189 "WFFINTBS.spad" 1935408 1935430 1937735 1937740) (-1188 "WEIER.spad" 1933630 1933641 1935398 1935403) (-1187 "VSPACE.spad" 1933303 1933314 1933598 1933625) (-1186 "VSPACE.spad" 1932996 1933009 1933293 1933298) (-1185 "VOID.spad" 1932673 1932682 1932986 1932991) (-1184 "VIEWDEF.spad" 1927874 1927883 1932663 1932668) (-1183 "VIEW3D.spad" 1911835 1911844 1927864 1927869) (-1182 "VIEW2D.spad" 1899734 1899743 1911825 1911830) (-1181 "VIEW.spad" 1897454 1897463 1899724 1899729) (-1180 "VECTOR2.spad" 1896093 1896106 1897444 1897449) (-1179 "VECTOR.spad" 1894499 1894510 1894750 1894765) (-1178 "VECTCAT.spad" 1892423 1892434 1894479 1894494) (-1177 "VECTCAT.spad" 1890144 1890157 1892202 1892207) (-1176 "VARIABLE.spad" 1889924 1889939 1890134 1890139) (-1175 "UTYPE.spad" 1889568 1889577 1889914 1889919) (-1174 "UTSODETL.spad" 1888863 1888887 1889524 1889529) (-1173 "UTSODE.spad" 1887079 1887099 1888853 1888858) (-1172 "UTSCAT.spad" 1884558 1884574 1886977 1887074) (-1171 "UTSCAT.spad" 1881705 1881723 1884126 1884131) (-1170 "UTS2.spad" 1881300 1881335 1881695 1881700) (-1169 "UTS.spad" 1876312 1876340 1879832 1879929) (-1168 "URAGG.spad" 1871033 1871044 1876302 1876307) (-1167 "URAGG.spad" 1865690 1865703 1870961 1870966) (-1166 "UPXSSING.spad" 1863458 1863484 1864894 1865027) (-1165 "UPXSCONS.spad" 1861276 1861296 1861649 1861798) (-1164 "UPXSCCA.spad" 1859847 1859867 1861122 1861271) (-1163 "UPXSCCA.spad" 1858560 1858582 1859837 1859842) (-1162 "UPXSCAT.spad" 1857149 1857165 1858406 1858555) (-1161 "UPXS2.spad" 1856692 1856745 1857139 1857144) (-1160 "UPXS.spad" 1854047 1854075 1854883 1855032) (-1159 "UPSQFREE.spad" 1852462 1852476 1854037 1854042) (-1158 "UPSCAT.spad" 1850257 1850281 1852360 1852457) (-1157 "UPSCAT.spad" 1847753 1847779 1849858 1849863) (-1156 "UPOLYC2.spad" 1847224 1847243 1847743 1847748) (-1155 "UPOLYC.spad" 1842304 1842315 1847066 1847219) (-1154 "UPOLYC.spad" 1837302 1837315 1842066 1842071) (-1153 "UPMP.spad" 1836234 1836247 1837292 1837297) (-1152 "UPDIVP.spad" 1835799 1835813 1836224 1836229) (-1151 "UPDECOMP.spad" 1834060 1834074 1835789 1835794) (-1150 "UPCDEN.spad" 1833277 1833293 1834050 1834055) (-1149 "UP2.spad" 1832641 1832662 1833267 1833272) (-1148 "UP.spad" 1830111 1830126 1830498 1830651) (-1147 "UNISEG2.spad" 1829608 1829621 1830067 1830072) (-1146 "UNISEG.spad" 1828961 1828972 1829527 1829532) (-1145 "UNIFACT.spad" 1828064 1828076 1828951 1828956) (-1144 "ULSCONS.spad" 1821910 1821930 1822280 1822429) (-1143 "ULSCCAT.spad" 1819647 1819667 1821756 1821905) (-1142 "ULSCCAT.spad" 1817492 1817514 1819603 1819608) (-1141 "ULSCAT.spad" 1815732 1815748 1817338 1817487) (-1140 "ULS2.spad" 1815246 1815299 1815722 1815727) (-1139 "ULS.spad" 1807279 1807307 1808224 1808647) (-1138 "UINT8.spad" 1807156 1807165 1807269 1807274) (-1137 "UINT64.spad" 1807032 1807041 1807146 1807151) (-1136 "UINT32.spad" 1806908 1806917 1807022 1807027) (-1135 "UINT16.spad" 1806784 1806793 1806898 1806903) (-1134 "UFD.spad" 1805849 1805858 1806710 1806779) (-1133 "UFD.spad" 1804976 1804987 1805839 1805844) (-1132 "UDVO.spad" 1803857 1803866 1804966 1804971) (-1131 "UDPO.spad" 1801438 1801449 1803813 1803818) (-1130 "TYPEAST.spad" 1801357 1801366 1801428 1801433) (-1129 "TYPE.spad" 1801289 1801298 1801347 1801352) (-1128 "TWOFACT.spad" 1799941 1799956 1801279 1801284) (-1127 "TUPLE.spad" 1799448 1799459 1799853 1799858) (-1126 "TUBETOOL.spad" 1796315 1796324 1799438 1799443) (-1125 "TUBE.spad" 1794962 1794979 1796305 1796310) (-1124 "TSETCAT.spad" 1783045 1783062 1794942 1794957) (-1123 "TSETCAT.spad" 1771102 1771121 1783001 1783006) (-1122 "TS.spad" 1769730 1769746 1770696 1770793) (-1121 "TRMANIP.spad" 1764094 1764111 1769418 1769423) (-1120 "TRIMAT.spad" 1763057 1763082 1764084 1764089) (-1119 "TRIGMNIP.spad" 1761584 1761601 1763047 1763052) (-1118 "TRIGCAT.spad" 1761096 1761105 1761574 1761579) (-1117 "TRIGCAT.spad" 1760606 1760617 1761086 1761091) (-1116 "TREE.spad" 1759197 1759208 1760229 1760244) (-1115 "TRANFUN.spad" 1759036 1759045 1759187 1759192) (-1114 "TRANFUN.spad" 1758873 1758884 1759026 1759031) (-1113 "TOPSP.spad" 1758547 1758556 1758863 1758868) (-1112 "TOOLSIGN.spad" 1758210 1758221 1758537 1758542) (-1111 "TEXTFILE.spad" 1756771 1756780 1758200 1758205) (-1110 "TEX1.spad" 1756327 1756338 1756761 1756766) (-1109 "TEX.spad" 1753521 1753530 1756317 1756322) (-1108 "TBCMPPK.spad" 1751622 1751645 1753511 1753516) (-1107 "TBAGG.spad" 1750877 1750900 1751602 1751617) (-1106 "TBAGG.spad" 1750140 1750165 1750867 1750872) (-1105 "TANEXP.spad" 1749548 1749559 1750130 1750135) (-1104 "TALGOP.spad" 1749272 1749283 1749538 1749543) (-1103 "TABLEAU.spad" 1748753 1748764 1749262 1749267) (-1102 "TABLE.spad" 1746453 1746476 1746723 1746738) (-1101 "TABLBUMP.spad" 1743232 1743243 1746443 1746448) (-1100 "SYSTEM.spad" 1742460 1742469 1743222 1743227) (-1099 "SYSSOLP.spad" 1739943 1739954 1742450 1742455) (-1098 "SYSPTR.spad" 1739842 1739851 1739933 1739938) (-1097 "SYSNNI.spad" 1739065 1739076 1739832 1739837) (-1096 "SYSINT.spad" 1738469 1738480 1739055 1739060) (-1095 "SYNTAX.spad" 1734803 1734812 1738459 1738464) (-1094 "SYMTAB.spad" 1732871 1732880 1734793 1734798) (-1093 "SYMS.spad" 1728900 1728909 1732861 1732866) (-1092 "SYMPOLY.spad" 1728033 1728044 1728115 1728242) (-1091 "SYMFUNC.spad" 1727534 1727545 1728023 1728028) (-1090 "SYMBOL.spad" 1725029 1725038 1727524 1727529) (-1089 "SUTS.spad" 1722142 1722170 1723561 1723658) (-1088 "SUPXS.spad" 1719484 1719512 1720333 1720482) (-1087 "SUPFRACF.spad" 1718589 1718607 1719474 1719479) (-1086 "SUP2.spad" 1717981 1717994 1718579 1718584) (-1085 "SUP.spad" 1715065 1715076 1715838 1715991) (-1084 "SUMRF.spad" 1714039 1714050 1715055 1715060) (-1083 "SUMFS.spad" 1713668 1713685 1714029 1714034) (-1082 "SULS.spad" 1705688 1705716 1706646 1707069) (-1081 "syntax.spad" 1705457 1705466 1705678 1705683) (-1080 "SUCH.spad" 1705147 1705162 1705447 1705452) (-1079 "SUBSPACE.spad" 1697278 1697293 1705137 1705142) (-1078 "SUBRESP.spad" 1696448 1696462 1697234 1697239) (-1077 "STTFNC.spad" 1692916 1692932 1696438 1696443) (-1076 "STTF.spad" 1689015 1689031 1692906 1692911) (-1075 "STTAYLOR.spad" 1681692 1681703 1688922 1688927) (-1074 "STRTBL.spad" 1679555 1679572 1679704 1679719) (-1073 "STRING.spad" 1678186 1678195 1678571 1678586) (-1072 "STREAM3.spad" 1677759 1677774 1678176 1678181) (-1071 "STREAM2.spad" 1676887 1676900 1677749 1677754) (-1070 "STREAM1.spad" 1676593 1676604 1676877 1676882) (-1069 "STREAM.spad" 1673543 1673554 1676034 1676049) (-1068 "STINPROD.spad" 1672479 1672495 1673533 1673538) (-1067 "STEPAST.spad" 1671713 1671722 1672469 1672474) (-1066 "STEP.spad" 1671030 1671039 1671703 1671708) (-1065 "STBL.spad" 1668833 1668861 1669000 1669015) (-1064 "STAGG.spad" 1667532 1667543 1668823 1668828) (-1063 "STAGG.spad" 1666229 1666242 1667522 1667527) (-1062 "STACK.spad" 1665663 1665674 1665913 1665928) (-1061 "SRING.spad" 1665423 1665432 1665653 1665658) (-1060 "SREGSET.spad" 1663006 1663023 1664908 1664923) (-1059 "SRDCMPK.spad" 1661583 1661603 1662996 1663001) (-1058 "SRAGG.spad" 1656778 1656787 1661563 1661578) (-1057 "SRAGG.spad" 1651981 1651992 1656768 1656773) (-1056 "SQMATRIX.spad" 1649670 1649688 1650586 1650661) (-1055 "SPLTREE.spad" 1644320 1644333 1649116 1649131) (-1054 "SPLNODE.spad" 1640940 1640953 1644310 1644315) (-1053 "SPFCAT.spad" 1639749 1639758 1640930 1640935) (-1052 "SPECOUT.spad" 1638301 1638310 1639739 1639744) (-1051 "SPADXPT.spad" 1630392 1630401 1638291 1638296) (-1050 "spad-parser.spad" 1629857 1629866 1630382 1630387) (-1049 "SPADAST.spad" 1629558 1629567 1629847 1629852) (-1048 "SPACEC.spad" 1613773 1613784 1629548 1629553) (-1047 "SPACE3.spad" 1613549 1613560 1613763 1613768) (-1046 "SORTPAK.spad" 1613098 1613111 1613505 1613510) (-1045 "SOLVETRA.spad" 1610861 1610872 1613088 1613093) (-1044 "SOLVESER.spad" 1609317 1609328 1610851 1610856) (-1043 "SOLVERAD.spad" 1605343 1605354 1609307 1609312) (-1042 "SOLVEFOR.spad" 1603805 1603823 1605333 1605338) (-1041 "SNTSCAT.spad" 1603417 1603434 1603785 1603800) (-1040 "SMTS.spad" 1601734 1601760 1603011 1603108) (-1039 "SMP.spad" 1599542 1599562 1599932 1600059) (-1038 "SMITH.spad" 1598387 1598412 1599532 1599537) (-1037 "SMATCAT.spad" 1596517 1596547 1598343 1598382) (-1036 "SMATCAT.spad" 1594567 1594599 1596395 1596400) (-1035 "aggcat.spad" 1594243 1594254 1594547 1594562) (-1034 "SKAGG.spad" 1593224 1593235 1594223 1594238) (-1033 "SINT.spad" 1592523 1592532 1593090 1593219) (-1032 "SIMPAN.spad" 1592251 1592260 1592513 1592518) (-1031 "SIGNRF.spad" 1591376 1591387 1592241 1592246) (-1030 "SIGNEF.spad" 1590662 1590679 1591366 1591371) (-1029 "syntax.spad" 1590079 1590088 1590652 1590657) (-1028 "SIG.spad" 1589441 1589450 1590069 1590074) (-1027 "SHP.spad" 1587385 1587400 1589397 1589402) (-1026 "SHDP.spad" 1576728 1576755 1577245 1577330) (-1025 "SGROUP.spad" 1576336 1576345 1576718 1576723) (-1024 "SGROUP.spad" 1575942 1575953 1576326 1576331) (-1023 "catdef.spad" 1575652 1575664 1575763 1575937) (-1022 "catdef.spad" 1575208 1575220 1575473 1575647) (-1021 "SGCF.spad" 1568347 1568356 1575198 1575203) (-1020 "SFRTCAT.spad" 1567305 1567322 1568327 1568342) (-1019 "SFRGCD.spad" 1566368 1566388 1567295 1567300) (-1018 "SFQCMPK.spad" 1561181 1561201 1566358 1566363) (-1017 "SEXOF.spad" 1561024 1561064 1561171 1561176) (-1016 "SEXCAT.spad" 1558852 1558892 1561014 1561019) (-1015 "SEX.spad" 1558744 1558753 1558842 1558847) (-1014 "SETMN.spad" 1557204 1557221 1558734 1558739) (-1013 "SETCAT.spad" 1556689 1556698 1557194 1557199) (-1012 "SETCAT.spad" 1556172 1556183 1556679 1556684) (-1011 "SETAGG.spad" 1552721 1552732 1556152 1556167) (-1010 "SETAGG.spad" 1549278 1549291 1552711 1552716) (-1009 "SET.spad" 1547436 1547447 1548535 1548562) (-1008 "syntax.spad" 1547139 1547148 1547426 1547431) (-1007 "SEGXCAT.spad" 1546295 1546308 1547129 1547134) (-1006 "SEGCAT.spad" 1545220 1545231 1546285 1546290) (-1005 "SEGBIND2.spad" 1544918 1544931 1545210 1545215) (-1004 "SEGBIND.spad" 1544676 1544687 1544865 1544870) (-1003 "SEGAST.spad" 1544406 1544415 1544666 1544671) (-1002 "SEG2.spad" 1543841 1543854 1544362 1544367) (-1001 "SEG.spad" 1543654 1543665 1543760 1543765) (-1000 "SDVAR.spad" 1542930 1542941 1543644 1543649) (-999 "SDPOL.spad" 1540623 1540633 1540913 1541040) (-998 "SCPKG.spad" 1538713 1538723 1540613 1540618) (-997 "SCOPE.spad" 1537891 1537899 1538703 1538708) (-996 "SCACHE.spad" 1536588 1536598 1537881 1537886) (-995 "SASTCAT.spad" 1536498 1536506 1536578 1536583) (-994 "SAOS.spad" 1536371 1536379 1536488 1536493) (-993 "SAERFFC.spad" 1536085 1536104 1536361 1536366) (-992 "SAEFACT.spad" 1535787 1535806 1536075 1536080) (-991 "SAE.spad" 1533438 1533453 1534048 1534183) (-990 "RURPK.spad" 1531098 1531113 1533428 1533433) (-989 "RULESET.spad" 1530552 1530575 1531088 1531093) (-988 "RULECOLD.spad" 1530405 1530417 1530542 1530547) (-987 "RULE.spad" 1528654 1528677 1530395 1530400) (-986 "RTVALUE.spad" 1528390 1528398 1528644 1528649) (-985 "syntax.spad" 1528108 1528116 1528380 1528385) (-984 "RSETGCD.spad" 1524551 1524570 1528098 1528103) (-983 "RSETCAT.spad" 1514532 1514548 1524531 1524546) (-982 "RSETCAT.spad" 1504521 1504539 1514522 1514527) (-981 "RSDCMPK.spad" 1503022 1503041 1504511 1504516) (-980 "RRCC.spad" 1501407 1501436 1503012 1503017) (-979 "RRCC.spad" 1499790 1499821 1501397 1501402) (-978 "RPTAST.spad" 1499493 1499501 1499780 1499785) (-977 "RPOLCAT.spad" 1478998 1479012 1499361 1499488) (-976 "RPOLCAT.spad" 1458296 1458312 1478661 1478666) (-975 "ROMAN.spad" 1457625 1457633 1458162 1458291) (-974 "ROIRC.spad" 1456706 1456737 1457615 1457620) (-973 "RNS.spad" 1455683 1455691 1456608 1456701) (-972 "RNS.spad" 1454746 1454756 1455673 1455678) (-971 "RNGBIND.spad" 1453907 1453920 1454701 1454706) (-970 "RNG.spad" 1453516 1453524 1453897 1453902) (-969 "RNG.spad" 1453123 1453133 1453506 1453511) (-968 "RMODULE.spad" 1452905 1452915 1453113 1453118) (-967 "RMCAT2.spad" 1452326 1452382 1452895 1452900) (-966 "RMATRIX.spad" 1451148 1451166 1451490 1451517) (-965 "RMATCAT.spad" 1446798 1446828 1451116 1451143) (-964 "RMATCAT.spad" 1442326 1442358 1446646 1446651) (-963 "RLINSET.spad" 1442031 1442041 1442316 1442321) (-962 "RINTERP.spad" 1441920 1441939 1442021 1442026) (-961 "RING.spad" 1441391 1441399 1441900 1441915) (-960 "RING.spad" 1440870 1440880 1441381 1441386) (-959 "RIDIST.spad" 1440263 1440271 1440860 1440865) (-958 "RGCHAIN.spad" 1438520 1438535 1439413 1439428) (-957 "RGBCSPC.spad" 1438310 1438321 1438510 1438515) (-956 "RGBCMDL.spad" 1437873 1437884 1438300 1438305) (-955 "RFFACTOR.spad" 1437336 1437346 1437863 1437868) (-954 "RFFACT.spad" 1437072 1437083 1437326 1437331) (-953 "RFDIST.spad" 1436069 1436077 1437062 1437067) (-952 "RF.spad" 1433744 1433754 1436059 1436064) (-951 "RETSOL.spad" 1433164 1433176 1433734 1433739) (-950 "RETRACT.spad" 1432593 1432603 1433154 1433159) (-949 "RETRACT.spad" 1432020 1432032 1432583 1432588) (-948 "RETAST.spad" 1431833 1431841 1432010 1432015) (-947 "RESRING.spad" 1431181 1431227 1431771 1431828) (-946 "RESLATC.spad" 1430506 1430516 1431171 1431176) (-945 "REPSQ.spad" 1430238 1430248 1430496 1430501) (-944 "REPDB.spad" 1429946 1429956 1430228 1430233) (-943 "REP2.spad" 1419661 1419671 1429788 1429793) (-942 "REP1.spad" 1413882 1413892 1419611 1419616) (-941 "REP.spad" 1411437 1411445 1413872 1413877) (-940 "REGSET.spad" 1409114 1409130 1410922 1410937) (-939 "REF.spad" 1408633 1408643 1409104 1409109) (-938 "REDORDER.spad" 1407840 1407856 1408623 1408628) (-937 "RECLOS.spad" 1406737 1406756 1407440 1407533) (-936 "REALSOLV.spad" 1405878 1405886 1406727 1406732) (-935 "REAL0Q.spad" 1403177 1403191 1405868 1405873) (-934 "REAL0.spad" 1400022 1400036 1403167 1403172) (-933 "REAL.spad" 1399895 1399903 1400012 1400017) (-932 "RDUCEAST.spad" 1399617 1399625 1399885 1399890) (-931 "RDIV.spad" 1399273 1399297 1399607 1399612) (-930 "RDIST.spad" 1398841 1398851 1399263 1399268) (-929 "RDETRS.spad" 1397706 1397723 1398831 1398836) (-928 "RDETR.spad" 1395846 1395863 1397696 1397701) (-927 "RDEEFS.spad" 1394946 1394962 1395836 1395841) (-926 "RDEEF.spad" 1393957 1393973 1394936 1394941) (-925 "RCFIELD.spad" 1391176 1391184 1393859 1393952) (-924 "RCFIELD.spad" 1388481 1388491 1391166 1391171) (-923 "RCAGG.spad" 1386418 1386428 1388471 1388476) (-922 "RCAGG.spad" 1384256 1384268 1386311 1386316) (-921 "RATRET.spad" 1383617 1383627 1384246 1384251) (-920 "RATFACT.spad" 1383310 1383321 1383607 1383612) (-919 "RANDSRC.spad" 1382630 1382638 1383300 1383305) (-918 "RADUTIL.spad" 1382387 1382395 1382620 1382625) (-917 "RADIX.spad" 1379432 1379445 1380977 1381070) (-916 "RADFF.spad" 1377349 1377385 1377467 1377623) (-915 "RADCAT.spad" 1376945 1376953 1377339 1377344) (-914 "RADCAT.spad" 1376539 1376549 1376935 1376940) (-913 "QUEUE.spad" 1375965 1375975 1376223 1376238) (-912 "QUATCT2.spad" 1375586 1375604 1375955 1375960) (-911 "QUATCAT.spad" 1373757 1373767 1375516 1375581) (-910 "QUATCAT.spad" 1371693 1371705 1373454 1373459) (-909 "QUAT.spad" 1370300 1370310 1370642 1370707) (-908 "QUAGG.spad" 1369146 1369156 1370280 1370295) (-907 "QQUTAST.spad" 1368915 1368923 1369136 1369141) (-906 "QFORM.spad" 1368534 1368548 1368905 1368910) (-905 "QFCAT2.spad" 1368227 1368243 1368524 1368529) (-904 "QFCAT.spad" 1366930 1366940 1368129 1368222) (-903 "QFCAT.spad" 1365266 1365278 1366467 1366472) (-902 "QEQUAT.spad" 1364825 1364833 1365256 1365261) (-901 "QCMPACK.spad" 1359740 1359759 1364815 1364820) (-900 "QALGSET2.spad" 1357736 1357754 1359730 1359735) (-899 "QALGSET.spad" 1353841 1353873 1357650 1357655) (-898 "PWFFINTB.spad" 1351257 1351278 1353831 1353836) (-897 "PUSHVAR.spad" 1350596 1350615 1351247 1351252) (-896 "PTRANFN.spad" 1346732 1346742 1350586 1350591) (-895 "PTPACK.spad" 1343820 1343830 1346722 1346727) (-894 "PTFUNC2.spad" 1343643 1343657 1343810 1343815) (-893 "PTCAT.spad" 1342910 1342920 1343623 1343638) (-892 "PSQFR.spad" 1342225 1342249 1342900 1342905) (-891 "PSEUDLIN.spad" 1341111 1341121 1342215 1342220) (-890 "PSETPK.spad" 1327816 1327832 1340989 1340994) (-889 "PSETCAT.spad" 1322226 1322249 1327806 1327811) (-888 "PSETCAT.spad" 1316600 1316625 1322182 1322187) (-887 "PSCURVE.spad" 1315599 1315607 1316590 1316595) (-886 "PSCAT.spad" 1314382 1314411 1315497 1315594) (-885 "PSCAT.spad" 1313255 1313286 1314372 1314377) (-884 "PRTITION.spad" 1311953 1311961 1313245 1313250) (-883 "PRTDAST.spad" 1311672 1311680 1311943 1311948) (-882 "PRS.spad" 1301290 1301307 1311628 1311633) (-881 "PRQAGG.spad" 1300737 1300747 1301270 1301285) (-880 "PROPLOG.spad" 1300341 1300349 1300727 1300732) (-879 "PROPFUN2.spad" 1299964 1299977 1300331 1300336) (-878 "PROPFUN1.spad" 1299370 1299381 1299954 1299959) (-877 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(-629 "MATLIN.spad" 939123 939147 941639 941644) (-628 "MATCAT2.spad" 938405 938453 939113 939118) (-627 "MATCAT.spad" 930113 930135 938385 938400) (-626 "MATCAT.spad" 921681 921705 929955 929960) (-625 "MAPPKG3.spad" 920596 920610 921671 921676) (-624 "MAPPKG2.spad" 919934 919946 920586 920591) (-623 "MAPPKG1.spad" 918762 918772 919924 919929) (-622 "MAPPAST.spad" 918101 918109 918752 918757) (-621 "MAPHACK3.spad" 917913 917927 918091 918096) (-620 "MAPHACK2.spad" 917682 917694 917903 917908) (-619 "MAPHACK1.spad" 917326 917336 917672 917677) (-618 "MAGMA.spad" 915132 915149 917316 917321) (-617 "MACROAST.spad" 914727 914735 915122 915127) (-616 "LZSTAGG.spad" 911981 911991 914717 914722) (-615 "LZSTAGG.spad" 909233 909245 911971 911976) (-614 "LWORD.spad" 905978 905995 909223 909228) (-613 "LSTAST.spad" 905762 905770 905968 905973) (-612 "LSQM.spad" 904052 904066 904446 904485) (-611 "LSPP.spad" 903587 903604 904042 904047) (-610 "LSMP1.spad" 901430 901444 903577 903582) (-609 "LSMP.spad" 900287 900315 901420 901425) (-608 "LSAGG.spad" 899968 899978 900267 900282) (-607 "LSAGG.spad" 899657 899669 899958 899963) (-606 "LPOLY.spad" 898619 898638 899513 899582) (-605 "LPEFRAC.spad" 897890 897900 898609 898614) (-604 "LOGIC.spad" 897492 897500 897880 897885) (-603 "LOGIC.spad" 897092 897102 897482 897487) (-602 "LODOOPS.spad" 896022 896034 897082 897087) (-601 "LODOF.spad" 895068 895085 895979 895984) (-600 "LODOCAT.spad" 893734 893744 895024 895063) (-599 "LODOCAT.spad" 892398 892410 893690 893695) (-598 "LODO2.spad" 891712 891724 892119 892158) (-597 "LODO1.spad" 891153 891163 891433 891472) (-596 "LODO.spad" 890578 890594 890874 890913) (-595 "LODEEF.spad" 889380 889398 890568 890573) (-594 "LO.spad" 888781 888795 889314 889341) (-593 "LNAGG.spad" 884968 884978 888771 888776) (-592 "LNAGG.spad" 881091 881103 884896 884901) (-591 "LMOPS.spad" 877859 877876 881081 881086) (-590 "LMODULE.spad" 877643 877653 877849 877854) (-589 "LMDICT.spad" 876875 876885 877123 877138) (-588 "LLINSET.spad" 876582 876592 876865 876870) (-587 "LITERAL.spad" 876488 876499 876572 876577) (-586 "LIST3.spad" 875799 875813 876478 876483) (-585 "LIST2MAP.spad" 872726 872738 875789 875794) (-584 "LIST2.spad" 871428 871440 872716 872721) (-583 "LIST.spad" 868997 869007 870340 870355) (-582 "LINSET.spad" 868776 868786 868987 868992) (-581 "LINFORM.spad" 868239 868251 868744 868771) (-580 "LINEXP.spad" 866982 866992 868229 868234) (-579 "LINELT.spad" 866353 866365 866865 866892) (-578 "LINDEP.spad" 865202 865214 866265 866270) (-577 "LINBASIS.spad" 864838 864853 865192 865197) (-576 "LIMITRF.spad" 862785 862795 864828 864833) (-575 "LIMITPS.spad" 861695 861708 862775 862780) (-574 "LIECAT.spad" 861179 861189 861621 861690) (-573 "LIECAT.spad" 860691 860703 861135 861140) (-572 "LIE.spad" 858695 858707 859969 860111) (-571 "LIB.spad" 856508 856516 856954 856969) (-570 "LGROBP.spad" 853861 853880 856498 856503) (-569 "LFCAT.spad" 852920 852928 853851 853856) (-568 "LF.spad" 851875 851891 852910 852915) (-567 "LEXTRIPK.spad" 847498 847513 851865 851870) (-566 "LEXP.spad" 845517 845544 847478 847493) (-565 "LETAST.spad" 845216 845224 845507 845512) (-564 "LEADCDET.spad" 843622 843639 845206 845211) (-563 "LAZM3PK.spad" 842366 842388 843612 843617) (-562 "LAUPOL.spad" 841033 841046 841933 842002) (-561 "LAPLACE.spad" 840616 840632 841023 841028) (-560 "LALG.spad" 840392 840402 840596 840611) (-559 "LALG.spad" 840176 840188 840382 840387) (-558 "LA.spad" 839616 839630 840098 840137) (-557 "KVTFROM.spad" 839359 839369 839606 839611) (-556 "KTVLOGIC.spad" 838903 838911 839349 839354) (-555 "KRCFROM.spad" 838649 838659 838893 838898) (-554 "KOVACIC.spad" 837380 837397 838639 838644) (-553 "KONVERT.spad" 837102 837112 837370 837375) (-552 "KOERCE.spad" 836839 836849 837092 837097) (-551 "KERNEL2.spad" 836542 836554 836829 836834) (-550 "KERNEL.spad" 835262 835272 836391 836396) (-549 "KDAGG.spad" 834371 834393 835242 835257) (-548 "KDAGG.spad" 833488 833512 834361 834366) (-547 "KAFILE.spad" 831854 831870 832089 832104) (-546 "JVMOP.spad" 831767 831775 831844 831849) (-545 "JVMMDACC.spad" 830821 830829 831757 831762) (-544 "JVMFDACC.spad" 830137 830145 830811 830816) (-543 "JVMCSTTG.spad" 828866 828874 830127 830132) (-542 "JVMCFACC.spad" 828312 828320 828856 828861) (-541 "JVMBCODE.spad" 828223 828231 828302 828307) (-540 "JORDAN.spad" 826040 826052 827501 827643) (-539 "JOINAST.spad" 825742 825750 826030 826035) (-538 "IXAGG.spad" 823875 823899 825732 825737) (-537 "IXAGG.spad" 821810 821836 823669 823674) (-536 "ITUPLE.spad" 820986 820996 821800 821805) (-535 "ITRIGMNP.spad" 819833 819852 820976 820981) (-534 "ITFUN3.spad" 819339 819353 819823 819828) (-533 "ITFUN2.spad" 819083 819095 819329 819334) (-532 "ITFORM.spad" 818438 818446 819073 819078) (-531 "ITAYLOR.spad" 816432 816447 818302 818399) (-530 "ISUPS.spad" 808881 808896 815418 815515) (-529 "ISUMP.spad" 808382 808398 808871 808876) (-528 "ISAST.spad" 808101 808109 808372 808377) (-527 "IRURPK.spad" 806818 806837 808091 808096) (-526 "IRSN.spad" 804822 804830 806808 806813) (-525 "IRRF2F.spad" 803315 803325 804778 804783) (-524 "IRREDFFX.spad" 802916 802927 803305 803310) (-523 "IROOT.spad" 801255 801265 802906 802911) (-522 "IRFORM.spad" 800579 800587 801245 801250) (-521 "IR2F.spad" 799793 799809 800569 800574) (-520 "IR2.spad" 798821 798837 799783 799788) (-519 "IR.spad" 796657 796671 798703 798730) (-518 "IPRNTPK.spad" 796417 796425 796647 796652) (-517 "IPF.spad" 795982 795994 796222 796315) (-516 "IPADIC.spad" 795751 795777 795908 795977) (-515 "IP4ADDR.spad" 795308 795316 795741 795746) (-514 "IOMODE.spad" 794830 794838 795298 795303) (-513 "IOBFILE.spad" 794215 794223 794820 794825) (-512 "IOBCON.spad" 794080 794088 794205 794210) (-511 "INVLAPLA.spad" 793729 793745 794070 794075) (-510 "INTTR.spad" 787123 787140 793719 793724) (-509 "INTTOOLS.spad" 784931 784947 786750 786755) (-508 "INTSLPE.spad" 784259 784267 784921 784926) (-507 "INTRVL.spad" 783825 783835 784173 784254) (-506 "INTRF.spad" 782257 782271 783815 783820) (-505 "INTRET.spad" 781689 781699 782247 782252) (-504 "INTRAT.spad" 780424 780441 781679 781684) (-503 "INTPM.spad" 778887 778903 780145 780150) (-502 "INTPAF.spad" 776763 776781 778816 778821) (-501 "INTHERTR.spad" 776037 776054 776753 776758) (-500 "INTHERAL.spad" 775707 775731 776027 776032) (-499 "INTHEORY.spad" 772146 772154 775697 775702) (-498 "INTG0.spad" 765910 765928 772075 772080) (-497 "INTFACT.spad" 764977 764987 765900 765905) (-496 "INTEF.spad" 763388 763404 764967 764972) (-495 "INTDOM.spad" 762011 762019 763314 763383) (-494 "INTDOM.spad" 760696 760706 762001 762006) (-493 "INTCAT.spad" 758963 758973 760610 760691) (-492 "INTBIT.spad" 758470 758478 758953 758958) (-491 "INTALG.spad" 757658 757685 758460 758465) (-490 "INTAF.spad" 757158 757174 757648 757653) (-489 "INTABL.spad" 754965 754996 755128 755143) (-488 "INT8.spad" 754845 754853 754955 754960) (-487 "INT64.spad" 754724 754732 754835 754840) (-486 "INT32.spad" 754603 754611 754714 754719) (-485 "INT16.spad" 754482 754490 754593 754598) (-484 "INT.spad" 754008 754016 754348 754477) (-483 "INS.spad" 751511 751519 753910 754003) (-482 "INS.spad" 749100 749110 751501 751506) (-481 "INPSIGN.spad" 748570 748583 749090 749095) (-480 "INPRODPF.spad" 747666 747685 748560 748565) (-479 "INPRODFF.spad" 746754 746778 747656 747661) (-478 "INNMFACT.spad" 745729 745746 746744 746749) (-477 "INMODGCD.spad" 745233 745263 745719 745724) (-476 "INFSP.spad" 743530 743552 745223 745228) (-475 "INFPROD0.spad" 742610 742629 743520 743525) (-474 "INFORM1.spad" 742235 742245 742600 742605) (-473 "INFORM.spad" 739446 739454 742225 742230) (-472 "INFINITY.spad" 738998 739006 739436 739441) (-471 "INETCLTS.spad" 738975 738983 738988 738993) (-470 "INEP.spad" 737521 737543 738965 738970) (-469 "INDE.spad" 737170 737187 737431 737436) (-468 "INCRMAPS.spad" 736607 736617 737160 737165) (-467 "INBFILE.spad" 735703 735711 736597 736602) (-466 "INBFF.spad" 731553 731564 735693 735698) (-465 "INBCON.spad" 729819 729827 731543 731548) (-464 "INBCON.spad" 728083 728093 729809 729814) (-463 "INAST.spad" 727744 727752 728073 728078) (-462 "IMPTAST.spad" 727452 727460 727734 727739) (-461 "IMATQF.spad" 726518 726562 727380 727385) (-460 "IMATLIN.spad" 725111 725135 726446 726451) (-459 "IFF.spad" 724524 724540 724795 724888) (-458 "IFAST.spad" 724138 724146 724514 724519) (-457 "IFARRAY.spad" 721352 721367 723050 723065) (-456 "IFAMON.spad" 721214 721231 721308 721313) (-455 "IEVALAB.spad" 720627 720639 721204 721209) (-454 "IEVALAB.spad" 720038 720052 720617 720622) (-453 "indexedp.spad" 719594 719606 720028 720033) (-452 "IDPOAMS.spad" 719272 719284 719506 719511) (-451 "IDPOAM.spad" 718914 718926 719184 719189) (-450 "IDPO.spad" 718328 718340 718826 718831) (-449 "IDPC.spad" 717043 717055 718318 718323) (-448 "IDPAM.spad" 716710 716722 716955 716960) (-447 "IDPAG.spad" 716379 716391 716622 716627) (-446 "IDENT.spad" 716031 716039 716369 716374) (-445 "catdef.spad" 715802 715813 715914 716026) (-444 "IDECOMP.spad" 713041 713059 715792 715797) (-443 "IDEAL.spad" 708003 708042 712989 712994) (-442 "ICDEN.spad" 707216 707232 707993 707998) (-441 "ICARD.spad" 706609 706617 707206 707211) (-440 "IBPTOOLS.spad" 705216 705233 706599 706604) (-439 "IBATOOL.spad" 702201 702220 705206 705211) (-438 "IBACHIN.spad" 700708 700723 702191 702196) (-437 "array2.spad" 700205 700227 700392 700407) (-436 "IARRAY1.spad" 698971 698986 699117 699132) (-435 "IAN.spad" 697353 697361 698802 698895) (-434 "IALGFACT.spad" 696964 696997 697343 697348) (-433 "HYPCAT.spad" 696388 696396 696954 696959) (-432 "HYPCAT.spad" 695810 695820 696378 696383) (-431 "HOSTNAME.spad" 695626 695634 695800 695805) (-430 "HOMOTOP.spad" 695369 695379 695616 695621) (-429 "HOAGG.spad" 694885 694895 695359 695364) (-428 "HOAGG.spad" 694223 694235 694699 694704) (-427 "HEXADEC.spad" 692448 692456 692813 692906) (-426 "HEUGCD.spad" 691539 691550 692438 692443) (-425 "HELLFDIV.spad" 691145 691169 691529 691534) (-424 "HEAP.spad" 690614 690624 690829 690844) (-423 "HEADAST.spad" 690155 690163 690604 690609) (-422 "HDP.spad" 679638 679654 680015 680100) (-421 "HDMP.spad" 677185 677200 677801 677928) (-420 "HB.spad" 675460 675468 677175 677180) (-419 "HASHTBL.spad" 673219 673250 673430 673445) (-418 "HASAST.spad" 672935 672943 673209 673214) (-417 "HACKPI.spad" 672426 672434 672837 672930) (-416 "GTSET.spad" 671204 671220 671911 671926) (-415 "GSTBL.spad" 669000 669035 669174 669189) (-414 "GSERIES.spad" 666372 666399 667191 667340) (-413 "GROUP.spad" 665645 665653 666352 666367) (-412 "GROUP.spad" 664926 664936 665635 665640) (-411 "GROEBSOL.spad" 663420 663441 664916 664921) (-410 "GRMOD.spad" 662001 662013 663410 663415) (-409 "GRMOD.spad" 660580 660594 661991 661996) (-408 "GRIMAGE.spad" 653493 653501 660570 660575) (-407 "GRDEF.spad" 651872 651880 653483 653488) (-406 "GRAY.spad" 650343 650351 651862 651867) (-405 "GRALG.spad" 649438 649450 650333 650338) (-404 "GRALG.spad" 648531 648545 649428 649433) (-403 "GPOLSET.spad" 647840 647863 648052 648067) (-402 "GOSPER.spad" 647117 647135 647830 647835) (-401 "GMODPOL.spad" 646265 646292 647085 647112) (-400 "GHENSEL.spad" 645348 645362 646255 646260) (-399 "GENUPS.spad" 641641 641654 645338 645343) (-398 "GENUFACT.spad" 641218 641228 641631 641636) (-397 "GENPGCD.spad" 640820 640837 641208 641213) (-396 "GENMFACT.spad" 640272 640291 640810 640815) (-395 "GENEEZ.spad" 638231 638244 640262 640267) (-394 "GDMP.spad" 635620 635637 636394 636521) (-393 "GCNAALG.spad" 629543 629570 635414 635481) (-392 "GCDDOM.spad" 628735 628743 629469 629538) (-391 "GCDDOM.spad" 627989 627999 628725 628730) (-390 "GBINTERN.spad" 624009 624047 627979 627984) (-389 "GBF.spad" 619792 619830 623999 624004) (-388 "GBEUCLID.spad" 617674 617712 619782 619787) (-387 "GB.spad" 615200 615238 617630 617635) (-386 "GAUSSFAC.spad" 614513 614521 615190 615195) (-385 "GALUTIL.spad" 612839 612849 614469 614474) (-384 "GALPOLYU.spad" 611293 611306 612829 612834) (-383 "GALFACTU.spad" 609506 609525 611283 611288) (-382 "GALFACT.spad" 599719 599730 609496 609501) (-381 "FUNDESC.spad" 599397 599405 599709 599714) (-380 "FUNCTION.spad" 599246 599258 599387 599392) (-379 "FT.spad" 597546 597554 599236 599241) (-378 "FSUPFACT.spad" 596460 596479 597496 597501) (-377 "FST.spad" 594546 594554 596450 596455) (-376 "FSRED.spad" 594026 594042 594536 594541) (-375 "FSPRMELT.spad" 592892 592908 593983 593988) (-374 "FSPECF.spad" 590983 590999 592882 592887) (-373 "FSINT.spad" 590643 590659 590973 590978) (-372 "FSERIES.spad" 589834 589846 590463 590562) (-371 "FSCINT.spad" 589151 589167 589824 589829) (-370 "FSAGG2.spad" 587886 587902 589141 589146) (-369 "FSAGG.spad" 587015 587025 587854 587881) (-368 "FSAGG.spad" 586094 586106 586935 586940) (-367 "FS2UPS.spad" 580609 580643 586084 586089) (-366 "FS2EXPXP.spad" 579750 579773 580599 580604) (-365 "FS2.spad" 579405 579421 579740 579745) (-364 "FS.spad" 573677 573687 579184 579400) (-363 "FS.spad" 567751 567763 573260 573265) (-362 "FRUTIL.spad" 566705 566715 567741 567746) (-361 "FRNAALG.spad" 561982 561992 566647 566700) (-360 "FRNAALG.spad" 557271 557283 561938 561943) (-359 "FRNAAF2.spad" 556719 556737 557261 557266) (-358 "FRMOD.spad" 556127 556157 556648 556653) (-357 "FRIDEAL2.spad" 555731 555763 556117 556122) (-356 "FRIDEAL.spad" 554956 554977 555711 555726) (-355 "FRETRCT.spad" 554475 554485 554946 554951) (-354 "FRETRCT.spad" 553901 553913 554374 554379) (-353 "FRAMALG.spad" 552281 552294 553857 553896) (-352 "FRAMALG.spad" 550693 550708 552271 552276) (-351 "FRAC2.spad" 550298 550310 550683 550688) (-350 "FRAC.spad" 548285 548295 548672 548845) (-349 "FR2.spad" 547621 547633 548275 548280) (-348 "FR.spad" 541409 541419 546682 546751) (-347 "FPS.spad" 538248 538256 541299 541404) (-346 "FPS.spad" 535115 535125 538168 538173) (-345 "FPC.spad" 534161 534169 535017 535110) (-344 "FPC.spad" 533293 533303 534151 534156) (-343 "FPATMAB.spad" 533055 533065 533283 533288) (-342 "FPARFRAC.spad" 531897 531914 533045 533050) (-341 "FORDER.spad" 531588 531612 531887 531892) (-340 "FNLA.spad" 531012 531034 531556 531583) (-339 "FNCAT.spad" 529607 529615 531002 531007) (-338 "FNAME.spad" 529499 529507 529597 529602) (-337 "FMONOID.spad" 529180 529190 529455 529460) (-336 "FMONCAT.spad" 526349 526359 529170 529175) (-335 "FMCAT.spad" 524025 524043 526317 526344) (-334 "FM1.spad" 523390 523402 523959 523986) (-333 "FM.spad" 523005 523017 523244 523271) (-332 "FLOATRP.spad" 520748 520762 522995 523000) (-331 "FLOATCP.spad" 518187 518201 520738 520743) (-330 "FLOAT.spad" 515278 515286 518053 518182) (-329 "FLINEXP.spad" 515000 515010 515268 515273) (-328 "FLINEXP.spad" 514679 514691 514949 514954) (-327 "FLASORT.spad" 514005 514017 514669 514674) (-326 "FLALG.spad" 511675 511694 513931 514000) (-325 "FLAGG2.spad" 510392 510408 511665 511670) (-324 "FLAGG.spad" 507468 507478 510382 510387) (-323 "FLAGG.spad" 504409 504421 507325 507330) (-322 "FINRALG.spad" 502494 502507 504365 504404) (-321 "FINRALG.spad" 500505 500520 502378 502383) (-320 "FINITE.spad" 499657 499665 500495 500500) (-319 "FINITE.spad" 498807 498817 499647 499652) (-318 "aggcat.spad" 495737 495747 498797 498802) (-317 "FINAGG.spad" 492632 492644 495694 495699) (-316 "FINAALG.spad" 481817 481827 492574 492627) (-315 "FINAALG.spad" 471014 471026 481773 481778) (-314 "FILECAT.spad" 469548 469565 471004 471009) (-313 "FILE.spad" 469131 469141 469538 469543) (-312 "FIELD.spad" 468537 468545 469033 469126) (-311 "FIELD.spad" 468029 468039 468527 468532) (-310 "FGROUP.spad" 466692 466702 468009 468024) (-309 "FGLMICPK.spad" 465487 465502 466682 466687) (-308 "FFX.spad" 464873 464888 465206 465299) (-307 "FFSLPE.spad" 464384 464405 464863 464868) (-306 "FFPOLY2.spad" 463444 463461 464374 464379) (-305 "FFPOLY.spad" 454786 454797 463434 463439) (-304 "FFP.spad" 454194 454214 454505 454598) (-303 "FFNBX.spad" 452717 452737 453913 454006) (-302 "FFNBP.spad" 451241 451258 452436 452529) (-301 "FFNB.spad" 449709 449730 450925 451018) (-300 "FFINTBAS.spad" 447223 447242 449699 449704) (-299 "FFIELDC.spad" 444808 444816 447125 447218) (-298 "FFIELDC.spad" 442479 442489 444798 444803) (-297 "FFHOM.spad" 441251 441268 442469 442474) (-296 "FFF.spad" 438694 438705 441241 441246) (-295 "FFCGX.spad" 437552 437572 438413 438506) (-294 "FFCGP.spad" 436452 436472 437271 437364) (-293 "FFCG.spad" 435247 435268 436136 436229) (-292 "FFCAT2.spad" 434994 435034 435237 435242) (-291 "FFCAT.spad" 428159 428181 434833 434989) (-290 "FFCAT.spad" 421403 421427 428079 428084) (-289 "FF.spad" 420854 420870 421087 421180) (-288 "FEVALAB.spad" 420562 420572 420844 420849) (-287 "FEVALAB.spad" 420046 420058 420330 420335) (-286 "FDIVCAT.spad" 418142 418166 420036 420041) (-285 "FDIVCAT.spad" 416236 416262 418132 418137) (-284 "FDIV2.spad" 415892 415932 416226 416231) (-283 "FDIV.spad" 415350 415374 415882 415887) (-282 "FCTRDATA.spad" 414358 414366 415340 415345) (-281 "FCOMP.spad" 413737 413747 414348 414353) (-280 "FAXF.spad" 406772 406786 413639 413732) (-279 "FAXF.spad" 399859 399875 406728 406733) (-278 "FARRAY.spad" 397738 397748 398771 398786) (-277 "FAMR.spad" 395882 395894 397636 397733) (-276 "FAMR.spad" 394010 394024 395766 395771) (-275 "FAMONOID.spad" 393694 393704 393964 393969) (-274 "FAMONC.spad" 392014 392026 393684 393689) (-273 "FAGROUP.spad" 391654 391664 391910 391937) (-272 "FACUTIL.spad" 389866 389883 391644 391649) (-271 "FACTFUNC.spad" 389068 389078 389856 389861) (-270 "EXPUPXS.spad" 385960 385983 387259 387408) (-269 "EXPRTUBE.spad" 383248 383256 385950 385955) (-268 "EXPRODE.spad" 380416 380432 383238 383243) (-267 "EXPR2UPS.spad" 376538 376551 380406 380411) (-266 "EXPR2.spad" 376243 376255 376528 376533) (-265 "EXPR.spad" 371888 371898 372602 372889) (-264 "EXPEXPAN.spad" 368833 368858 369465 369558) (-263 "EXITAST.spad" 368569 368577 368823 368828) (-262 "EXIT.spad" 368240 368248 368559 368564) (-261 "EVALCYC.spad" 367700 367714 368230 368235) (-260 "EVALAB.spad" 367280 367290 367690 367695) (-259 "EVALAB.spad" 366858 366870 367270 367275) (-258 "EUCDOM.spad" 364448 364456 366784 366853) (-257 "EUCDOM.spad" 362100 362110 364438 364443) (-256 "ES2.spad" 361613 361629 362090 362095) (-255 "ES1.spad" 361183 361199 361603 361608) (-254 "ES.spad" 354054 354062 361173 361178) (-253 "ES.spad" 346846 346856 353967 353972) (-252 "ERROR.spad" 344173 344181 346836 346841) (-251 "EQTBL.spad" 341934 341956 342143 342158) (-250 "EQ2.spad" 341652 341664 341924 341929) (-249 "EQ.spad" 336558 336568 339353 339459) (-248 "EP.spad" 332884 332894 336548 336553) (-247 "ENV.spad" 331562 331570 332874 332879) (-246 "ENTIRER.spad" 331230 331238 331506 331557) (-245 "ENTIRER.spad" 330942 330952 331220 331225) (-244 "EMR.spad" 330230 330271 330868 330937) (-243 "ELTAGG.spad" 328484 328503 330220 330225) (-242 "ELTAGG.spad" 326674 326695 328412 328417) (-241 "ELTAB.spad" 326149 326162 326664 326669) (-240 "ELFUTS.spad" 325584 325603 326139 326144) (-239 "ELEMFUN.spad" 325273 325281 325574 325579) (-238 "ELEMFUN.spad" 324960 324970 325263 325268) (-237 "ELAGG.spad" 322931 322941 324940 324955) (-236 "ELAGG.spad" 320841 320853 322852 322857) (-235 "ELABOR.spad" 320187 320195 320831 320836) (-234 "ELABEXPR.spad" 319119 319127 320177 320182) (-233 "EFUPXS.spad" 315895 315925 319075 319080) (-232 "EFULS.spad" 312731 312754 315851 315856) (-231 "EFSTRUC.spad" 310746 310762 312721 312726) (-230 "EF.spad" 305522 305538 310736 310741) (-229 "EAB.spad" 303822 303830 305512 305517) (-228 "DVARCAT.spad" 300828 300838 303812 303817) (-227 "DVARCAT.spad" 297832 297844 300818 300823) (-226 "DSMP.spad" 295565 295579 295870 295997) (-225 "DSEXT.spad" 294867 294877 295555 295560) (-224 "DSEXT.spad" 294089 294101 294779 294784) (-223 "DROPT1.spad" 293754 293764 294079 294084) (-222 "DROPT0.spad" 288619 288627 293744 293749) (-221 "DROPT.spad" 282578 282586 288609 288614) (-220 "DRAWPT.spad" 280751 280759 282568 282573) (-219 "DRAWHACK.spad" 280059 280069 280741 280746) (-218 "DRAWCX.spad" 277537 277545 280049 280054) (-217 "DRAWCURV.spad" 277084 277099 277527 277532) (-216 "DRAWCFUN.spad" 266616 266624 277074 277079) (-215 "DRAW.spad" 259492 259505 266606 266611) (-214 "DQAGG.spad" 257682 257692 259472 259487) (-213 "DPOLCAT.spad" 253039 253055 257550 257677) (-212 "DPOLCAT.spad" 248482 248500 252995 253000) (-211 "DPMO.spad" 241035 241051 241173 241367) (-210 "DPMM.spad" 233601 233619 233726 233920) (-209 "DOMTMPLT.spad" 233372 233380 233591 233596) (-208 "DOMCTOR.spad" 233127 233135 233362 233367) (-207 "DOMAIN.spad" 232238 232246 233117 233122) (-206 "DMP.spad" 229831 229846 230401 230528) (-205 "DMEXT.spad" 229698 229708 229799 229826) (-204 "DLP.spad" 229058 229068 229688 229693) (-203 "DLIST.spad" 227366 227376 227970 227985) (-202 "DLAGG.spad" 225783 225793 227356 227361) (-201 "DIVRING.spad" 225325 225333 225727 225778) (-200 "DIVRING.spad" 224911 224921 225315 225320) (-199 "DISPLAY.spad" 223101 223109 224901 224906) (-198 "DIRPROD2.spad" 221919 221937 223091 223096) (-197 "DIRPROD.spad" 211139 211155 211779 211864) (-196 "DIRPCAT.spad" 210434 210450 211049 211134) (-195 "DIRPCAT.spad" 209343 209361 209960 209965) (-194 "DIOSP.spad" 208168 208176 209333 209338) (-193 "DIOPS.spad" 207164 207174 208148 208163) (-192 "DIOPS.spad" 206107 206119 207093 207098) (-191 "catdef.spad" 205965 205973 206097 206102) (-190 "DIFRING.spad" 205803 205811 205945 205960) (-189 "DIFFSPC.spad" 205382 205390 205793 205798) (-188 "DIFFSPC.spad" 204959 204969 205372 205377) (-187 "DIFFMOD.spad" 204448 204458 204927 204954) (-186 "DIFFDOM.spad" 203613 203624 204438 204443) (-185 "DIFFDOM.spad" 202776 202789 203603 203608) (-184 "DIFEXT.spad" 202595 202605 202756 202771) (-183 "DIAGG.spad" 202225 202235 202575 202590) (-182 "DIAGG.spad" 201863 201875 202215 202220) (-181 "DHMATRIX.spad" 200252 200262 201397 201412) (-180 "DFSFUN.spad" 193892 193900 200242 200247) (-179 "DFLOAT.spad" 190499 190507 193782 193887) (-178 "DFINTTLS.spad" 188730 188746 190489 190494) (-177 "DERHAM.spad" 186644 186676 188710 188725) (-176 "DEQUEUE.spad" 186045 186055 186328 186343) (-175 "DEGRED.spad" 185662 185676 186035 186040) (-174 "DEFINTRF.spad" 183244 183254 185652 185657) (-173 "DEFINTEF.spad" 181782 181798 183234 183239) (-172 "DEFAST.spad" 181166 181174 181772 181777) (-171 "DECIMAL.spad" 179395 179403 179756 179849) (-170 "DDFACT.spad" 177216 177233 179385 179390) (-169 "DBLRESP.spad" 176816 176840 177206 177211) (-168 "DBASIS.spad" 176442 176457 176806 176811) (-167 "DBASE.spad" 175106 175116 176432 176437) (-166 "DATAARY.spad" 174592 174605 175096 175101) (-165 "CYCLOTOM.spad" 174098 174106 174582 174587) (-164 "CYCLES.spad" 170884 170892 174088 174093) (-163 "CVMP.spad" 170301 170311 170874 170879) (-162 "CTRIGMNP.spad" 168801 168817 170291 170296) (-161 "CTORKIND.spad" 168404 168412 168791 168796) (-160 "CTORCAT.spad" 167645 167653 168394 168399) (-159 "CTORCAT.spad" 166884 166894 167635 167640) (-158 "CTORCALL.spad" 166473 166483 166874 166879) (-157 "CTOR.spad" 166164 166172 166463 166468) (-156 "CSTTOOLS.spad" 165409 165422 166154 166159) (-155 "CRFP.spad" 159181 159194 165399 165404) (-154 "CRCEAST.spad" 158901 158909 159171 159176) (-153 "CRAPACK.spad" 157968 157978 158891 158896) (-152 "CPMATCH.spad" 157469 157484 157890 157895) (-151 "CPIMA.spad" 157174 157193 157459 157464) (-150 "COORDSYS.spad" 152183 152193 157164 157169) (-149 "CONTOUR.spad" 151610 151618 152173 152178) (-148 "CONTFRAC.spad" 147360 147370 151512 151605) (-147 "CONDUIT.spad" 147118 147126 147350 147355) (-146 "COMRING.spad" 146792 146800 147056 147113) (-145 "COMPPROP.spad" 146310 146318 146782 146787) (-144 "COMPLPAT.spad" 146077 146092 146300 146305) (-143 "COMPLEX2.spad" 145792 145804 146067 146072) (-142 "COMPLEX.spad" 141498 141508 141742 142000) (-141 "COMPILER.spad" 141047 141055 141488 141493) (-140 "COMPFACT.spad" 140649 140663 141037 141042) (-139 "COMPCAT.spad" 138724 138734 140386 140644) (-138 "COMPCAT.spad" 136540 136552 138204 138209) (-137 "COMMUPC.spad" 136288 136306 136530 136535) (-136 "COMMONOP.spad" 135821 135829 136278 136283) (-135 "COMMAAST.spad" 135584 135592 135811 135816) (-134 "COMM.spad" 135395 135403 135574 135579) (-133 "COMBOPC.spad" 134318 134326 135385 135390) (-132 "COMBINAT.spad" 133085 133095 134308 134313) (-131 "COMBF.spad" 130507 130523 133075 133080) (-130 "COLOR.spad" 129344 129352 130497 130502) (-129 "COLONAST.spad" 129010 129018 129334 129339) (-128 "CMPLXRT.spad" 128721 128738 129000 129005) (-127 "CLLCTAST.spad" 128383 128391 128711 128716) (-126 "CLIP.spad" 124491 124499 128373 128378) (-125 "CLIF.spad" 123146 123162 124447 124486) (-124 "CLAGG.spad" 121138 121148 123136 123141) (-123 "CLAGG.spad" 118989 119001 120989 120994) (-122 "CINTSLPE.spad" 118344 118357 118979 118984) (-121 "CHVAR.spad" 116482 116504 118334 118339) (-120 "CHARZ.spad" 116397 116405 116462 116477) (-119 "CHARPOL.spad" 115923 115933 116387 116392) (-118 "CHARNZ.spad" 115685 115693 115903 115918) (-117 "CHAR.spad" 113053 113061 115675 115680) (-116 "CFCAT.spad" 112381 112389 113043 113048) (-115 "CDEN.spad" 111601 111615 112371 112376) (-114 "CCLASS.spad" 109670 109678 110932 110959) (-113 "CATEGORY.spad" 108744 108752 109660 109665) (-112 "CATCTOR.spad" 108635 108643 108734 108739) (-111 "CATAST.spad" 108261 108269 108625 108630) (-110 "CASEAST.spad" 107975 107983 108251 108256) (-109 "CARTEN2.spad" 107365 107392 107965 107970) (-108 "CARTEN.spad" 103117 103141 107355 107360) (-107 "CARD.spad" 100412 100420 103091 103112) (-106 "CAPSLAST.spad" 100194 100202 100402 100407) (-105 "CACHSET.spad" 99818 99826 100184 100189) (-104 "CABMON.spad" 99373 99381 99808 99813) (-103 "BYTEORD.spad" 99048 99056 99363 99368) (-102 "BYTEBUF.spad" 96858 96866 98064 98079) (-101 "BYTE.spad" 96333 96341 96848 96853) (-100 "BTREE.spad" 95422 95432 95956 95971) (-99 "BTOURN.spad" 94444 94453 95045 95060) (-98 "BTCAT.spad" 94014 94023 94424 94439) (-97 "BTCAT.spad" 93592 93603 94004 94009) (-96 "BTAGG.spad" 93071 93078 93572 93587) (-95 "BTAGG.spad" 92558 92567 93061 93066) (-94 "BSTREE.spad" 91316 91325 92181 92196) (-93 "BRILL.spad" 89522 89532 91306 91311) (-92 "BRAGG.spad" 88479 88488 89512 89517) (-91 "BRAGG.spad" 87372 87383 88407 88412) (-90 "BPADICRT.spad" 85432 85443 85678 85771) (-89 "BPADIC.spad" 85105 85116 85358 85427) (-88 "BOUNDZRO.spad" 84762 84778 85095 85100) (-87 "BOP1.spad" 82221 82230 84752 84757) (-86 "BOP.spad" 77364 77371 82211 82216) (-85 "BOOLEAN.spad" 76913 76920 77354 77359) (-84 "BOOLE.spad" 76564 76571 76903 76908) (-83 "BOOLE.spad" 76213 76222 76554 76559) (-82 "BMODULE.spad" 75926 75937 76181 76208) (-81 "BITS.spad" 75127 75134 75341 75356) (-80 "catdef.spad" 75010 75020 75117 75122) (-79 "catdef.spad" 74761 74771 75000 75005) (-78 "BINDING.spad" 74183 74190 74751 74756) (-77 "BINARY.spad" 72418 72425 72773 72866) (-76 "BGAGG.spad" 71738 71747 72398 72413) (-75 "BGAGG.spad" 71066 71077 71728 71733) (-74 "BEZOUT.spad" 70207 70233 71016 71021) (-73 "BBTREE.spad" 67101 67110 69830 69845) (-72 "BASTYPE.spad" 66601 66608 67091 67096) (-71 "BASTYPE.spad" 66099 66108 66591 66596) (-70 "BALFACT.spad" 65559 65571 66089 66094) (-69 "AUTOMOR.spad" 65010 65019 65539 65554) (-68 "ATTREG.spad" 62142 62149 64786 65005) (-67 "ATTRAST.spad" 61859 61866 62132 62137) (-66 "ATRIG.spad" 61329 61336 61849 61854) (-65 "ATRIG.spad" 60797 60806 61319 61324) (-64 "ASTCAT.spad" 60701 60708 60787 60792) (-63 "ASTCAT.spad" 60603 60612 60691 60696) (-62 "ASTACK.spad" 60019 60028 60287 60302) (-61 "ASSOCEQ.spad" 58853 58864 59975 59980) (-60 "ARRAY2.spad" 58388 58397 58537 58552) (-59 "ARRAY12.spad" 57101 57112 58378 58383) (-58 "ARRAY1.spad" 55667 55676 56013 56028) (-57 "ARR2CAT.spad" 51719 51740 55647 55662) (-56 "ARR2CAT.spad" 47779 47802 51709 51714) (-55 "ARITY.spad" 47151 47158 47769 47774) (-54 "APPRULE.spad" 46435 46457 47141 47146) (-53 "APPLYORE.spad" 46054 46067 46425 46430) (-52 "ANY1.spad" 45125 45134 46044 46049) (-51 "ANY.spad" 43976 43983 45115 45120) (-50 "ANTISYM.spad" 42421 42437 43956 43971) (-49 "ANON.spad" 42130 42137 42411 42416) (-48 "AN.spad" 40598 40605 41961 42054) (-47 "AMR.spad" 38783 38794 40496 40593) (-46 "AMR.spad" 36831 36844 38546 38551) (-45 "ALIST.spad" 33066 33087 33416 33431) (-44 "ALGSC.spad" 32201 32227 32938 32991) (-43 "ALGPKG.spad" 27984 27995 32157 32162) (-42 "ALGMFACT.spad" 27177 27191 27974 27979) (-41 "ALGMANIP.spad" 24678 24693 27021 27026) (-40 "ALGFF.spad" 22496 22523 22713 22869) (-39 "ALGFACT.spad" 21615 21625 22486 22491) (-38 "ALGEBRA.spad" 21448 21457 21571 21610) (-37 "ALGEBRA.spad" 21313 21324 21438 21443) (-36 "ALAGG.spad" 20841 20862 21293 21308) (-35 "AHYP.spad" 20222 20229 20831 20836) (-34 "AGG.spad" 19129 19136 20212 20217) (-33 "AGG.spad" 18034 18043 19119 19124) (-32 "AF.spad" 16479 16494 17983 17988) (-31 "ADDAST.spad" 16165 16172 16469 16474) (-30 "ACPLOT.spad" 15042 15049 16155 16160) (-29 "ACFS.spad" 12899 12908 14944 15037) (-28 "ACFS.spad" 10842 10853 12889 12894) (-27 "ACF.spad" 7596 7603 10744 10837) (-26 "ACF.spad" 4436 4445 7586 7591) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 2944 2951 3506 3511) (-22 "ABELMON.spad" 2370 2379 2934 2939) (-21 "ABELGRP.spad" 2035 2042 2360 2365) (-20 "ABELGRP.spad" 1698 1707 2025 2030) (-19 "A1AGG.spad" 860 869 1678 1693) (-18 "A1AGG.spad" 30 41 850 855)) 
\ No newline at end of file
+((-3 NIL 1968340 1968345 1968350 1968355) (-2 NIL 1968320 1968325 1968330 1968335) (-1 NIL 1968300 1968305 1968310 1968315) (0 NIL 1968280 1968285 1968290 1968295) (-1210 "ZMOD.spad" 1968089 1968102 1968218 1968275) (-1209 "ZLINDEP.spad" 1967187 1967198 1968079 1968084) (-1208 "ZDSOLVE.spad" 1957148 1957170 1967177 1967182) (-1207 "YSTREAM.spad" 1956643 1956654 1957138 1957143) (-1206 "YDIAGRAM.spad" 1956277 1956286 1956633 1956638) (-1205 "XRPOLY.spad" 1955497 1955517 1956133 1956202) (-1204 "XPR.spad" 1953292 1953305 1955215 1955314) (-1203 "XPOLYC.spad" 1952611 1952627 1953218 1953287) (-1202 "XPOLY.spad" 1952166 1952177 1952467 1952536) (-1201 "XPBWPOLY.spad" 1950637 1950657 1951972 1952041) (-1200 "XFALG.spad" 1947685 1947701 1950563 1950632) (-1199 "XF.spad" 1946148 1946163 1947587 1947680) (-1198 "XF.spad" 1944591 1944608 1946032 1946037) (-1197 "XEXPPKG.spad" 1943850 1943876 1944581 1944586) (-1196 "XDPOLY.spad" 1943464 1943480 1943706 1943775) (-1195 "XALG.spad" 1943132 1943143 1943420 1943459) (-1194 "WUTSET.spad" 1938996 1939013 1942627 1942632) (-1193 "WP.spad" 1938203 1938247 1938854 1938921) (-1192 "WHILEAST.spad" 1938001 1938010 1938193 1938198) (-1191 "WHEREAST.spad" 1937672 1937681 1937991 1937996) (-1190 "WFFINTBS.spad" 1935335 1935357 1937662 1937667) (-1189 "WEIER.spad" 1933557 1933568 1935325 1935330) (-1188 "VSPACE.spad" 1933230 1933241 1933525 1933552) (-1187 "VSPACE.spad" 1932923 1932936 1933220 1933225) (-1186 "VOID.spad" 1932600 1932609 1932913 1932918) (-1185 "VIEWDEF.spad" 1927801 1927810 1932590 1932595) (-1184 "VIEW3D.spad" 1911762 1911771 1927791 1927796) (-1183 "VIEW2D.spad" 1899661 1899670 1911752 1911757) (-1182 "VIEW.spad" 1897381 1897390 1899651 1899656) (-1181 "VECTOR2.spad" 1896020 1896033 1897371 1897376) (-1180 "VECTOR.spad" 1894436 1894447 1894687 1894692) (-1179 "VECTCAT.spad" 1892370 1892381 1894426 1894431) (-1178 "VECTCAT.spad" 1890091 1890104 1892149 1892154) (-1177 "VARIABLE.spad" 1889871 1889886 1890081 1890086) (-1176 "UTYPE.spad" 1889515 1889524 1889861 1889866) (-1175 "UTSODETL.spad" 1888810 1888834 1889471 1889476) (-1174 "UTSODE.spad" 1887026 1887046 1888800 1888805) (-1173 "UTSCAT.spad" 1884505 1884521 1886924 1887021) (-1172 "UTSCAT.spad" 1881652 1881670 1884073 1884078) (-1171 "UTS2.spad" 1881247 1881282 1881642 1881647) (-1170 "UTS.spad" 1876259 1876287 1879779 1879876) (-1169 "URAGG.spad" 1870980 1870991 1876249 1876254) (-1168 "URAGG.spad" 1865637 1865650 1870908 1870913) (-1167 "UPXSSING.spad" 1863405 1863431 1864841 1864974) (-1166 "UPXSCONS.spad" 1861223 1861243 1861596 1861745) (-1165 "UPXSCCA.spad" 1859794 1859814 1861069 1861218) (-1164 "UPXSCCA.spad" 1858507 1858529 1859784 1859789) (-1163 "UPXSCAT.spad" 1857096 1857112 1858353 1858502) (-1162 "UPXS2.spad" 1856639 1856692 1857086 1857091) (-1161 "UPXS.spad" 1853994 1854022 1854830 1854979) (-1160 "UPSQFREE.spad" 1852409 1852423 1853984 1853989) (-1159 "UPSCAT.spad" 1850204 1850228 1852307 1852404) (-1158 "UPSCAT.spad" 1847700 1847726 1849805 1849810) (-1157 "UPOLYC2.spad" 1847171 1847190 1847690 1847695) (-1156 "UPOLYC.spad" 1842251 1842262 1847013 1847166) (-1155 "UPOLYC.spad" 1837249 1837262 1842013 1842018) (-1154 "UPMP.spad" 1836181 1836194 1837239 1837244) (-1153 "UPDIVP.spad" 1835746 1835760 1836171 1836176) (-1152 "UPDECOMP.spad" 1834007 1834021 1835736 1835741) (-1151 "UPCDEN.spad" 1833224 1833240 1833997 1834002) (-1150 "UP2.spad" 1832588 1832609 1833214 1833219) (-1149 "UP.spad" 1830058 1830073 1830445 1830598) (-1148 "UNISEG2.spad" 1829555 1829568 1830014 1830019) (-1147 "UNISEG.spad" 1828908 1828919 1829474 1829479) (-1146 "UNIFACT.spad" 1828011 1828023 1828898 1828903) (-1145 "ULSCONS.spad" 1821857 1821877 1822227 1822376) (-1144 "ULSCCAT.spad" 1819594 1819614 1821703 1821852) (-1143 "ULSCCAT.spad" 1817439 1817461 1819550 1819555) (-1142 "ULSCAT.spad" 1815679 1815695 1817285 1817434) (-1141 "ULS2.spad" 1815193 1815246 1815669 1815674) (-1140 "ULS.spad" 1807226 1807254 1808171 1808594) (-1139 "UINT8.spad" 1807103 1807112 1807216 1807221) (-1138 "UINT64.spad" 1806979 1806988 1807093 1807098) (-1137 "UINT32.spad" 1806855 1806864 1806969 1806974) (-1136 "UINT16.spad" 1806731 1806740 1806845 1806850) (-1135 "UFD.spad" 1805796 1805805 1806657 1806726) (-1134 "UFD.spad" 1804923 1804934 1805786 1805791) (-1133 "UDVO.spad" 1803804 1803813 1804913 1804918) (-1132 "UDPO.spad" 1801385 1801396 1803760 1803765) (-1131 "TYPEAST.spad" 1801304 1801313 1801375 1801380) (-1130 "TYPE.spad" 1801236 1801245 1801294 1801299) (-1129 "TWOFACT.spad" 1799888 1799903 1801226 1801231) (-1128 "TUPLE.spad" 1799395 1799406 1799800 1799805) (-1127 "TUBETOOL.spad" 1796262 1796271 1799385 1799390) (-1126 "TUBE.spad" 1794909 1794926 1796252 1796257) (-1125 "TSETCAT.spad" 1783002 1783019 1794899 1794904) (-1124 "TSETCAT.spad" 1771059 1771078 1782958 1782963) (-1123 "TS.spad" 1769687 1769703 1770653 1770750) (-1122 "TRMANIP.spad" 1764051 1764068 1769375 1769380) (-1121 "TRIMAT.spad" 1763014 1763039 1764041 1764046) (-1120 "TRIGMNIP.spad" 1761541 1761558 1763004 1763009) (-1119 "TRIGCAT.spad" 1761053 1761062 1761531 1761536) (-1118 "TRIGCAT.spad" 1760563 1760574 1761043 1761048) (-1117 "TREE.spad" 1759164 1759175 1760196 1760201) (-1116 "TRANFUN.spad" 1759003 1759012 1759154 1759159) (-1115 "TRANFUN.spad" 1758840 1758851 1758993 1758998) (-1114 "TOPSP.spad" 1758514 1758523 1758830 1758835) (-1113 "TOOLSIGN.spad" 1758177 1758188 1758504 1758509) (-1112 "TEXTFILE.spad" 1756738 1756747 1758167 1758172) (-1111 "TEX1.spad" 1756294 1756305 1756728 1756733) (-1110 "TEX.spad" 1753488 1753497 1756284 1756289) (-1109 "TBCMPPK.spad" 1751589 1751612 1753478 1753483) (-1108 "TBAGG.spad" 1750854 1750877 1751579 1751584) (-1107 "TBAGG.spad" 1750117 1750142 1750844 1750849) (-1106 "TANEXP.spad" 1749525 1749536 1750107 1750112) (-1105 "TALGOP.spad" 1749249 1749260 1749515 1749520) (-1104 "TABLEAU.spad" 1748730 1748741 1749239 1749244) (-1103 "TABLE.spad" 1746440 1746463 1746710 1746715) (-1102 "TABLBUMP.spad" 1743219 1743230 1746430 1746435) (-1101 "SYSTEM.spad" 1742447 1742456 1743209 1743214) (-1100 "SYSSOLP.spad" 1739930 1739941 1742437 1742442) (-1099 "SYSPTR.spad" 1739829 1739838 1739920 1739925) (-1098 "SYSNNI.spad" 1739052 1739063 1739819 1739824) (-1097 "SYSINT.spad" 1738456 1738467 1739042 1739047) (-1096 "SYNTAX.spad" 1734790 1734799 1738446 1738451) (-1095 "SYMTAB.spad" 1732858 1732867 1734780 1734785) (-1094 "SYMS.spad" 1728887 1728896 1732848 1732853) (-1093 "SYMPOLY.spad" 1728020 1728031 1728102 1728229) (-1092 "SYMFUNC.spad" 1727521 1727532 1728010 1728015) (-1091 "SYMBOL.spad" 1725016 1725025 1727511 1727516) (-1090 "SUTS.spad" 1722129 1722157 1723548 1723645) (-1089 "SUPXS.spad" 1719471 1719499 1720320 1720469) (-1088 "SUPFRACF.spad" 1718576 1718594 1719461 1719466) (-1087 "SUP2.spad" 1717968 1717981 1718566 1718571) (-1086 "SUP.spad" 1715052 1715063 1715825 1715978) (-1085 "SUMRF.spad" 1714026 1714037 1715042 1715047) (-1084 "SUMFS.spad" 1713655 1713672 1714016 1714021) (-1083 "SULS.spad" 1705675 1705703 1706633 1707056) (-1082 "syntax.spad" 1705444 1705453 1705665 1705670) (-1081 "SUCH.spad" 1705134 1705149 1705434 1705439) (-1080 "SUBSPACE.spad" 1697265 1697280 1705124 1705129) (-1079 "SUBRESP.spad" 1696435 1696449 1697221 1697226) (-1078 "STTFNC.spad" 1692903 1692919 1696425 1696430) (-1077 "STTF.spad" 1689002 1689018 1692893 1692898) (-1076 "STTAYLOR.spad" 1681679 1681690 1688909 1688914) (-1075 "STRTBL.spad" 1679552 1679569 1679701 1679706) (-1074 "STRING.spad" 1678193 1678202 1678578 1678583) (-1073 "STREAM3.spad" 1677766 1677781 1678183 1678188) (-1072 "STREAM2.spad" 1676894 1676907 1677756 1677761) (-1071 "STREAM1.spad" 1676600 1676611 1676884 1676889) (-1070 "STREAM.spad" 1673560 1673571 1676051 1676056) (-1069 "STINPROD.spad" 1672496 1672512 1673550 1673555) (-1068 "STEPAST.spad" 1671730 1671739 1672486 1672491) (-1067 "STEP.spad" 1671047 1671056 1671720 1671725) (-1066 "STBL.spad" 1668860 1668888 1669027 1669032) (-1065 "STAGG.spad" 1667559 1667570 1668850 1668855) (-1064 "STAGG.spad" 1666256 1666269 1667549 1667554) (-1063 "STACK.spad" 1665700 1665711 1665950 1665955) (-1062 "SRING.spad" 1665460 1665469 1665690 1665695) (-1061 "SREGSET.spad" 1663053 1663070 1664955 1664960) (-1060 "SRDCMPK.spad" 1661630 1661650 1663043 1663048) (-1059 "SRAGG.spad" 1656835 1656844 1661620 1661625) (-1058 "SRAGG.spad" 1652038 1652049 1656825 1656830) (-1057 "SQMATRIX.spad" 1649727 1649745 1650643 1650718) (-1056 "SPLTREE.spad" 1644387 1644400 1649183 1649188) (-1055 "SPLNODE.spad" 1641007 1641020 1644377 1644382) (-1054 "SPFCAT.spad" 1639816 1639825 1640997 1641002) (-1053 "SPECOUT.spad" 1638368 1638377 1639806 1639811) (-1052 "SPADXPT.spad" 1630459 1630468 1638358 1638363) (-1051 "spad-parser.spad" 1629924 1629933 1630449 1630454) (-1050 "SPADAST.spad" 1629625 1629634 1629914 1629919) (-1049 "SPACEC.spad" 1613840 1613851 1629615 1629620) (-1048 "SPACE3.spad" 1613616 1613627 1613830 1613835) (-1047 "SORTPAK.spad" 1613165 1613178 1613572 1613577) (-1046 "SOLVETRA.spad" 1610928 1610939 1613155 1613160) (-1045 "SOLVESER.spad" 1609384 1609395 1610918 1610923) (-1044 "SOLVERAD.spad" 1605410 1605421 1609374 1609379) (-1043 "SOLVEFOR.spad" 1603872 1603890 1605400 1605405) (-1042 "SNTSCAT.spad" 1603494 1603511 1603862 1603867) (-1041 "SMTS.spad" 1601811 1601837 1603088 1603185) (-1040 "SMP.spad" 1599619 1599639 1600009 1600136) (-1039 "SMITH.spad" 1598464 1598489 1599609 1599614) (-1038 "SMATCAT.spad" 1596594 1596624 1598420 1598459) (-1037 "SMATCAT.spad" 1594644 1594676 1596472 1596477) (-1036 "aggcat.spad" 1594330 1594341 1594634 1594639) (-1035 "SKAGG.spad" 1593321 1593332 1594320 1594325) (-1034 "SINT.spad" 1592620 1592629 1593187 1593316) (-1033 "SIMPAN.spad" 1592348 1592357 1592610 1592615) (-1032 "SIGNRF.spad" 1591473 1591484 1592338 1592343) (-1031 "SIGNEF.spad" 1590759 1590776 1591463 1591468) (-1030 "syntax.spad" 1590176 1590185 1590749 1590754) (-1029 "SIG.spad" 1589538 1589547 1590166 1590171) (-1028 "SHP.spad" 1587482 1587497 1589494 1589499) (-1027 "SHDP.spad" 1576825 1576852 1577342 1577427) (-1026 "SGROUP.spad" 1576433 1576442 1576815 1576820) (-1025 "SGROUP.spad" 1576039 1576050 1576423 1576428) (-1024 "catdef.spad" 1575749 1575761 1575860 1576034) (-1023 "catdef.spad" 1575305 1575317 1575570 1575744) (-1022 "SGCF.spad" 1568444 1568453 1575295 1575300) (-1021 "SFRTCAT.spad" 1567412 1567429 1568434 1568439) (-1020 "SFRGCD.spad" 1566475 1566495 1567402 1567407) (-1019 "SFQCMPK.spad" 1561288 1561308 1566465 1566470) (-1018 "SEXOF.spad" 1561131 1561171 1561278 1561283) (-1017 "SEXCAT.spad" 1558959 1558999 1561121 1561126) (-1016 "SEX.spad" 1558851 1558860 1558949 1558954) (-1015 "SETMN.spad" 1557311 1557328 1558841 1558846) (-1014 "SETCAT.spad" 1556796 1556805 1557301 1557306) (-1013 "SETCAT.spad" 1556279 1556290 1556786 1556791) (-1012 "SETAGG.spad" 1552828 1552839 1556259 1556274) (-1011 "SETAGG.spad" 1549385 1549398 1552818 1552823) (-1010 "SET.spad" 1547555 1547566 1548654 1548669) (-1009 "syntax.spad" 1547258 1547267 1547545 1547550) (-1008 "SEGXCAT.spad" 1546414 1546427 1547248 1547253) (-1007 "SEGCAT.spad" 1545339 1545350 1546404 1546409) (-1006 "SEGBIND2.spad" 1545037 1545050 1545329 1545334) (-1005 "SEGBIND.spad" 1544795 1544806 1544984 1544989) (-1004 "SEGAST.spad" 1544525 1544534 1544785 1544790) (-1003 "SEG2.spad" 1543960 1543973 1544481 1544486) (-1002 "SEG.spad" 1543773 1543784 1543879 1543884) (-1001 "SDVAR.spad" 1543049 1543060 1543763 1543768) (-1000 "SDPOL.spad" 1540741 1540752 1541032 1541159) (-999 "SCPKG.spad" 1538831 1538841 1540731 1540736) (-998 "SCOPE.spad" 1538009 1538017 1538821 1538826) (-997 "SCACHE.spad" 1536706 1536716 1537999 1538004) (-996 "SASTCAT.spad" 1536616 1536624 1536696 1536701) (-995 "SAOS.spad" 1536489 1536497 1536606 1536611) (-994 "SAERFFC.spad" 1536203 1536222 1536479 1536484) (-993 "SAEFACT.spad" 1535905 1535924 1536193 1536198) (-992 "SAE.spad" 1533556 1533571 1534166 1534301) (-991 "RURPK.spad" 1531216 1531231 1533546 1533551) (-990 "RULESET.spad" 1530670 1530693 1531206 1531211) (-989 "RULECOLD.spad" 1530523 1530535 1530660 1530665) (-988 "RULE.spad" 1528772 1528795 1530513 1530518) (-987 "RTVALUE.spad" 1528508 1528516 1528762 1528767) (-986 "syntax.spad" 1528226 1528234 1528498 1528503) (-985 "RSETGCD.spad" 1524669 1524688 1528216 1528221) (-984 "RSETCAT.spad" 1514660 1514676 1524659 1524664) (-983 "RSETCAT.spad" 1504649 1504667 1514650 1514655) (-982 "RSDCMPK.spad" 1503150 1503169 1504639 1504644) (-981 "RRCC.spad" 1501535 1501564 1503140 1503145) (-980 "RRCC.spad" 1499918 1499949 1501525 1501530) (-979 "RPTAST.spad" 1499621 1499629 1499908 1499913) (-978 "RPOLCAT.spad" 1479126 1479140 1499489 1499616) (-977 "RPOLCAT.spad" 1458424 1458440 1478789 1478794) (-976 "ROMAN.spad" 1457753 1457761 1458290 1458419) (-975 "ROIRC.spad" 1456834 1456865 1457743 1457748) (-974 "RNS.spad" 1455811 1455819 1456736 1456829) (-973 "RNS.spad" 1454874 1454884 1455801 1455806) (-972 "RNGBIND.spad" 1454035 1454048 1454829 1454834) (-971 "RNG.spad" 1453644 1453652 1454025 1454030) (-970 "RNG.spad" 1453251 1453261 1453634 1453639) (-969 "RMODULE.spad" 1453033 1453043 1453241 1453246) (-968 "RMCAT2.spad" 1452454 1452510 1453023 1453028) (-967 "RMATRIX.spad" 1451276 1451294 1451618 1451645) (-966 "RMATCAT.spad" 1446926 1446956 1451244 1451271) (-965 "RMATCAT.spad" 1442454 1442486 1446774 1446779) (-964 "RLINSET.spad" 1442159 1442169 1442444 1442449) (-963 "RINTERP.spad" 1442048 1442067 1442149 1442154) (-962 "RING.spad" 1441519 1441527 1442028 1442043) (-961 "RING.spad" 1440998 1441008 1441509 1441514) (-960 "RIDIST.spad" 1440391 1440399 1440988 1440993) (-959 "RGCHAIN.spad" 1438658 1438673 1439551 1439556) (-958 "RGBCSPC.spad" 1438448 1438459 1438648 1438653) (-957 "RGBCMDL.spad" 1438011 1438022 1438438 1438443) (-956 "RFFACTOR.spad" 1437474 1437484 1438001 1438006) (-955 "RFFACT.spad" 1437210 1437221 1437464 1437469) (-954 "RFDIST.spad" 1436207 1436215 1437200 1437205) (-953 "RF.spad" 1433882 1433892 1436197 1436202) (-952 "RETSOL.spad" 1433302 1433314 1433872 1433877) (-951 "RETRACT.spad" 1432731 1432741 1433292 1433297) (-950 "RETRACT.spad" 1432158 1432170 1432721 1432726) (-949 "RETAST.spad" 1431971 1431979 1432148 1432153) (-948 "RESRING.spad" 1431319 1431365 1431909 1431966) (-947 "RESLATC.spad" 1430644 1430654 1431309 1431314) (-946 "REPSQ.spad" 1430376 1430386 1430634 1430639) (-945 "REPDB.spad" 1430084 1430094 1430366 1430371) (-944 "REP2.spad" 1419799 1419809 1429926 1429931) (-943 "REP1.spad" 1414020 1414030 1419749 1419754) (-942 "REP.spad" 1411575 1411583 1414010 1414015) (-941 "REGSET.spad" 1409262 1409278 1411070 1411075) (-940 "REF.spad" 1408781 1408791 1409252 1409257) (-939 "REDORDER.spad" 1407988 1408004 1408771 1408776) (-938 "RECLOS.spad" 1406885 1406904 1407588 1407681) (-937 "REALSOLV.spad" 1406026 1406034 1406875 1406880) (-936 "REAL0Q.spad" 1403325 1403339 1406016 1406021) (-935 "REAL0.spad" 1400170 1400184 1403315 1403320) (-934 "REAL.spad" 1400043 1400051 1400160 1400165) (-933 "RDUCEAST.spad" 1399765 1399773 1400033 1400038) (-932 "RDIV.spad" 1399421 1399445 1399755 1399760) (-931 "RDIST.spad" 1398989 1398999 1399411 1399416) (-930 "RDETRS.spad" 1397854 1397871 1398979 1398984) (-929 "RDETR.spad" 1395994 1396011 1397844 1397849) (-928 "RDEEFS.spad" 1395094 1395110 1395984 1395989) (-927 "RDEEF.spad" 1394105 1394121 1395084 1395089) (-926 "RCFIELD.spad" 1391324 1391332 1394007 1394100) (-925 "RCFIELD.spad" 1388629 1388639 1391314 1391319) (-924 "RCAGG.spad" 1386566 1386576 1388619 1388624) (-923 "RCAGG.spad" 1384404 1384416 1386459 1386464) (-922 "RATRET.spad" 1383765 1383775 1384394 1384399) (-921 "RATFACT.spad" 1383458 1383469 1383755 1383760) (-920 "RANDSRC.spad" 1382778 1382786 1383448 1383453) (-919 "RADUTIL.spad" 1382535 1382543 1382768 1382773) (-918 "RADIX.spad" 1379580 1379593 1381125 1381218) (-917 "RADFF.spad" 1377497 1377533 1377615 1377771) (-916 "RADCAT.spad" 1377093 1377101 1377487 1377492) (-915 "RADCAT.spad" 1376687 1376697 1377083 1377088) (-914 "QUEUE.spad" 1376123 1376133 1376381 1376386) (-913 "QUATCT2.spad" 1375744 1375762 1376113 1376118) (-912 "QUATCAT.spad" 1373915 1373925 1375674 1375739) (-911 "QUATCAT.spad" 1371851 1371863 1373612 1373617) (-910 "QUAT.spad" 1370458 1370468 1370800 1370865) (-909 "QUAGG.spad" 1369314 1369324 1370448 1370453) (-908 "QQUTAST.spad" 1369083 1369091 1369304 1369309) (-907 "QFORM.spad" 1368702 1368716 1369073 1369078) (-906 "QFCAT2.spad" 1368395 1368411 1368692 1368697) (-905 "QFCAT.spad" 1367098 1367108 1368297 1368390) (-904 "QFCAT.spad" 1365434 1365446 1366635 1366640) (-903 "QEQUAT.spad" 1364993 1365001 1365424 1365429) (-902 "QCMPACK.spad" 1359908 1359927 1364983 1364988) (-901 "QALGSET2.spad" 1357904 1357922 1359898 1359903) (-900 "QALGSET.spad" 1354009 1354041 1357818 1357823) (-899 "PWFFINTB.spad" 1351425 1351446 1353999 1354004) (-898 "PUSHVAR.spad" 1350764 1350783 1351415 1351420) (-897 "PTRANFN.spad" 1346900 1346910 1350754 1350759) (-896 "PTPACK.spad" 1343988 1343998 1346890 1346895) (-895 "PTFUNC2.spad" 1343811 1343825 1343978 1343983) (-894 "PTCAT.spad" 1343088 1343098 1343801 1343806) (-893 "PSQFR.spad" 1342403 1342427 1343078 1343083) (-892 "PSEUDLIN.spad" 1341289 1341299 1342393 1342398) (-891 "PSETPK.spad" 1327994 1328010 1341167 1341172) (-890 "PSETCAT.spad" 1322404 1322427 1327984 1327989) (-889 "PSETCAT.spad" 1316778 1316803 1322360 1322365) (-888 "PSCURVE.spad" 1315777 1315785 1316768 1316773) (-887 "PSCAT.spad" 1314560 1314589 1315675 1315772) (-886 "PSCAT.spad" 1313433 1313464 1314550 1314555) (-885 "PRTITION.spad" 1312131 1312139 1313423 1313428) (-884 "PRTDAST.spad" 1311850 1311858 1312121 1312126) (-883 "PRS.spad" 1301468 1301485 1311806 1311811) (-882 "PRQAGG.spad" 1300925 1300935 1301458 1301463) (-881 "PROPLOG.spad" 1300529 1300537 1300915 1300920) (-880 "PROPFUN2.spad" 1300152 1300165 1300519 1300524) (-879 "PROPFUN1.spad" 1299558 1299569 1300142 1300147) (-878 "PROPFRML.spad" 1298126 1298137 1299548 1299553) (-877 "PROPERTY.spad" 1297622 1297630 1298116 1298121) (-876 "PRODUCT.spad" 1295319 1295331 1295603 1295658) (-875 "PRINT.spad" 1295071 1295079 1295309 1295314) (-874 "PRIMES.spad" 1293332 1293342 1295061 1295066) (-873 "PRIMELT.spad" 1291453 1291467 1293322 1293327) (-872 "PRIMCAT.spad" 1291096 1291104 1291443 1291448) (-871 "PRIMARR2.spad" 1289863 1289875 1291086 1291091) (-870 "PRIMARR.spad" 1288615 1288625 1288785 1288790) (-869 "PREASSOC.spad" 1287997 1288009 1288605 1288610) (-868 "PR.spad" 1286515 1286527 1287214 1287341) (-867 "PPCURVE.spad" 1285652 1285660 1286505 1286510) (-866 "PORTNUM.spad" 1285443 1285451 1285642 1285647) (-865 "POLYROOT.spad" 1284292 1284314 1285399 1285404) (-864 "POLYLIFT.spad" 1283557 1283580 1284282 1284287) (-863 "POLYCATQ.spad" 1281683 1281705 1283547 1283552) (-862 "POLYCAT.spad" 1275185 1275206 1281551 1281678) (-861 "POLYCAT.spad" 1268207 1268230 1274575 1274580) (-860 "POLY2UP.spad" 1267659 1267673 1268197 1268202) (-859 "POLY2.spad" 1267256 1267268 1267649 1267654) (-858 "POLY.spad" 1264924 1264934 1265439 1265566) (-857 "POLUTIL.spad" 1263889 1263918 1264880 1264885) (-856 "POLTOPOL.spad" 1262637 1262652 1263879 1263884) (-855 "POINT.spad" 1261217 1261227 1261304 1261309) (-854 "PNTHEORY.spad" 1257919 1257927 1261207 1261212) (-853 "PMTOOLS.spad" 1256694 1256708 1257909 1257914) (-852 "PMSYM.spad" 1256243 1256253 1256684 1256689) (-851 "PMQFCAT.spad" 1255834 1255848 1256233 1256238) (-850 "PMPREDFS.spad" 1255296 1255318 1255824 1255829) (-849 "PMPRED.spad" 1254783 1254797 1255286 1255291) (-848 "PMPLCAT.spad" 1253860 1253878 1254712 1254717) (-847 "PMLSAGG.spad" 1253445 1253459 1253850 1253855) (-846 "PMKERNEL.spad" 1253024 1253036 1253435 1253440) (-845 "PMINS.spad" 1252604 1252614 1253014 1253019) (-844 "PMFS.spad" 1252181 1252199 1252594 1252599) (-843 "PMDOWN.spad" 1251471 1251485 1252171 1252176) (-842 "PMASSFS.spad" 1250446 1250462 1251461 1251466) (-841 "PMASS.spad" 1249464 1249472 1250436 1250441) (-840 "PLOTTOOL.spad" 1249244 1249252 1249454 1249459) (-839 "PLOT3D.spad" 1245708 1245716 1249234 1249239) (-838 "PLOT1.spad" 1244881 1244891 1245698 1245703) (-837 "PLOT.spad" 1239804 1239812 1244871 1244876) (-836 "PLEQN.spad" 1227206 1227233 1239794 1239799) (-835 "PINTERPA.spad" 1226990 1227006 1227196 1227201) (-834 "PINTERP.spad" 1226612 1226631 1226980 1226985) (-833 "PID.spad" 1225586 1225594 1226538 1226607) (-832 "PICOERCE.spad" 1225243 1225253 1225576 1225581) (-831 "PI.spad" 1224860 1224868 1225217 1225238) (-830 "PGROEB.spad" 1223469 1223483 1224850 1224855) (-829 "PGE.spad" 1215142 1215150 1223459 1223464) (-828 "PGCD.spad" 1214096 1214113 1215132 1215137) (-827 "PFRPAC.spad" 1213245 1213255 1214086 1214091) (-826 "PFR.spad" 1209948 1209958 1213147 1213240) (-825 "PFOTOOLS.spad" 1209206 1209222 1209938 1209943) (-824 "PFOQ.spad" 1208576 1208594 1209196 1209201) (-823 "PFO.spad" 1207995 1208022 1208566 1208571) (-822 "PFECAT.spad" 1205705 1205713 1207921 1207990) (-821 "PFECAT.spad" 1203443 1203453 1205661 1205666) (-820 "PFBRU.spad" 1201331 1201343 1203433 1203438) (-819 "PFBR.spad" 1198891 1198914 1201321 1201326) (-818 "PF.spad" 1198465 1198477 1198696 1198789) (-817 "PERMGRP.spad" 1193235 1193245 1198455 1198460) (-816 "PERMCAT.spad" 1191896 1191906 1193215 1193230) (-815 "PERMAN.spad" 1190452 1190466 1191886 1191891) (-814 "PERM.spad" 1186262 1186272 1190285 1190300) (-813 "PENDTREE.spad" 1185615 1185625 1185895 1185900) (-812 "PDSPC.spad" 1184428 1184438 1185605 1185610) (-811 "PDSPC.spad" 1183239 1183251 1184418 1184423) (-810 "PDRING.spad" 1183081 1183091 1183219 1183234) (-809 "PDMOD.spad" 1182897 1182909 1183049 1183076) (-808 "PDECOMP.spad" 1182367 1182384 1182887 1182892) (-807 "PDDOM.spad" 1181805 1181818 1182357 1182362) (-806 "PDDOM.spad" 1181241 1181256 1181795 1181800) (-805 "PCOMP.spad" 1181094 1181107 1181231 1181236) (-804 "PBWLB.spad" 1179692 1179709 1181084 1181089) (-803 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1159949 1159957 1160527 1160532) (-784 "PALETTE.spad" 1159063 1159071 1159939 1159944) (-783 "PAIR.spad" 1158137 1158150 1158706 1158711) (-782 "PADICRC.spad" 1155542 1155560 1156705 1156798) (-781 "PADICRAT.spad" 1153602 1153614 1153815 1153908) (-780 "PADICCT.spad" 1152151 1152163 1153528 1153597) (-779 "PADIC.spad" 1151854 1151866 1152077 1152146) (-778 "PADEPAC.spad" 1150543 1150562 1151844 1151849) (-777 "PADE.spad" 1149295 1149311 1150533 1150538) (-776 "OWP.spad" 1148543 1148573 1149153 1149220) (-775 "OVERSET.spad" 1148116 1148124 1148533 1148538) (-774 "OVAR.spad" 1147897 1147920 1148106 1148111) (-773 "OUTFORM.spad" 1137305 1137313 1147887 1147892) (-772 "OUTBFILE.spad" 1136739 1136747 1137295 1137300) (-771 "OUTBCON.spad" 1135809 1135817 1136729 1136734) (-770 "OUTBCON.spad" 1134877 1134887 1135799 1135804) (-769 "OUT.spad" 1133995 1134003 1134867 1134872) (-768 "OSI.spad" 1133470 1133478 1133985 1133990) (-767 "OSGROUP.spad" 1133388 1133396 1133460 1133465) (-766 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1110522 1110527) (-747 "OPERCAT.spad" 1109462 1109474 1109988 1109993) (-746 "OP.spad" 1109204 1109214 1109284 1109351) (-745 "ONECOMP2.spad" 1108628 1108640 1109194 1109199) (-744 "ONECOMP.spad" 1107434 1107444 1108236 1108265) (-743 "OMSAGG.spad" 1107246 1107256 1107414 1107429) (-742 "OMLO.spad" 1106679 1106691 1107132 1107171) (-741 "OINTDOM.spad" 1106442 1106450 1106605 1106674) (-740 "OFMONOID.spad" 1104581 1104591 1106398 1106403) (-739 "ODVAR.spad" 1103842 1103852 1104571 1104576) (-738 "ODR.spad" 1103486 1103512 1103654 1103803) (-737 "ODPOL.spad" 1101134 1101144 1101474 1101601) (-736 "ODP.spad" 1090621 1090641 1090994 1091079) (-735 "ODETOOLS.spad" 1089270 1089289 1090611 1090616) (-734 "ODESYS.spad" 1086964 1086981 1089260 1089265) (-733 "ODERTRIC.spad" 1082997 1083014 1086921 1086926) (-732 "ODERED.spad" 1082396 1082420 1082987 1082992) (-731 "ODERAT.spad" 1080029 1080046 1082386 1082391) (-730 "ODEPRRIC.spad" 1077122 1077144 1080019 1080024) (-729 "ODEPRIM.spad" 1074520 1074542 1077112 1077117) (-728 "ODEPAL.spad" 1073906 1073930 1074510 1074515) (-727 "ODEINT.spad" 1073341 1073357 1073896 1073901) (-726 "ODEEF.spad" 1068836 1068852 1073331 1073336) (-725 "ODECONST.spad" 1068381 1068399 1068826 1068831) (-724 "OCTCT2.spad" 1068022 1068040 1068371 1068376) (-723 "OCT.spad" 1066337 1066347 1067051 1067090) (-722 "OCAMON.spad" 1066185 1066193 1066327 1066332) (-721 "OC.spad" 1063981 1063991 1066141 1066180) (-720 "OC.spad" 1061516 1061528 1063678 1063683) (-719 "OASGP.spad" 1061331 1061339 1061506 1061511) (-718 "OAMONS.spad" 1060853 1060861 1061321 1061326) (-717 "OAMON.spad" 1060611 1060619 1060843 1060848) (-716 "OAMON.spad" 1060367 1060377 1060601 1060606) (-715 "OAGROUP.spad" 1059905 1059913 1060357 1060362) (-714 "OAGROUP.spad" 1059441 1059451 1059895 1059900) (-713 "NUMTUBE.spad" 1059032 1059048 1059431 1059436) (-712 "NUMQUAD.spad" 1047008 1047016 1059022 1059027) (-711 "NUMODE.spad" 1038360 1038368 1046998 1047003) (-710 "NUMFMT.spad" 1037200 1037208 1038350 1038355) (-709 "NUMERIC.spad" 1029315 1029325 1037006 1037011) (-708 "NTSCAT.spad" 1027845 1027861 1029305 1029310) (-707 "NTPOLFN.spad" 1027422 1027432 1027788 1027793) (-706 "NSUP2.spad" 1026814 1026826 1027412 1027417) (-705 "NSUP.spad" 1020251 1020261 1024671 1024824) (-704 "NSMP.spad" 1017163 1017182 1017455 1017582) (-703 "NREP.spad" 1015565 1015579 1017153 1017158) (-702 "NPCOEF.spad" 1014811 1014831 1015555 1015560) (-701 "NORMRETR.spad" 1014409 1014448 1014801 1014806) (-700 "NORMPK.spad" 1012351 1012370 1014399 1014404) (-699 "NORMMA.spad" 1012039 1012065 1012341 1012346) (-698 "NONE1.spad" 1011715 1011725 1012029 1012034) (-697 "NONE.spad" 1011456 1011464 1011705 1011710) (-696 "NODE1.spad" 1010943 1010959 1011446 1011451) (-695 "NNI.spad" 1009838 1009846 1010917 1010938) (-694 "NLINSOL.spad" 1008464 1008474 1009828 1009833) (-693 "NFINTBAS.spad" 1006024 1006041 1008454 1008459) (-692 "NETCLT.spad" 1005998 1006009 1006014 1006019) (-691 "NCODIV.spad" 1004222 1004238 1005988 1005993) (-690 "NCNTFRAC.spad" 1003864 1003878 1004212 1004217) (-689 "NCEP.spad" 1002030 1002044 1003854 1003859) (-688 "NASRING.spad" 1001634 1001642 1002020 1002025) (-687 "NASRING.spad" 1001236 1001246 1001624 1001629) (-686 "NARNG.spad" 1000636 1000644 1001226 1001231) (-685 "NARNG.spad" 1000034 1000044 1000626 1000631) (-684 "NAALG.spad" 999599 999609 1000002 1000029) (-683 "NAALG.spad" 999184 999196 999589 999594) (-682 "MULTSQFR.spad" 996142 996159 999174 999179) (-681 "MULTFACT.spad" 995525 995542 996132 996137) (-680 "MTSCAT.spad" 993619 993640 995423 995520) (-679 "MTHING.spad" 993278 993288 993609 993614) (-678 "MSYSCMD.spad" 992712 992720 993268 993273) (-677 "MSETAGG.spad" 992569 992579 992692 992707) (-676 "MSET.spad" 990379 990389 992126 992141) (-675 "MRING.spad" 987356 987368 990087 990154) (-674 "MRF2.spad" 986918 986932 987346 987351) (-673 "MRATFAC.spad" 986464 986481 986908 986913) (-672 "MPRFF.spad" 984504 984523 986454 986459) (-671 "MPOLY.spad" 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965337 965342) (-650 "MODMON.spad" 962148 962160 962863 963016) (-649 "MODFIELD.spad" 961510 961549 962050 962143) (-648 "MMLFORM.spad" 960370 960378 961500 961505) (-647 "MMAP.spad" 960112 960146 960360 960365) (-646 "MLO.spad" 958571 958581 960068 960107) (-645 "MLIFT.spad" 957183 957200 958561 958566) (-644 "MKUCFUNC.spad" 956718 956736 957173 957178) (-643 "MKRECORD.spad" 956306 956319 956708 956713) (-642 "MKFUNC.spad" 955713 955723 956296 956301) (-641 "MKFLCFN.spad" 954681 954691 955703 955708) (-640 "MKBCFUNC.spad" 954176 954194 954671 954676) (-639 "MHROWRED.spad" 952687 952697 954166 954171) (-638 "MFINFACT.spad" 952087 952109 952677 952682) (-637 "MESH.spad" 949882 949890 952077 952082) (-636 "MDDFACT.spad" 948101 948111 949872 949877) (-635 "MDAGG.spad" 947402 947412 948091 948096) (-634 "MCDEN.spad" 946612 946624 947392 947397) (-633 "MAYBE.spad" 945912 945923 946602 946607) (-632 "MATSTOR.spad" 943228 943238 945902 945907) (-631 "MATRIX.spad" 942029 942039 942513 942518) (-630 "MATLIN.spad" 939397 939421 941913 941918) (-629 "MATCAT2.spad" 938679 938727 939387 939392) (-628 "MATCAT.spad" 930397 930419 938669 938674) (-627 "MATCAT.spad" 921965 921989 930239 930244) (-626 "MAPPKG3.spad" 920880 920894 921955 921960) (-625 "MAPPKG2.spad" 920218 920230 920870 920875) (-624 "MAPPKG1.spad" 919046 919056 920208 920213) (-623 "MAPPAST.spad" 918385 918393 919036 919041) (-622 "MAPHACK3.spad" 918197 918211 918375 918380) (-621 "MAPHACK2.spad" 917966 917978 918187 918192) (-620 "MAPHACK1.spad" 917610 917620 917956 917961) (-619 "MAGMA.spad" 915416 915433 917600 917605) (-618 "MACROAST.spad" 915011 915019 915406 915411) (-617 "LZSTAGG.spad" 912265 912275 915001 915006) (-616 "LZSTAGG.spad" 909517 909529 912255 912260) (-615 "LWORD.spad" 906262 906279 909507 909512) (-614 "LSTAST.spad" 906046 906054 906252 906257) (-613 "LSQM.spad" 904336 904350 904730 904769) (-612 "LSPP.spad" 903871 903888 904326 904331) (-611 "LSMP1.spad" 901714 901728 903861 903866) (-610 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877432) (-589 "LLINSET.spad" 876886 876896 877169 877174) (-588 "LITERAL.spad" 876792 876803 876876 876881) (-587 "LIST3.spad" 876103 876117 876782 876787) (-586 "LIST2MAP.spad" 873030 873042 876093 876098) (-585 "LIST2.spad" 871732 871744 873020 873025) (-584 "LIST.spad" 869311 869321 870654 870659) (-583 "LINSET.spad" 869090 869100 869301 869306) (-582 "LINFORM.spad" 868553 868565 869058 869085) (-581 "LINEXP.spad" 867296 867306 868543 868548) (-580 "LINELT.spad" 866667 866679 867179 867206) (-579 "LINDEP.spad" 865516 865528 866579 866584) (-578 "LINBASIS.spad" 865152 865167 865506 865511) (-577 "LIMITRF.spad" 863099 863109 865142 865147) (-576 "LIMITPS.spad" 862009 862022 863089 863094) (-575 "LIECAT.spad" 861493 861503 861935 862004) (-574 "LIECAT.spad" 861005 861017 861449 861454) (-573 "LIE.spad" 859009 859021 860283 860425) (-572 "LIB.spad" 856832 856840 857278 857283) (-571 "LGROBP.spad" 854185 854204 856822 856827) (-570 "LFCAT.spad" 853244 853252 854175 854180) (-569 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"IDENT.spad" 716395 716403 716733 716738) (-446 "catdef.spad" 716166 716177 716278 716390) (-445 "IDECOMP.spad" 713405 713423 716156 716161) (-444 "IDEAL.spad" 708367 708406 713353 713358) (-443 "ICDEN.spad" 707580 707596 708357 708362) (-442 "ICARD.spad" 706973 706981 707570 707575) (-441 "IBPTOOLS.spad" 705580 705597 706963 706968) (-440 "boolean.spad" 704872 704885 705005 705010) (-439 "IBATOOL.spad" 701857 701876 704862 704867) (-438 "IBACHIN.spad" 700364 700379 701847 701852) (-437 "array2.spad" 699871 699893 700058 700063) (-436 "IARRAY1.spad" 698647 698662 698793 698798) (-435 "IAN.spad" 697029 697037 698478 698571) (-434 "IALGFACT.spad" 696640 696673 697019 697024) (-433 "HYPCAT.spad" 696064 696072 696630 696635) (-432 "HYPCAT.spad" 695486 695496 696054 696059) (-431 "HOSTNAME.spad" 695302 695310 695476 695481) (-430 "HOMOTOP.spad" 695045 695055 695292 695297) (-429 "HOAGG.spad" 694561 694571 695035 695040) (-428 "HOAGG.spad" 693899 693911 694375 694380) (-427 "HEXADEC.spad" 692124 692132 692489 692582) (-426 "HEUGCD.spad" 691215 691226 692114 692119) (-425 "HELLFDIV.spad" 690821 690845 691205 691210) (-424 "HEAP.spad" 690300 690310 690515 690520) (-423 "HEADAST.spad" 689841 689849 690290 690295) (-422 "HDP.spad" 679324 679340 679701 679786) (-421 "HDMP.spad" 676871 676886 677487 677614) (-420 "HB.spad" 675146 675154 676861 676866) (-419 "HASHTBL.spad" 672915 672946 673126 673131) (-418 "HASAST.spad" 672631 672639 672905 672910) (-417 "HACKPI.spad" 672122 672130 672533 672626) (-416 "GTSET.spad" 670910 670926 671617 671622) (-415 "GSTBL.spad" 668716 668751 668890 668895) (-414 "GSERIES.spad" 666088 666115 666907 667056) (-413 "GROUP.spad" 665361 665369 666068 666083) (-412 "GROUP.spad" 664642 664652 665351 665356) (-411 "GROEBSOL.spad" 663136 663157 664632 664637) (-410 "GRMOD.spad" 661717 661729 663126 663131) (-409 "GRMOD.spad" 660296 660310 661707 661712) (-408 "GRIMAGE.spad" 653209 653217 660286 660291) (-407 "GRDEF.spad" 651588 651596 653199 653204) (-406 "GRAY.spad" 650059 650067 651578 651583) (-405 "GRALG.spad" 649154 649166 650049 650054) (-404 "GRALG.spad" 648247 648261 649144 649149) (-403 "GPOLSET.spad" 647566 647589 647778 647783) (-402 "GOSPER.spad" 646843 646861 647556 647561) (-401 "GMODPOL.spad" 645991 646018 646811 646838) (-400 "GHENSEL.spad" 645074 645088 645981 645986) (-399 "GENUPS.spad" 641367 641380 645064 645069) (-398 "GENUFACT.spad" 640944 640954 641357 641362) (-397 "GENPGCD.spad" 640546 640563 640934 640939) (-396 "GENMFACT.spad" 639998 640017 640536 640541) (-395 "GENEEZ.spad" 637957 637970 639988 639993) (-394 "GDMP.spad" 635346 635363 636120 636247) (-393 "GCNAALG.spad" 629269 629296 635140 635207) (-392 "GCDDOM.spad" 628461 628469 629195 629264) (-391 "GCDDOM.spad" 627715 627725 628451 628456) (-390 "GBINTERN.spad" 623735 623773 627705 627710) (-389 "GBF.spad" 619518 619556 623725 623730) (-388 "GBEUCLID.spad" 617400 617438 619508 619513) (-387 "GB.spad" 614926 614964 617356 617361) (-386 "GAUSSFAC.spad" 614239 614247 614916 614921) (-385 "GALUTIL.spad" 612565 612575 614195 614200) (-384 "GALPOLYU.spad" 611019 611032 612555 612560) (-383 "GALFACTU.spad" 609232 609251 611009 611014) (-382 "GALFACT.spad" 599445 599456 609222 609227) (-381 "FUNDESC.spad" 599123 599131 599435 599440) (-380 "FUNCTION.spad" 598972 598984 599113 599118) (-379 "FT.spad" 597272 597280 598962 598967) (-378 "FSUPFACT.spad" 596186 596205 597222 597227) (-377 "FST.spad" 594272 594280 596176 596181) (-376 "FSRED.spad" 593752 593768 594262 594267) (-375 "FSPRMELT.spad" 592618 592634 593709 593714) (-374 "FSPECF.spad" 590709 590725 592608 592613) (-373 "FSINT.spad" 590369 590385 590699 590704) (-372 "FSERIES.spad" 589560 589572 590189 590288) (-371 "FSCINT.spad" 588877 588893 589550 589555) (-370 "FSAGG2.spad" 587612 587628 588867 588872) (-369 "FSAGG.spad" 586753 586763 587592 587607) (-368 "FSAGG.spad" 585832 585844 586673 586678) (-367 "FS2UPS.spad" 580347 580381 585822 585827) (-366 "FS2EXPXP.spad" 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"FPC.spad" 533899 533907 534755 534848) (-344 "FPC.spad" 533031 533041 533889 533894) (-343 "FPATMAB.spad" 532793 532803 533021 533026) (-342 "FPARFRAC.spad" 531635 531652 532783 532788) (-341 "FORDER.spad" 531326 531350 531625 531630) (-340 "FNLA.spad" 530750 530772 531294 531321) (-339 "FNCAT.spad" 529345 529353 530740 530745) (-338 "FNAME.spad" 529237 529245 529335 529340) (-337 "FMONOID.spad" 528918 528928 529193 529198) (-336 "FMONCAT.spad" 526087 526097 528908 528913) (-335 "FMCAT.spad" 523763 523781 526055 526082) (-334 "FM1.spad" 523128 523140 523697 523724) (-333 "FM.spad" 522743 522755 522982 523009) (-332 "FLOATRP.spad" 520486 520500 522733 522738) (-331 "FLOATCP.spad" 517925 517939 520476 520481) (-330 "FLOAT.spad" 515016 515024 517791 517920) (-329 "FLINEXP.spad" 514738 514748 515006 515011) (-328 "FLINEXP.spad" 514417 514429 514687 514692) (-327 "FLASORT.spad" 513743 513755 514407 514412) (-326 "FLALG.spad" 511413 511432 513669 513738) (-325 "FLAGG2.spad" 510130 510146 511403 511408) (-324 "FLAGG.spad" 507206 507216 510120 510125) (-323 "FLAGG.spad" 504147 504159 507063 507068) (-322 "FINRALG.spad" 502232 502245 504103 504142) (-321 "FINRALG.spad" 500243 500258 502116 502121) (-320 "FINITE.spad" 499395 499403 500233 500238) (-319 "FINITE.spad" 498545 498555 499385 499390) (-318 "aggcat.spad" 495475 495485 498535 498540) (-317 "FINAGG.spad" 492370 492382 495432 495437) (-316 "FINAALG.spad" 481555 481565 492312 492365) (-315 "FINAALG.spad" 470752 470764 481511 481516) (-314 "FILECAT.spad" 469286 469303 470742 470747) (-313 "FILE.spad" 468869 468879 469276 469281) (-312 "FIELD.spad" 468275 468283 468771 468864) (-311 "FIELD.spad" 467767 467777 468265 468270) (-310 "FGROUP.spad" 466430 466440 467747 467762) (-309 "FGLMICPK.spad" 465225 465240 466420 466425) (-308 "FFX.spad" 464611 464626 464944 465037) (-307 "FFSLPE.spad" 464122 464143 464601 464606) (-306 "FFPOLY2.spad" 463182 463199 464112 464117) (-305 "FFPOLY.spad" 454524 454535 463172 463177) (-304 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415969) (-283 "FDIV.spad" 415088 415112 415620 415625) (-282 "FCTRDATA.spad" 414096 414104 415078 415083) (-281 "FCOMP.spad" 413475 413485 414086 414091) (-280 "FAXF.spad" 406510 406524 413377 413470) (-279 "FAXF.spad" 399597 399613 406466 406471) (-278 "FARRAY.spad" 397486 397496 398519 398524) (-277 "FAMR.spad" 395630 395642 397384 397481) (-276 "FAMR.spad" 393758 393772 395514 395519) (-275 "FAMONOID.spad" 393442 393452 393712 393717) (-274 "FAMONC.spad" 391762 391774 393432 393437) (-273 "FAGROUP.spad" 391402 391412 391658 391685) (-272 "FACUTIL.spad" 389614 389631 391392 391397) (-271 "FACTFUNC.spad" 388816 388826 389604 389609) (-270 "EXPUPXS.spad" 385708 385731 387007 387156) (-269 "EXPRTUBE.spad" 382996 383004 385698 385703) (-268 "EXPRODE.spad" 380164 380180 382986 382991) (-267 "EXPR2UPS.spad" 376286 376299 380154 380159) (-266 "EXPR2.spad" 375991 376003 376276 376281) (-265 "EXPR.spad" 371636 371646 372350 372637) (-264 "EXPEXPAN.spad" 368581 368606 369213 369306) (-263 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"ELTAGG.spad" 326432 326453 328170 328175) (-241 "ELTAB.spad" 325907 325920 326422 326427) (-240 "ELFUTS.spad" 325342 325361 325897 325902) (-239 "ELEMFUN.spad" 325031 325039 325332 325337) (-238 "ELEMFUN.spad" 324718 324728 325021 325026) (-237 "ELAGG.spad" 322699 322709 324708 324713) (-236 "ELAGG.spad" 320609 320621 322620 322625) (-235 "ELABOR.spad" 319955 319963 320599 320604) (-234 "ELABEXPR.spad" 318887 318895 319945 319950) (-233 "EFUPXS.spad" 315663 315693 318843 318848) (-232 "EFULS.spad" 312499 312522 315619 315624) (-231 "EFSTRUC.spad" 310514 310530 312489 312494) (-230 "EF.spad" 305290 305306 310504 310509) (-229 "EAB.spad" 303590 303598 305280 305285) (-228 "DVARCAT.spad" 300596 300606 303580 303585) (-227 "DVARCAT.spad" 297600 297612 300586 300591) (-226 "DSMP.spad" 295333 295347 295638 295765) (-225 "DSEXT.spad" 294635 294645 295323 295328) (-224 "DSEXT.spad" 293857 293869 294547 294552) (-223 "DROPT1.spad" 293522 293532 293847 293852) (-222 "DROPT0.spad" 288387 288395 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 0ea97bbf..f41447fd 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,299 +1,299 @@
 
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. -104) T) ((-1204 . -590) 200475) ((-1204 . -1194) 200459) ((-1204 . -654) 200429) ((-1204 . -582) 200399) ((-1204 . -968) 200383) ((-1204 . -963) 200367) ((-1204 . -82) 200346) ((-1204 . -38) 200316) ((-1204 . -1199) 200295) ((-1203 . -961) T) ((-1203 . -663) T) ((-1203 . -1061) T) ((-1203 . -1025) T) ((-1203 . -970) T) ((-1203 . -21) T) ((-1203 . -588) 200254) ((-1203 . -23) T) ((-1203 . -1013) T) ((-1203 . -552) 200236) ((-1203 . -1129) T) ((-1203 . -13) T) ((-1203 . -72) T) ((-1203 . -25) T) ((-1203 . -104) T) ((-1203 . -590) 200210) ((-1203 . -555) 200166) ((-1203 . -1194) 200150) ((-1203 . -654) 200120) ((-1203 . -582) 200090) ((-1203 . -968) 200074) ((-1203 . -963) 200058) ((-1203 . -82) 200037) ((-1203 . -38) 200007) ((-1203 . -335) 199986) ((-1203 . -950) 199970) ((-1201 . -1202) 199946) ((-1201 . -950) 199920) ((-1201 . -555) 199866) ((-1201 . -961) T) ((-1201 . -663) T) ((-1201 . -1061) T) ((-1201 . -1025) T) ((-1201 . -970) T) ((-1201 . -21) T) ((-1201 . -588) 199825) ((-1201 . -23) T) ((-1201 . -1013) T) ((-1201 . -552) 199807) ((-1201 . -1129) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -590) 199781) ((-1201 . -1194) 199765) ((-1201 . -654) 199735) ((-1201 . -582) 199705) ((-1201 . -968) 199689) ((-1201 . -963) 199673) ((-1201 . -82) 199652) ((-1201 . -38) 199622) ((-1201 . -1199) 199598) ((-1200 . -1202) 199577) ((-1200 . -950) 199534) ((-1200 . -555) 199463) ((-1200 . -961) T) ((-1200 . -663) T) ((-1200 . -1061) T) ((-1200 . -1025) T) ((-1200 . -970) T) ((-1200 . -21) T) ((-1200 . -588) 199422) ((-1200 . -23) T) ((-1200 . -1013) T) ((-1200 . -552) 199404) ((-1200 . -1129) T) ((-1200 . -13) T) ((-1200 . -72) T) ((-1200 . -25) T) ((-1200 . -104) T) ((-1200 . -590) 199378) ((-1200 . -1194) 199362) ((-1200 . -654) 199332) ((-1200 . -582) 199302) ((-1200 . -968) 199286) ((-1200 . -963) 199270) ((-1200 . -82) 199249) ((-1200 . -38) 199219) ((-1200 . -1199) 199198) ((-1200 . -335) 199170) ((-1195 . -335) 199142) ((-1195 . -555) 199091) ((-1195 . -950) 199068) ((-1195 . -582) 199038) ((-1195 . -654) 199008) ((-1195 . -590) 198982) ((-1195 . -588) 198941) ((-1195 . -104) T) ((-1195 . -25) T) ((-1195 . -72) T) ((-1195 . -13) T) ((-1195 . -1129) T) ((-1195 . -552) 198923) ((-1195 . -1013) T) ((-1195 . -23) T) ((-1195 . -21) T) ((-1195 . -968) 198907) ((-1195 . -963) 198891) ((-1195 . -82) 198870) ((-1195 . -1202) 198849) ((-1195 . -961) T) ((-1195 . -663) T) ((-1195 . -1061) T) ((-1195 . -1025) T) ((-1195 . -970) T) ((-1195 . -1194) 198833) ((-1195 . -38) 198803) ((-1195 . -1199) 198782) ((-1193 . -1124) 198751) ((-1193 . -1035) 198735) ((-1193 . -552) 198697) ((-1193 . -124) 198681) ((-1193 . -34) T) ((-1193 . -13) T) ((-1193 . -1129) T) ((-1193 . -72) T) ((-1193 . -260) 198619) ((-1193 . -455) 198552) ((-1193 . -1013) T) ((-1193 . -429) 198536) ((-1193 . -553) 198497) ((-1193 . -318) 198481) ((-1193 . -889) 198450) ((-1192 . -961) T) ((-1192 . -663) T) ((-1192 . -1061) T) ((-1192 . 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T) ((-1169 . -186) 196798) ((-1169 . -13) T) ((-1169 . -1129) T) ((-1169 . -189) 196757) ((-1169 . -241) 196722) ((-1169 . -809) 196635) ((-1169 . -806) 196523) ((-1169 . -811) 196436) ((-1169 . -886) 196406) ((-1169 . -38) 196303) ((-1169 . -82) 196168) ((-1169 . -963) 196054) ((-1169 . -968) 195940) ((-1169 . -582) 195837) ((-1169 . -654) 195734) ((-1169 . -118) 195713) ((-1169 . -120) 195692) ((-1169 . -146) 195646) ((-1169 . -495) 195625) ((-1169 . -246) 195604) ((-1169 . -47) 195581) ((-1169 . -1158) 195558) ((-1169 . -35) 195524) ((-1169 . -66) 195490) ((-1169 . -239) 195456) ((-1169 . -433) 195422) ((-1169 . -1118) 195388) ((-1169 . -1115) 195354) ((-1169 . -915) 195320) ((-1166 . -277) 195264) ((-1166 . -950) 195230) ((-1166 . -355) 195196) ((-1166 . -38) 195053) ((-1166 . -555) 194927) ((-1166 . -590) 194816) ((-1166 . -588) 194690) ((-1166 . -970) T) ((-1166 . -1025) T) ((-1166 . -1061) T) ((-1166 . -663) T) ((-1166 . -961) T) ((-1166 . -82) 194540) ((-1166 . -963) 194429) 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T) ((-1160 . -663) T) ((-1160 . -961) T) ((-1160 . -82) 189958) ((-1160 . -963) 189799) ((-1160 . -968) 189640) ((-1160 . -21) T) ((-1160 . -23) T) ((-1160 . -1013) T) ((-1160 . -552) 189622) ((-1160 . -1129) T) ((-1160 . -13) T) ((-1160 . -72) T) ((-1160 . -25) T) ((-1160 . -104) T) ((-1160 . -246) 189576) ((-1160 . -201) 189555) ((-1160 . -915) 189521) ((-1160 . -1115) 189487) ((-1160 . -1118) 189453) ((-1160 . -433) 189419) ((-1160 . -239) 189385) ((-1160 . -66) 189351) ((-1160 . -35) 189317) ((-1160 . -1158) 189287) ((-1160 . -47) 189257) ((-1160 . -120) 189236) ((-1160 . -118) 189215) ((-1160 . -886) 189178) ((-1160 . -811) 189084) ((-1160 . -806) 188965) ((-1160 . -809) 188871) ((-1160 . -241) 188829) ((-1160 . -189) 188781) ((-1160 . -186) 188727) ((-1160 . -190) 188679) ((-1160 . -1162) 188663) ((-1160 . -950) 188598) ((-1148 . -1155) 188582) ((-1148 . -1066) 188560) ((-1148 . -553) NIL) ((-1148 . -260) 188547) ((-1148 . -455) 188495) ((-1148 . -277) 188472) ((-1148 . -950) 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. -1129) T) ((-1148 . -189) T) ((-1148 . -225) 185898) ((-1148 . -184) 185882) ((-1146 . -1006) 185866) ((-1146 . -557) 185850) ((-1146 . -1013) 185828) ((-1146 . -552) 185795) ((-1146 . -1129) 185773) ((-1146 . -13) 185751) ((-1146 . -72) 185729) ((-1146 . -1007) 185686) ((-1144 . -1143) 185665) ((-1144 . -915) 185631) ((-1144 . -1115) 185597) ((-1144 . -1118) 185563) ((-1144 . -433) 185529) ((-1144 . -239) 185495) ((-1144 . -66) 185461) ((-1144 . -35) 185427) ((-1144 . -1158) 185404) ((-1144 . -47) 185381) ((-1144 . -555) 185136) ((-1144 . -654) 184956) ((-1144 . -582) 184776) ((-1144 . -590) 184587) ((-1144 . -588) 184445) ((-1144 . -968) 184259) ((-1144 . -963) 184073) ((-1144 . -82) 183861) ((-1144 . -38) 183681) ((-1144 . -886) 183651) ((-1144 . -241) 183551) ((-1144 . -1141) 183535) ((-1144 . -970) T) ((-1144 . -1025) T) ((-1144 . -1061) T) ((-1144 . -663) T) ((-1144 . -961) T) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1013) T) ((-1144 . -552) 183517) ((-1144 . -1129) T) ((-1144 . -13) T) ((-1144 . -72) T) ((-1144 . -25) T) ((-1144 . -104) T) ((-1144 . -118) 183445) ((-1144 . -120) 183327) ((-1144 . -553) 183000) ((-1144 . -184) 182970) ((-1144 . -809) 182824) ((-1144 . -811) 182624) ((-1144 . -806) 182422) ((-1144 . -225) 182392) ((-1144 . -189) 182254) ((-1144 . -186) 182110) ((-1144 . -190) 182018) ((-1144 . -312) 181997) ((-1144 . -1134) 181976) ((-1144 . -832) 181955) ((-1144 . -495) 181909) ((-1144 . -146) 181843) ((-1144 . -392) 181822) ((-1144 . -258) 181801) ((-1144 . -246) 181755) ((-1144 . -201) 181734) ((-1144 . -288) 181704) ((-1144 . -455) 181564) ((-1144 . -260) 181503) ((-1144 . -329) 181473) ((-1144 . -580) 181381) ((-1144 . -343) 181351) ((-1144 . -796) 181224) ((-1144 . -740) 181177) ((-1144 . -714) 181130) ((-1144 . -716) 181083) ((-1144 . -756) 180985) ((-1144 . -759) 180887) ((-1144 . -718) 180840) ((-1144 . -721) 180793) ((-1144 . -755) 180746) ((-1144 . -794) 180716) ((-1144 . -821) 180669) ((-1144 . -933) 180622) ((-1144 . -950) 180411) ((-1144 . -1066) 180363) ((-1144 . -904) 180333) ((-1139 . -1143) 180294) ((-1139 . -915) 180260) ((-1139 . -1115) 180226) ((-1139 . -1118) 180192) ((-1139 . -433) 180158) ((-1139 . -239) 180124) ((-1139 . -66) 180090) ((-1139 . -35) 180056) ((-1139 . -1158) 180033) ((-1139 . -47) 180010) ((-1139 . -555) 179811) ((-1139 . -654) 179613) ((-1139 . -582) 179415) ((-1139 . -590) 179270) ((-1139 . -588) 179110) ((-1139 . -968) 178906) ((-1139 . -963) 178702) ((-1139 . -82) 178454) ((-1139 . -38) 178256) ((-1139 . -886) 178226) ((-1139 . -241) 178054) ((-1139 . -1141) 178038) ((-1139 . -970) T) ((-1139 . -1025) T) ((-1139 . -1061) T) ((-1139 . -663) T) ((-1139 . -961) T) ((-1139 . -21) T) ((-1139 . -23) T) ((-1139 . -1013) T) ((-1139 . -552) 178020) ((-1139 . -1129) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -25) T) ((-1139 . -104) T) ((-1139 . -118) 177930) ((-1139 . -120) 177840) ((-1139 . -553) NIL) ((-1139 . -184) 177792) ((-1139 . -809) 177628) ((-1139 . -811) 177392) ((-1139 . -806) 177131) ((-1139 . -225) 177083) ((-1139 . -189) 176909) ((-1139 . -186) 176729) ((-1139 . -190) 176619) ((-1139 . -312) 176598) ((-1139 . -1134) 176577) ((-1139 . -832) 176556) ((-1139 . -495) 176510) ((-1139 . -146) 176444) ((-1139 . -392) 176423) ((-1139 . -258) 176402) ((-1139 . -246) 176356) ((-1139 . -201) 176335) ((-1139 . -288) 176287) ((-1139 . -455) 176021) ((-1139 . -260) 175906) ((-1139 . -329) 175858) ((-1139 . -580) 175810) ((-1139 . -343) 175762) ((-1139 . -796) NIL) ((-1139 . -740) NIL) ((-1139 . -714) NIL) ((-1139 . -716) NIL) ((-1139 . -756) NIL) ((-1139 . -759) NIL) ((-1139 . -718) NIL) ((-1139 . -721) NIL) ((-1139 . -755) NIL) ((-1139 . -794) 175714) ((-1139 . -821) NIL) ((-1139 . -933) NIL) ((-1139 . -950) 175680) ((-1139 . -1066) NIL) ((-1139 . -904) 175632) ((-1138 . -752) T) ((-1138 . -759) T) ((-1138 . -756) T) ((-1138 . -1013) T) ((-1138 . -552) 175614) ((-1138 . -1129) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -604) T) ((-1137 . -752) T) ((-1137 . -759) T) ((-1137 . -756) T) ((-1137 . -1013) T) ((-1137 . -552) 175596) ((-1137 . -1129) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -604) T) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1013) T) ((-1136 . -552) 175578) ((-1136 . -1129) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1013) T) ((-1135 . -552) 175560) ((-1135 . -1129) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -320) T) ((-1135 . -604) T) ((-1130 . -995) T) ((-1130 . -430) 175541) ((-1130 . -552) 175507) ((-1130 . -555) 175488) ((-1130 . -1013) T) ((-1130 . -1129) T) ((-1130 . -13) T) ((-1130 . -72) T) ((-1130 . -64) T) ((-1127 . -430) 175465) ((-1127 . -552) 175406) ((-1127 . -555) 175383) ((-1127 . -1013) 175361) ((-1127 . -1129) 175339) ((-1127 . -13) 175317) ((-1127 . -72) 175295) ((-1122 . -679) 175271) ((-1122 . -35) 175237) ((-1122 . -66) 175203) ((-1122 . -239) 175169) ((-1122 . -433) 175135) ((-1122 . -1118) 175101) ((-1122 . -1115) 175067) ((-1122 . -915) 175033) ((-1122 . -47) 175002) ((-1122 . -38) 174899) ((-1122 . -582) 174796) ((-1122 . -654) 174693) ((-1122 . -555) 174575) ((-1122 . -246) 174554) ((-1122 . -495) 174533) ((-1122 . -82) 174398) ((-1122 . -963) 174284) ((-1122 . -968) 174170) ((-1122 . -146) 174124) ((-1122 . -120) 174103) ((-1122 . -118) 174082) ((-1122 . -590) 174007) ((-1122 . -588) 173917) ((-1122 . -886) 173878) ((-1122 . -811) 173859) ((-1122 . -1129) T) ((-1122 . -13) T) ((-1122 . -806) 173838) ((-1122 . -961) T) ((-1122 . -663) T) ((-1122 . -1061) T) ((-1122 . -1025) T) ((-1122 . -970) T) ((-1122 . -21) T) ((-1122 . -23) T) ((-1122 . -1013) T) ((-1122 . -552) 173820) ((-1122 . -72) T) ((-1122 . -25) T) ((-1122 . -104) T) ((-1122 . -809) 173801) ((-1122 . -455) 173768) ((-1122 . -260) 173755) ((-1116 . -923) 173739) ((-1116 . -34) T) ((-1116 . -13) T) ((-1116 . -1129) T) ((-1116 . -72) 173693) ((-1116 . -552) 173628) ((-1116 . -260) 173566) ((-1116 . -455) 173499) ((-1116 . -1013) 173477) ((-1116 . -429) 173461) ((-1116 . -318) 173445) ((-1116 . -1035) 173429) ((-1111 . -314) 173403) ((-1111 . -72) T) ((-1111 . -13) T) ((-1111 . -1129) T) ((-1111 . -552) 173385) ((-1111 . -1013) T) ((-1109 . -1013) T) ((-1109 . -552) 173367) ((-1109 . -1129) T) ((-1109 . -13) T) ((-1109 . -72) T) ((-1109 . -555) 173349) ((-1104 . -747) 173333) ((-1104 . -72) T) ((-1104 . -13) T) ((-1104 . -1129) T) ((-1104 . -552) 173315) ((-1104 . -1013) T) ((-1102 . -1107) 173294) ((-1102 . -183) 173242) ((-1102 . -76) 173190) ((-1102 . -1035) 173125) ((-1102 . -124) 173073) ((-1102 . -553) NIL) ((-1102 . -193) 173021) ((-1102 . -538) 173000) ((-1102 . -260) 172798) ((-1102 . -455) 172550) ((-1102 . -429) 172485) ((-1102 . -241) 172464) ((-1102 . -243) 172443) ((-1102 . -549) 172422) ((-1102 . -1013) T) ((-1102 . -552) 172404) ((-1102 . -72) T) ((-1102 . -1129) T) ((-1102 . -13) T) ((-1102 . -34) T) ((-1102 . -318) 172352) ((-1098 . -1013) T) ((-1098 . -552) 172334) ((-1098 . -1129) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1097 . -752) T) ((-1097 . -759) T) ((-1097 . -756) T) ((-1097 . -1013) T) ((-1097 . -552) 172316) ((-1097 . -1129) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1097 . -604) T) ((-1096 . -752) T) ((-1096 . -759) T) ((-1096 . -756) T) ((-1096 . -1013) T) ((-1096 . -552) 172298) ((-1096 . -1129) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -320) T) ((-1095 . -1175) T) ((-1095 . -1013) T) ((-1095 . -552) 172265) ((-1095 . -1129) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -950) 172201) ((-1095 . -555) 172137) ((-1094 . -552) 172119) ((-1093 . -552) 172101) ((-1092 . -277) 172078) ((-1092 . -950) 171976) ((-1092 . -355) 171960) ((-1092 . -38) 171857) ((-1092 . -555) 171714) ((-1092 . -590) 171639) ((-1092 . -588) 171549) ((-1092 . -970) T) ((-1092 . -1025) T) ((-1092 . -1061) T) ((-1092 . -663) T) ((-1092 . -961) T) ((-1092 . -82) 171414) ((-1092 . -963) 171300) ((-1092 . -968) 171186) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1013) T) ((-1092 . -552) 171168) ((-1092 . -1129) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -582) 171065) ((-1092 . -654) 170962) ((-1092 . -118) 170941) ((-1092 . -120) 170920) ((-1092 . -146) 170874) ((-1092 . -495) 170853) ((-1092 . -246) 170832) ((-1092 . -47) 170809) ((-1090 . -756) T) ((-1090 . -552) 170791) ((-1090 . -1013) T) ((-1090 . -72) T) ((-1090 . -13) T) ((-1090 . -1129) T) ((-1090 . -759) T) ((-1090 . -553) 170713) ((-1090 . -555) 170679) ((-1090 . -950) 170661) ((-1090 . -796) 170628) ((-1089 . -1172) 170612) ((-1089 . -190) 170571) ((-1089 . -555) 170453) ((-1089 . -590) 170378) ((-1089 . -588) 170288) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -552) 170270) ((-1089 . -1013) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -970) T) ((-1089 . -1025) T) ((-1089 . -1061) T) ((-1089 . -663) T) ((-1089 . -961) T) ((-1089 . -186) 170223) ((-1089 . -13) T) ((-1089 . -1129) T) ((-1089 . -189) 170182) ((-1089 . -241) 170147) ((-1089 . -809) 170060) ((-1089 . -806) 169948) ((-1089 . -811) 169861) ((-1089 . -886) 169831) ((-1089 . -38) 169728) ((-1089 . -82) 169593) ((-1089 . -963) 169479) ((-1089 . -968) 169365) ((-1089 . -582) 169262) ((-1089 . -654) 169159) ((-1089 . -118) 169138) ((-1089 . -120) 169117) ((-1089 . -146) 169071) ((-1089 . -495) 169050) ((-1089 . -246) 169029) ((-1089 . -47) 169006) ((-1089 . -1158) 168983) ((-1089 . -35) 168949) ((-1089 . -66) 168915) ((-1089 . -239) 168881) ((-1089 . -433) 168847) ((-1089 . -1118) 168813) ((-1089 . -1115) 168779) ((-1089 . -915) 168745) ((-1088 . -1164) 168706) ((-1088 . -312) 168685) ((-1088 . -1134) 168664) ((-1088 . -832) 168643) ((-1088 . -495) 168597) ((-1088 . -146) 168531) ((-1088 . -555) 168280) ((-1088 . -654) 168127) ((-1088 . -582) 167974) ((-1088 . -38) 167821) ((-1088 . -392) 167800) ((-1088 . -258) 167779) ((-1088 . -590) 167679) ((-1088 . -588) 167564) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1061) T) ((-1088 . -663) T) ((-1088 . -961) T) ((-1088 . -82) 167384) ((-1088 . -963) 167225) ((-1088 . -968) 167066) ((-1088 . -21) T) ((-1088 . -23) T) ((-1088 . -1013) T) ((-1088 . -552) 167048) ((-1088 . -1129) T) ((-1088 . -13) T) ((-1088 . -72) T) ((-1088 . -25) T) ((-1088 . -104) T) ((-1088 . -246) 167002) ((-1088 . -201) 166981) ((-1088 . -915) 166947) ((-1088 . -1115) 166913) ((-1088 . -1118) 166879) ((-1088 . -433) 166845) ((-1088 . -239) 166811) ((-1088 . -66) 166777) ((-1088 . -35) 166743) ((-1088 . -1158) 166713) ((-1088 . -47) 166683) ((-1088 . -120) 166662) ((-1088 . -118) 166641) ((-1088 . -886) 166604) ((-1088 . -811) 166510) ((-1088 . -806) 166391) ((-1088 . -809) 166297) ((-1088 . -241) 166255) ((-1088 . -189) 166207) ((-1088 . -186) 166153) ((-1088 . -190) 166105) ((-1088 . -1162) 166089) ((-1088 . -950) 166024) ((-1085 . -1155) 166008) ((-1085 . -1066) 165986) ((-1085 . -553) NIL) ((-1085 . -260) 165973) ((-1085 . -455) 165921) ((-1085 . -277) 165898) ((-1085 . -950) 165781) ((-1085 . -355) 165765) ((-1085 . -38) 165597) ((-1085 . -82) 165402) ((-1085 . -963) 165228) ((-1085 . -968) 165054) ((-1085 . -588) 164964) ((-1085 . -590) 164853) ((-1085 . -582) 164685) ((-1085 . -654) 164517) ((-1085 . -555) 164294) ((-1085 . -118) 164273) ((-1085 . -120) 164252) ((-1085 . -47) 164229) ((-1085 . -329) 164213) ((-1085 . -580) 164161) ((-1085 . -809) 164105) ((-1085 . -806) 164012) ((-1085 . -811) 163923) ((-1085 . -796) NIL) ((-1085 . -821) 163902) ((-1085 . -1134) 163881) ((-1085 . -861) 163851) ((-1085 . -832) 163830) ((-1085 . -495) 163744) ((-1085 . -246) 163658) ((-1085 . -146) 163552) ((-1085 . -392) 163486) ((-1085 . -258) 163465) ((-1085 . -241) 163392) ((-1085 . -190) T) ((-1085 . -104) T) ((-1085 . -25) T) ((-1085 . -72) T) ((-1085 . -552) 163374) ((-1085 . -1013) T) ((-1085 . -23) T) ((-1085 . -21) T) ((-1085 . -970) T) ((-1085 . -1025) T) ((-1085 . -1061) T) ((-1085 . -663) T) ((-1085 . -961) T) ((-1085 . -186) 163361) ((-1085 . -13) T) ((-1085 . -1129) T) ((-1085 . -189) T) ((-1085 . -225) 163345) ((-1085 . -184) 163329) ((-1082 . -1143) 163290) ((-1082 . -915) 163256) ((-1082 . -1115) 163222) ((-1082 . -1118) 163188) ((-1082 . -433) 163154) ((-1082 . -239) 163120) ((-1082 . -66) 163086) ((-1082 . -35) 163052) ((-1082 . -1158) 163029) ((-1082 . -47) 163006) ((-1082 . -555) 162807) ((-1082 . -654) 162609) ((-1082 . -582) 162411) ((-1082 . -590) 162266) ((-1082 . -588) 162106) ((-1082 . -968) 161902) ((-1082 . -963) 161698) ((-1082 . -82) 161450) ((-1082 . -38) 161252) ((-1082 . -886) 161222) ((-1082 . -241) 161050) ((-1082 . -1141) 161034) ((-1082 . -970) T) ((-1082 . -1025) T) ((-1082 . -1061) T) ((-1082 . -663) T) ((-1082 . -961) T) ((-1082 . -21) T) ((-1082 . -23) T) ((-1082 . -1013) T) ((-1082 . -552) 161016) ((-1082 . -1129) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -25) T) ((-1082 . -104) T) ((-1082 . -118) 160926) ((-1082 . -120) 160836) ((-1082 . -553) NIL) ((-1082 . -184) 160788) ((-1082 . -809) 160624) ((-1082 . -811) 160388) ((-1082 . -806) 160127) ((-1082 . -225) 160079) ((-1082 . -189) 159905) ((-1082 . -186) 159725) ((-1082 . -190) 159615) ((-1082 . -312) 159594) ((-1082 . -1134) 159573) ((-1082 . -832) 159552) ((-1082 . -495) 159506) ((-1082 . -146) 159440) ((-1082 . -392) 159419) ((-1082 . -258) 159398) ((-1082 . -246) 159352) ((-1082 . -201) 159331) ((-1082 . -288) 159283) ((-1082 . -455) 159017) ((-1082 . -260) 158902) ((-1082 . -329) 158854) ((-1082 . -580) 158806) ((-1082 . -343) 158758) ((-1082 . -796) NIL) ((-1082 . -740) NIL) ((-1082 . -714) NIL) ((-1082 . -716) NIL) ((-1082 . -756) NIL) ((-1082 . -759) NIL) ((-1082 . -718) NIL) ((-1082 . -721) NIL) ((-1082 . -755) NIL) ((-1082 . -794) 158710) ((-1082 . -821) NIL) ((-1082 . -933) NIL) ((-1082 . -950) 158676) ((-1082 . -1066) NIL) ((-1082 . -904) 158628) ((-1081 . -995) T) ((-1081 . -430) 158609) ((-1081 . -552) 158575) ((-1081 . -555) 158556) ((-1081 . -1013) T) ((-1081 . -1129) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -64) T) ((-1080 . -1013) T) ((-1080 . -552) 158538) ((-1080 . -1129) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1079 . -1013) T) ((-1079 . -552) 158520) ((-1079 . -1129) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1074 . -1107) 158496) ((-1074 . -183) 158441) ((-1074 . -76) 158386) ((-1074 . -1035) 158318) ((-1074 . -124) 158263) ((-1074 . -553) NIL) ((-1074 . -193) 158208) ((-1074 . -538) 158184) ((-1074 . -260) 157973) ((-1074 . -455) 157713) ((-1074 . -429) 157645) ((-1074 . -241) 157621) ((-1074 . -243) 157597) ((-1074 . -549) 157573) ((-1074 . -1013) T) ((-1074 . -552) 157555) ((-1074 . -72) T) ((-1074 . -1129) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 157500) ((-1073 . -1058) T) ((-1073 . -324) 157482) ((-1073 . -759) T) ((-1073 . -756) T) ((-1073 . -124) 157464) ((-1073 . -553) NIL) ((-1073 . -241) 157414) ((-1073 . -538) 157389) ((-1073 . -243) 157364) ((-1073 . -593) 157346) ((-1073 . -429) 157328) ((-1073 . -1013) T) ((-1073 . -455) NIL) ((-1073 . -260) NIL) ((-1073 . -552) 157310) ((-1073 . -72) T) ((-1073 . -1129) T) ((-1073 . -13) T) ((-1073 . -34) T) ((-1073 . -318) 157292) ((-1073 . -1035) 157274) ((-1073 . -19) 157256) ((-1069 . -616) 157240) ((-1069 . -593) 157224) ((-1069 . -243) 157201) ((-1069 . -241) 157153) ((-1069 . -538) 157130) ((-1069 . -553) 157091) ((-1069 . -429) 157075) ((-1069 . -1013) 157053) ((-1069 . -455) 156986) ((-1069 . -260) 156924) ((-1069 . -552) 156859) ((-1069 . -72) 156813) ((-1069 . -1129) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -124) 156797) ((-1069 . -1168) 156781) ((-1069 . -923) 156765) ((-1069 . -1064) 156749) ((-1069 . -555) 156726) ((-1069 . -1035) 156710) ((-1067 . -995) T) ((-1067 . -430) 156691) ((-1067 . -552) 156657) ((-1067 . -555) 156638) ((-1067 . -1013) T) ((-1067 . -1129) T) ((-1067 . -13) T) ((-1067 . -72) T) ((-1067 . -64) T) ((-1065 . -1107) 156617) ((-1065 . -183) 156565) ((-1065 . -76) 156513) ((-1065 . -1035) 156448) ((-1065 . -124) 156396) ((-1065 . -553) NIL) ((-1065 . -193) 156344) ((-1065 . -538) 156323) ((-1065 . -260) 156121) ((-1065 . -455) 155873) ((-1065 . -429) 155808) ((-1065 . -241) 155787) ((-1065 . -243) 155766) ((-1065 . -549) 155745) ((-1065 . -1013) T) ((-1065 . -552) 155727) ((-1065 . -72) T) ((-1065 . -1129) T) ((-1065 . -13) T) ((-1065 . -34) T) ((-1065 . -318) 155675) ((-1062 . -1034) 155659) ((-1062 . -318) 155643) ((-1062 . -1035) 155627) ((-1062 . -34) T) ((-1062 . -13) T) ((-1062 . -1129) T) ((-1062 . -72) 155581) ((-1062 . -552) 155516) ((-1062 . -260) 155454) ((-1062 . -455) 155387) ((-1062 . -1013) 155365) ((-1062 . -429) 155349) ((-1062 . -76) 155333) ((-1060 . -1020) 155302) ((-1060 . -1124) 155271) ((-1060 . -1035) 155255) ((-1060 . -552) 155217) ((-1060 . -124) 155201) ((-1060 . -34) T) ((-1060 . -13) T) ((-1060 . -1129) T) ((-1060 . -72) T) ((-1060 . -260) 155139) ((-1060 . -455) 155072) ((-1060 . -1013) T) ((-1060 . -429) 155056) ((-1060 . -553) 155017) ((-1060 . -318) 155001) ((-1060 . -889) 154970) ((-1060 . -983) 154939) ((-1056 . -1037) 154884) ((-1056 . -318) 154868) ((-1056 . -34) T) ((-1056 . -260) 154806) ((-1056 . -455) 154739) ((-1056 . -429) 154723) ((-1056 . -965) 154663) ((-1056 . -950) 154561) ((-1056 . -555) 154480) ((-1056 . -355) 154464) ((-1056 . -580) 154412) ((-1056 . -590) 154350) ((-1056 . -329) 154334) ((-1056 . -190) 154313) ((-1056 . -186) 154261) ((-1056 . -189) 154215) ((-1056 . -225) 154199) ((-1056 . -806) 154123) ((-1056 . -811) 154049) ((-1056 . -809) 154008) ((-1056 . -184) 153992) ((-1056 . -654) 153927) ((-1056 . -582) 153862) ((-1056 . -588) 153821) ((-1056 . -104) T) ((-1056 . -25) T) ((-1056 . -72) T) ((-1056 . -13) T) ((-1056 . -1129) T) ((-1056 . -552) 153783) ((-1056 . -1013) T) ((-1056 . -23) T) ((-1056 . -21) T) ((-1056 . -968) 153767) ((-1056 . -963) 153751) ((-1056 . -82) 153730) ((-1056 . -961) T) ((-1056 . -663) T) ((-1056 . -1061) T) ((-1056 . -1025) T) 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-392) 151035) ((-1039 . -580) 150983) ((-1039 . -590) 150872) ((-1039 . -329) 150856) ((-1039 . -47) 150828) ((-1039 . -38) 150680) ((-1039 . -582) 150532) ((-1039 . -654) 150384) ((-1039 . -246) 150318) ((-1039 . -495) 150252) ((-1039 . -82) 150077) ((-1039 . -963) 149923) ((-1039 . -968) 149769) ((-1039 . -146) 149683) ((-1039 . -120) 149662) ((-1039 . -118) 149641) ((-1039 . -588) 149551) ((-1039 . -104) T) ((-1039 . -25) T) ((-1039 . -72) T) ((-1039 . -13) T) ((-1039 . -1129) T) ((-1039 . -552) 149533) ((-1039 . -1013) T) ((-1039 . -23) T) ((-1039 . -21) T) ((-1039 . -961) T) ((-1039 . -663) T) ((-1039 . -1061) T) ((-1039 . -1025) T) ((-1039 . -970) T) ((-1039 . -355) 149517) ((-1039 . -277) 149489) ((-1039 . -260) 149476) ((-1039 . -553) 149224) ((-1033 . -483) T) ((-1033 . -1134) T) ((-1033 . -1066) T) ((-1033 . -950) 149206) ((-1033 . -553) 149121) ((-1033 . -933) T) ((-1033 . -796) 149103) ((-1033 . -755) T) ((-1033 . -721) T) ((-1033 . -718) T) ((-1033 . -759) T) ((-1033 . -756) T) ((-1033 . -716) T) ((-1033 . -714) T) ((-1033 . -740) T) ((-1033 . -590) 149075) ((-1033 . -580) 149057) ((-1033 . -832) T) ((-1033 . -495) T) ((-1033 . -246) T) ((-1033 . -146) T) ((-1033 . -555) 149029) ((-1033 . -654) 149016) ((-1033 . -582) 149003) ((-1033 . -968) 148990) ((-1033 . -963) 148977) ((-1033 . -82) 148962) ((-1033 . -38) 148949) ((-1033 . -392) T) ((-1033 . -258) T) ((-1033 . -189) T) ((-1033 . -186) 148936) ((-1033 . -190) T) ((-1033 . -116) T) ((-1033 . -961) T) ((-1033 . -663) T) ((-1033 . -1061) T) ((-1033 . -1025) T) ((-1033 . -970) T) ((-1033 . -21) T) ((-1033 . -588) 148908) ((-1033 . -23) T) ((-1033 . -1013) T) ((-1033 . -552) 148890) ((-1033 . -1129) T) ((-1033 . -13) T) ((-1033 . -72) T) ((-1033 . -25) T) ((-1033 . -104) T) ((-1033 . -120) T) ((-1033 . -752) T) ((-1033 . -320) T) ((-1033 . -84) T) ((-1033 . -604) T) ((-1029 . -995) T) ((-1029 . -430) 148871) ((-1029 . -552) 148837) ((-1029 . -555) 148818) ((-1029 . -1013) T) ((-1029 . -1129) T) 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-806) 146787) ((-1026 . -811) 146661) ((-1026 . -809) 146594) ((-1026 . -184) 146564) ((-1026 . -552) 146261) ((-1026 . -968) 146186) ((-1026 . -963) 146091) ((-1026 . -82) 146011) ((-1026 . -104) 145886) ((-1026 . -25) 145723) ((-1026 . -72) 145460) ((-1026 . -13) T) ((-1026 . -1129) T) ((-1026 . -1013) 145216) ((-1026 . -23) 145072) ((-1026 . -21) 144987) ((-1022 . -1023) 144971) ((-1022 . |MappingCategory|) 144945) ((-1022 . -1129) T) ((-1022 . -80) 144929) ((-1022 . -1013) T) ((-1022 . -552) 144911) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 144875) ((-1017 . -72) T) ((-1017 . -552) 144857) ((-1017 . -1013) T) ((-1017 . -241) 144813) ((-1017 . -1129) T) ((-1017 . -13) T) ((-1017 . -557) 144728) ((-1015 . -1016) 144680) ((-1015 . -72) T) ((-1015 . -552) 144662) ((-1015 . -1013) T) ((-1015 . -241) 144618) ((-1015 . -1129) T) ((-1015 . -13) T) ((-1015 . -557) 144521) ((-1014 . -320) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1129) T) ((-1014 . -552) 144503) ((-1014 . -1013) T) ((-1009 . -369) 144487) ((-1009 . -1011) 144471) ((-1009 . -318) 144455) ((-1009 . -320) 144434) ((-1009 . -193) 144418) ((-1009 . -553) 144379) ((-1009 . -124) 144363) ((-1009 . -1035) 144347) ((-1009 . -34) T) ((-1009 . -13) T) ((-1009 . -1129) T) ((-1009 . -72) T) ((-1009 . -552) 144329) ((-1009 . -260) 144267) ((-1009 . -455) 144200) ((-1009 . -1013) T) ((-1009 . -429) 144184) ((-1009 . -76) 144168) ((-1009 . -183) 144152) ((-1008 . -995) T) ((-1008 . -430) 144133) ((-1008 . -552) 144099) ((-1008 . -555) 144080) ((-1008 . -1013) T) ((-1008 . -1129) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1129) T) ((-1004 . -13) T) ((-1004 . -1013) 144050) ((-1004 . -552) 144009) ((-1004 . -72) 143979) ((-1003 . -995) T) ((-1003 . -430) 143960) ((-1003 . -552) 143926) ((-1003 . -555) 143907) ((-1003 . -1013) T) ((-1003 . -1129) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 143891) ((-1001 . -557) 143875) ((-1001 . -1013) 143853) ((-1001 . -552) 143820) ((-1001 . -1129) 143798) ((-1001 . -13) 143776) ((-1001 . -72) 143754) ((-1001 . -1007) 143712) ((-1000 . -228) 143696) ((-1000 . -555) 143680) ((-1000 . -950) 143664) ((-1000 . -759) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -552) 143646) ((-1000 . -756) T) ((-1000 . -186) 143633) ((-1000 . -13) T) ((-1000 . -1129) T) ((-1000 . -189) T) ((-999 . -213) 143570) ((-999 . -555) 143313) ((-999 . -950) 143142) ((-999 . -553) NIL) ((-999 . -277) 143103) ((-999 . -355) 143087) ((-999 . -38) 142939) ((-999 . -82) 142764) ((-999 . -963) 142610) ((-999 . -968) 142456) ((-999 . -588) 142366) ((-999 . -590) 142255) ((-999 . -582) 142107) ((-999 . -654) 141959) ((-999 . -118) 141938) ((-999 . -120) 141917) ((-999 . -146) 141831) ((-999 . -495) 141765) ((-999 . -246) 141699) ((-999 . -47) 141660) ((-999 . -329) 141644) ((-999 . -580) 141592) ((-999 . -392) 141546) ((-999 . -455) 141409) ((-999 . -809) 141344) ((-999 . -806) 141242) ((-999 . -811) 141144) ((-999 . -796) NIL) ((-999 . -821) 141123) ((-999 . -1134) 141102) ((-999 . -861) 141047) ((-999 . -260) 141034) ((-999 . -190) 141013) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -552) 140995) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1061) T) ((-999 . -663) T) ((-999 . -961) T) ((-999 . -186) 140943) ((-999 . -13) T) ((-999 . -1129) T) ((-999 . -189) 140897) ((-999 . -225) 140881) ((-999 . -184) 140865) ((-997 . -552) 140847) ((-994 . -756) T) ((-994 . -552) 140829) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1129) T) ((-994 . -759) T) ((-994 . -553) 140810) ((-991 . -661) 140789) ((-991 . -950) 140687) ((-991 . -355) 140671) ((-991 . -580) 140619) ((-991 . -590) 140496) ((-991 . -329) 140480) ((-991 . -322) 140459) ((-991 . -120) 140438) ((-991 . -555) 140263) ((-991 . -654) 140137) ((-991 . -582) 140011) ((-991 . -588) 139909) ((-991 . -968) 139822) ((-991 . -963) 139735) ((-991 . -82) 139627) ((-991 . -38) 139501) ((-991 . -353) 139480) ((-991 . -345) 139459) ((-991 . -118) 139413) ((-991 . -1066) 139392) ((-991 . -299) 139371) ((-991 . -320) 139325) ((-991 . -201) 139279) ((-991 . -246) 139233) ((-991 . -258) 139187) ((-991 . -392) 139141) ((-991 . -495) 139095) ((-991 . -832) 139049) ((-991 . -1134) 139003) ((-991 . -312) 138957) ((-991 . -190) 138885) ((-991 . -186) 138761) ((-991 . -189) 138643) ((-991 . -225) 138613) ((-991 . -806) 138485) ((-991 . -811) 138359) ((-991 . -809) 138292) ((-991 . -184) 138262) ((-991 . -553) 138246) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -552) 138228) ((-991 . -1129) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -961) T) ((-991 . -663) T) ((-991 . -1061) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -552) 138210) ((-989 . -1129) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 138189) ((-988 . -1013) T) ((-988 . -552) 138171) ((-988 . -1129) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -552) 138153) ((-987 . -1129) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 138132) ((-987 . -950) 138109) ((-987 . -555) 138086) ((-986 . -1129) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -430) 138067) ((-985 . -552) 138033) ((-985 . -555) 138014) ((-985 . -1013) T) ((-985 . -1129) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -430) 137995) ((-978 . -552) 137961) ((-978 . -555) 137942) ((-978 . -1013) T) ((-978 . -1129) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) ((-975 . -1134) T) ((-975 . -1066) T) ((-975 . -950) 137924) ((-975 . -553) 137839) ((-975 . -933) T) ((-975 . -796) 137821) ((-975 . -755) T) ((-975 . -721) T) ((-975 . -718) T) ((-975 . -759) T) ((-975 . -756) T) ((-975 . -716) T) ((-975 . -714) T) ((-975 . -740) T) ((-975 . -590) 137793) ((-975 . -580) 137775) ((-975 . -832) T) ((-975 . -495) T) ((-975 . -246) T) ((-975 . -146) T) 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. -590) 137126) ((-966 . -588) 137095) ((-966 . -104) T) ((-966 . -25) T) ((-966 . -72) T) ((-966 . -13) T) ((-966 . -1129) T) ((-966 . -552) 137057) ((-966 . -1013) T) ((-966 . -23) T) ((-966 . -21) T) ((-966 . -968) 137041) ((-966 . -963) 137025) ((-966 . -82) 137004) ((-966 . -1187) 136974) ((-966 . -553) 136935) ((-958 . -983) 136864) ((-958 . -889) 136793) ((-958 . -318) 136758) ((-958 . -553) 136700) ((-958 . -429) 136665) ((-958 . -1013) T) ((-958 . -455) 136549) ((-958 . -260) 136457) ((-958 . -552) 136400) ((-958 . -72) T) ((-958 . -1129) T) ((-958 . -13) T) ((-958 . -34) T) ((-958 . -124) 136365) ((-958 . -1035) 136330) ((-958 . -1124) 136259) ((-948 . -995) T) ((-948 . -430) 136240) ((-948 . -552) 136206) ((-948 . -555) 136187) ((-948 . -1013) T) ((-948 . -1129) T) ((-948 . -13) T) ((-948 . -72) T) ((-948 . -64) T) ((-947 . -146) T) ((-947 . -555) 136156) ((-947 . -970) T) ((-947 . -1025) T) ((-947 . -1061) T) ((-947 . -663) T) ((-947 . -961) T) ((-947 . -590) 136130) ((-947 . -588) 136089) ((-947 . -104) T) ((-947 . -25) T) ((-947 . -72) T) ((-947 . -13) T) ((-947 . -1129) T) ((-947 . -552) 136071) ((-947 . -1013) T) ((-947 . -23) T) ((-947 . -21) T) ((-947 . -968) 136045) ((-947 . -963) 136019) ((-947 . -82) 135986) ((-947 . -38) 135970) ((-947 . -582) 135954) ((-947 . -654) 135938) ((-940 . -983) 135907) ((-940 . -889) 135876) ((-940 . -318) 135860) ((-940 . -553) 135821) ((-940 . -429) 135805) ((-940 . -1013) T) ((-940 . -455) 135738) ((-940 . -260) 135676) ((-940 . -552) 135638) ((-940 . -72) T) ((-940 . -1129) T) ((-940 . -13) T) ((-940 . -34) T) ((-940 . -124) 135622) ((-940 . -1035) 135606) ((-940 . -1124) 135575) ((-939 . -1013) T) ((-939 . -552) 135557) ((-939 . -1129) T) ((-939 . -13) T) ((-939 . -72) T) ((-937 . -925) T) ((-937 . -915) T) ((-937 . -714) T) ((-937 . -716) T) ((-937 . -756) T) ((-937 . -759) T) ((-937 . -718) T) ((-937 . -721) T) ((-937 . -755) T) ((-937 . -950) 135442) ((-937 . -355) 135404) ((-937 . -201) T) ((-937 . -246) T) 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119433) ((-780 . -455) 119296) ((-780 . -288) 119273) ((-780 . -201) T) ((-780 . -82) 119190) ((-780 . -963) 119135) ((-780 . -968) 119080) ((-780 . -246) T) ((-780 . -654) 119025) ((-780 . -582) 118970) ((-780 . -588) 118900) ((-780 . -38) 118845) ((-780 . -258) T) ((-780 . -392) T) ((-780 . -146) T) ((-780 . -495) T) ((-780 . -832) T) ((-780 . -1134) T) ((-780 . -312) T) ((-780 . -190) NIL) ((-780 . -186) NIL) ((-780 . -189) NIL) ((-780 . -225) 118822) ((-780 . -806) NIL) ((-780 . -811) NIL) ((-780 . -809) NIL) ((-780 . -184) 118799) ((-780 . -120) T) ((-780 . -118) NIL) ((-780 . -104) T) ((-780 . -25) T) ((-780 . -72) T) ((-780 . -13) T) ((-780 . -1129) T) ((-780 . -552) 118781) ((-780 . -1013) T) ((-780 . -23) T) ((-780 . -21) T) ((-780 . -961) T) ((-780 . -663) T) ((-780 . -1061) T) ((-780 . -1025) T) ((-780 . -970) T) ((-778 . -779) 118765) ((-778 . -832) T) ((-778 . -495) T) ((-778 . -246) T) ((-778 . -146) T) ((-778 . -555) 118737) ((-778 . -654) 118724) ((-778 . -582) 118711) 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-13) T) ((-774 . -72) T) ((-773 . -752) T) ((-773 . -759) T) ((-773 . -756) T) ((-773 . -1013) T) ((-773 . -552) 118156) ((-773 . -1129) T) ((-773 . -13) T) ((-773 . -72) T) ((-773 . -320) T) ((-773 . -553) 118078) ((-772 . -1013) T) ((-772 . -552) 118060) ((-772 . -1129) T) ((-772 . -13) T) ((-772 . -72) T) ((-771 . -770) T) ((-771 . -147) T) ((-771 . -552) 118042) ((-767 . -756) T) ((-767 . -552) 118024) ((-767 . -1013) T) ((-767 . -72) T) ((-767 . -13) T) ((-767 . -1129) T) ((-767 . -759) T) ((-764 . -761) 118008) ((-764 . -950) 117906) ((-764 . -555) 117804) ((-764 . -355) 117788) ((-764 . -654) 117758) ((-764 . -582) 117728) ((-764 . -590) 117702) ((-764 . -588) 117661) ((-764 . -104) T) ((-764 . -25) T) ((-764 . -72) T) ((-764 . -13) T) ((-764 . -1129) T) ((-764 . -552) 117643) ((-764 . -1013) T) ((-764 . -23) T) ((-764 . -21) T) ((-764 . -968) 117627) ((-764 . -963) 117611) ((-764 . -82) 117590) ((-764 . -961) T) ((-764 . -663) T) ((-764 . -1061) T) ((-764 . -1025) T) ((-764 . -970) T) ((-764 . -38) 117560) ((-763 . -761) 117544) ((-763 . -950) 117442) ((-763 . -555) 117361) ((-763 . -355) 117345) ((-763 . -654) 117315) ((-763 . -582) 117285) ((-763 . -590) 117259) ((-763 . -588) 117218) ((-763 . -104) T) ((-763 . -25) T) ((-763 . -72) T) ((-763 . -13) T) ((-763 . -1129) T) ((-763 . -552) 117200) ((-763 . -1013) T) ((-763 . -23) T) ((-763 . -21) T) ((-763 . -968) 117184) ((-763 . -963) 117168) ((-763 . -82) 117147) ((-763 . -961) T) ((-763 . -663) T) ((-763 . -1061) T) ((-763 . -1025) T) ((-763 . -970) T) ((-763 . -38) 117117) ((-757 . -759) T) ((-757 . -1129) T) ((-757 . -13) T) ((-757 . -72) T) ((-757 . -430) 117101) ((-757 . -552) 117049) ((-757 . -555) 117033) ((-750 . -1013) T) ((-750 . -552) 117015) ((-750 . -1129) T) ((-750 . -13) T) ((-750 . -72) T) ((-750 . -355) 116999) ((-750 . -555) 116872) ((-750 . -950) 116770) ((-750 . -21) 116725) ((-750 . -588) 116645) ((-750 . -23) 116600) ((-750 . -25) 116555) ((-750 . -104) 116510) ((-750 . -755) 116489) 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-552) 115720) ((-743 . -1129) T) ((-743 . -13) T) ((-743 . -72) T) ((-743 . -355) 115704) ((-743 . -555) 115577) ((-743 . -950) 115475) ((-743 . -21) 115430) ((-743 . -588) 115350) ((-743 . -23) 115305) ((-743 . -25) 115260) ((-743 . -104) 115215) ((-743 . -755) 115194) ((-743 . -721) 115173) ((-743 . -718) 115152) ((-743 . -759) 115131) ((-743 . -756) 115110) ((-743 . -716) 115089) ((-743 . -714) 115068) ((-743 . -961) 115047) ((-743 . -663) 115026) ((-743 . -1061) 115005) ((-743 . -1025) 114984) ((-743 . -970) 114963) ((-743 . -590) 114936) ((-743 . -120) 114915) ((-741 . -645) 114899) ((-741 . -555) 114854) ((-741 . -654) 114824) ((-741 . -582) 114794) ((-741 . -590) 114768) ((-741 . -588) 114727) ((-741 . -104) T) ((-741 . -25) T) ((-741 . -72) T) ((-741 . -13) T) ((-741 . -1129) T) ((-741 . -552) 114709) ((-741 . -1013) T) ((-741 . -23) T) ((-741 . -21) T) ((-741 . -968) 114693) ((-741 . -963) 114677) ((-741 . -82) 114656) ((-741 . -961) T) ((-741 . -663) T) ((-741 . -1061) T) 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106292) ((-722 . -582) 106276) ((-722 . -590) 106250) ((-722 . -588) 106209) ((-722 . -104) T) ((-722 . -25) T) ((-722 . -72) T) ((-722 . -13) T) ((-722 . -1129) T) ((-722 . -552) 106191) ((-722 . -1013) T) ((-722 . -23) T) ((-722 . -21) T) ((-722 . -968) 106175) ((-722 . -963) 106159) ((-722 . -82) 106138) ((-722 . -961) T) ((-722 . -663) T) ((-722 . -1061) T) ((-722 . -1025) T) ((-722 . -970) T) ((-722 . -38) 106122) ((-704 . -1155) 106106) ((-704 . -1066) 106084) ((-704 . -553) NIL) ((-704 . -260) 106071) ((-704 . -455) 106019) ((-704 . -277) 105996) ((-704 . -950) 105858) ((-704 . -355) 105842) ((-704 . -38) 105674) ((-704 . -82) 105479) ((-704 . -963) 105305) ((-704 . -968) 105131) ((-704 . -588) 105041) ((-704 . -590) 104930) ((-704 . -582) 104762) ((-704 . -654) 104594) ((-704 . -555) 104350) ((-704 . -118) 104329) ((-704 . -120) 104308) ((-704 . -47) 104285) ((-704 . -329) 104269) ((-704 . -580) 104217) ((-704 . -809) 104161) ((-704 . -806) 104068) ((-704 . -811) 103979) ((-704 . -796) NIL) ((-704 . -821) 103958) ((-704 . -1134) 103937) ((-704 . -861) 103907) ((-704 . -832) 103886) ((-704 . -495) 103800) ((-704 . -246) 103714) ((-704 . -146) 103608) ((-704 . -392) 103542) ((-704 . -258) 103521) ((-704 . -241) 103448) ((-704 . -190) T) ((-704 . -104) T) ((-704 . -25) T) ((-704 . -72) T) ((-704 . -552) 103409) ((-704 . -1013) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1061) T) ((-704 . -663) T) ((-704 . -961) T) ((-704 . -186) 103396) ((-704 . -13) T) ((-704 . -1129) T) ((-704 . -189) T) ((-704 . -225) 103380) ((-704 . -184) 103364) ((-703 . -977) 103331) ((-703 . -553) 102966) ((-703 . -260) 102953) ((-703 . -455) 102905) ((-703 . -277) 102877) ((-703 . -950) 102736) ((-703 . -355) 102720) ((-703 . -38) 102572) ((-703 . -555) 102345) ((-703 . -590) 102234) ((-703 . -588) 102144) ((-703 . -970) T) ((-703 . -1025) T) ((-703 . -1061) T) ((-703 . -663) T) ((-703 . -961) T) ((-703 . -82) 101969) ((-703 . -963) 101815) ((-703 . -968) 101661) ((-703 . -21) T) ((-703 . -23) T) ((-703 . -1013) T) ((-703 . -552) 101575) ((-703 . -1129) T) ((-703 . -13) T) ((-703 . -72) T) ((-703 . -25) T) ((-703 . -104) T) ((-703 . -582) 101427) ((-703 . -654) 101279) ((-703 . -118) 101258) ((-703 . -120) 101237) ((-703 . -146) 101151) ((-703 . -495) 101085) ((-703 . -246) 101019) ((-703 . -47) 100991) ((-703 . -329) 100975) ((-703 . -580) 100923) ((-703 . -392) 100877) ((-703 . -809) 100861) ((-703 . -806) 100843) ((-703 . -811) 100827) ((-703 . -796) 100686) ((-703 . -821) 100665) ((-703 . -1134) 100644) ((-703 . -861) 100611) ((-696 . -1013) T) ((-696 . -552) 100593) ((-696 . -1129) T) ((-696 . -13) T) ((-696 . -72) T) ((-694 . -717) T) ((-694 . -104) T) ((-694 . -25) T) ((-694 . -72) T) ((-694 . -13) T) ((-694 . -1129) T) ((-694 . -552) 100575) ((-694 . -1013) T) ((-694 . -23) T) ((-694 . -716) T) ((-694 . -756) T) ((-694 . -759) T) ((-694 . -718) T) ((-694 . -721) T) ((-694 . -663) T) ((-694 . -1025) T) ((-675 . -676) 100559) ((-675 . -1011) 100543) ((-675 . -193) 100527) ((-675 . -553) 100488) ((-675 . -124) 100472) ((-675 . -1035) 100456) ((-675 . -34) T) ((-675 . -13) T) ((-675 . -1129) T) ((-675 . -72) T) ((-675 . -552) 100438) ((-675 . -260) 100376) ((-675 . -455) 100309) ((-675 . -1013) T) ((-675 . -429) 100293) ((-675 . -76) 100277) ((-675 . -634) 100261) ((-675 . -318) 100245) ((-674 . -961) T) ((-674 . -663) T) ((-674 . -1061) T) ((-674 . -1025) T) ((-674 . -970) T) ((-674 . -21) T) ((-674 . -588) 100190) ((-674 . -23) T) ((-674 . -1013) T) ((-674 . -552) 100172) ((-674 . -1129) T) ((-674 . -13) T) ((-674 . -72) T) ((-674 . -25) T) ((-674 . -104) T) ((-674 . -590) 100132) ((-674 . -555) 100088) ((-674 . -950) 100059) ((-674 . -120) 100038) ((-674 . -118) 100017) ((-674 . -38) 99987) ((-674 . -82) 99952) ((-674 . -963) 99922) ((-674 . -968) 99892) ((-674 . -582) 99862) ((-674 . -654) 99832) ((-674 . -320) 99785) ((-670 . -861) 99738) ((-670 . -555) 99530) ((-670 . -950) 99408) ((-670 . 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. -588) 90070) ((-596 . -970) T) ((-596 . -1025) T) ((-596 . -1061) T) ((-596 . -663) T) ((-596 . -961) T) ((-596 . -82) 90049) ((-596 . -963) 90033) ((-596 . -968) 90017) ((-596 . -21) T) ((-596 . -23) T) ((-596 . -1013) T) ((-596 . -552) 89999) ((-596 . -72) T) ((-596 . -25) T) ((-596 . -104) T) ((-596 . -582) 89969) ((-596 . -654) 89939) ((-596 . -355) 89923) ((-596 . -950) 89821) ((-596 . -761) 89805) ((-596 . -1129) T) ((-596 . -13) T) ((-596 . -241) 89784) ((-594 . -654) 89768) ((-594 . -582) 89752) ((-594 . -590) 89736) ((-594 . -588) 89705) ((-594 . -104) T) ((-594 . -25) T) ((-594 . -72) T) ((-594 . -13) T) ((-594 . -1129) T) ((-594 . -552) 89687) ((-594 . -1013) T) ((-594 . -23) T) ((-594 . -21) T) ((-594 . -968) 89671) ((-594 . -963) 89655) ((-594 . -82) 89634) ((-594 . -714) 89613) ((-594 . -716) 89592) ((-594 . -756) 89571) ((-594 . -759) 89550) ((-594 . -718) 89529) ((-594 . -721) 89508) ((-591 . -1013) T) ((-591 . -552) 89490) ((-591 . -1129) T) ((-591 . -13) T) ((-591 . 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. -756) T) ((-507 . -495) T) ((-507 . -246) T) ((-507 . -146) T) ((-507 . -555) 79980) ((-507 . -654) 79967) ((-507 . -582) 79954) ((-507 . -590) 79941) ((-507 . -588) 79913) ((-507 . -104) T) ((-507 . -25) T) ((-507 . -72) T) ((-507 . -13) T) ((-507 . -1129) T) ((-507 . -552) 79895) ((-507 . -1013) T) ((-507 . -23) T) ((-507 . -21) T) ((-507 . -968) 79882) ((-507 . -963) 79869) ((-507 . -82) 79854) ((-507 . -961) T) ((-507 . -663) T) ((-507 . -1061) T) ((-507 . -1025) T) ((-507 . -970) T) ((-507 . -38) 79841) ((-507 . -392) T) ((-489 . -1107) 79820) ((-489 . -183) 79768) ((-489 . -76) 79716) ((-489 . -1035) 79651) ((-489 . -124) 79599) ((-489 . -553) NIL) ((-489 . -193) 79547) ((-489 . -538) 79526) ((-489 . -260) 79324) ((-489 . -455) 79076) ((-489 . -429) 79011) ((-489 . -241) 78990) ((-489 . -243) 78969) ((-489 . -549) 78948) ((-489 . -1013) T) ((-489 . -552) 78930) ((-489 . -72) T) ((-489 . -1129) T) ((-489 . -13) T) ((-489 . -34) T) ((-489 . -318) 78878) ((-488 . -752) T) ((-488 . 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. -1013) T) ((-342 . -552) 54563) ((-342 . -1129) T) ((-342 . -13) T) ((-342 . -72) T) ((-342 . -189) T) ((-342 . -186) 54550) ((-342 . -553) 54527) ((-340 . -683) 54511) ((-340 . -657) T) ((-340 . -685) T) ((-340 . -82) 54490) ((-340 . -963) 54474) ((-340 . -968) 54458) ((-340 . -21) T) ((-340 . -588) 54427) ((-340 . -23) T) ((-340 . -1013) T) ((-340 . -552) 54409) ((-340 . -1129) T) ((-340 . -13) T) ((-340 . -72) T) ((-340 . -25) T) ((-340 . -104) T) ((-340 . -590) 54393) ((-340 . -582) 54377) ((-340 . -654) 54361) ((-338 . -339) T) ((-338 . -72) T) ((-338 . -13) T) ((-338 . -1129) T) ((-338 . -552) 54327) ((-338 . -1013) T) ((-338 . -555) 54308) ((-338 . -430) 54289) ((-337 . -336) 54273) ((-337 . -555) 54257) ((-337 . -950) 54241) ((-337 . -759) 54220) ((-337 . -756) 54199) ((-337 . -1025) T) ((-337 . -72) T) ((-337 . -13) T) ((-337 . -1129) T) ((-337 . -552) 54181) ((-337 . -1013) T) ((-337 . -663) T) ((-334 . -335) 54160) ((-334 . -555) 54144) ((-334 . -950) 54128) ((-334 . -582) 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\ No newline at end of file
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188607) ((-1149 . -355) 188591) ((-1149 . -38) 188423) ((-1149 . -82) 188228) ((-1149 . -964) 188054) ((-1149 . -969) 187880) ((-1149 . -589) 187790) ((-1149 . -591) 187679) ((-1149 . -583) 187511) ((-1149 . -655) 187343) ((-1149 . -556) 187099) ((-1149 . -118) 187078) ((-1149 . -120) 187057) ((-1149 . -47) 187034) ((-1149 . -329) 187018) ((-1149 . -581) 186966) ((-1149 . -810) 186910) ((-1149 . -807) 186817) ((-1149 . -812) 186728) ((-1149 . -797) NIL) ((-1149 . -822) 186707) ((-1149 . -1135) 186686) ((-1149 . -862) 186656) ((-1149 . -833) 186635) ((-1149 . -496) 186549) ((-1149 . -246) 186463) ((-1149 . -146) 186357) ((-1149 . -392) 186291) ((-1149 . -258) 186270) ((-1149 . -241) 186197) ((-1149 . -190) T) ((-1149 . -104) T) ((-1149 . -25) T) ((-1149 . -72) T) ((-1149 . -553) 186179) ((-1149 . -1014) T) ((-1149 . -23) T) ((-1149 . -21) T) ((-1149 . -971) T) ((-1149 . -1026) T) ((-1149 . -1062) T) ((-1149 . -664) T) ((-1149 . -962) T) ((-1149 . -186) 186166) ((-1149 . -13) T) ((-1149 . -1130) T) ((-1149 . -189) T) ((-1149 . -225) 186150) ((-1149 . -184) 186134) ((-1147 . -1007) 186118) ((-1147 . -558) 186102) ((-1147 . -1014) 186080) ((-1147 . -553) 186047) ((-1147 . -1130) 186025) ((-1147 . -13) 186003) ((-1147 . -72) 185981) ((-1147 . -1008) 185938) ((-1145 . -1144) 185917) ((-1145 . -916) 185883) ((-1145 . -1116) 185849) ((-1145 . -1119) 185815) ((-1145 . -433) 185781) ((-1145 . -239) 185747) ((-1145 . -66) 185713) ((-1145 . -35) 185679) ((-1145 . -1159) 185656) ((-1145 . -47) 185633) ((-1145 . -556) 185388) ((-1145 . -655) 185208) ((-1145 . -583) 185028) ((-1145 . -591) 184839) ((-1145 . -589) 184697) ((-1145 . -969) 184511) ((-1145 . -964) 184325) ((-1145 . -82) 184113) ((-1145 . -38) 183933) ((-1145 . -887) 183903) ((-1145 . -241) 183803) ((-1145 . -1142) 183787) ((-1145 . -971) T) ((-1145 . -1026) T) ((-1145 . -1062) T) ((-1145 . -664) T) ((-1145 . -962) T) ((-1145 . -21) T) ((-1145 . -23) T) ((-1145 . -1014) T) ((-1145 . -553) 183769) ((-1145 . -1130) T) ((-1145 . -13) T) ((-1145 . -72) T) ((-1145 . -25) T) ((-1145 . -104) T) ((-1145 . -118) 183697) ((-1145 . -120) 183579) ((-1145 . -554) 183252) ((-1145 . -184) 183222) ((-1145 . -810) 183076) ((-1145 . -812) 182876) ((-1145 . -807) 182674) ((-1145 . -225) 182644) ((-1145 . -189) 182506) ((-1145 . -186) 182362) ((-1145 . -190) 182270) ((-1145 . -312) 182249) ((-1145 . -1135) 182228) ((-1145 . -833) 182207) ((-1145 . -496) 182161) ((-1145 . -146) 182095) ((-1145 . -392) 182074) ((-1145 . -258) 182053) ((-1145 . -246) 182007) ((-1145 . -201) 181986) ((-1145 . -288) 181956) ((-1145 . -456) 181816) ((-1145 . -260) 181755) ((-1145 . -329) 181725) ((-1145 . -581) 181633) ((-1145 . -343) 181603) ((-1145 . -797) 181476) ((-1145 . -741) 181429) ((-1145 . -715) 181382) ((-1145 . -717) 181335) ((-1145 . -757) 181237) ((-1145 . -760) 181139) ((-1145 . -719) 181092) ((-1145 . -722) 181045) ((-1145 . -756) 180998) ((-1145 . -795) 180968) ((-1145 . -822) 180921) ((-1145 . -934) 180874) ((-1145 . -951) 180663) ((-1145 . -1067) 180615) ((-1145 . -905) 180585) ((-1140 . -1144) 180546) ((-1140 . -916) 180512) ((-1140 . -1116) 180478) ((-1140 . -1119) 180444) ((-1140 . -433) 180410) ((-1140 . -239) 180376) ((-1140 . -66) 180342) ((-1140 . -35) 180308) ((-1140 . -1159) 180285) ((-1140 . -47) 180262) ((-1140 . -556) 180063) ((-1140 . -655) 179865) ((-1140 . -583) 179667) ((-1140 . -591) 179522) ((-1140 . -589) 179362) ((-1140 . -969) 179158) ((-1140 . -964) 178954) ((-1140 . -82) 178706) ((-1140 . -38) 178508) ((-1140 . -887) 178478) ((-1140 . -241) 178306) ((-1140 . -1142) 178290) ((-1140 . -971) T) ((-1140 . -1026) T) ((-1140 . -1062) T) ((-1140 . -664) T) ((-1140 . -962) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1014) T) ((-1140 . -553) 178272) ((-1140 . -1130) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -25) T) ((-1140 . -104) T) ((-1140 . -118) 178182) ((-1140 . -120) 178092) ((-1140 . -554) NIL) ((-1140 . -184) 178044) ((-1140 . -810) 177880) ((-1140 . -812) 177644) ((-1140 . -807) 177383) ((-1140 . -225) 177335) ((-1140 . -189) 177161) ((-1140 . -186) 176981) ((-1140 . -190) 176871) ((-1140 . -312) 176850) ((-1140 . -1135) 176829) ((-1140 . -833) 176808) ((-1140 . -496) 176762) ((-1140 . -146) 176696) ((-1140 . -392) 176675) ((-1140 . -258) 176654) ((-1140 . -246) 176608) ((-1140 . -201) 176587) ((-1140 . -288) 176539) ((-1140 . -456) 176273) ((-1140 . -260) 176158) ((-1140 . -329) 176110) ((-1140 . -581) 176062) ((-1140 . -343) 176014) ((-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) 175966) ((-1140 . -822) NIL) ((-1140 . -934) NIL) ((-1140 . -951) 175932) ((-1140 . -1067) NIL) ((-1140 . -905) 175884) ((-1139 . -753) T) ((-1139 . -760) T) ((-1139 . -757) T) ((-1139 . -1014) T) ((-1139 . -553) 175866) ((-1139 . -1130) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -320) T) ((-1139 . -605) T) ((-1138 . -753) T) ((-1138 . -760) T) ((-1138 . -757) T) ((-1138 . -1014) T) ((-1138 . -553) 175848) ((-1138 . -1130) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -605) T) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1014) T) ((-1137 . -553) 175830) ((-1137 . -1130) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1014) T) ((-1136 . -553) 175812) ((-1136 . -1130) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -605) T) ((-1131 . -996) T) ((-1131 . -430) 175793) ((-1131 . -553) 175759) ((-1131 . -556) 175740) ((-1131 . -1014) T) ((-1131 . -1130) T) ((-1131 . -13) T) ((-1131 . -72) T) ((-1131 . -64) T) ((-1128 . -430) 175717) ((-1128 . -553) 175658) ((-1128 . -556) 175635) ((-1128 . -1014) 175613) ((-1128 . -1130) 175591) ((-1128 . -13) 175569) ((-1128 . -72) 175547) ((-1123 . -680) 175523) ((-1123 . -35) 175489) ((-1123 . -66) 175455) ((-1123 . -239) 175421) ((-1123 . -433) 175387) ((-1123 . -1119) 175353) ((-1123 . -1116) 175319) ((-1123 . -916) 175285) ((-1123 . -47) 175254) ((-1123 . -38) 175151) ((-1123 . -583) 175048) ((-1123 . -655) 174945) ((-1123 . -556) 174827) ((-1123 . -246) 174806) ((-1123 . -496) 174785) ((-1123 . -82) 174650) ((-1123 . -964) 174536) ((-1123 . -969) 174422) ((-1123 . -146) 174376) ((-1123 . -120) 174355) ((-1123 . -118) 174334) ((-1123 . -591) 174259) ((-1123 . -589) 174169) ((-1123 . -887) 174130) ((-1123 . -812) 174111) ((-1123 . -1130) T) ((-1123 . -13) T) ((-1123 . -807) 174090) ((-1123 . -962) T) ((-1123 . -664) T) ((-1123 . -1062) T) ((-1123 . -1026) T) ((-1123 . -971) T) ((-1123 . -21) T) ((-1123 . -23) T) ((-1123 . -1014) T) ((-1123 . -553) 174072) ((-1123 . -72) T) ((-1123 . -25) T) ((-1123 . -104) T) ((-1123 . -810) 174053) ((-1123 . -456) 174020) ((-1123 . -260) 174007) ((-1117 . -924) 173991) ((-1117 . -34) T) ((-1117 . -13) T) ((-1117 . -1130) T) ((-1117 . -72) 173945) ((-1117 . -553) 173880) ((-1117 . -260) 173818) ((-1117 . -456) 173751) ((-1117 . -1014) 173729) ((-1117 . -429) 173713) ((-1117 . -318) 173697) ((-1117 . -1036) 173681) ((-1112 . -314) 173655) ((-1112 . -72) T) ((-1112 . -13) T) ((-1112 . -1130) T) ((-1112 . -553) 173637) ((-1112 . -1014) T) ((-1110 . -1014) T) ((-1110 . -553) 173619) ((-1110 . -1130) T) ((-1110 . -13) T) ((-1110 . -72) T) ((-1110 . -556) 173601) ((-1105 . -748) 173585) ((-1105 . -72) T) ((-1105 . -13) T) ((-1105 . -1130) T) ((-1105 . -553) 173567) ((-1105 . -1014) T) ((-1103 . -1108) 173546) ((-1103 . -183) 173494) ((-1103 . -76) 173442) ((-1103 . -1036) 173377) ((-1103 . -124) 173325) ((-1103 . -554) NIL) ((-1103 . -193) 173273) ((-1103 . -539) 173252) ((-1103 . -260) 173050) ((-1103 . -456) 172802) ((-1103 . -429) 172737) ((-1103 . -241) 172716) ((-1103 . -243) 172695) ((-1103 . -550) 172674) ((-1103 . -1014) T) ((-1103 . -553) 172656) ((-1103 . -72) T) ((-1103 . -1130) T) ((-1103 . -13) T) ((-1103 . -34) T) ((-1103 . -318) 172604) ((-1099 . -1014) T) ((-1099 . -553) 172586) ((-1099 . -1130) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1098 . -753) T) ((-1098 . -760) T) ((-1098 . -757) T) ((-1098 . -1014) T) ((-1098 . -553) 172568) ((-1098 . -1130) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -320) T) ((-1098 . -605) T) ((-1097 . -753) T) ((-1097 . -760) T) ((-1097 . -757) T) ((-1097 . -1014) T) ((-1097 . -553) 172550) ((-1097 . -1130) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1096 . -1176) T) ((-1096 . -1014) T) ((-1096 . -553) 172517) ((-1096 . -1130) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -951) 172453) ((-1096 . -556) 172389) ((-1095 . -553) 172371) ((-1094 . -553) 172353) ((-1093 . -277) 172330) ((-1093 . -951) 172228) ((-1093 . -355) 172212) ((-1093 . -38) 172109) ((-1093 . -556) 171966) ((-1093 . -591) 171891) ((-1093 . -589) 171801) ((-1093 . -971) T) ((-1093 . -1026) T) ((-1093 . -1062) T) ((-1093 . -664) T) ((-1093 . -962) T) ((-1093 . -82) 171666) ((-1093 . -964) 171552) ((-1093 . -969) 171438) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1014) T) ((-1093 . -553) 171420) ((-1093 . -1130) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -25) T) ((-1093 . -104) T) ((-1093 . -583) 171317) ((-1093 . -655) 171214) ((-1093 . -118) 171193) ((-1093 . -120) 171172) ((-1093 . -146) 171126) ((-1093 . -496) 171105) ((-1093 . -246) 171084) ((-1093 . -47) 171061) ((-1091 . -757) T) ((-1091 . -553) 171043) ((-1091 . -1014) T) ((-1091 . -72) T) ((-1091 . -13) T) ((-1091 . -1130) T) ((-1091 . -760) T) ((-1091 . -554) 170965) ((-1091 . -556) 170931) ((-1091 . -951) 170913) ((-1091 . -797) 170880) ((-1090 . -1173) 170864) ((-1090 . -190) 170823) ((-1090 . -556) 170705) ((-1090 . -591) 170630) ((-1090 . -589) 170540) ((-1090 . -104) T) ((-1090 . -25) T) ((-1090 . -72) T) ((-1090 . -553) 170522) ((-1090 . -1014) T) ((-1090 . -23) T) ((-1090 . -21) T) ((-1090 . -971) T) ((-1090 . -1026) T) ((-1090 . -1062) T) ((-1090 . -664) T) ((-1090 . -962) T) ((-1090 . -186) 170475) ((-1090 . -13) T) ((-1090 . -1130) T) ((-1090 . -189) 170434) ((-1090 . -241) 170399) ((-1090 . -810) 170312) ((-1090 . -807) 170200) ((-1090 . -812) 170113) ((-1090 . -887) 170083) ((-1090 . -38) 169980) ((-1090 . -82) 169845) ((-1090 . -964) 169731) ((-1090 . -969) 169617) ((-1090 . -583) 169514) ((-1090 . -655) 169411) ((-1090 . -118) 169390) ((-1090 . -120) 169369) ((-1090 . -146) 169323) ((-1090 . -496) 169302) ((-1090 . -246) 169281) ((-1090 . -47) 169258) ((-1090 . -1159) 169235) ((-1090 . -35) 169201) ((-1090 . -66) 169167) ((-1090 . -239) 169133) ((-1090 . -433) 169099) ((-1090 . -1119) 169065) ((-1090 . -1116) 169031) ((-1090 . -916) 168997) ((-1089 . -1165) 168958) ((-1089 . -312) 168937) ((-1089 . -1135) 168916) ((-1089 . -833) 168895) ((-1089 . -496) 168849) ((-1089 . -146) 168783) ((-1089 . -556) 168532) ((-1089 . -655) 168379) ((-1089 . -583) 168226) ((-1089 . -38) 168073) ((-1089 . -392) 168052) ((-1089 . -258) 168031) ((-1089 . -591) 167931) ((-1089 . -589) 167816) ((-1089 . -971) T) ((-1089 . -1026) T) ((-1089 . -1062) T) ((-1089 . -664) T) ((-1089 . -962) T) ((-1089 . -82) 167636) ((-1089 . -964) 167477) ((-1089 . -969) 167318) ((-1089 . -21) T) ((-1089 . -23) T) ((-1089 . -1014) T) ((-1089 . -553) 167300) ((-1089 . -1130) T) ((-1089 . -13) T) ((-1089 . -72) T) ((-1089 . -25) T) ((-1089 . -104) T) ((-1089 . -246) 167254) ((-1089 . -201) 167233) ((-1089 . -916) 167199) ((-1089 . -1116) 167165) ((-1089 . -1119) 167131) ((-1089 . -433) 167097) ((-1089 . -239) 167063) ((-1089 . -66) 167029) ((-1089 . -35) 166995) ((-1089 . -1159) 166965) ((-1089 . -47) 166935) ((-1089 . -120) 166914) ((-1089 . -118) 166893) ((-1089 . -887) 166856) ((-1089 . -812) 166762) ((-1089 . -807) 166643) ((-1089 . -810) 166549) ((-1089 . -241) 166507) ((-1089 . -189) 166459) ((-1089 . -186) 166405) ((-1089 . -190) 166357) ((-1089 . -1163) 166341) ((-1089 . -951) 166276) ((-1086 . -1156) 166260) ((-1086 . -1067) 166238) ((-1086 . -554) NIL) ((-1086 . -260) 166225) ((-1086 . -456) 166173) ((-1086 . -277) 166150) ((-1086 . -951) 166033) ((-1086 . -355) 166017) ((-1086 . -38) 165849) ((-1086 . -82) 165654) ((-1086 . -964) 165480) ((-1086 . -969) 165306) ((-1086 . -589) 165216) ((-1086 . -591) 165105) ((-1086 . -583) 164937) ((-1086 . -655) 164769) ((-1086 . -556) 164546) ((-1086 . -118) 164525) ((-1086 . -120) 164504) ((-1086 . -47) 164481) ((-1086 . -329) 164465) ((-1086 . -581) 164413) ((-1086 . -810) 164357) ((-1086 . -807) 164264) ((-1086 . -812) 164175) ((-1086 . -797) NIL) ((-1086 . -822) 164154) ((-1086 . -1135) 164133) ((-1086 . -862) 164103) ((-1086 . -833) 164082) ((-1086 . -496) 163996) ((-1086 . -246) 163910) ((-1086 . -146) 163804) ((-1086 . -392) 163738) ((-1086 . -258) 163717) ((-1086 . -241) 163644) ((-1086 . -190) T) ((-1086 . -104) T) ((-1086 . -25) T) ((-1086 . -72) T) ((-1086 . -553) 163626) ((-1086 . -1014) T) ((-1086 . -23) T) ((-1086 . -21) T) ((-1086 . -971) T) ((-1086 . -1026) T) ((-1086 . -1062) T) ((-1086 . -664) T) ((-1086 . -962) T) ((-1086 . -186) 163613) ((-1086 . -13) T) ((-1086 . -1130) T) ((-1086 . -189) T) ((-1086 . -225) 163597) ((-1086 . -184) 163581) ((-1083 . -1144) 163542) ((-1083 . -916) 163508) ((-1083 . -1116) 163474) ((-1083 . -1119) 163440) ((-1083 . -433) 163406) ((-1083 . -239) 163372) ((-1083 . -66) 163338) ((-1083 . -35) 163304) ((-1083 . -1159) 163281) ((-1083 . -47) 163258) ((-1083 . -556) 163059) ((-1083 . -655) 162861) ((-1083 . -583) 162663) ((-1083 . -591) 162518) ((-1083 . -589) 162358) ((-1083 . -969) 162154) ((-1083 . -964) 161950) ((-1083 . -82) 161702) ((-1083 . -38) 161504) ((-1083 . -887) 161474) ((-1083 . -241) 161302) ((-1083 . -1142) 161286) ((-1083 . -971) T) ((-1083 . -1026) T) ((-1083 . -1062) T) ((-1083 . -664) T) ((-1083 . -962) T) ((-1083 . -21) T) ((-1083 . -23) T) ((-1083 . -1014) T) ((-1083 . -553) 161268) ((-1083 . -1130) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1083 . -25) T) ((-1083 . -104) T) ((-1083 . -118) 161178) ((-1083 . -120) 161088) ((-1083 . -554) NIL) ((-1083 . -184) 161040) ((-1083 . -810) 160876) ((-1083 . -812) 160640) ((-1083 . -807) 160379) ((-1083 . -225) 160331) ((-1083 . -189) 160157) ((-1083 . -186) 159977) ((-1083 . -190) 159867) ((-1083 . -312) 159846) ((-1083 . -1135) 159825) ((-1083 . -833) 159804) ((-1083 . -496) 159758) ((-1083 . -146) 159692) ((-1083 . -392) 159671) ((-1083 . -258) 159650) ((-1083 . -246) 159604) ((-1083 . -201) 159583) ((-1083 . -288) 159535) ((-1083 . -456) 159269) ((-1083 . -260) 159154) ((-1083 . -329) 159106) ((-1083 . -581) 159058) ((-1083 . -343) 159010) ((-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) 158962) ((-1083 . -822) NIL) ((-1083 . -934) NIL) ((-1083 . -951) 158928) ((-1083 . -1067) NIL) ((-1083 . -905) 158880) ((-1082 . -996) T) ((-1082 . -430) 158861) ((-1082 . -553) 158827) ((-1082 . -556) 158808) ((-1082 . -1014) T) ((-1082 . -1130) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -64) T) ((-1081 . -1014) T) ((-1081 . -553) 158790) ((-1081 . -1130) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1080 . -1014) T) ((-1080 . -553) 158772) ((-1080 . -1130) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1075 . -1108) 158748) ((-1075 . -183) 158693) ((-1075 . -76) 158638) ((-1075 . -1036) 158570) ((-1075 . -124) 158515) ((-1075 . -554) NIL) ((-1075 . -193) 158460) ((-1075 . -539) 158436) ((-1075 . -260) 158225) ((-1075 . -456) 157965) ((-1075 . -429) 157897) ((-1075 . -241) 157873) ((-1075 . -243) 157849) ((-1075 . -550) 157825) ((-1075 . -1014) T) ((-1075 . -553) 157807) ((-1075 . -72) T) ((-1075 . -1130) T) ((-1075 . -13) T) ((-1075 . -34) T) ((-1075 . -318) 157752) ((-1074 . -1059) T) ((-1074 . -324) 157734) ((-1074 . -760) T) ((-1074 . -757) T) ((-1074 . -124) 157716) ((-1074 . -554) NIL) ((-1074 . -241) 157666) ((-1074 . -539) 157641) ((-1074 . -243) 157616) ((-1074 . -594) 157598) ((-1074 . -429) 157580) ((-1074 . -1014) T) ((-1074 . -456) NIL) ((-1074 . -260) NIL) ((-1074 . -553) 157562) ((-1074 . -72) T) ((-1074 . -1130) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 157544) ((-1074 . -1036) 157526) ((-1074 . -19) 157508) ((-1070 . -617) 157492) ((-1070 . -594) 157476) ((-1070 . -243) 157453) ((-1070 . -241) 157405) ((-1070 . -539) 157382) ((-1070 . -554) 157343) ((-1070 . -429) 157327) ((-1070 . -1014) 157305) ((-1070 . -456) 157238) ((-1070 . -260) 157176) ((-1070 . -553) 157111) ((-1070 . -72) 157065) ((-1070 . -1130) T) ((-1070 . -13) T) ((-1070 . -34) T) ((-1070 . -124) 157049) ((-1070 . -1169) 157033) ((-1070 . -924) 157017) ((-1070 . -1065) 157001) ((-1070 . -556) 156978) ((-1070 . -1036) 156962) ((-1068 . -996) T) ((-1068 . -430) 156943) ((-1068 . -553) 156909) ((-1068 . -556) 156890) ((-1068 . -1014) T) ((-1068 . -1130) T) ((-1068 . -13) T) ((-1068 . -72) T) ((-1068 . -64) T) ((-1066 . -1108) 156869) ((-1066 . -183) 156817) ((-1066 . -76) 156765) ((-1066 . -1036) 156700) ((-1066 . -124) 156648) ((-1066 . -554) NIL) ((-1066 . -193) 156596) ((-1066 . -539) 156575) ((-1066 . -260) 156373) ((-1066 . -456) 156125) ((-1066 . -429) 156060) ((-1066 . -241) 156039) ((-1066 . -243) 156018) ((-1066 . -550) 155997) ((-1066 . -1014) T) ((-1066 . -553) 155979) ((-1066 . -72) T) ((-1066 . -1130) T) ((-1066 . -13) T) ((-1066 . -34) T) ((-1066 . -318) 155927) ((-1063 . -1035) 155911) ((-1063 . -318) 155895) ((-1063 . -1036) 155879) ((-1063 . -34) T) ((-1063 . -13) T) ((-1063 . -1130) T) ((-1063 . -72) 155833) ((-1063 . -553) 155768) ((-1063 . -260) 155706) ((-1063 . -456) 155639) ((-1063 . -1014) 155617) ((-1063 . -429) 155601) ((-1063 . -76) 155585) ((-1061 . -1021) 155554) ((-1061 . -1125) 155523) ((-1061 . -1036) 155507) ((-1061 . -553) 155469) ((-1061 . -124) 155453) ((-1061 . -34) T) ((-1061 . -13) T) ((-1061 . -1130) T) ((-1061 . -72) T) ((-1061 . -260) 155391) ((-1061 . -456) 155324) ((-1061 . -1014) T) ((-1061 . -429) 155308) ((-1061 . -554) 155269) ((-1061 . -318) 155253) ((-1061 . -890) 155222) ((-1061 . -984) 155191) ((-1057 . -1038) 155136) ((-1057 . -318) 155120) ((-1057 . -34) T) ((-1057 . -260) 155058) ((-1057 . -456) 154991) ((-1057 . -429) 154975) ((-1057 . -966) 154915) ((-1057 . -951) 154813) ((-1057 . -556) 154732) ((-1057 . -355) 154716) ((-1057 . -581) 154664) ((-1057 . -591) 154602) ((-1057 . -329) 154586) ((-1057 . -190) 154565) ((-1057 . -186) 154513) ((-1057 . -189) 154467) ((-1057 . -225) 154451) ((-1057 . -807) 154375) ((-1057 . -812) 154301) ((-1057 . -810) 154260) ((-1057 . -184) 154244) ((-1057 . -655) 154179) ((-1057 . -583) 154114) ((-1057 . -589) 154073) ((-1057 . -104) T) ((-1057 . -25) T) ((-1057 . -72) T) ((-1057 . -13) T) ((-1057 . -1130) T) ((-1057 . -553) 154035) ((-1057 . -1014) T) ((-1057 . -23) T) ((-1057 . -21) T) ((-1057 . -969) 154019) ((-1057 . -964) 154003) ((-1057 . -82) 153982) ((-1057 . -962) T) ((-1057 . -664) T) ((-1057 . -1062) T) ((-1057 . -1026) T) ((-1057 . -971) T) ((-1057 . -38) 153942) ((-1057 . -554) 153903) ((-1056 . -924) 153874) ((-1056 . -34) T) ((-1056 . -13) T) ((-1056 . -1130) T) ((-1056 . -72) T) ((-1056 . -553) 153856) ((-1056 . -260) 153782) ((-1056 . -456) 153690) ((-1056 . -1014) T) ((-1056 . -429) 153661) ((-1056 . -318) 153632) ((-1056 . -1036) 153603) ((-1055 . -1014) T) ((-1055 . -553) 153585) ((-1055 . -1130) T) ((-1055 . -13) T) ((-1055 . -72) T) ((-1050 . -1052) T) ((-1050 . -1176) T) ((-1050 . -64) T) ((-1050 . -72) T) ((-1050 . -13) T) ((-1050 . -1130) T) ((-1050 . -553) 153551) ((-1050 . -1014) T) ((-1050 . -556) 153532) ((-1050 . -430) 153513) ((-1050 . -996) T) ((-1048 . -1049) 153497) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1130) T) ((-1048 . -553) 153479) ((-1048 . -1014) T) ((-1041 . -680) 153458) ((-1041 . -35) 153424) ((-1041 . -66) 153390) ((-1041 . -239) 153356) ((-1041 . -433) 153322) ((-1041 . -1119) 153288) ((-1041 . -1116) 153254) ((-1041 . -916) 153220) ((-1041 . -47) 153192) ((-1041 . -38) 153089) ((-1041 . -583) 152986) ((-1041 . -655) 152883) ((-1041 . -556) 152765) ((-1041 . -246) 152744) ((-1041 . -496) 152723) ((-1041 . -82) 152588) ((-1041 . -964) 152474) ((-1041 . -969) 152360) ((-1041 . -146) 152314) ((-1041 . -120) 152293) ((-1041 . -118) 152272) ((-1041 . -591) 152197) ((-1041 . -589) 152107) ((-1041 . -887) 152074) ((-1041 . -812) 152058) ((-1041 . -1130) T) ((-1041 . -13) T) ((-1041 . -807) 152040) ((-1041 . -962) T) ((-1041 . -664) T) ((-1041 . -1062) T) ((-1041 . -1026) T) ((-1041 . -971) T) ((-1041 . -21) T) ((-1041 . -23) T) ((-1041 . -1014) T) ((-1041 . -553) 152022) ((-1041 . -72) T) ((-1041 . -25) T) ((-1041 . -104) T) ((-1041 . -810) 152006) ((-1041 . -456) 151976) ((-1041 . -260) 151963) ((-1040 . -862) 151930) ((-1040 . -556) 151729) ((-1040 . -951) 151614) ((-1040 . -1135) 151593) ((-1040 . -822) 151572) ((-1040 . -797) 151431) ((-1040 . -812) 151415) ((-1040 . -807) 151397) ((-1040 . -810) 151381) ((-1040 . -456) 151333) ((-1040 . -392) 151287) ((-1040 . -581) 151235) ((-1040 . -591) 151124) ((-1040 . -329) 151108) ((-1040 . -47) 151080) ((-1040 . -38) 150932) ((-1040 . -583) 150784) ((-1040 . -655) 150636) ((-1040 . -246) 150570) ((-1040 . -496) 150504) ((-1040 . -82) 150329) ((-1040 . -964) 150175) ((-1040 . -969) 150021) ((-1040 . -146) 149935) ((-1040 . -120) 149914) ((-1040 . -118) 149893) ((-1040 . -589) 149803) ((-1040 . -104) T) ((-1040 . -25) T) ((-1040 . -72) T) ((-1040 . -13) T) ((-1040 . -1130) T) ((-1040 . -553) 149785) ((-1040 . -1014) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -962) T) ((-1040 . -664) T) ((-1040 . -1062) T) ((-1040 . -1026) T) ((-1040 . -971) T) ((-1040 . -355) 149769) ((-1040 . -277) 149741) ((-1040 . -260) 149728) ((-1040 . -554) 149476) ((-1034 . -484) T) ((-1034 . -1135) T) ((-1034 . -1067) T) ((-1034 . -951) 149458) ((-1034 . -554) 149373) ((-1034 . -934) T) ((-1034 . -797) 149355) ((-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) 149327) ((-1034 . -581) 149309) ((-1034 . -833) T) ((-1034 . -496) T) ((-1034 . -246) T) ((-1034 . -146) T) ((-1034 . -556) 149281) ((-1034 . -655) 149268) ((-1034 . -583) 149255) ((-1034 . -969) 149242) ((-1034 . -964) 149229) ((-1034 . -82) 149214) ((-1034 . -38) 149201) ((-1034 . -392) T) ((-1034 . -258) T) ((-1034 . -189) T) ((-1034 . -186) 149188) ((-1034 . -190) T) ((-1034 . -116) T) ((-1034 . -962) T) ((-1034 . -664) T) ((-1034 . -1062) T) ((-1034 . -1026) T) ((-1034 . -971) T) ((-1034 . -21) T) ((-1034 . -589) 149160) ((-1034 . -23) T) ((-1034 . -1014) T) ((-1034 . -553) 149142) ((-1034 . -1130) T) ((-1034 . -13) T) ((-1034 . -72) T) ((-1034 . -25) T) ((-1034 . -104) T) ((-1034 . -120) T) ((-1034 . -753) T) ((-1034 . -320) T) ((-1034 . -84) T) ((-1034 . -605) T) ((-1030 . -996) T) ((-1030 . -430) 149123) ((-1030 . -553) 149089) ((-1030 . -556) 149070) ((-1030 . -1014) T) ((-1030 . -1130) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1030 . -64) T) ((-1029 . -1014) T) ((-1029 . -553) 149052) ((-1029 . -1130) T) ((-1029 . -13) T) ((-1029 . -72) T) ((-1027 . -196) 149031) ((-1027 . -1188) 149001) ((-1027 . -722) 148980) ((-1027 . -719) 148959) ((-1027 . -760) 148913) ((-1027 . -757) 148867) ((-1027 . -717) 148846) ((-1027 . -718) 148825) ((-1027 . -655) 148770) ((-1027 . -583) 148695) ((-1027 . -243) 148672) ((-1027 . -241) 148649) ((-1027 . -539) 148626) ((-1027 . -951) 148455) ((-1027 . -556) 148259) ((-1027 . -355) 148228) ((-1027 . -581) 148136) ((-1027 . -591) 147975) ((-1027 . -329) 147945) ((-1027 . -429) 147929) ((-1027 . -456) 147862) ((-1027 . -260) 147800) ((-1027 . -34) T) ((-1027 . -318) 147784) ((-1027 . -320) 147763) ((-1027 . -190) 147716) ((-1027 . -589) 147504) ((-1027 . -971) 147483) ((-1027 . -1026) 147462) ((-1027 . -1062) 147441) ((-1027 . -664) 147420) ((-1027 . -962) 147399) ((-1027 . -186) 147295) ((-1027 . -189) 147197) ((-1027 . -225) 147167) ((-1027 . -807) 147039) ((-1027 . -812) 146913) ((-1027 . -810) 146846) ((-1027 . -184) 146816) ((-1027 . -553) 146513) ((-1027 . -969) 146438) ((-1027 . -964) 146343) ((-1027 . -82) 146263) ((-1027 . -104) 146138) ((-1027 . -25) 145975) ((-1027 . -72) 145712) ((-1027 . -13) T) ((-1027 . -1130) T) ((-1027 . -1014) 145468) ((-1027 . -23) 145324) ((-1027 . -21) 145239) ((-1023 . -1024) 145223) ((-1023 . |MappingCategory|) 145197) ((-1023 . -1130) T) ((-1023 . -80) 145181) ((-1023 . -1014) T) ((-1023 . -553) 145163) ((-1023 . -13) T) ((-1023 . -72) T) ((-1018 . -1017) 145127) ((-1018 . -72) T) ((-1018 . -553) 145109) ((-1018 . -1014) T) ((-1018 . -241) 145065) ((-1018 . -1130) T) ((-1018 . -13) T) ((-1018 . -558) 144980) ((-1016 . -1017) 144932) ((-1016 . -72) T) ((-1016 . -553) 144914) ((-1016 . -1014) T) ((-1016 . -241) 144870) ((-1016 . -1130) T) ((-1016 . -13) T) ((-1016 . -558) 144773) ((-1015 . -320) T) ((-1015 . -72) T) ((-1015 . -13) T) ((-1015 . -1130) T) ((-1015 . -553) 144755) ((-1015 . -1014) T) ((-1010 . -369) 144739) ((-1010 . -1012) 144723) ((-1010 . -318) 144707) ((-1010 . -320) 144686) ((-1010 . -193) 144670) ((-1010 . -554) 144631) ((-1010 . -124) 144615) ((-1010 . -1036) 144599) ((-1010 . -34) T) ((-1010 . -13) T) ((-1010 . -1130) T) ((-1010 . -72) T) ((-1010 . -553) 144581) ((-1010 . -260) 144519) ((-1010 . -456) 144452) ((-1010 . -1014) T) ((-1010 . -429) 144436) ((-1010 . -76) 144420) ((-1010 . -183) 144404) ((-1009 . -996) T) ((-1009 . -430) 144385) ((-1009 . -553) 144351) ((-1009 . -556) 144332) ((-1009 . -1014) T) ((-1009 . -1130) T) ((-1009 . -13) T) ((-1009 . -72) T) ((-1009 . -64) T) ((-1005 . -1130) T) ((-1005 . -13) T) ((-1005 . -1014) 144302) ((-1005 . -553) 144261) ((-1005 . -72) 144231) ((-1004 . -996) T) ((-1004 . -430) 144212) ((-1004 . -553) 144178) ((-1004 . -556) 144159) ((-1004 . -1014) T) ((-1004 . -1130) T) ((-1004 . -13) T) ((-1004 . -72) T) ((-1004 . -64) T) ((-1002 . -1007) 144143) ((-1002 . -558) 144127) ((-1002 . -1014) 144105) ((-1002 . -553) 144072) ((-1002 . -1130) 144050) ((-1002 . -13) 144028) ((-1002 . -72) 144006) ((-1002 . -1008) 143964) ((-1001 . -228) 143948) ((-1001 . -556) 143932) ((-1001 . -951) 143916) ((-1001 . -760) T) ((-1001 . -72) T) ((-1001 . -1014) T) ((-1001 . -553) 143898) ((-1001 . -757) T) ((-1001 . -186) 143885) ((-1001 . -13) T) ((-1001 . -1130) T) ((-1001 . -189) T) ((-1000 . -213) 143822) ((-1000 . -556) 143565) ((-1000 . -951) 143394) ((-1000 . -554) NIL) ((-1000 . -277) 143355) ((-1000 . -355) 143339) ((-1000 . -38) 143191) ((-1000 . -82) 143016) ((-1000 . -964) 142862) ((-1000 . -969) 142708) ((-1000 . -589) 142618) ((-1000 . -591) 142507) ((-1000 . -583) 142359) ((-1000 . -655) 142211) ((-1000 . -118) 142190) ((-1000 . -120) 142169) ((-1000 . -146) 142083) ((-1000 . -496) 142017) ((-1000 . -246) 141951) ((-1000 . -47) 141912) ((-1000 . -329) 141896) ((-1000 . -581) 141844) ((-1000 . -392) 141798) ((-1000 . -456) 141661) ((-1000 . -810) 141596) ((-1000 . -807) 141494) ((-1000 . -812) 141396) ((-1000 . -797) NIL) ((-1000 . -822) 141375) ((-1000 . -1135) 141354) ((-1000 . -862) 141299) ((-1000 . -260) 141286) ((-1000 . -190) 141265) ((-1000 . -104) T) ((-1000 . -25) T) ((-1000 . -72) T) ((-1000 . -553) 141247) ((-1000 . -1014) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -971) T) ((-1000 . -1026) T) ((-1000 . -1062) T) ((-1000 . -664) T) ((-1000 . -962) T) ((-1000 . -186) 141195) ((-1000 . -13) T) ((-1000 . -1130) T) ((-1000 . -189) 141149) ((-1000 . -225) 141133) ((-1000 . -184) 141117) ((-998 . -553) 141099) ((-995 . -757) T) ((-995 . -553) 141081) ((-995 . -1014) T) ((-995 . -72) T) ((-995 . -13) T) ((-995 . -1130) T) ((-995 . -760) T) ((-995 . -554) 141062) ((-992 . -662) 141041) ((-992 . -951) 140939) ((-992 . -355) 140923) ((-992 . -581) 140871) ((-992 . -591) 140748) ((-992 . -329) 140732) ((-992 . -322) 140711) ((-992 . -120) 140690) ((-992 . -556) 140515) ((-992 . -655) 140389) ((-992 . -583) 140263) ((-992 . -589) 140161) ((-992 . -969) 140074) ((-992 . -964) 139987) ((-992 . -82) 139879) ((-992 . -38) 139753) ((-992 . -353) 139732) ((-992 . -345) 139711) ((-992 . -118) 139665) ((-992 . -1067) 139644) ((-992 . -299) 139623) ((-992 . -320) 139577) ((-992 . -201) 139531) ((-992 . -246) 139485) ((-992 . -258) 139439) ((-992 . -392) 139393) ((-992 . -496) 139347) ((-992 . -833) 139301) ((-992 . -1135) 139255) ((-992 . -312) 139209) ((-992 . -190) 139137) ((-992 . -186) 139013) ((-992 . -189) 138895) ((-992 . -225) 138865) ((-992 . -807) 138737) ((-992 . -812) 138611) ((-992 . -810) 138544) ((-992 . -184) 138514) ((-992 . -554) 138498) ((-992 . -21) T) ((-992 . -23) T) ((-992 . -1014) T) ((-992 . -553) 138480) ((-992 . -1130) T) ((-992 . -13) T) ((-992 . -72) T) ((-992 . -25) T) ((-992 . -104) T) ((-992 . -962) T) ((-992 . -664) T) ((-992 . -1062) T) ((-992 . -1026) T) ((-992 . -971) T) ((-992 . -146) T) ((-990 . -1014) T) ((-990 . -553) 138462) ((-990 . -1130) T) ((-990 . -13) T) ((-990 . -72) T) ((-990 . -241) 138441) ((-989 . -1014) T) ((-989 . -553) 138423) ((-989 . -1130) T) ((-989 . -13) T) ((-989 . -72) T) ((-988 . -1014) T) ((-988 . -553) 138405) ((-988 . -1130) T) ((-988 . -13) T) ((-988 . -72) T) ((-988 . -241) 138384) ((-988 . -951) 138361) ((-988 . -556) 138338) ((-987 . -1130) T) ((-987 . -13) T) ((-986 . -996) T) ((-986 . -430) 138319) ((-986 . -553) 138285) ((-986 . -556) 138266) ((-986 . -1014) T) ((-986 . -1130) T) ((-986 . -13) T) ((-986 . -72) T) ((-986 . -64) T) ((-979 . -996) T) ((-979 . -430) 138247) ((-979 . -553) 138213) ((-979 . -556) 138194) ((-979 . -1014) T) ((-979 . -1130) T) ((-979 . -13) T) ((-979 . -72) T) ((-979 . -64) T) ((-976 . -484) T) ((-976 . -1135) T) ((-976 . -1067) T) ((-976 . -951) 138176) ((-976 . -554) 138091) ((-976 . -934) T) ((-976 . -797) 138073) ((-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) 138045) ((-976 . -581) 138027) ((-976 . -833) T) ((-976 . -496) T) ((-976 . -246) T) ((-976 . -146) T) ((-976 . -556) 137999) ((-976 . -655) 137986) ((-976 . -583) 137973) ((-976 . -969) 137960) ((-976 . -964) 137947) ((-976 . -82) 137932) ((-976 . -38) 137919) ((-976 . -392) T) ((-976 . -258) T) ((-976 . -189) T) ((-976 . -186) 137906) ((-976 . -190) T) ((-976 . -116) T) ((-976 . -962) T) ((-976 . -664) T) ((-976 . -1062) T) ((-976 . -1026) T) ((-976 . -971) T) ((-976 . -21) T) ((-976 . -589) 137878) ((-976 . -23) T) ((-976 . -1014) T) ((-976 . -553) 137860) ((-976 . -1130) T) ((-976 . -13) T) ((-976 . -72) T) ((-976 . -25) T) ((-976 . -104) T) ((-976 . -120) T) ((-976 . -558) 137841) ((-975 . -981) 137820) ((-975 . -72) T) ((-975 . -13) T) ((-975 . -1130) T) ((-975 . -553) 137802) ((-975 . -1014) T) ((-972 . -1130) T) ((-972 . -13) T) ((-972 . -1014) 137780) ((-972 . -553) 137747) ((-972 . -72) 137725) ((-967 . -966) 137665) ((-967 . -583) 137610) ((-967 . -655) 137555) ((-967 . -429) 137539) ((-967 . -456) 137472) ((-967 . -260) 137410) ((-967 . -34) T) ((-967 . -318) 137394) ((-967 . -591) 137378) ((-967 . -589) 137347) ((-967 . -104) T) ((-967 . -25) T) ((-967 . -72) T) ((-967 . -13) T) ((-967 . -1130) T) ((-967 . -553) 137309) ((-967 . -1014) T) ((-967 . -23) T) ((-967 . -21) T) ((-967 . -969) 137293) ((-967 . -964) 137277) ((-967 . -82) 137256) ((-967 . -1188) 137226) ((-967 . -554) 137187) ((-959 . -984) 137116) ((-959 . -890) 137045) ((-959 . -318) 137010) ((-959 . -554) 136952) ((-959 . -429) 136917) ((-959 . -1014) T) ((-959 . -456) 136801) ((-959 . -260) 136709) ((-959 . -553) 136652) ((-959 . -72) T) ((-959 . -1130) T) ((-959 . -13) T) ((-959 . -34) T) ((-959 . -124) 136617) ((-959 . -1036) 136582) ((-959 . -1125) 136511) ((-949 . -996) T) ((-949 . -430) 136492) ((-949 . -553) 136458) ((-949 . -556) 136439) ((-949 . -1014) T) ((-949 . -1130) T) ((-949 . -13) T) ((-949 . -72) T) ((-949 . -64) T) ((-948 . -146) T) ((-948 . -556) 136408) ((-948 . -971) T) ((-948 . -1026) T) ((-948 . -1062) T) ((-948 . -664) T) 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134775) ((-918 . -756) T) ((-918 . -722) T) ((-918 . -719) T) ((-918 . -760) T) ((-918 . -757) T) ((-918 . -717) T) ((-918 . -715) T) ((-918 . -741) T) ((-918 . -797) 134757) ((-918 . -343) 134739) ((-918 . -581) 134721) ((-918 . -329) 134703) ((-918 . -241) NIL) ((-918 . -260) NIL) ((-918 . -456) NIL) ((-918 . -288) 134685) ((-918 . -201) T) ((-918 . -82) 134612) ((-918 . -964) 134562) ((-918 . -969) 134512) ((-918 . -246) T) ((-918 . -655) 134462) ((-918 . -583) 134412) ((-918 . -591) 134362) ((-918 . -589) 134312) ((-918 . -38) 134262) ((-918 . -258) T) ((-918 . -392) T) ((-918 . -146) T) ((-918 . -496) T) ((-918 . -833) T) ((-918 . -1135) T) ((-918 . -312) T) ((-918 . -190) T) ((-918 . -186) 134249) ((-918 . -189) T) ((-918 . -225) 134231) ((-918 . -807) NIL) ((-918 . -812) NIL) ((-918 . -810) NIL) ((-918 . -184) 134213) ((-918 . -120) T) ((-918 . -118) NIL) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1130) T) ((-918 . -553) 134173) ((-918 . 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-320) NIL) ((-917 . -299) NIL) ((-917 . -1067) NIL) ((-917 . -118) 133063) ((-917 . -345) NIL) ((-917 . -353) 133035) ((-917 . -120) 133007) ((-917 . -322) 132979) ((-917 . -329) 132956) ((-917 . -581) 132890) ((-917 . -355) 132867) ((-917 . -951) 132744) ((-917 . -662) 132716) ((-914 . -909) 132700) ((-914 . -318) 132684) ((-914 . -1036) 132668) ((-914 . -34) T) ((-914 . -13) T) ((-914 . -1130) T) ((-914 . -72) 132622) ((-914 . -553) 132557) ((-914 . -260) 132495) ((-914 . -456) 132428) ((-914 . -1014) 132406) ((-914 . -429) 132390) ((-914 . -76) 132374) ((-910 . -912) 132358) ((-910 . -760) 132337) ((-910 . -757) 132316) ((-910 . -951) 132214) ((-910 . -355) 132198) ((-910 . -581) 132146) ((-910 . -591) 132048) ((-910 . -329) 132032) ((-910 . -241) 131990) ((-910 . -260) 131955) ((-910 . -456) 131867) ((-910 . -288) 131851) ((-910 . -38) 131799) ((-910 . -82) 131677) ((-910 . -964) 131576) ((-910 . -969) 131475) ((-910 . -589) 131398) ((-910 . -583) 131346) ((-910 . -655) 131294) 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-1014) T) ((-900 . -553) 130503) ((-900 . -1130) T) ((-900 . -13) T) ((-900 . -72) T) ((-885 . -722) T) ((-885 . -719) T) ((-885 . -760) T) ((-885 . -757) T) ((-885 . -717) T) ((-885 . -23) T) ((-885 . -1014) T) ((-885 . -553) 130463) ((-885 . -1130) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -25) T) ((-885 . -104) T) ((-884 . -996) T) ((-884 . -430) 130444) ((-884 . -553) 130410) ((-884 . -556) 130391) ((-884 . -1014) T) ((-884 . -1130) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -64) T) ((-878 . -881) T) ((-878 . -72) T) ((-878 . -553) 130373) ((-878 . -1014) T) ((-878 . -605) T) ((-878 . -13) T) ((-878 . -1130) T) ((-878 . -84) T) ((-878 . -556) 130357) ((-877 . -553) 130339) ((-876 . -1014) T) ((-876 . -553) 130321) ((-876 . -1130) T) ((-876 . -13) T) ((-876 . -72) T) ((-876 . -320) 130274) ((-876 . -664) 130176) ((-876 . -1026) 130078) ((-876 . -23) 129892) ((-876 . -25) 129706) ((-876 . -104) 129564) ((-876 . -413) 129517) ((-876 . -21) 129472) ((-876 . -589) 129416) ((-876 . -718) 129369) ((-876 . -717) 129322) ((-876 . -757) 129224) ((-876 . -760) 129126) ((-876 . -719) 129079) ((-876 . -722) 129032) ((-870 . -19) 129016) ((-870 . -1036) 129000) ((-870 . -318) 128984) ((-870 . -34) T) ((-870 . -13) T) ((-870 . -1130) T) ((-870 . -72) 128918) ((-870 . -553) 128833) ((-870 . -260) 128771) ((-870 . -456) 128704) ((-870 . -1014) 128657) ((-870 . -429) 128641) ((-870 . -594) 128625) ((-870 . -243) 128602) ((-870 . -241) 128554) ((-870 . -539) 128531) ((-870 . -554) 128492) ((-870 . -124) 128476) ((-870 . -757) 128455) ((-870 . -760) 128434) ((-870 . -324) 128418) ((-868 . -277) 128397) ((-868 . -951) 128295) ((-868 . -355) 128279) ((-868 . -38) 128176) ((-868 . -556) 128033) ((-868 . -591) 127958) ((-868 . -589) 127868) ((-868 . -971) T) ((-868 . -1026) T) ((-868 . -1062) T) ((-868 . -664) T) ((-868 . -962) T) ((-868 . -82) 127733) ((-868 . -964) 127619) ((-868 . -969) 127505) ((-868 . -21) T) ((-868 . -23) T) ((-868 . -1014) T) ((-868 . -553) 127487) ((-868 . -1130) T) ((-868 . -13) T) ((-868 . -72) T) ((-868 . -25) T) ((-868 . -104) T) ((-868 . -583) 127384) ((-868 . -655) 127281) ((-868 . -118) 127260) ((-868 . -120) 127239) ((-868 . -146) 127193) ((-868 . -496) 127172) ((-868 . -246) 127151) ((-868 . -47) 127130) ((-866 . -1014) T) ((-866 . -553) 127096) ((-866 . -1130) T) ((-866 . -13) T) ((-866 . -72) T) ((-858 . -862) 127057) ((-858 . -556) 126853) ((-858 . -951) 126735) ((-858 . -1135) 126714) ((-858 . -822) 126693) ((-858 . -797) 126618) ((-858 . -812) 126599) ((-858 . -807) 126578) ((-858 . -810) 126559) ((-858 . -456) 126505) ((-858 . -392) 126459) ((-858 . -581) 126407) ((-858 . -591) 126296) ((-858 . -329) 126280) ((-858 . -47) 126249) ((-858 . -38) 126101) ((-858 . -583) 125953) ((-858 . -655) 125805) ((-858 . -246) 125739) ((-858 . -496) 125673) ((-858 . -82) 125498) ((-858 . -964) 125344) ((-858 . -969) 125190) ((-858 . -146) 125104) ((-858 . -120) 125083) ((-858 . -118) 125062) ((-858 . -589) 124972) ((-858 . -104) T) 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T) ((-831 . -1014) T) ((-831 . -553) 124032) ((-831 . -1130) T) ((-831 . -13) T) ((-831 . -72) T) ((-831 . -25) T) ((-831 . -664) T) ((-831 . -1026) T) ((-826 . -312) T) ((-826 . -1135) T) ((-826 . -833) T) ((-826 . -496) T) ((-826 . -146) T) ((-826 . -556) 123969) ((-826 . -655) 123921) ((-826 . -583) 123873) ((-826 . -38) 123825) ((-826 . -392) T) ((-826 . -258) T) ((-826 . -591) 123777) ((-826 . -589) 123714) ((-826 . -971) T) ((-826 . -1026) T) ((-826 . -1062) T) ((-826 . -664) T) ((-826 . -962) T) ((-826 . -82) 123645) ((-826 . -964) 123597) ((-826 . -969) 123549) ((-826 . -21) T) ((-826 . -23) T) ((-826 . -1014) T) ((-826 . -553) 123531) ((-826 . -1130) T) ((-826 . -13) T) ((-826 . -72) T) ((-826 . -25) T) ((-826 . -104) T) ((-826 . -246) T) ((-826 . -201) T) ((-818 . -299) T) ((-818 . -1067) T) ((-818 . -320) T) ((-818 . -118) T) ((-818 . -312) T) ((-818 . -1135) T) ((-818 . -833) T) ((-818 . -496) T) ((-818 . -146) T) ((-818 . -556) 123481) ((-818 . -655) 123446) ((-818 . -583) 123411) ((-818 . -38) 123376) ((-818 . -392) T) ((-818 . -258) T) ((-818 . -82) 123325) ((-818 . -964) 123290) ((-818 . -969) 123255) ((-818 . -589) 123205) ((-818 . -591) 123170) ((-818 . -246) T) ((-818 . -201) T) ((-818 . -345) T) ((-818 . -189) T) ((-818 . -1130) T) ((-818 . -13) T) ((-818 . -186) 123157) ((-818 . -962) T) ((-818 . -664) T) ((-818 . -1062) T) ((-818 . -1026) T) ((-818 . -971) T) ((-818 . -21) T) ((-818 . -23) T) ((-818 . -1014) T) ((-818 . -553) 123139) ((-818 . -72) T) ((-818 . -25) T) ((-818 . -104) T) ((-818 . -190) T) ((-818 . -280) 123126) ((-818 . -120) 123108) ((-818 . -951) 123095) ((-818 . -1188) 123082) ((-818 . -1199) 123069) ((-818 . -554) 123051) ((-817 . -1014) T) ((-817 . -553) 123033) ((-817 . -1130) T) ((-817 . -13) T) ((-817 . -72) T) ((-814 . -816) 123017) ((-814 . -760) 122971) ((-814 . -757) 122925) ((-814 . -664) T) ((-814 . -1014) T) ((-814 . -553) 122907) ((-814 . -72) T) ((-814 . -1026) T) ((-814 . -413) T) ((-814 . -1130) T) ((-814 . -13) T) ((-814 . -241) 122886) ((-813 . -92) 122870) ((-813 . -429) 122854) ((-813 . -1014) 122832) ((-813 . -456) 122765) ((-813 . -260) 122703) ((-813 . -553) 122617) ((-813 . -72) 122571) ((-813 . -1130) T) ((-813 . -13) T) ((-813 . -34) T) ((-813 . -924) 122555) ((-804 . -757) T) ((-804 . -553) 122537) ((-804 . -1014) T) ((-804 . -72) T) ((-804 . -13) T) ((-804 . -1130) T) ((-804 . -760) T) ((-804 . -951) 122514) ((-804 . -556) 122491) ((-801 . -1014) T) ((-801 . -553) 122473) ((-801 . -1130) T) ((-801 . -13) T) ((-801 . -72) T) ((-801 . -951) 122441) ((-801 . -556) 122409) ((-799 . -1014) T) ((-799 . -553) 122391) ((-799 . -1130) T) ((-799 . -13) T) ((-799 . -72) T) ((-796 . -1014) T) ((-796 . -553) 122373) ((-796 . -1130) T) ((-796 . -13) T) ((-796 . -72) T) ((-786 . -996) T) ((-786 . -430) 122354) ((-786 . -553) 122320) ((-786 . -556) 122301) ((-786 . -1014) T) ((-786 . -1130) T) ((-786 . -13) T) ((-786 . -72) T) ((-786 . -64) T) ((-786 . -1176) T) ((-784 . -1014) T) ((-784 . -553) 122283) ((-784 . -1130) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -556) 122265) ((-783 . -1130) T) ((-783 . -13) T) ((-783 . -553) 122140) ((-783 . -1014) 122091) ((-783 . -72) 122042) ((-782 . -905) 122026) ((-782 . -1067) 122004) ((-782 . -951) 121871) ((-782 . -556) 121770) ((-782 . -554) 121573) ((-782 . -934) 121552) ((-782 . -822) 121531) ((-782 . -795) 121515) ((-782 . -756) 121494) ((-782 . -722) 121473) ((-782 . -719) 121452) ((-782 . -760) 121406) ((-782 . -757) 121360) ((-782 . -717) 121339) ((-782 . -715) 121318) ((-782 . -741) 121297) ((-782 . -797) 121222) ((-782 . -343) 121206) ((-782 . -581) 121154) ((-782 . -591) 121070) ((-782 . -329) 121054) ((-782 . -241) 121012) ((-782 . -260) 120977) ((-782 . -456) 120889) ((-782 . -288) 120873) ((-782 . -201) T) ((-782 . -82) 120804) ((-782 . -964) 120756) ((-782 . -969) 120708) ((-782 . -246) T) ((-782 . -655) 120660) ((-782 . -583) 120612) ((-782 . -589) 120549) ((-782 . -38) 120501) ((-782 . -258) T) ((-782 . -392) T) 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. -583) 116020) ((-746 . -655) 115990) ((-744 . -1014) T) ((-744 . -553) 115972) ((-744 . -1130) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -355) 115956) ((-744 . -556) 115829) ((-744 . -951) 115727) ((-744 . -21) 115682) ((-744 . -589) 115602) ((-744 . -23) 115557) ((-744 . -25) 115512) ((-744 . -104) 115467) ((-744 . -756) 115446) ((-744 . -722) 115425) ((-744 . -719) 115404) ((-744 . -760) 115383) ((-744 . -757) 115362) ((-744 . -717) 115341) ((-744 . -715) 115320) ((-744 . -962) 115299) ((-744 . -664) 115278) ((-744 . -1062) 115257) ((-744 . -1026) 115236) ((-744 . -971) 115215) ((-744 . -591) 115188) ((-744 . -120) 115167) ((-742 . -646) 115151) ((-742 . -556) 115106) ((-742 . -655) 115076) ((-742 . -583) 115046) ((-742 . -591) 115020) ((-742 . -589) 114979) ((-742 . -104) T) ((-742 . -25) T) ((-742 . -72) T) ((-742 . -13) T) ((-742 . -1130) T) ((-742 . -553) 114961) ((-742 . -1014) T) ((-742 . -23) T) ((-742 . -21) T) ((-742 . -969) 114945) ((-742 . -964) 114929) ((-742 . -82) 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. -807) 104320) ((-705 . -812) 104231) ((-705 . -797) NIL) ((-705 . -822) 104210) ((-705 . -1135) 104189) ((-705 . -862) 104159) ((-705 . -833) 104138) ((-705 . -496) 104052) ((-705 . -246) 103966) ((-705 . -146) 103860) ((-705 . -392) 103794) ((-705 . -258) 103773) ((-705 . -241) 103700) ((-705 . -190) T) ((-705 . -104) T) ((-705 . -25) T) ((-705 . -72) T) ((-705 . -553) 103661) ((-705 . -1014) T) ((-705 . -23) T) ((-705 . -21) T) ((-705 . -971) T) ((-705 . -1026) T) ((-705 . -1062) T) ((-705 . -664) T) ((-705 . -962) T) ((-705 . -186) 103648) ((-705 . -13) T) ((-705 . -1130) T) ((-705 . -189) T) ((-705 . -225) 103632) ((-705 . -184) 103616) ((-704 . -978) 103583) ((-704 . -554) 103218) ((-704 . -260) 103205) ((-704 . -456) 103157) ((-704 . -277) 103129) ((-704 . -951) 102988) ((-704 . -355) 102972) ((-704 . -38) 102824) ((-704 . -556) 102597) ((-704 . -591) 102486) ((-704 . -589) 102396) ((-704 . -971) T) ((-704 . -1026) T) ((-704 . -1062) T) ((-704 . -664) T) ((-704 . -962) T) 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. -964) 81082) ((-520 . -82) 81043) ((-520 . -951) 81027) ((-520 . -556) 81011) ((-518 . -299) T) ((-518 . -1067) T) ((-518 . -320) T) ((-518 . -118) T) ((-518 . -312) T) ((-518 . -1135) T) ((-518 . -833) T) ((-518 . -496) T) ((-518 . -146) T) ((-518 . -556) 80961) ((-518 . -655) 80926) ((-518 . -583) 80891) ((-518 . -38) 80856) ((-518 . -392) T) ((-518 . -258) T) ((-518 . -82) 80805) ((-518 . -964) 80770) ((-518 . -969) 80735) ((-518 . -589) 80685) ((-518 . -591) 80650) ((-518 . -246) T) ((-518 . -201) T) ((-518 . -345) T) ((-518 . -189) T) ((-518 . -1130) T) ((-518 . -13) T) ((-518 . -186) 80637) ((-518 . -962) T) ((-518 . -664) T) ((-518 . -1062) T) ((-518 . -1026) T) ((-518 . -971) T) ((-518 . -21) T) ((-518 . -23) T) ((-518 . -1014) T) ((-518 . -553) 80619) ((-518 . -72) T) ((-518 . -25) T) ((-518 . -104) T) ((-518 . -190) T) ((-518 . -280) 80606) ((-518 . -120) 80588) ((-518 . -951) 80575) ((-518 . -1188) 80562) ((-518 . -1199) 80549) ((-518 . -554) 80531) ((-517 . -780) 80515) 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-1130) T) ((-431 . -13) T) ((-431 . -72) T) ((-427 . -905) 74286) ((-427 . -1067) T) ((-427 . -556) 74236) ((-427 . -951) 74196) ((-427 . -554) 74126) ((-427 . -934) T) ((-427 . -822) NIL) ((-427 . -795) 74108) ((-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) 74090) ((-427 . -343) 74072) ((-427 . -581) 74054) ((-427 . -329) 74036) ((-427 . -241) NIL) ((-427 . -260) NIL) ((-427 . -456) NIL) ((-427 . -288) 74018) ((-427 . -201) T) ((-427 . -82) 73945) ((-427 . -964) 73895) ((-427 . -969) 73845) ((-427 . -246) T) ((-427 . -655) 73795) ((-427 . -583) 73745) ((-427 . -591) 73695) ((-427 . -589) 73645) ((-427 . -38) 73595) ((-427 . -258) T) ((-427 . -392) T) ((-427 . -146) T) ((-427 . -496) T) ((-427 . -833) T) ((-427 . -1135) T) ((-427 . -312) T) ((-427 . -190) T) ((-427 . -186) 73582) ((-427 . -189) T) ((-427 . -225) 73564) ((-427 . -807) NIL) ((-427 . -812) NIL) ((-427 . -810) NIL) ((-427 . -184) 73546) ((-427 . -120) T) ((-427 . -118) NIL) ((-427 . -104) T) ((-427 . -25) T) ((-427 . -72) T) ((-427 . -13) T) ((-427 . -1130) T) ((-427 . -553) 73488) ((-427 . -1014) T) ((-427 . -23) T) ((-427 . -21) T) ((-427 . -962) T) ((-427 . -664) T) ((-427 . -1062) T) ((-427 . -1026) T) ((-427 . -971) T) ((-425 . -286) 73457) ((-425 . -104) T) ((-425 . -25) T) ((-425 . -72) T) ((-425 . -13) T) ((-425 . -1130) T) ((-425 . -553) 73439) ((-425 . -1014) T) ((-425 . -23) T) ((-425 . -589) 73421) ((-425 . -21) T) ((-424 . -882) 73405) ((-424 . -318) 73389) ((-424 . -1036) 73373) ((-424 . -34) T) ((-424 . -13) T) ((-424 . -1130) T) ((-424 . -72) 73327) ((-424 . -553) 73262) ((-424 . -260) 73200) ((-424 . -456) 73133) ((-424 . -1014) 73111) ((-424 . -429) 73095) ((-424 . -76) 73079) ((-423 . -996) T) ((-423 . -430) 73060) ((-423 . -553) 73026) ((-423 . -556) 73007) ((-423 . -1014) T) ((-423 . -1130) T) ((-423 . -13) T) ((-423 . -72) T) ((-423 . -64) T) ((-422 . -196) 72986) 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T) ((-422 . -1130) T) ((-422 . -1014) 69423) ((-422 . -23) 69279) ((-422 . -21) 69194) ((-421 . -862) 69139) ((-421 . -556) 68931) ((-421 . -951) 68809) ((-421 . -1135) 68788) ((-421 . -822) 68767) ((-421 . -797) NIL) ((-421 . -812) 68744) ((-421 . -807) 68719) ((-421 . -810) 68696) ((-421 . -456) 68634) ((-421 . -392) 68588) ((-421 . -581) 68536) ((-421 . -591) 68425) ((-421 . -329) 68409) ((-421 . -47) 68366) ((-421 . -38) 68218) ((-421 . -583) 68070) ((-421 . -655) 67922) ((-421 . -246) 67856) ((-421 . -496) 67790) ((-421 . -82) 67615) ((-421 . -964) 67461) ((-421 . -969) 67307) ((-421 . -146) 67221) ((-421 . -120) 67200) ((-421 . -118) 67179) ((-421 . -589) 67089) ((-421 . -104) T) ((-421 . -25) T) ((-421 . -72) T) ((-421 . -13) T) ((-421 . -1130) T) ((-421 . -553) 67071) ((-421 . -1014) T) ((-421 . -23) T) ((-421 . -21) T) ((-421 . -962) T) ((-421 . -664) T) ((-421 . -1062) T) ((-421 . -1026) T) ((-421 . -971) T) ((-421 . -355) 67055) ((-421 . -277) 67012) ((-421 . -260) 66999) ((-421 . -554) 66860) ((-419 . -1108) 66839) ((-419 . -183) 66787) ((-419 . -76) 66735) ((-419 . -1036) 66670) ((-419 . -124) 66618) ((-419 . -554) NIL) ((-419 . -193) 66566) ((-419 . -539) 66545) ((-419 . -260) 66343) ((-419 . -456) 66095) ((-419 . -429) 66030) ((-419 . -241) 66009) ((-419 . -243) 65988) ((-419 . -550) 65967) ((-419 . -1014) T) ((-419 . -553) 65949) ((-419 . -72) T) ((-419 . -1130) T) ((-419 . -13) T) ((-419 . -34) T) ((-419 . -318) 65897) ((-418 . -996) T) ((-418 . -430) 65878) ((-418 . -553) 65844) ((-418 . -556) 65825) ((-418 . -1014) T) ((-418 . -1130) T) ((-418 . -13) T) ((-418 . -72) T) ((-418 . -64) T) ((-417 . -312) T) ((-417 . -1135) T) ((-417 . -833) T) ((-417 . -496) T) ((-417 . -146) T) ((-417 . -556) 65775) ((-417 . -655) 65740) ((-417 . -583) 65705) ((-417 . -38) 65670) ((-417 . -392) T) ((-417 . -258) T) ((-417 . -591) 65635) ((-417 . -589) 65585) ((-417 . -971) T) ((-417 . -1026) T) ((-417 . -1062) T) ((-417 . -664) T) ((-417 . -962) T) ((-417 . -82) 65534) ((-417 . -964) 65499) ((-417 . -969) 65464) ((-417 . -21) T) ((-417 . -23) T) ((-417 . -1014) T) ((-417 . -553) 65416) ((-417 . -1130) T) ((-417 . -13) T) ((-417 . -72) T) ((-417 . -25) T) ((-417 . -104) T) ((-417 . -246) T) ((-417 . -201) T) ((-417 . -120) T) ((-417 . -951) 65376) ((-417 . -934) T) ((-417 . -554) 65298) ((-416 . -1125) 65267) ((-416 . -1036) 65251) ((-416 . -553) 65213) ((-416 . -124) 65197) ((-416 . -34) T) ((-416 . -13) T) ((-416 . -1130) T) ((-416 . -72) T) ((-416 . -260) 65135) ((-416 . -456) 65068) ((-416 . -1014) T) ((-416 . -429) 65052) ((-416 . -554) 65013) ((-416 . -318) 64997) ((-416 . -890) 64966) ((-415 . -1108) 64945) ((-415 . -183) 64893) ((-415 . -76) 64841) ((-415 . -1036) 64776) ((-415 . -124) 64724) ((-415 . -554) NIL) ((-415 . -193) 64672) ((-415 . -539) 64651) ((-415 . -260) 64449) ((-415 . -456) 64201) ((-415 . -429) 64136) ((-415 . -241) 64115) ((-415 . -243) 64094) ((-415 . -550) 64073) ((-415 . -1014) T) ((-415 . -553) 64055) ((-415 . -72) T) ((-415 . -1130) T) ((-415 . -13) T) ((-415 . -34) T) ((-415 . -318) 64003) ((-414 . -1163) 63987) ((-414 . -190) 63939) ((-414 . -186) 63885) ((-414 . -189) 63837) ((-414 . -241) 63795) ((-414 . -810) 63701) ((-414 . -807) 63582) ((-414 . -812) 63488) ((-414 . -887) 63451) ((-414 . -38) 63298) ((-414 . -82) 63118) ((-414 . -964) 62959) ((-414 . -969) 62800) ((-414 . -589) 62685) ((-414 . -591) 62585) ((-414 . -583) 62432) ((-414 . -655) 62279) ((-414 . -556) 62111) ((-414 . -118) 62090) ((-414 . -120) 62069) ((-414 . -47) 62039) ((-414 . -1159) 62009) ((-414 . -35) 61975) ((-414 . -66) 61941) ((-414 . -239) 61907) ((-414 . -433) 61873) ((-414 . -1119) 61839) ((-414 . -1116) 61805) ((-414 . -916) 61771) ((-414 . -201) 61750) ((-414 . -246) 61704) ((-414 . -104) T) ((-414 . -25) T) ((-414 . -72) T) ((-414 . -13) T) ((-414 . -1130) T) ((-414 . -553) 61686) ((-414 . -1014) T) ((-414 . -23) T) ((-414 . -21) T) ((-414 . -962) T) ((-414 . -664) T) ((-414 . -1062) T) ((-414 . -1026) T) ((-414 . -971) T) ((-414 . -258) 61665) ((-414 . -392) 61644) ((-414 . -146) 61578) ((-414 . -496) 61532) ((-414 . -833) 61511) ((-414 . -1135) 61490) ((-414 . -312) 61469) ((-408 . -1014) T) ((-408 . -553) 61451) ((-408 . -1130) T) ((-408 . -13) T) ((-408 . -72) T) ((-403 . -890) 61420) ((-403 . -318) 61404) ((-403 . -554) 61365) ((-403 . -429) 61349) ((-403 . -1014) T) ((-403 . -456) 61282) ((-403 . -260) 61220) ((-403 . -553) 61182) ((-403 . -72) T) ((-403 . -1130) T) ((-403 . -13) T) ((-403 . -34) T) ((-403 . -124) 61166) ((-403 . -1036) 61150) ((-401 . -655) 61121) ((-401 . -583) 61092) ((-401 . -591) 61063) ((-401 . -589) 61019) ((-401 . -104) T) ((-401 . -25) T) ((-401 . -72) T) ((-401 . -13) T) ((-401 . -1130) T) ((-401 . -553) 61001) ((-401 . -1014) T) ((-401 . -23) T) ((-401 . -21) T) ((-401 . -969) 60972) ((-401 . -964) 60943) ((-401 . -82) 60904) ((-394 . -862) 60871) ((-394 . -556) 60663) ((-394 . -951) 60541) ((-394 . -1135) 60520) ((-394 . -822) 60499) ((-394 . -797) NIL) ((-394 . -812) 60476) ((-394 . -807) 60451) ((-394 . -810) 60428) ((-394 . -456) 60366) ((-394 . -392) 60320) ((-394 . -581) 60268) ((-394 . -591) 60157) ((-394 . -329) 60141) ((-394 . -47) 60120) ((-394 . -38) 59972) ((-394 . -583) 59824) ((-394 . -655) 59676) ((-394 . -246) 59610) ((-394 . -496) 59544) ((-394 . -82) 59369) ((-394 . -964) 59215) ((-394 . -969) 59061) ((-394 . -146) 58975) ((-394 . -120) 58954) ((-394 . -118) 58933) ((-394 . -589) 58843) ((-394 . -104) T) ((-394 . -25) T) ((-394 . -72) T) ((-394 . -13) T) ((-394 . -1130) T) ((-394 . -553) 58825) ((-394 . -1014) T) ((-394 . -23) T) ((-394 . -21) T) ((-394 . -962) T) ((-394 . -664) T) ((-394 . -1062) T) ((-394 . -1026) T) ((-394 . -971) T) ((-394 . -355) 58809) ((-394 . -277) 58788) ((-394 . -260) 58775) ((-394 . -554) 58636) ((-393 . -361) 58606) ((-393 . -684) 58576) ((-393 . -658) T) ((-393 . -686) T) ((-393 . -82) 58527) ((-393 . -964) 58497) ((-393 . -969) 58467) ((-393 . -21) T) ((-393 . -589) 58382) ((-393 . -23) T) ((-393 . -1014) T) ((-393 . -553) 58364) ((-393 . -72) T) ((-393 . -25) T) ((-393 . -104) T) ((-393 . -591) 58294) ((-393 . -583) 58264) ((-393 . -655) 58234) ((-393 . -316) 58204) ((-393 . -1130) T) ((-393 . -13) T) ((-393 . -241) 58167) ((-381 . -1014) T) ((-381 . -553) 58149) ((-381 . -1130) T) ((-381 . -13) T) ((-381 . -72) T) ((-380 . -1014) T) ((-380 . -553) 58131) ((-380 . -1130) T) ((-380 . -13) T) ((-380 . -72) T) ((-379 . -1014) T) ((-379 . -553) 58113) ((-379 . -1130) T) ((-379 . -13) T) ((-379 . -72) T) ((-377 . -553) 58095) ((-372 . -38) 58079) ((-372 . -556) 58048) ((-372 . -591) 58022) ((-372 . -589) 57981) ((-372 . -971) T) ((-372 . -1026) T) ((-372 . -1062) T) ((-372 . -664) T) ((-372 . -962) T) ((-372 . -82) 57960) ((-372 . -964) 57944) ((-372 . -969) 57928) ((-372 . -21) T) ((-372 . -23) T) ((-372 . -1014) T) ((-372 . -553) 57910) ((-372 . -1130) T) ((-372 . -13) T) ((-372 . -72) T) ((-372 . -25) T) ((-372 . -104) T) ((-372 . -583) 57894) ((-372 . -655) 57878) ((-358 . -664) T) ((-358 . -1014) T) ((-358 . -553) 57860) ((-358 . -1130) T) ((-358 . -13) T) ((-358 . -72) T) ((-358 . -1026) T) ((-356 . -413) T) ((-356 . -1026) T) ((-356 . -72) T) ((-356 . -13) T) ((-356 . -1130) T) ((-356 . -553) 57842) ((-356 . -1014) T) ((-356 . -664) T) ((-350 . -905) 57826) ((-350 . -1067) 57804) ((-350 . -951) 57671) ((-350 . -556) 57570) ((-350 . -554) 57373) ((-350 . -934) 57352) ((-350 . -822) 57331) ((-350 . -795) 57315) ((-350 . -756) 57294) ((-350 . -722) 57273) ((-350 . -719) 57252) ((-350 . -760) 57206) ((-350 . -757) 57160) ((-350 . -717) 57139) ((-350 . -715) 57118) ((-350 . -741) 57097) ((-350 . -797) 57022) ((-350 . -343) 57006) ((-350 . -581) 56954) ((-350 . -591) 56870) ((-350 . -329) 56854) ((-350 . -241) 56812) ((-350 . -260) 56777) ((-350 . -456) 56689) ((-350 . -288) 56673) ((-350 . -201) T) ((-350 . -82) 56604) ((-350 . -964) 56556) ((-350 . -969) 56508) ((-350 . -246) T) ((-350 . -655) 56460) ((-350 . -583) 56412) ((-350 . -589) 56349) ((-350 . -38) 56301) ((-350 . -258) T) ((-350 . -392) T) ((-350 . -146) T) ((-350 . -496) T) ((-350 . -833) T) ((-350 . -1135) T) ((-350 . -312) T) ((-350 . -190) 56280) ((-350 . -186) 56228) ((-350 . -189) 56182) ((-350 . -225) 56166) ((-350 . -807) 56090) ((-350 . -812) 56016) ((-350 . -810) 55975) ((-350 . -184) 55959) ((-350 . -120) 55913) ((-350 . -118) 55892) ((-350 . -104) T) ((-350 . -25) T) ((-350 . -72) T) ((-350 . -13) T) ((-350 . -1130) T) ((-350 . -553) 55874) ((-350 . -1014) T) ((-350 . -23) T) ((-350 . -21) T) ((-350 . -962) T) ((-350 . -664) T) ((-350 . -1062) T) ((-350 . -1026) T) ((-350 . -971) T) ((-348 . -496) T) ((-348 . -246) T) ((-348 . -146) T) ((-348 . -556) 55783) ((-348 . -655) 55757) ((-348 . -583) 55731) ((-348 . -591) 55705) ((-348 . -589) 55664) ((-348 . -104) T) ((-348 . -25) T) ((-348 . -72) T) ((-348 . -13) T) ((-348 . -1130) T) ((-348 . -553) 55646) ((-348 . -1014) T) ((-348 . -23) T) ((-348 . -21) T) ((-348 . -969) 55620) ((-348 . -964) 55594) ((-348 . -82) 55561) ((-348 . -962) T) ((-348 . -664) T) ((-348 . -1062) T) ((-348 . -1026) T) ((-348 . -971) T) ((-348 . -38) 55535) ((-348 . -184) 55519) ((-348 . -810) 55478) ((-348 . -812) 55404) ((-348 . -807) 55328) ((-348 . -225) 55312) ((-348 . -189) 55266) ((-348 . -186) 55214) ((-348 . -190) 55193) ((-348 . -288) 55177) ((-348 . -456) 55019) ((-348 . -260) 54958) ((-348 . -241) 54886) ((-348 . -355) 54870) ((-348 . -951) 54768) ((-348 . -392) 54721) ((-348 . -934) 54700) ((-348 . -554) 54603) ((-348 . -1135) 54581) ((-342 . -1014) T) ((-342 . -553) 54563) ((-342 . -1130) T) ((-342 . -13) T) ((-342 . -72) T) ((-342 . -189) T) ((-342 . -186) 54550) ((-342 . -554) 54527) ((-340 . -684) 54511) ((-340 . -658) T) ((-340 . -686) T) ((-340 . -82) 54490) ((-340 . -964) 54474) ((-340 . -969) 54458) ((-340 . -21) T) ((-340 . -589) 54427) ((-340 . -23) T) ((-340 . -1014) T) ((-340 . -553) 54409) ((-340 . -1130) T) ((-340 . -13) T) ((-340 . -72) T) ((-340 . -25) T) ((-340 . -104) T) ((-340 . -591) 54393) ((-340 . -583) 54377) ((-340 . -655) 54361) ((-338 . -339) T) ((-338 . -72) T) ((-338 . -13) T) ((-338 . -1130) T) ((-338 . -553) 54327) ((-338 . -1014) T) ((-338 . -556) 54308) ((-338 . -430) 54289) ((-337 . -336) 54273) ((-337 . -556) 54257) ((-337 . -951) 54241) ((-337 . -760) 54220) ((-337 . -757) 54199) ((-337 . -1026) T) ((-337 . -72) T) ((-337 . -13) T) ((-337 . -1130) T) ((-337 . -553) 54181) ((-337 . -1014) T) ((-337 . -664) T) ((-334 . -335) 54160) ((-334 . -556) 54144) ((-334 . -951) 54128) ((-334 . -583) 54098) ((-334 . -655) 54068) ((-334 . -591) 54052) ((-334 . -589) 54021) ((-334 . -104) T) ((-334 . -25) T) ((-334 . -72) T) ((-334 . -13) T) ((-334 . -1130) T) ((-334 . -553) 54003) ((-334 . -1014) T) ((-334 . -23) T) ((-334 . -21) T) ((-334 . -969) 53987) ((-334 . -964) 53971) ((-334 . -82) 53950) ((-333 . -82) 53929) ((-333 . -964) 53913) ((-333 . -969) 53897) ((-333 . -21) T) ((-333 . -589) 53866) ((-333 . -23) T) ((-333 . -1014) T) ((-333 . -553) 53848) ((-333 . -1130) T) ((-333 . -13) T) ((-333 . -72) T) ((-333 . -25) T) ((-333 . -104) T) ((-333 . -591) 53832) ((-333 . -450) 53811) ((-333 . -558) 53776) ((-333 . -655) 53746) ((-333 . -583) 53716) ((-330 . -347) T) ((-330 . -120) T) ((-330 . -556) 53666) ((-330 . -591) 53631) ((-330 . -589) 53581) ((-330 . -104) T) ((-330 . -25) T) ((-330 . -72) T) ((-330 . -13) T) ((-330 . -1130) T) ((-330 . -553) 53548) ((-330 . -1014) T) ((-330 . -23) T) ((-330 . -21) T) ((-330 . -971) T) ((-330 . -1026) T) ((-330 . -1062) T) ((-330 . -664) T) ((-330 . -962) T) ((-330 . -554) 53462) ((-330 . -312) T) ((-330 . -1135) T) ((-330 . -833) T) ((-330 . -496) T) ((-330 . -146) T) ((-330 . -655) 53427) ((-330 . -583) 53392) ((-330 . -38) 53357) ((-330 . -392) T) ((-330 . -258) T) ((-330 . -82) 53306) ((-330 . -964) 53271) ((-330 . -969) 53236) ((-330 . -246) T) ((-330 . -201) T) ((-330 . -756) T) ((-330 . -722) T) ((-330 . -719) T) ((-330 . -760) T) ((-330 . -757) T) ((-330 . -717) T) ((-330 . -715) T) ((-330 . -797) 53218) ((-330 . -916) T) ((-330 . -934) T) ((-330 . -951) 53178) ((-330 . -974) T) ((-330 . -190) T) ((-330 . -186) 53165) ((-330 . -189) T) ((-330 . -1116) T) ((-330 . -1119) T) ((-330 . -433) T) ((-330 . -239) T) ((-330 . -66) T) ((-330 . -35) T) ((-330 . -558) 53147) ((-313 . -314) 53124) ((-313 . -72) T) ((-313 . -13) T) ((-313 . -1130) T) ((-313 . -553) 53106) ((-313 . -1014) T) ((-310 . -413) T) ((-310 . -1026) T) ((-310 . -72) T) ((-310 . -13) T) ((-310 . -1130) T) ((-310 . -553) 53088) ((-310 . -1014) T) ((-310 . -664) T) ((-310 . -951) 53072) ((-310 . -556) 53056) ((-308 . -280) 53040) ((-308 . -190) 53019) ((-308 . -186) 52992) ((-308 . -189) 52971) ((-308 . -320) 52950) ((-308 . -1067) 52929) ((-308 . -299) 52908) ((-308 . -120) 52887) ((-308 . -556) 52824) ((-308 . -591) 52776) ((-308 . -589) 52713) ((-308 . -104) T) ((-308 . -25) T) ((-308 . -72) T) ((-308 . -13) T) ((-308 . -1130) T) ((-308 . -553) 52695) ((-308 . -1014) T) ((-308 . -23) T) ((-308 . -21) T) ((-308 . -971) T) ((-308 . -1026) T) ((-308 . -1062) T) ((-308 . -664) T) ((-308 . -962) T) ((-308 . -312) T) ((-308 . -1135) T) ((-308 . -833) T) ((-308 . -496) T) ((-308 . -146) T) ((-308 . -655) 52647) ((-308 . -583) 52599) ((-308 . -38) 52564) ((-308 . -392) T) ((-308 . -258) T) ((-308 . -82) 52495) ((-308 . -964) 52447) ((-308 . -969) 52399) ((-308 . -246) T) ((-308 . -201) T) ((-308 . -345) 52353) ((-308 . -118) 52307) ((-308 . -951) 52291) ((-308 . -1188) 52275) ((-308 . -1199) 52259) ((-304 . -280) 52243) ((-304 . -190) 52222) ((-304 . -186) 52195) ((-304 . -189) 52174) ((-304 . -320) 52153) ((-304 . -1067) 52132) ((-304 . -299) 52111) ((-304 . -120) 52090) ((-304 . -556) 52027) ((-304 . -591) 51979) ((-304 . -589) 51916) ((-304 . -104) T) ((-304 . -25) T) ((-304 . -72) T) ((-304 . -13) T) ((-304 . -1130) T) ((-304 . -553) 51898) ((-304 . -1014) T) ((-304 . -23) T) ((-304 . -21) T) ((-304 . -971) T) ((-304 . -1026) T) ((-304 . -1062) T) ((-304 . -664) T) ((-304 . -962) T) 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. -655) 51053) ((-303 . -583) 51005) ((-303 . -38) 50970) ((-303 . -392) T) ((-303 . -258) T) ((-303 . -82) 50901) ((-303 . -964) 50853) ((-303 . -969) 50805) ((-303 . -246) T) ((-303 . -201) T) ((-303 . -345) 50759) ((-303 . -118) 50713) ((-303 . -951) 50697) ((-303 . -1188) 50681) ((-303 . -1199) 50665) ((-302 . -280) 50649) ((-302 . -190) 50628) ((-302 . -186) 50601) ((-302 . -189) 50580) ((-302 . -320) 50559) ((-302 . -1067) 50538) ((-302 . -299) 50517) ((-302 . -120) 50496) ((-302 . -556) 50433) ((-302 . -591) 50385) ((-302 . -589) 50322) ((-302 . -104) T) ((-302 . -25) T) ((-302 . -72) T) ((-302 . -13) T) ((-302 . -1130) T) ((-302 . -553) 50304) ((-302 . -1014) T) ((-302 . -23) T) ((-302 . -21) T) ((-302 . -971) T) ((-302 . -1026) T) ((-302 . -1062) T) ((-302 . -664) T) ((-302 . -962) T) ((-302 . -312) T) ((-302 . -1135) T) ((-302 . -833) T) ((-302 . -496) T) ((-302 . -146) T) ((-302 . -655) 50256) ((-302 . -583) 50208) ((-302 . -38) 50173) ((-302 . -392) T) ((-302 . -258) T) 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. -1014) T) ((-177 . -553) 16868) ((-177 . -1130) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -951) 16845) ((-176 . -214) 16829) ((-176 . -1035) 16813) ((-176 . -76) 16797) ((-176 . -429) 16781) ((-176 . -1014) 16759) ((-176 . -456) 16692) ((-176 . -260) 16630) ((-176 . -553) 16565) ((-176 . -72) 16519) ((-176 . -1130) T) ((-176 . -13) T) ((-176 . -34) T) ((-176 . -1036) 16503) ((-176 . -318) 16487) ((-176 . -909) 16471) ((-172 . -996) T) ((-172 . -430) 16452) ((-172 . -553) 16418) ((-172 . -556) 16399) ((-172 . -1014) T) ((-172 . -1130) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -905) 16381) ((-171 . -1067) T) ((-171 . -556) 16331) ((-171 . -951) 16291) ((-171 . -554) 16221) ((-171 . -934) T) ((-171 . -822) NIL) ((-171 . -795) 16203) ((-171 . -756) T) ((-171 . -722) T) ((-171 . -719) T) ((-171 . -760) T) ((-171 . -757) T) ((-171 . -717) T) ((-171 . -715) T) ((-171 . -741) T) ((-171 . -797) 16185) ((-171 . -343) 16167) ((-171 . -581) 16149) ((-171 . -329) 16131) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -456) NIL) ((-171 . -288) 16113) ((-171 . -201) T) ((-171 . -82) 16040) ((-171 . -964) 15990) ((-171 . -969) 15940) ((-171 . -246) T) ((-171 . -655) 15890) ((-171 . -583) 15840) ((-171 . -591) 15790) ((-171 . -589) 15740) ((-171 . -38) 15690) ((-171 . -258) T) ((-171 . -392) T) ((-171 . -146) T) ((-171 . -496) T) ((-171 . -833) T) ((-171 . -1135) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15677) ((-171 . -189) T) ((-171 . -225) 15659) ((-171 . -807) NIL) ((-171 . -812) NIL) ((-171 . -810) NIL) ((-171 . -184) 15641) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1130) T) ((-171 . -553) 15583) ((-171 . -1014) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -962) T) ((-171 . -664) T) ((-171 . -1062) T) ((-171 . -1026) T) ((-171 . -971) T) ((-168 . -753) T) ((-168 . -760) T) ((-168 . -757) T) ((-168 . -1014) T) ((-168 . -553) 15565) ((-168 . -1130) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -320) T) ((-167 . -1014) T) ((-167 . -553) 15547) ((-167 . -1130) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -556) 15524) ((-166 . -1014) T) ((-166 . -553) 15506) ((-166 . -1130) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1014) T) ((-161 . -553) 15488) ((-161 . -1130) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1014) T) ((-158 . -553) 15470) ((-158 . -1130) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1014) T) ((-157 . -553) 15452) ((-157 . -1130) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -748) 15434) ((-154 . -996) T) ((-154 . -430) 15415) ((-154 . -553) 15381) ((-154 . -556) 15362) ((-154 . -1014) T) ((-154 . -1130) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -553) 15344) ((-148 . -38) 15276) ((-148 . -556) 15193) ((-148 . -591) 15125) ((-148 . -589) 15042) ((-148 . -971) T) ((-148 . -1026) T) ((-148 . -1062) T) ((-148 . -664) T) ((-148 . -962) T) ((-148 . -82) 14941) ((-148 . -964) 14873) ((-148 . -969) 14805) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1014) T) ((-148 . -553) 14787) ((-148 . -1130) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . -583) 14719) ((-148 . -655) 14651) ((-148 . -312) T) ((-148 . -1135) T) ((-148 . -833) T) ((-148 . -496) T) ((-148 . -146) T) ((-148 . -392) T) ((-148 . -258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1014) T) ((-145 . -553) 14633) ((-145 . -1130) T) ((-145 . -13) T) ((-145 . -72) T) ((-142 . -139) 14617) ((-142 . -35) 14595) ((-142 . -66) 14573) ((-142 . -239) 14551) ((-142 . -433) 14529) ((-142 . -1119) 14507) ((-142 . -1116) 14485) ((-142 . -916) 14437) ((-142 . -822) 14390) ((-142 . -554) 14158) ((-142 . -795) 14142) ((-142 . -320) 14096) ((-142 . -299) 14075) ((-142 . -1067) 14054) ((-142 . -345) 14033) ((-142 . -353) 14004) ((-142 . -38) 13838) ((-142 . -82) 13730) ((-142 . -964) 13643) ((-142 . -969) 13556) ((-142 . -583) 13390) ((-142 . -655) 13224) 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. -1014) T) ((-111 . -1130) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -996) T) ((-110 . -430) 10338) ((-110 . -553) 10304) ((-110 . -556) 10285) ((-110 . -1014) T) ((-110 . -1130) T) ((-110 . -13) T) ((-110 . -72) T) ((-110 . -64) T) ((-108 . -405) 10262) ((-108 . -556) 10158) ((-108 . -951) 10142) ((-108 . -1014) T) ((-108 . -553) 10124) ((-108 . -1130) T) ((-108 . -13) T) ((-108 . -72) T) ((-108 . -410) 10079) ((-108 . -241) 10056) ((-107 . -757) T) ((-107 . -553) 10038) ((-107 . -1014) T) ((-107 . -72) T) ((-107 . -13) T) ((-107 . -1130) T) ((-107 . -760) T) ((-107 . -23) T) ((-107 . -25) T) ((-107 . -664) T) ((-107 . -1026) T) ((-107 . -951) 10020) ((-107 . -556) 10002) ((-106 . -996) T) ((-106 . -430) 9983) ((-106 . -553) 9949) ((-106 . -556) 9930) ((-106 . -1014) T) ((-106 . -1130) T) ((-106 . -13) T) ((-106 . -72) T) ((-106 . -64) T) ((-103 . -1014) T) ((-103 . -553) 9912) ((-103 . -1130) T) ((-103 . -13) T) ((-103 . -72) T) ((-102 . -19) 9894) ((-102 . 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9144) ((-99 . -553) 9079) ((-99 . -260) 9017) ((-99 . -456) 8950) ((-99 . -1014) 8928) ((-99 . -429) 8912) ((-99 . -92) 8896) ((-94 . -98) 8880) ((-94 . -1036) 8864) ((-94 . -318) 8848) ((-94 . -924) 8832) ((-94 . -34) T) ((-94 . -13) T) ((-94 . -1130) T) ((-94 . -72) 8786) ((-94 . -553) 8721) ((-94 . -260) 8659) ((-94 . -456) 8592) ((-94 . -1014) 8570) ((-94 . -429) 8554) ((-94 . -92) 8538) ((-90 . -905) 8516) ((-90 . -1067) NIL) ((-90 . -951) 8494) ((-90 . -556) 8425) ((-90 . -554) NIL) ((-90 . -934) NIL) ((-90 . -822) NIL) ((-90 . -795) 8403) ((-90 . -756) NIL) ((-90 . -722) NIL) ((-90 . -719) NIL) ((-90 . -760) NIL) ((-90 . -757) NIL) ((-90 . -717) NIL) ((-90 . -715) NIL) ((-90 . -741) NIL) ((-90 . -797) NIL) ((-90 . -343) 8381) ((-90 . -581) 8359) ((-90 . -591) 8305) ((-90 . -329) 8283) ((-90 . -241) 8217) ((-90 . -260) 8164) ((-90 . -456) 8034) ((-90 . -288) 8012) ((-90 . -201) T) ((-90 . -82) 7931) ((-90 . -964) 7877) ((-90 . -969) 7823) ((-90 . -246) T) ((-90 . -655) 7769) ((-90 . -583) 7715) ((-90 . -589) 7646) ((-90 . -38) 7592) ((-90 . -258) T) ((-90 . -392) T) ((-90 . -146) T) ((-90 . -496) T) ((-90 . -833) T) ((-90 . -1135) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7570) ((-90 . -807) NIL) ((-90 . -812) NIL) ((-90 . -810) NIL) ((-90 . -184) 7548) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1130) T) ((-90 . -553) 7530) ((-90 . -1014) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -962) T) ((-90 . -664) T) ((-90 . -1062) T) ((-90 . -1026) T) ((-90 . -971) T) ((-89 . -780) 7514) ((-89 . -833) T) ((-89 . -496) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -556) 7486) ((-89 . -655) 7473) ((-89 . -583) 7460) ((-89 . -969) 7447) ((-89 . -964) 7434) ((-89 . -82) 7419) ((-89 . -38) 7406) ((-89 . -392) T) ((-89 . -258) T) ((-89 . -962) T) ((-89 . -664) T) ((-89 . -1062) T) ((-89 . -1026) T) ((-89 . -971) T) ((-89 . -21) T) ((-89 . -589) 7378) ((-89 . -23) T) ((-89 . -1014) T) ((-89 . -553) 7360) ((-89 . -1130) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -591) 7347) ((-89 . -120) T) ((-86 . -757) T) ((-86 . -553) 7329) ((-86 . -1014) T) ((-86 . -72) T) ((-86 . -13) T) ((-86 . -1130) T) ((-86 . -760) T) ((-86 . -748) 7310) ((-85 . -753) T) ((-85 . -760) T) ((-85 . -757) T) ((-85 . -1014) T) ((-85 . -553) 7292) ((-85 . -1130) T) ((-85 . -13) T) ((-85 . -72) T) ((-85 . -320) T) ((-85 . -881) T) ((-85 . -605) T) ((-85 . -84) T) ((-85 . -554) 7274) ((-81 . -96) T) ((-81 . -324) 7257) ((-81 . -760) T) ((-81 . -757) T) ((-81 . -124) 7240) ((-81 . -554) 7222) ((-81 . -241) 7173) ((-81 . -539) 7149) ((-81 . -243) 7125) ((-81 . -594) 7108) ((-81 . -429) 7091) ((-81 . -1014) T) ((-81 . -456) NIL) ((-81 . -260) NIL) ((-81 . -553) 7073) ((-81 . -72) T) ((-81 . -34) T) ((-81 . -318) 7056) ((-81 . -1036) 7039) ((-81 . -19) 7022) ((-81 . -605) T) ((-81 . -13) T) ((-81 . -1130) T) ((-81 . -84) T) ((-79 . -80) 7006) ((-79 . -1130) T) ((-79 . |MappingCategory|) 6980) ((-79 . -1014) T) ((-79 . -553) 6962) ((-79 . -13) T) ((-79 . -72) T) ((-78 . -553) 6944) ((-77 . -905) 6926) ((-77 . -1067) T) ((-77 . -556) 6876) ((-77 . -951) 6836) ((-77 . -554) 6766) ((-77 . -934) T) ((-77 . -822) NIL) ((-77 . -795) 6748) ((-77 . -756) T) ((-77 . -722) T) ((-77 . -719) T) ((-77 . -760) T) ((-77 . -757) T) ((-77 . -717) T) ((-77 . -715) T) ((-77 . -741) T) ((-77 . -797) 6730) ((-77 . -343) 6712) ((-77 . -581) 6694) ((-77 . -329) 6676) ((-77 . -241) NIL) ((-77 . -260) NIL) ((-77 . -456) NIL) ((-77 . -288) 6658) ((-77 . -201) T) ((-77 . -82) 6585) ((-77 . -964) 6535) ((-77 . -969) 6485) ((-77 . -246) T) ((-77 . -655) 6435) ((-77 . -583) 6385) ((-77 . -591) 6335) ((-77 . -589) 6285) ((-77 . -38) 6235) ((-77 . -258) T) ((-77 . -392) T) ((-77 . -146) T) ((-77 . -496) T) ((-77 . -833) T) ((-77 . -1135) T) ((-77 . -312) T) ((-77 . -190) T) ((-77 . -186) 6222) ((-77 . -189) T) ((-77 . -225) 6204) ((-77 . -807) NIL) ((-77 . -812) NIL) ((-77 . -810) NIL) ((-77 . -184) 6186) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1130) T) ((-77 . -553) 6129) ((-77 . -1014) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -962) T) ((-77 . -664) T) ((-77 . -1062) T) ((-77 . -1026) T) ((-77 . -971) T) ((-73 . -98) 6113) ((-73 . -1036) 6097) ((-73 . -318) 6081) ((-73 . -924) 6065) ((-73 . -34) T) ((-73 . -13) T) ((-73 . -1130) T) ((-73 . -72) 6019) ((-73 . -553) 5954) ((-73 . -260) 5892) ((-73 . -456) 5825) ((-73 . -1014) 5803) ((-73 . -429) 5787) ((-73 . -92) 5771) ((-69 . -413) T) ((-69 . -1026) T) ((-69 . -72) T) ((-69 . -13) T) ((-69 . -1130) T) ((-69 . -553) 5753) ((-69 . -1014) T) ((-69 . -664) T) ((-69 . -241) 5732) ((-67 . -996) T) ((-67 . -430) 5713) ((-67 . -553) 5679) ((-67 . -556) 5660) ((-67 . -1014) T) ((-67 . -1130) T) ((-67 . -13) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1035) 5644) ((-62 . -318) 5628) ((-62 . -1036) 5612) ((-62 . -34) T) ((-62 . -13) T) ((-62 . -1130) T) ((-62 . -72) 5566) ((-62 . -553) 5501) ((-62 . -260) 5439) ((-62 . -456) 5372) ((-62 . -1014) 5350) ((-62 . -429) 5334) ((-62 . -76) 5318) ((-60 . -57) 5280) ((-60 . -1036) 5264) ((-60 . -429) 5248) ((-60 . -1014) 5226) ((-60 . -456) 5159) ((-60 . -260) 5097) ((-60 . -553) 5032) ((-60 . -72) 4986) ((-60 . -1130) T) ((-60 . -13) T) ((-60 . -34) T) ((-60 . -318) 4970) ((-58 . -19) 4954) ((-58 . -1036) 4938) ((-58 . -318) 4922) ((-58 . -34) T) ((-58 . -13) T) ((-58 . -1130) T) ((-58 . -72) 4856) ((-58 . -553) 4771) ((-58 . -260) 4709) ((-58 . -456) 4642) ((-58 . -1014) 4595) ((-58 . -429) 4579) ((-58 . -594) 4563) ((-58 . -243) 4540) ((-58 . -241) 4492) ((-58 . -539) 4469) ((-58 . -554) 4430) ((-58 . -124) 4414) ((-58 . -757) 4393) ((-58 . -760) 4372) ((-58 . -324) 4356) ((-55 . -1014) T) ((-55 . -553) 4338) ((-55 . -1130) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -951) 4320) ((-55 . -556) 4302) ((-51 . -1014) T) ((-51 . -553) 4284) ((-51 . -1130) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -561) 4268) ((-50 . -556) 4237) ((-50 . -591) 4211) ((-50 . -589) 4170) ((-50 . -971) T) ((-50 . -1026) T) ((-50 . -1062) T) ((-50 . -664) T) ((-50 . -962) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1014) T) ((-50 . -553) 4152) ((-50 . -1130) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -951) 4136) ((-49 . -1014) T) ((-49 . -553) 4118) ((-49 . -1130) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -254) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1130) T) ((-48 . -553) 4100) ((-48 . -1014) T) ((-48 . -556) 4001) ((-48 . -951) 3944) ((-48 . -456) 3910) ((-48 . -260) 3897) ((-48 . -27) T) ((-48 . -916) T) ((-48 . -201) T) ((-48 . -82) 3846) ((-48 . -964) 3811) ((-48 . -969) 3776) ((-48 . -246) T) ((-48 . -655) 3741) ((-48 . -583) 3706) ((-48 . -591) 3656) ((-48 . -589) 3606) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -962) T) ((-48 . -664) T) ((-48 . -1062) T) ((-48 . -1026) T) ((-48 . -971) T) ((-48 . -38) 3571) ((-48 . -258) T) ((-48 . -392) T) ((-48 . -146) T) ((-48 . -496) T) ((-48 . -833) T) ((-48 . -1135) T) ((-48 . -312) T) ((-48 . -581) 3531) ((-48 . -934) T) ((-48 . -554) 3476) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3463) ((-48 . -189) T) ((-45 . -36) 3442) ((-45 . -550) 3421) ((-45 . -1036) 3356) ((-45 . -243) 3279) ((-45 . -241) 3177) ((-45 . -429) 3112) ((-45 . -456) 2864) ((-45 . -260) 2662) ((-45 . -539) 2585) ((-45 . -193) 2533) ((-45 . -76) 2481) ((-45 . -183) 2429) ((-45 . -1108) 2408) ((-45 . -237) 2356) ((-45 . -124) 2304) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1130) T) ((-45 . -72) T) ((-45 . -553) 2286) ((-45 . -1014) T) ((-45 . -554) NIL) ((-45 . -594) 2234) ((-45 . -324) 2182) ((-45 . -760) NIL) ((-45 . -757) NIL) ((-45 . -318) 2130) ((-45 . -1065) 2078) ((-45 . -924) 2026) ((-45 . -1169) 1974) ((-45 . -609) 1922) ((-44 . -361) 1906) ((-44 . -684) 1890) ((-44 . -658) T) ((-44 . -686) T) ((-44 . -82) 1869) ((-44 . -964) 1853) ((-44 . -969) 1837) ((-44 . -21) T) ((-44 . -589) 1780) ((-44 . -23) T) ((-44 . -1014) T) ((-44 . -553) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -104) T) ((-44 . -591) 1720) ((-44 . -583) 1704) ((-44 . -655) 1688) ((-44 . -316) 1672) ((-44 . -1130) T) ((-44 . -13) T) ((-44 . -241) 1649) ((-40 . -291) 1623) ((-40 . -146) T) ((-40 . -556) 1553) ((-40 . -971) T) ((-40 . -1026) T) ((-40 . -1062) T) ((-40 . -664) T) ((-40 . -962) T) ((-40 . -591) 1455) ((-40 . -589) 1385) ((-40 . -104) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -13) T) ((-40 . -1130) T) ((-40 . -553) 1367) ((-40 . -1014) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -969) 1312) ((-40 . -964) 1257) ((-40 . -82) 1174) ((-40 . -554) 1158) ((-40 . -184) 1135) ((-40 . -810) 1087) ((-40 . -812) 999) ((-40 . -807) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -312) T) ((-40 . -1135) T) ((-40 . -833) T) ((-40 . -496) T) ((-40 . -655) 677) ((-40 . -583) 622) ((-40 . -38) 567) ((-40 . -392) T) ((-40 . -258) T) ((-40 . -246) T) ((-40 . -201) T) ((-40 . -320) NIL) ((-40 . -299) NIL) ((-40 . -1067) NIL) ((-40 . -118) 539) ((-40 . -345) NIL) ((-40 . -353) 511) ((-40 . -120) 483) ((-40 . -322) 455) ((-40 . -329) 432) ((-40 . -581) 366) ((-40 . -355) 343) ((-40 . -951) 220) ((-40 . -662) 192) ((-31 . -996) T) ((-31 . -430) 173) ((-31 . -553) 139) ((-31 . -556) 120) ((-31 . -1014) T) ((-31 . -1130) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -867) T) ((-30 . -553) 102) ((0 . |EnumerationCategory|) T) ((0 . -553) 84) ((0 . -1014) T) ((0 . -72) T) ((0 . -1130) T) ((-2 . |RecordCategory|) T) ((-2 . -553) 66) ((-2 . -1014) T) ((-2 . -72) T) ((-2 . -1130) T) ((-3 . |UnionCategory|) T) ((-3 . -553) 48) ((-3 . -1014) T) ((-3 . -72) T) ((-3 . -1130) T) ((-1 . -1014) T) ((-1 . -553) 30) ((-1 . -1130) T) ((-1 . -13) T) ((-1 . -72) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 1d642ebe..abcdc820 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3578003924)            
-(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3578007596)            
+(4000 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -139,7 +139,7 @@
  |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname|
  |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor|
  |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |InnerTwoDimensionalArray|
- |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools|
+ |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits|
  |IntegralBasisPolynomialTools| |IndexCard| |InnerCommonDenominator|
  |PolynomialIdeals| |IdealDecompositionPackage| |IdempotentOperatorCategory|
  |Identifier| |IndexedDirectProductAbelianGroup|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 5f6b3740..b4716686 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4049 +1,4052 @@
 
-(2789160 . 3578003932)       
-((-1735 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1733 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3789 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-1146 (-484)) |#2|) 44 T ELT)) (-2297 (($ $) 80 T ELT)) (-3843 ((|#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)) (-3420 (((-484) (-1 (-85) |#2|) $) 27 T ELT) (((-484) |#2| $) NIL T ELT) (((-484) |#2| $ (-484)) 96 T ELT)) (-3519 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2609 (((-583 |#2|) $) 13 T ELT)) (-3327 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3959 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2304 (($ |#2| $ (-484)) NIL T ELT) (($ $ $ (-484)) 67 T ELT)) (-1354 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1731 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3801 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-484)) NIL T ELT) (($ $ (-1146 (-484))) 66 T ELT)) (-2305 (($ $ (-484)) 76 T ELT) (($ $ (-1146 (-484))) 75 T ELT)) (-1730 (((-694) |#2| $) NIL T ELT) (((-694) (-1 (-85) |#2|) $) 34 T ELT)) (-1734 (($ $ $ (-484)) 69 T ELT)) (-3401 (($ $) 68 T ELT)) (-3531 (($ (-583 |#2|)) 73 T ELT)) (-3803 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-583 $)) 85 T ELT)) (-3947 (((-772) $) 92 T ELT)) (-1732 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3057 (((-85) $ $) 95 T ELT)) (-2686 (((-85) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -7 (-15 -3057 ((-85) |#1| |#1|)) (-15 -3947 ((-772) |#1|)) (-15 -3327 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2686 ((-85) |#1| |#1|)) (-15 -1733 (|#1| |#1|)) (-15 -1733 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2297 (|#1| |#1|)) (-15 -1734 (|#1| |#1| |#1| (-484))) (-15 -1735 ((-85) |#1|)) (-15 -3519 (|#1| |#1| |#1|)) (-15 -3420 ((-484) |#2| |#1| (-484))) (-15 -3420 ((-484) |#2| |#1|)) (-15 -3420 ((-484) (-1 (-85) |#2|) |#1|)) (-15 -1735 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3519 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -1732 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1731 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1730 ((-694) (-1 (-85) |#2|) |#1|)) (-15 -2609 ((-583 |#2|) |#1|)) (-15 -3843 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3843 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1730 ((-694) |#2| |#1|)) (-15 -3843 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3789 (|#2| |#1| (-1146 (-484)) |#2|)) (-15 -2304 (|#1| |#1| |#1| (-484))) (-15 -2304 (|#1| |#2| |#1| (-484))) (-15 -2305 (|#1| |#1| (-1146 (-484)))) (-15 -2305 (|#1| |#1| (-484))) (-15 -3959 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3803 (|#1| (-583 |#1|))) (-15 -3803 (|#1| |#1| |#1|)) (-15 -3803 (|#1| |#2| |#1|)) (-15 -3803 (|#1| |#1| |#2|)) (-15 -3801 (|#1| |#1| (-1146 (-484)))) (-15 -3531 (|#1| (-583 |#2|))) (-15 -1354 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -3801 (|#2| |#1| (-484))) (-15 -3801 (|#2| |#1| (-484) |#2|)) (-15 -3789 (|#2| |#1| (-484) |#2|)) (-15 -3959 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3401 (|#1| |#1|))) (-19 |#2|) (-1129)) (T -18)) 
+(2793113 . 3578007604)       
+((-1736 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1734 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3790 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-1147 (-485)) |#2|) 44 T ELT)) (-2298 (($ $) 80 T ELT)) (-3844 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3421 (((-485) (-1 (-85) |#2|) $) 27 T ELT) (((-485) |#2| $) NIL T ELT) (((-485) |#2| $ (-485)) 96 T ELT)) (-3520 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2610 (((-584 |#2|) $) 13 T ELT)) (-3328 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3960 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2305 (($ |#2| $ (-485)) NIL T ELT) (($ $ $ (-485)) 67 T ELT)) (-1355 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1732 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3802 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-485)) NIL T ELT) (($ $ (-1147 (-485))) 66 T ELT)) (-2306 (($ $ (-485)) 76 T ELT) (($ $ (-1147 (-485))) 75 T ELT)) (-1731 (((-695) |#2| $) NIL T ELT) (((-695) (-1 (-85) |#2|) $) 34 T ELT)) (-1735 (($ $ $ (-485)) 69 T ELT)) (-3402 (($ $) 68 T ELT)) (-3532 (($ (-584 |#2|)) 73 T ELT)) (-3804 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-584 $)) 85 T ELT)) (-3948 (((-773) $) 92 T ELT)) (-1733 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3058 (((-85) $ $) 95 T ELT)) (-2687 (((-85) $ $) 99 T ELT))) 
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 NIL 
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+(((-19 |#1|) (-113) (-1130)) (T -19)) 
 NIL 
-(-13 (-324 |t#1|) (-1035 |t#1|)) 
-(((-34) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-756)) (|has| |#1| (-72))) ((-552 (-772)) OR (|has| |#1| (-1013)) (|has| |#1| (-756)) (|has| |#1| (-552 (-772)))) ((-124 |#1|) . T) ((-553 (-473)) |has| |#1| (-553 (-473))) ((-241 (-484) |#1|) . T) ((-241 (-1146 (-484)) $) . T) ((-243 (-484) |#1|) . T) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-318 |#1|) . T) ((-324 |#1|) . T) ((-429 |#1|) . T) ((-538 (-484) |#1|) . T) ((-455 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-593 |#1|) . T) ((-756) |has| |#1| (-756)) ((-759) |has| |#1| (-756)) ((-1013) OR (|has| |#1| (-1013)) (|has| |#1| (-756))) ((-1035 |#1|) . T) ((-1129) . T)) 
-((-1312 (((-3 $ "failed") $ $) 12 T ELT)) (-1214 (((-85) $ $) 27 T ELT)) (-3838 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) 16 T ELT) (($ (-484) $) 25 T ELT))) 
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+(-13 (-324 |t#1|) (-1036 |t#1|)) 
+(((-34) . T) ((-72) OR (|has| |#1| (-1014)) (|has| |#1| (-757)) (|has| |#1| (-72))) ((-553 (-773)) OR (|has| |#1| (-1014)) (|has| |#1| (-757)) (|has| |#1| (-553 (-773)))) ((-124 |#1|) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-241 (-485) |#1|) . T) ((-241 (-1147 (-485)) $) . T) ((-243 (-485) |#1|) . T) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-318 |#1|) . T) ((-324 |#1|) . T) ((-429 |#1|) . T) ((-539 (-485) |#1|) . T) ((-456 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-13) . T) ((-594 |#1|) . T) ((-757) |has| |#1| (-757)) ((-760) |has| |#1| (-757)) ((-1014) OR (|has| |#1| (-1014)) (|has| |#1| (-757))) ((-1036 |#1|) . T) ((-1130) . T)) 
+((-1313 (((-3 $ "failed") $ $) 12 T ELT)) (-1215 (((-85) $ $) 27 T ELT)) (-3839 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) 16 T ELT) (($ (-485) $) 25 T ELT))) 
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 NIL 
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+((-2570 (((-85) $ $) 7 T ELT)) (-3190 (((-85) $) 22 T ELT)) (-1313 (((-3 $ "failed") $ $) 26 T ELT)) (-3726 (($) 23 T CONST)) (-1215 (((-85) $ $) 20 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1034) $) 12 T ELT)) (-3948 (((-773) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2662 (($) 24 T CONST)) (-3058 (((-85) $ $) 8 T ELT)) (-3839 (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (-3841 (($ $ $) 18 T ELT)) (* (($ (-831) $) 17 T ELT) (($ (-695) $) 21 T ELT) (($ (-485) $) 30 T ELT))) 
 (((-21) (-113)) (T -21)) 
-((-3838 (*1 *1 *1) (-4 *1 (-21))) (-3838 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-104) (-588 (-484)) (-10 -8 (-15 -3838 ($ $)) (-15 -3838 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-1013) . T) ((-1129) . T)) 
-((-3189 (((-85) $) 10 T ELT)) (-3725 (($) 15 T CONST)) (-1214 (((-85) $ $) 22 T ELT)) (* (($ (-830) $) 14 T ELT) (($ (-694) $) 19 T ELT))) 
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+((-3839 (*1 *1 *1) (-4 *1 (-21))) (-3839 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-104) (-589 (-485)) (-10 -8 (-15 -3839 ($ $)) (-15 -3839 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-1014) . T) ((-1130) . T)) 
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 NIL 
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 NIL 
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-NIL 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-350 (-485))) . T) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) . T) ((-27) . T) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) . T) ((-82 |#1| |#1|) |has| |#1| (-146)) ((-82 $ $) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-350 (-485))) . T) ((-556 (-350 (-858 |#1|))) |has| |#1| (-496)) ((-556 (-485)) . T) ((-556 (-551 $)) . T) ((-556 (-858 |#1|)) |has| |#1| (-962)) ((-556 (-1091)) . T) ((-556 |#1|) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-146) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-554 (-801 (-330))) |has| |#1| (-554 (-801 (-330)))) ((-554 (-801 (-485))) |has| |#1| (-554 (-801 (-485)))) ((-201) . T) ((-246) . T) ((-258) . T) ((-260 $) . T) ((-254) . T) ((-312) . T) ((-329 |#1|) |has| |#1| (-962)) ((-343 |#1|) . T) ((-355 |#1|) . T) ((-364 |#1|) . T) ((-392) . T) ((-413) |has| |#1| (-413)) ((-456 (-551 $) $) . T) ((-456 $ $) . T) ((-496) . T) ((-13) . T) ((-589 (-350 (-485))) . T) ((-589 (-485)) . T) ((-589 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-146))) ((-589 $) . T) ((-591 (-350 (-485))) . T) ((-591 (-485)) -12 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-591 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-146))) ((-591 $) . T) ((-583 (-350 (-485))) . T) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) . T) ((-581 (-485)) -12 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-581 |#1|) |has| |#1| (-962)) ((-655 (-350 (-485))) . T) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) . T) ((-664) . T) ((-807 $ (-1091)) |has| |#1| (-962)) ((-810 (-1091)) |has| |#1| (-962)) ((-812 (-1091)) |has| |#1| (-962)) ((-797 (-330)) |has| |#1| (-797 (-330))) ((-797 (-485)) |has| |#1| (-797 (-485))) ((-795 |#1|) . T) ((-833) . T) ((-916) . T) ((-951 (-350 (-485))) OR (|has| |#1| (-951 (-350 (-485)))) (-12 (|has| |#1| (-496)) (|has| |#1| (-951 (-485))))) ((-951 (-350 (-858 |#1|))) |has| |#1| (-496)) ((-951 (-485)) |has| |#1| (-951 (-485))) ((-951 (-551 $)) . T) ((-951 (-858 |#1|)) |has| |#1| (-962)) ((-951 (-1091)) . T) ((-951 |#1|) . T) ((-964 (-350 (-485))) . T) ((-964 |#1|) |has| |#1| (-146)) ((-964 $) . T) ((-969 (-350 (-485))) . T) ((-969 |#1|) |has| |#1| (-146)) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T) ((-1135) . T)) 
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-NIL 
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+NIL 
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 (((-38 |#1|) (-113) (-146)) (T -38)) 
 NIL 
-(-13 (-961) (-654 |t#1|) (-555 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-555 (-484)) . T) ((-555 |#1|) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-582 |#1|) . T) ((-654 |#1|) . T) ((-663) . T) ((-963 |#1|) . T) ((-968 |#1|) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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ELT) (($ $ (-584 (-1091))) NIL (OR (-12 (|has| (-350 |#2|) (-312)) (|has| (-350 |#2|) (-810 (-1091)))) (-12 (|has| (-350 |#2|) (-312)) (|has| (-350 |#2|) (-812 (-1091))))) ELT) (($ $ (-1091)) NIL (OR (-12 (|has| (-350 |#2|) (-312)) (|has| (-350 |#2|) (-810 (-1091)))) (-12 (|has| (-350 |#2|) (-312)) (|has| (-350 |#2|) (-812 (-1091))))) ELT) (($ $ (-695)) NIL (OR (-12 (|has| (-350 |#2|) (-190)) (|has| (-350 |#2|) (-312))) (-12 (|has| (-350 |#2|) (-189)) (|has| (-350 |#2|) (-312))) (|has| (-350 |#2|) (-299))) ELT) (($ $) NIL (OR (-12 (|has| (-350 |#2|) (-190)) (|has| (-350 |#2|) (-312))) (-12 (|has| (-350 |#2|) (-189)) (|has| (-350 |#2|) (-312))) (|has| (-350 |#2|) (-299))) ELT)) (-3058 (((-85) $ $) NIL T ELT)) (-3951 (($ $ $) NIL (|has| (-350 |#2|) (-312)) ELT)) (-3839 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3841 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) NIL (|has| (-350 |#2|) (-312)) ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T 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+NIL 
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+NIL 
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 (((-64) (-113)) (T -64)) 
 NIL 
-(-13 (-1013) (-430 (-1095))) 
-(((-72) . T) ((-555 (-1095)) . T) ((-552 (-772)) . T) ((-552 (-1095)) . T) ((-430 (-1095)) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
-((-3489 (($ $) 10 T ELT)) (-3490 (($ $) 12 T ELT))) 
-(((-65 |#1|) (-10 -7 (-15 -3490 (|#1| |#1|)) (-15 -3489 (|#1| |#1|))) (-66)) (T -65)) 
+(-13 (-1014) (-430 (-1096))) 
+(((-72) . T) ((-556 (-1096)) . T) ((-553 (-773)) . T) ((-553 (-1096)) . T) ((-430 (-1096)) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
+((-3490 (($ $) 10 T ELT)) (-3491 (($ $) 12 T ELT))) 
+(((-65 |#1|) (-10 -7 (-15 -3491 (|#1| |#1|)) (-15 -3490 (|#1| |#1|))) (-66)) (T -65)) 
 NIL 
-((-3487 (($ $) 11 T ELT)) (-3485 (($ $) 10 T ELT)) (-3489 (($ $) 9 T ELT)) (-3490 (($ $) 8 T ELT)) (-3488 (($ $) 7 T ELT)) (-3486 (($ $) 6 T ELT))) 
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 (((-66) (-113)) (T -66)) 
-((-3487 (*1 *1 *1) (-4 *1 (-66))) (-3485 (*1 *1 *1) (-4 *1 (-66))) (-3489 (*1 *1 *1) (-4 *1 (-66))) (-3490 (*1 *1 *1) (-4 *1 (-66))) (-3488 (*1 *1 *1) (-4 *1 (-66))) (-3486 (*1 *1 *1) (-4 *1 (-66)))) 
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-((-3543 (*1 *2 *1) (-12 (-5 *2 (-1049)) (-5 *1 (-67))))) 
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+((-3544 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-67))))) 
 NIL 
 (((-68) (-113)) (T -68)) 
 NIL 
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-((-1264 (*1 *2 *3 *4) (-12 (-5 *4 (-583 *3)) (-4 *3 (-1155 *5)) (-4 *5 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *5 *3)))) (-1264 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *4 *3)) (-4 *3 (-1155 *4))))) 
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-NIL 
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+((-2570 (((-85) $ $) 13 T ELT)) (-1266 (((-85) $ $) 14 T ELT)) (-3058 (((-85) $ $) 11 T ELT))) 
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+NIL 
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 (((-72) (-113)) (T -72)) 
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-(-13 (-1129) (-10 -8 (-15 -3057 ((-85) $ $)) (-15 -2569 ((-85) $ $)) (-15 -1265 ((-85) $ $)))) 
-(((-13) . T) ((-1129) . T)) 
-((-2569 (((-85) $ $) NIL (|has| |#1| (-72)) ELT)) (-3403 ((|#1| $) NIL T ELT)) (-3026 ((|#1| $ |#1|) 24 (|has| $ (-1035 |#1|)) ELT)) (-1293 (($ $ $) NIL (|has| $ (-1035 |#1|)) ELT)) (-1294 (($ $ $) NIL (|has| $ (-1035 |#1|)) ELT)) (-1268 (($ $ (-583 |#1|)) 30 T ELT)) (-3789 ((|#1| $ #1="value" |#1|) NIL (|has| $ (-1035 |#1|)) ELT) (($ $ #2="left" $) NIL (|has| $ (-1035 |#1|)) ELT) (($ $ #3="right" $) NIL (|has| $ (-1035 |#1|)) ELT)) (-3027 (($ $ (-583 $)) NIL (|has| $ (-1035 |#1|)) ELT)) (-3725 (($) NIL T CONST)) (-3138 (($ $) 12 T ELT)) (-3843 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) NIL (|has| |#1| (-72)) ELT) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) NIL T ELT) ((|#1| (-1 |#1| |#1| |#1|) $) NIL T ELT)) (-3032 (((-583 $) $) NIL T ELT)) (-3028 (((-85) $ $) NIL (|has| |#1| (-72)) ELT)) (-1302 (($ $ |#1| $) 32 T ELT)) (-2609 (((-583 |#1|) $) NIL T ELT)) (-3246 (((-85) |#1| $) NIL (|has| |#1| (-72)) ELT)) (-1267 ((|#1| $ (-1 |#1| |#1| |#1|)) 40 T ELT) (($ $ $ (-1 |#1| |#1| |#1| |#1| |#1|)) 45 T ELT)) (-1266 (($ $ |#1| (-1 |#1| |#1| |#1|)) 46 T ELT) (($ $ |#1| (-1 (-583 |#1|) |#1| |#1| |#1|)) 49 T ELT)) (-3327 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-3959 (($ (-1 |#1| |#1|) $) NIL T ELT)) (-3139 (($ $) 11 T ELT)) (-3031 (((-583 |#1|) $) NIL T ELT)) (-3528 (((-85) $) 13 T ELT)) (-3243 (((-1073) $) NIL (|has| |#1| (-1013)) ELT)) (-3244 (((-1033) $) NIL (|has| |#1| (-1013)) ELT)) (-1731 (((-85) (-1 (-85) |#1|) $) NIL T ELT)) (-3769 (($ $ (-583 (-249 |#1|))) NIL (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ (-249 |#1|)) NIL (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ |#1| |#1|) NIL (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ (-583 |#1|) (-583 |#1|)) NIL (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT)) (-1222 (((-85) $ $) NIL T ELT)) (-3404 (((-85) $) 9 T ELT)) (-3566 (($) 31 T ELT)) (-3801 ((|#1| $ #1#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $ #3#) NIL T ELT)) (-3030 (((-484) $ $) NIL T ELT)) (-3634 (((-85) $) NIL T ELT)) (-1730 (((-694) |#1| $) NIL (|has| |#1| (-72)) ELT) (((-694) (-1 (-85) |#1|) $) NIL T ELT)) (-3401 (($ $) NIL T ELT)) (-3947 (((-772) $) NIL (|has| |#1| (-552 (-772))) ELT)) (-3523 (((-583 $) $) NIL T ELT)) (-3029 (((-85) $ $) NIL (|has| |#1| (-72)) ELT)) (-1265 (((-85) $ $) NIL (|has| |#1| (-72)) ELT)) (-1269 (($ (-694) |#1|) 33 T ELT)) (-1732 (((-85) (-1 (-85) |#1|) $) NIL T ELT)) (-3057 (((-85) $ $) NIL (|has| |#1| (-72)) ELT)) (-3958 (((-694) $) NIL T ELT))) 
-(((-73 |#1|) (-13 (-98 |#1|) (-10 -8 (-15 -1269 ($ (-694) |#1|)) (-15 -1268 ($ $ (-583 |#1|))) (-15 -1267 (|#1| $ (-1 |#1| |#1| |#1|))) (-15 -1267 ($ $ $ (-1 |#1| |#1| |#1| |#1| |#1|))) (-15 -1266 ($ $ |#1| (-1 |#1| |#1| |#1|))) (-15 -1266 ($ $ |#1| (-1 (-583 |#1|) |#1| |#1| |#1|))))) (-1013)) (T -73)) 
-((-1269 (*1 *1 *2 *3) (-12 (-5 *2 (-694)) (-5 *1 (-73 *3)) (-4 *3 (-1013)))) (-1268 (*1 *1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1013)) (-5 *1 (-73 *3)))) (-1267 (*1 *2 *1 *3) (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-73 *2)) (-4 *2 (-1013)))) (-1267 (*1 *1 *1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1013)) (-5 *1 (-73 *3)))) (-1266 (*1 *1 *1 *2 *3) (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1013)) (-5 *1 (-73 *2)))) (-1266 (*1 *1 *1 *2 *3) (-12 (-5 *3 (-1 (-583 *2) *2 *2 *2)) (-4 *2 (-1013)) (-5 *1 (-73 *2))))) 
-((-1270 ((|#3| |#2| |#2|) 34 T ELT)) (-1272 ((|#1| |#2| |#2|) 46 (|has| |#1| (-6 (-3998 #1="*"))) ELT)) (-1271 ((|#3| |#2| |#2|) 36 T ELT)) (-1273 ((|#1| |#2|) 53 (|has| |#1| (-6 (-3998 #1#))) ELT))) 
-(((-74 |#1| |#2| |#3| |#4| |#5|) (-10 -7 (-15 -1270 (|#3| |#2| |#2|)) (-15 -1271 (|#3| |#2| |#2|)) (IF (|has| |#1| (-6 (-3998 "*"))) (PROGN (-15 -1272 (|#1| |#2| |#2|)) (-15 -1273 (|#1| |#2|))) |%noBranch|)) (-961) (-1155 |#1|) (-627 |#1| |#4| |#5|) (-324 |#1|) (-324 |#1|)) (T -74)) 
-((-1273 (*1 *2 *3) (-12 (|has| *2 (-6 (-3998 #1="*"))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) (-4 *2 (-961)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1155 *2)) (-4 *4 (-627 *2 *5 *6)))) (-1272 (*1 *2 *3 *3) (-12 (|has| *2 (-6 (-3998 #1#))) (-4 *5 (-324 *2)) (-4 *6 (-324 *2)) (-4 *2 (-961)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1155 *2)) (-4 *4 (-627 *2 *5 *6)))) (-1271 (*1 *2 *3 *3) (-12 (-4 *4 (-961)) (-4 *2 (-627 *4 *5 *6)) (-5 *1 (-74 *4 *3 *2 *5 *6)) (-4 *3 (-1155 *4)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)))) (-1270 (*1 *2 *3 *3) (-12 (-4 *4 (-961)) (-4 *2 (-627 *4 *5 *6)) (-5 *1 (-74 *4 *3 *2 *5 *6)) (-4 *3 (-1155 *4)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4))))) 
-((-1276 (($ (-583 |#2|)) 11 T ELT))) 
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-NIL 
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-NIL 
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-(((-34) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-72))) ((-552 (-772)) OR (|has| |#1| (-1013)) (|has| |#1| (-552 (-772)))) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-429 |#1|) . T) ((-455 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-923 |#1|) . T) ((-1013) |has| |#1| (-1013)) ((-1129) . T)) 
-((-1297 (((-85) |#1|) 29 T ELT)) (-1296 (((-694) (-694)) 28 T ELT) (((-694)) 27 T ELT)) (-1295 (((-85) |#1| (-85)) 30 T ELT) (((-85) |#1|) 31 T ELT))) 
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-(((-94 |#1|) (-13 (-98 |#1|) (-10 -8 (-15 -1299 ($ (-583 |#1|))) (-15 -3610 ($ |#1| $)) (-15 -1298 ($ |#1| $)) (-15 -3419 ((-2 (|:| |less| $) (|:| |greater| $)) |#1| $)))) (-756)) (T -94)) 
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-((-2313 (($ $) 13 T ELT)) (-2561 (($ $) 11 T ELT)) (-1300 (($ $ $) 23 T ELT)) (-1301 (($ $ $) 21 T ELT)) (-2311 (($ $ $) 19 T ELT)) (-2312 (($ $ $) 17 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 
 (-13 (-193 |t#1|)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-186 $) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-190) |has| |#1| (-190)) ((-189) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-810 (-1091)) |has| |#1| (-810 (-1091))) ((-812 (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-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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 (((-190) (-113)) (T -190)) 
 NIL 
-(-13 (-961) (-189)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-555 (-484)) . T) ((-552 (-772)) . T) ((-186 $) . T) ((-189) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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 (((-191) (-113)) (T -191)) 
 NIL 
-(-13 (-716) (-1061)) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-663) . T) ((-716) . T) ((-718) . T) ((-756) . T) ((-759) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
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-NIL 
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ELT) (($ $ (-1090)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-1090) (-694)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090)) (-583 (-694))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-694)) NIL (|has| |#1| (-189)) ELT)) (-3057 (((-85) $ $) NIL T ELT)) (-3950 (($ $ |#1|) NIL (|has| |#1| (-312)) ELT)) (-3838 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3840 (($ $ $) NIL T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) NIL T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-350 (-484))) NIL (|has| |#1| (-38 (-350 (-484)))) ELT) (($ (-350 (-484)) $) NIL (|has| |#1| (-38 (-350 (-484)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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-NIL 
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-NIL 
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(-915))))) (-1545 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1544 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1543 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1542 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1541 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1540 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1539 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1538 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1537 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1536 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-915))))) (-1535 (*1 *2 *2) (-12 (-4 *3 (-495)) (-5 *1 (-230 *3 *2)) (-4 *2 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ELT) (($ $) NIL (OR (-12 (|has| |#3| (-190)) (|has| |#3| (-962))) (-12 (|has| |#3| (-189)) (|has| |#3| (-962)))) ELT)) (-2568 (((-85) $ $) NIL (|has| |#3| (-757)) ELT)) (-2569 (((-85) $ $) NIL (|has| |#3| (-757)) ELT)) (-3058 (((-85) $ $) NIL T ELT)) (-2686 (((-85) $ $) NIL (|has| |#3| (-757)) ELT)) (-2687 (((-85) $ $) NIL (|has| |#3| (-757)) ELT)) (-3951 (($ $ |#3|) NIL (|has| |#3| (-312)) ELT)) (-3839 (($ $ $) NIL T ELT) (($ $) NIL T ELT)) (-3841 (($ $ $) NIL T ELT)) (** (($ $ (-695)) NIL (|has| |#3| (-962)) ELT) (($ $ (-831)) NIL (|has| |#3| (-962)) ELT)) (* (($ |#2| $) 13 T ELT) (($ (-485) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-831) $) NIL T ELT) (($ $ |#3|) NIL (|has| |#3| (-664)) ELT) (($ |#3| $) NIL (|has| |#3| (-664)) ELT) (($ $ $) NIL (|has| |#3| (-962)) ELT)) (-3959 (((-695) $) NIL T ELT))) 
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+NIL 
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+NIL 
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ELT) (($ $ (-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) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-695)) NIL (|has| |#1| (-189)) ELT)) (-1490 (((-584 |#2|) $) NIL T ELT)) (-3950 (((-470 |#3|) $) NIL T ELT) (((-695) $ |#3|) NIL T ELT) (((-584 (-695)) $ (-584 |#3|)) NIL T ELT) (((-695) $ |#2|) NIL T ELT)) (-3974 (((-801 (-330)) $) NIL (-12 (|has| |#1| (-554 (-801 (-330)))) (|has| |#3| (-554 (-801 (-330))))) ELT) (((-801 (-485)) $) NIL (-12 (|has| |#1| (-554 (-801 (-485)))) (|has| |#3| (-554 (-801 (-485))))) ELT) (((-474) $) NIL (-12 (|has| |#1| (-554 (-474))) (|has| |#3| (-554 (-474)))) ELT)) (-2819 ((|#1| $) NIL (|has| |#1| (-392)) ELT) (($ $ |#3|) NIL (|has| |#1| (-392)) ELT)) (-2705 (((-3 (-1180 $) #1#) (-631 $)) NIL (-12 (|has| $ (-118)) (|has| |#1| 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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) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-695)) NIL (|has| |#1| (-189)) ELT)) (-3058 (((-85) $ $) NIL T ELT)) (-3951 (($ $ |#1|) NIL (|has| |#1| (-312)) ELT)) (-3839 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3841 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-350 (-485))) NIL (|has| |#1| (-38 (-350 (-485)))) ELT) (($ (-350 (-485)) $) NIL (|has| |#1| (-38 (-350 (-485)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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+NIL 
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+NIL 
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-NIL 
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+NIL 
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+NIL 
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 (((-246) (-113)) (T -246)) 
 NIL 
-(-13 (-961) (-82 $ $) (-10 -7 (-6 -3989))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-555 (-484)) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-963 $) . T) ((-968 $) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
-((-1584 (((-583 (-997)) $) 10 T ELT)) (-1582 (($ (-446) (-446) (-1015) $) 19 T ELT)) (-1580 (($ (-446) (-583 (-876)) $) 23 T ELT)) (-1578 (($) 25 T ELT)) (-1583 (((-632 (-1015)) (-446) (-446) $) 18 T ELT)) (-1581 (((-583 (-876)) (-446) $) 22 T ELT)) (-3566 (($) 7 T ELT)) (-1579 (($) 24 T ELT)) (-3947 (((-772) $) 29 T ELT)) (-1577 (($) 26 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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+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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(-818 |#1|) (-320)) ELT)) (-1628 (((-1086 (-818 |#1|)) $) NIL (|has| (-818 |#1|) (-320)) ELT)) (-1627 (((-1086 (-818 |#1|)) $) NIL (|has| (-818 |#1|) (-320)) ELT) (((-3 (-1086 (-818 |#1|)) #1#) $ $) NIL (|has| (-818 |#1|) (-320)) ELT)) (-1629 (($ $ (-1086 (-818 |#1|))) NIL (|has| (-818 |#1|) (-320)) ELT)) (-1895 (($ $ $) NIL T ELT) (($ (-584 $)) NIL T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-2486 (($ $) NIL T ELT)) (-3448 (($) NIL (|has| (-818 |#1|) (-320)) CONST)) (-2401 (($ (-831)) NIL (|has| (-818 |#1|) (-320)) ELT)) (-3933 (((-85) $) NIL T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-2410 (($) NIL (|has| (-818 |#1|) (-320)) ELT)) (-2710 (((-1086 $) (-1086 $) (-1086 $)) NIL T ELT)) (-3146 (($ $ $) NIL T ELT) (($ (-584 $)) NIL T ELT)) (-1677 (((-584 (-2 (|:| -3734 (-485)) (|:| -2402 (-485))))) NIL (|has| (-818 |#1|) (-320)) ELT)) (-3734 (((-348 $) $) NIL T ELT)) (-3932 (((-744 (-831))) NIL T ELT) (((-831)) NIL T ELT)) (-1607 (((-2 (|:| |coef1| $) (|:| |coef2| $) (|:| -2410 $)) $ $) NIL T 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(($ (-350 (-485)) $) NIL T ELT) (($ $ (-818 |#1|)) NIL T ELT) (($ (-818 |#1|) $) NIL T ELT))) 
+(((-289 |#1| |#2|) (-280 (-818 |#1|)) (-831) (-831)) (T -289)) 
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-NIL 
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-(((-308 |#1| |#2|) (-280 |#1|) (-299) (-830)) (T -308)) 
-NIL 
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-NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 |#2|) . T) ((-590 |#2|) . T) ((-574 |#2|) . T) ((-582 |#2|) . T) ((-654 |#2|) . T) ((-963 |#2|) . T) ((-968 |#2|) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
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-NIL 
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-(((-337 |#1|) (-336 |#1|) (-1013)) (T -337)) 
-NIL 
-((-2569 (((-85) $ $) NIL T ELT)) (-1756 (((-85) $) 25 T ELT)) (-1757 (((-85) $) 22 T ELT)) (-3615 (($ (-1073) (-1073) (-1073)) 26 T ELT)) (-3543 (((-1073) $) 16 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-1761 (($ (-1073) (-1073) (-1073)) 14 T ELT)) (-1759 (((-1073) $) 17 T ELT)) (-1758 (((-85) $) 18 T ELT)) (-1760 (((-1073) $) 15 T ELT)) (-3947 (((-772) $) 12 T ELT) (($ (-1073)) 13 T ELT) (((-1073) $) 9 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) 7 T ELT))) 
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+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
+((-1786 (((-631 |#2|) (-1180 $)) 45 T ELT)) (-1796 (($ (-1180 |#2|) (-1180 $)) 39 T ELT)) (-1785 (((-631 |#2|) $ (-1180 $)) 47 T ELT)) (-3759 ((|#2| (-1180 $)) 13 T ELT)) (-3226 (((-1180 |#2|) $ (-1180 $)) NIL T ELT) (((-631 |#2|) (-1180 $) (-1180 $)) 27 T ELT))) 
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+NIL 
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+(((-322 |#1| |#2|) (-113) (-146) (-1156 |t#1|)) (T -322)) 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
+((-1736 (((-85) (-1 (-85) |#2| |#2|) $) NIL T ELT) (((-85) $) 18 T ELT)) (-1734 (($ (-1 (-85) |#2| |#2|) $) NIL T ELT) (($ $) 28 T ELT)) (-2911 (($ (-1 (-85) |#2| |#2|) $) 27 T ELT) (($ $) 22 T ELT)) (-2299 (($ $) 25 T ELT)) (-3421 (((-485) (-1 (-85) |#2|) $) NIL T ELT) (((-485) |#2| $) 11 T ELT) (((-485) |#2| $ (-485)) NIL T ELT)) (-3520 (($ (-1 (-85) |#2| |#2|) $ $) NIL T ELT) (($ $ $) 20 T ELT))) 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-322 |#1| |#2|) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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+(((-355 |#1|) (-113) (-1130)) (T -355)) 
+NIL 
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+((-3960 ((|#3| (-1 |#4| |#2|) |#1|) 29 T ELT))) 
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-((-1893 (((-694) |#4|) 12 T ELT)) (-1881 (((-583 (-2 (|:| |totdeg| (-694)) (|:| -2004 |#4|))) |#4| (-694) (-583 (-2 (|:| |totdeg| (-694)) (|:| -2004 |#4|)))) 39 T ELT)) (-1883 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 49 T ELT)) (-1882 ((|#4| (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 52 T ELT)) (-1871 ((|#4| |#4| (-583 |#4|)) 54 T ELT)) (-1879 (((-2 (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (-583 |#4|)) 96 T ELT)) (-1886 (((-1185) |#4|) 59 T ELT)) (-1889 (((-1185) (-583 |#4|)) 69 T ELT)) (-1887 (((-484) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (-484) (-484) (-484)) 66 T ELT)) (-1890 (((-1185) (-484)) 110 T ELT)) (-1884 (((-583 |#4|) (-583 |#4|)) 104 T ELT)) (-1892 (((-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (-2 (|:| |totdeg| (-694)) (|:| -2004 |#4|)) |#4| (-694)) 31 T ELT)) (-1885 (((-484) |#4|) 109 T ELT)) (-1880 ((|#4| |#4|) 37 T ELT)) (-1872 (((-583 |#4|) (-583 |#4|) (-484) (-484)) 74 T ELT)) (-1888 (((-484) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (-484) (-484) (-484) (-484)) 123 T ELT)) (-1891 (((-85) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 20 T ELT)) (-1873 (((-85) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 78 T ELT)) (-1878 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 76 T ELT)) (-1877 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 47 T ELT)) (-1874 (((-85) |#2| |#2|) 75 T ELT)) (-1876 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 48 T ELT)) (-1875 (((-85) |#2| |#2| |#2| |#2|) 80 T ELT)) (-1870 ((|#4| |#4| (-583 |#4|)) 97 T ELT))) 
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-((-1893 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-694)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1892 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-2 (|:| |totdeg| (-694)) (|:| -2004 *4))) (-5 *5 (-694)) (-4 *4 (-861 *6 *7 *8)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756)) (-5 *2 (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4))) (-5 *1 (-390 *6 *7 *8 *4)))) (-1891 (*1 *2 *3 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1890 (*1 *2 *3) (-12 (-5 *3 (-484)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1185)) (-5 *1 (-390 *4 *5 *6 *7)) (-4 *7 (-861 *4 *5 *6)))) (-1889 (*1 *2 *3) (-12 (-5 *3 (-583 *7)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1185)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1888 (*1 *2 *3 *4 *4 *2 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756)) (-5 *1 (-390 *5 *6 *7 *4)))) (-1887 (*1 *2 *3 *4 *4 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756)) (-5 *1 (-390 *5 *6 *7 *4)))) (-1886 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1185)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1885 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-484)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1884 (*1 *2 *2) (-12 (-5 *2 (-583 *6)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1883 (*1 *2 *2 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1882 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *2) (|:| |polj| *2))) (-4 *5 (-717)) (-4 *2 (-861 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2)) (-4 *4 (-392)) (-4 *6 (-756)))) (-1881 (*1 *2 *3 *4 *2) (-12 (-5 *2 (-583 (-2 (|:| |totdeg| (-694)) (|:| -2004 *3)))) (-5 *4 (-694)) (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-5 *1 (-390 *5 *6 *7 *3)))) (-1880 (*1 *2 *2) (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *2)) (-4 *2 (-861 *3 *4 *5)))) (-1879 (*1 *2 *3 *4) (-12 (-5 *4 (-583 *3)) (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) (-5 *1 (-390 *5 *6 *7 *3)))) (-1878 (*1 *2 *3 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *3 (-717)) (-4 *6 (-861 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-756)) (-5 *1 (-390 *4 *3 *5 *6)))) (-1877 (*1 *2 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1876 (*1 *2 *3 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *3) (|:| |polj| *3)))) (-4 *5 (-717)) (-4 *3 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *3)))) (-1875 (*1 *2 *3 *3 *3 *3) (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85)) (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5)))) (-1874 (*1 *2 *3 *3) (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85)) (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5)))) (-1873 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1872 (*1 *2 *2 *3 *3) (-12 (-5 *2 (-583 *7)) (-5 *3 (-484)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1871 (*1 *2 *2 *3) (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2)))) (-1870 (*1 *2 *2 *3) (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2))))) 
-((-1894 (($ $ $) 14 T ELT) (($ (-583 $)) 21 T ELT)) (-2709 (((-1085 $) (-1085 $) (-1085 $)) 45 T ELT)) (-3145 (($ $ $) NIL T ELT) (($ (-583 $)) 22 T ELT))) 
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-NIL 
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+((-1895 (($ $ $) 14 T ELT) (($ (-584 $)) 21 T ELT)) (-2710 (((-1086 $) (-1086 $) (-1086 $)) 45 T ELT)) (-3146 (($ $ $) NIL T ELT) (($ (-584 $)) 22 T ELT))) 
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+NIL 
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+NIL 
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-NIL 
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+NIL 
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-NIL 
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+((-3948 (*1 *1 *2) (-12 (-5 *2 (-1177 *4)) (-14 *4 (-1091)) (-5 *1 (-414 *3 *4 *5)) (-4 *3 (-962)) (-14 *5 *3))) (-3948 (*1 *1 *2) (-12 (-5 *2 (-1161 *3 *4 *5)) (-4 *3 (-962)) (-14 *4 (-1091)) (-14 *5 *3) (-5 *1 (-414 *3 *4 *5)))) (-3814 (*1 *1 *1 *2) (-12 (-5 *2 (-1177 *4)) (-14 *4 (-1091)) (-5 *1 (-414 *3 *4 *5)) (-4 *3 (-38 (-350 (-485)))) (-4 *3 (-962)) (-14 *5 *3)))) 
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$ (-318 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ELT) (((-3 |#2| #1#) |#1| $) 16 T ELT)) (-3408 (($ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL (-12 (|has| $ (-318 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72))) ELT) (($ (-1 (-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL (|has| $ (-318 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) ELT)) (-3844 (((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) NIL (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) ELT) (((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) NIL T ELT) (((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-1577 ((|#2| $ |#1| |#2|) NIL (|has| $ (-1036 |#2|)) ELT)) (-3114 ((|#2| $ |#1|) NIL T ELT)) (-2201 ((|#1| $) NIL (|has| |#1| (-757)) ELT)) (-2610 (((-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-3247 (((-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) ELT)) (-2202 ((|#1| $) NIL (|has| |#1| (-757)) ELT)) (-3328 (($ (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT) (($ (-1 |#2| |#2|) $) NIL T ELT)) (-3960 (($ (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT) (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) NIL T ELT)) (-3244 (((-1074) $) NIL (OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| |#2| (-1014))) ELT)) (-2233 (((-584 |#1|) $) NIL T ELT)) (-2234 (((-85) |#1| $) NIL T ELT)) (-1275 (((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL T ELT)) (-3611 (($ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL T ELT)) (-2204 (((-584 |#1|) $) NIL T ELT)) (-2205 (((-85) |#1| $) NIL T ELT)) (-3245 (((-1034) $) NIL (OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| |#2| (-1014))) ELT)) (-3803 ((|#2| $) NIL (|has| |#1| (-757)) ELT)) (-1355 (((-3 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) #1#) (-1 (-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-2200 (($ $ |#2|) NIL (|has| $ (-1036 |#2|)) ELT)) (-1276 (((-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL T ELT)) (-1732 (((-85) (-1 (-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-3770 (($ $ (-584 (-249 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-249 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-249 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-584 (-249 |#2|))) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-249 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT) (($ $ (-584 (-249 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))))) NIL (-12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ELT)) (-1223 (((-85) $ $) NIL T ELT)) (-2203 (((-85) |#2| $) NIL (-12 (|has| $ (-318 |#2|)) (|has| |#2| (-72))) ELT)) (-2206 (((-584 |#2|) $) NIL T ELT)) (-3405 (((-85) $) NIL T ELT)) (-3567 (($) NIL T ELT)) (-3802 ((|#2| $ |#1|) 13 T ELT) ((|#2| $ |#1| |#2|) NIL T ELT)) (-1467 (($) NIL T ELT) (($ (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-1731 (((-695) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) $) NIL (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) ELT) (((-695) (-1 (-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-3402 (($ $) NIL T ELT)) (-3974 (((-474) $) NIL (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-554 (-474))) ELT)) (-3532 (($ (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-3948 (((-773) $) NIL (OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-553 (-773)))) ELT)) (-1266 (((-85) $ $) NIL (OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-72))) ELT)) (-1277 (($ (-584 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-1733 (((-85) (-1 (-85) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-3058 (((-85) $ $) NIL (OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-72))) ELT)) (-3959 (((-695) $) NIL T ELT))) 
+(((-415 |#1| |#2| |#3| |#4|) (-1108 |#1| |#2|) (-1014) (-1014) (-1108 |#1| |#2|) |#2|) (T -415)) 
+NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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 (((-147) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-((-2434 (($ $ (-830)) 17 T ELT))) 
-(((-682 |#1| |#2|) (-10 -7 (-15 -2434 (|#1| |#1| (-830)))) (-683 |#2|) (-146)) (T -682)) 
-NIL 
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-(((-683 |#1|) (-113) (-146)) (T -683)) 
-((-2434 (*1 *1 *1 *2) (-12 (-5 *2 (-830)) (-4 *1 (-683 *3)) (-4 *3 (-146))))) 
-(-13 (-685) (-654 |t#1|) (-10 -8 (-15 -2434 ($ $ (-830))))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-590 |#1|) . T) ((-582 |#1|) . T) ((-654 |#1|) . T) ((-657) . T) ((-685) . T) ((-963 |#1|) . T) ((-968 |#1|) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
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-(((-685) (-113)) (T -685)) 
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-((-3947 (((-772) $) NIL T ELT) (($ (-484)) 10 T ELT))) 
-(((-686 |#1|) (-10 -7 (-15 -3947 (|#1| (-484))) (-15 -3947 ((-772) |#1|))) (-687)) (T -686)) 
-NIL 
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-NIL 
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-NIL 
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+NIL 
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T ELT)) (-1706 (((-1086 |#2|) $) NIL (|has| |#2| (-496)) ELT)) (-1794 ((|#2|) NIL T ELT) ((|#2| (-1180 $)) NIL T ELT)) (-1724 (((-1086 |#2|) $) NIL T ELT)) (-1718 (((-85)) NIL T ELT)) (-3159 (((-3 (-485) #1#) $) NIL (|has| |#2| (-951 (-485))) ELT) (((-3 (-350 (-485)) #1#) $) NIL (|has| |#2| (-951 (-350 (-485)))) ELT) (((-3 |#2| #1#) $) NIL T ELT)) (-3158 (((-485) $) NIL (|has| |#2| (-951 (-485))) ELT) (((-350 (-485)) $) NIL (|has| |#2| (-951 (-350 (-485)))) ELT) ((|#2| $) NIL T ELT)) (-1796 (($ (-1180 |#2|)) NIL T ELT) (($ (-1180 |#2|) (-1180 $)) NIL T ELT)) (-2280 (((-631 (-485)) (-631 $)) NIL (|has| |#2| (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 (-485))) (|:| |vec| (-1180 (-485)))) (-631 $) (-1180 $)) NIL (|has| |#2| (-581 (-485))) ELT) (((-2 (|:| |mat| (-631 |#2|)) (|:| |vec| (-1180 |#2|))) (-631 $) (-1180 $)) NIL T ELT) (((-631 |#2|) (-631 $)) NIL T ELT)) (-3844 ((|#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| (-72)) ELT)) (-3469 (((-3 $ #1#) $) NIL T ELT)) (-3110 (((-695) $) NIL (|has| |#2| (-496)) ELT) (((-831)) 42 T ELT)) (-3114 ((|#2| $ (-485) (-485)) NIL T ELT)) (-1715 (((-85)) NIL T ELT)) (-2435 (($ $ (-831)) NIL T ELT)) (-1215 (((-85) $ $) NIL T ELT)) (-2411 (((-85) $) NIL T ELT)) (-3109 (((-695) $) NIL (|has| |#2| (-496)) ELT)) (-3108 (((-584 (-197 |#1| |#2|)) $) NIL (|has| |#2| (-496)) ELT)) (-3116 (((-695) $) NIL T ELT)) (-1711 (((-85)) NIL T ELT)) (-3115 (((-695) $) NIL T ELT)) (-3329 ((|#2| $) NIL (|has| |#2| (-6 (-3999 #2="*"))) ELT)) (-3120 (((-485) $) NIL T ELT)) (-3118 (((-485) $) NIL T ELT)) (-2610 (((-584 |#2|) $) NIL T ELT)) (-3247 (((-85) |#2| $) NIL (|has| |#2| (-72)) ELT)) (-3119 (((-485) $) NIL T ELT)) (-3117 (((-485) $) NIL T ELT)) (-3125 (($ (-584 (-584 |#2|))) NIL T ELT)) (-3960 (($ (-1 |#2| |#2| |#2|) $ $) NIL T ELT) (($ (-1 |#2| |#2|) $) NIL T ELT)) (-3596 (((-584 (-584 |#2|)) $) NIL T ELT)) (-1709 (((-85)) NIL T ELT)) (-1713 (((-85)) NIL T 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ELT)) (-1710 (((-85)) NIL T ELT)) (-1712 (((-85)) NIL T ELT)) (-1714 (((-85)) NIL T ELT)) (-3592 (((-3 $ #1#) $) NIL (|has| |#2| (-312)) ELT)) (-3245 (((-1034) $) NIL T ELT)) (-1717 (((-85)) NIL T ELT)) (-3468 (((-3 $ #1#) $ |#2|) NIL (|has| |#2| (-496)) ELT)) (-1732 (((-85) (-1 (-85) |#2|) $) NIL T ELT)) (-3770 (($ $ (-584 (-249 |#2|))) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-249 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ELT)) (-1223 (((-85) $ $) NIL T ELT)) (-3405 (((-85) $) NIL T ELT)) (-3567 (($) NIL T ELT)) (-3802 ((|#2| $ (-485) (-485) |#2|) NIL T ELT) ((|#2| $ (-485) (-485)) 27 T ELT) ((|#2| $ (-485)) NIL T ELT)) (-3760 (($ $ (-1 |#2| |#2|) (-695)) NIL T ELT) (($ $ (-1 |#2| |#2|)) NIL T ELT) (($ $) NIL (|has| |#2| (-189)) ELT) (($ $ (-695)) NIL (|has| |#2| (-189)) ELT) (($ $ (-1091)) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-584 (-1091))) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-1091) (-695)) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| |#2| (-812 (-1091))) ELT)) (-3331 ((|#2| $) NIL T ELT)) (-3334 (($ (-584 |#2|)) NIL T ELT)) (-3123 (((-85) $) NIL T ELT)) (-3333 (((-197 |#1| |#2|) $) NIL T ELT)) (-3330 ((|#2| $) NIL (|has| |#2| (-6 (-3999 #2#))) ELT)) (-1731 (((-695) (-1 (-85) |#2|) $) NIL T ELT) (((-695) |#2| $) NIL (|has| |#2| (-72)) ELT)) (-3402 (($ $) NIL T ELT)) (-3226 (((-631 |#2|) (-1180 $)) NIL T ELT) (((-1180 |#2|) $) NIL T ELT) (((-631 |#2|) (-1180 $) (-1180 $)) NIL T ELT) (((-1180 |#2|) $ (-1180 $)) 30 T ELT)) (-3974 (($ (-1180 |#2|)) NIL T ELT) (((-1180 |#2|) $) NIL T ELT)) (-1896 (((-584 (-858 |#2|))) NIL T ELT) (((-584 (-858 |#2|)) (-1180 $)) NIL T ELT)) (-2437 (($ $ $) NIL T ELT)) (-1723 (((-85)) NIL T ELT)) (-3112 (((-197 |#1| |#2|) $ (-485)) NIL T ELT)) (-3948 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ (-350 (-485))) NIL (|has| |#2| (-951 (-350 (-485)))) ELT) (($ |#2|) NIL T ELT) (((-631 |#2|) $) NIL T ELT)) (-3128 (((-695)) NIL T CONST)) (-1266 (((-85) $ $) NIL T ELT)) (-2013 (((-1180 $)) 40 T ELT)) (-1708 (((-584 (-1180 |#2|))) NIL (|has| |#2| (-496)) ELT)) (-2438 (($ $ $ $) NIL T ELT)) (-1721 (((-85)) NIL T ELT)) (-2547 (($ (-631 |#2|) $) NIL T ELT)) (-1733 (((-85) (-1 (-85) |#2|) $) NIL T ELT)) (-3121 (((-85) $) NIL T ELT)) (-2436 (($ $ $) NIL T ELT)) (-1722 (((-85)) NIL T ELT)) (-1720 (((-85)) NIL T ELT)) (-3127 (((-85) $ $) NIL T ELT)) (-1716 (((-85)) NIL T ELT)) (-2662 (($) NIL T CONST)) (-2668 (($) NIL T CONST)) (-2671 (($ $ (-1 |#2| |#2|) (-695)) NIL T ELT) (($ $ (-1 |#2| |#2|)) NIL T ELT) (($ $) NIL (|has| |#2| (-189)) ELT) (($ $ (-695)) NIL (|has| |#2| (-189)) ELT) (($ $ (-1091)) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-584 (-1091))) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-1091) (-695)) NIL (|has| |#2| (-812 (-1091))) ELT) (($ $ (-584 (-1091)) (-584 (-695))) NIL (|has| |#2| (-812 (-1091))) ELT)) (-3058 (((-85) $ $) NIL T ELT)) (-3951 (($ $ |#2|) NIL (|has| |#2| (-312)) ELT)) (-3839 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3841 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) NIL (|has| |#2| (-312)) ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) NIL T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) NIL T ELT)) (-3959 (((-695) $) NIL T ELT))) 
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+NIL 
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+((-3250 (*1 *2 *1) (-12 (-5 *2 (-584 (-1050))) (-5 *1 (-614))))) 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 $) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-120) . T) ((-555 (-484)) . T) ((-555 $) . T) ((-552 (-772)) . T) ((-146) . T) ((-246) . T) ((-495) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-582 $) . T) ((-654 $) . T) ((-663) . T) ((-714) . T) ((-716) . T) ((-718) . T) ((-721) . T) ((-755) . T) ((-756) . T) ((-759) . T) ((-963 $) . T) ((-968 $) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
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+(((-721 |#1|) (-113) (-146)) (T -721)) 
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+(((-722) (-113)) (T -722)) 
+NIL 
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(-3841 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-485) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-350 (-485))) NIL (|has| |#1| (-38 (-350 (-485)))) ELT) (($ (-350 (-485)) $) NIL (|has| |#1| (-38 (-350 (-485)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL T ELT))) 
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 (((-755) (-113)) (T -755)) 
 NIL 
-(-13 (-714) (-120) (-663)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-555 (-484)) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-714) . T) ((-716) . T) ((-718) . T) ((-721) . T) ((-756) . T) ((-759) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-664) . T) ((-767) . T) ((-757) . T) ((-760) . T) ((-1026) . T) ((-1014) . T) ((-1130) . T)) 
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 (((-756) (-113)) (T -756)) 
 NIL 
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-(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-759) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-(((-766) (-113)) (T -766)) 
-NIL 
-(-13 (-756) (-1025)) 
-(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-756) . T) ((-759) . T) ((-1025) . T) ((-1013) . T) ((-1129) . T)) 
-((-2569 (((-85) $ $) NIL T ELT)) (-3403 (((-484) $) 14 T ELT)) (-2532 (($ $ $) NIL T ELT)) (-2858 (($ $ $) NIL T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3947 (((-772) $) 20 T ELT) (($ (-484)) 13 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-2567 (((-85) $ $) NIL T ELT)) (-2568 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) 10 T ELT)) (-2685 (((-85) $ $) NIL T ELT)) (-2686 (((-85) $ $) 12 T ELT))) 
-(((-767) (-13 (-756) (-10 -8 (-15 -3947 ($ (-484))) (-15 -3403 ((-484) $))))) (T -767)) 
-((-3947 (*1 *1 *2) (-12 (-5 *2 (-484)) (-5 *1 (-767)))) (-3403 (*1 *2 *1) (-12 (-5 *2 (-484)) (-5 *1 (-767))))) 
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-NIL 
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+(-13 (-715) (-120) (-664)) 
+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-715) . T) ((-717) . T) ((-719) . T) ((-722) . T) ((-757) . T) ((-760) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
+((-2570 (((-85) $ $) 7 T ELT)) (-2533 (($ $ $) 23 T ELT)) (-2859 (($ $ $) 22 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1034) $) 12 T ELT)) (-3948 (((-773) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2568 (((-85) $ $) 21 T ELT)) (-2569 (((-85) $ $) 19 T ELT)) (-3058 (((-85) $ $) 8 T ELT)) (-2686 (((-85) $ $) 20 T ELT)) (-2687 (((-85) $ $) 18 T ELT))) 
+(((-757) (-113)) (T -757)) 
+NIL 
+(-13 (-1014) (-760)) 
+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-760) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
+((-2533 (($ $ $) 16 T ELT)) (-2859 (($ $ $) 15 T ELT)) (-1266 (((-85) $ $) 17 T ELT)) (-2568 (((-85) $ $) 12 T ELT)) (-2569 (((-85) $ $) 9 T ELT)) (-3058 (((-85) $ $) 14 T ELT)) (-2686 (((-85) $ $) 11 T ELT))) 
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+NIL 
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+(((-760) (-113)) (T -760)) 
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+(((-72) . T) ((-13) . 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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-((-3243 (((-1073) $) 10 T ELT)) (-3244 (((-1033) $) 8 T ELT))) 
-(((-1012 |#1|) (-10 -7 (-15 -3243 ((-1073) |#1|)) (-15 -3244 ((-1033) |#1|))) (-1013)) (T -1012)) 
-NIL 
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-(((-1013) (-113)) (T -1013)) 
-((-3244 (*1 *2 *1) (-12 (-4 *1 (-1013)) (-5 *2 (-1033)))) (-3243 (*1 *2 *1) (-12 (-4 *1 (-1013)) (-5 *2 (-1073))))) 
-(-13 (-72) (-552 (-772)) (-10 -8 (-15 -3244 ((-1033) $)) (-15 -3243 ((-1073) $)))) 
-(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-1129) . T)) 
-((-2569 (((-85) $ $) NIL T ELT)) (-3137 (((-694)) 36 T ELT)) (-3248 (($ (-583 (-830))) 70 T ELT)) (-3250 (((-3 $ #1="failed") $ (-830) (-830)) 81 T ELT)) (-2995 (($) 40 T ELT)) (-3246 (((-85) (-830) $) 42 T ELT)) (-2010 (((-830) $) 64 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-2400 (($ (-830)) 39 T ELT)) (-3251 (((-3 $ #1#) $ (-830)) 77 T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3247 (((-1179 $)) 47 T ELT)) (-3249 (((-583 (-830)) $) 27 T ELT)) (-3245 (((-694) $ (-830) (-830)) 78 T ELT)) (-3947 (((-772) $) 32 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) 24 T ELT))) 
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-(((-1015) (-1016 (-1073) (-1090) (-484) (-179) (-772))) (T -1015)) 
-NIL 
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-(((-1016 |#1| |#2| |#3| |#4| |#5|) (-113) (-1013) (-1013) (-1013) (-1013) (-1013)) (T -1016)) 
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-(((-72) . T) ((-552 (-772)) . T) ((-557 (-583 $)) . T) ((-557 |#1|) . T) ((-557 |#2|) . T) ((-557 |#3|) . T) ((-557 |#4|) . T) ((-557 |#5|) . T) ((-241 (-484) $) . T) ((-241 (-583 (-484)) $) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
-((-2569 (((-85) $ $) NIL T ELT)) (-3261 (((-85) $) 45 T ELT)) (-3257 ((|#2| $) 48 T ELT)) (-3262 (((-85) $) 20 T ELT)) (-3536 ((|#1| $) 21 T ELT)) (-3264 (((-85) $) 42 T ELT)) (-3266 (((-85) $) 14 T ELT)) (-3263 (((-85) $) 44 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3260 (((-85) $) 46 T ELT)) (-3256 ((|#3| $) 50 T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3259 (((-85) $) 47 T ELT)) (-3255 ((|#4| $) 49 T ELT)) (-3254 ((|#5| $) 51 T ELT)) (-3267 (((-85) $ $) 41 T ELT)) (-3801 (($ $ (-484)) 62 T ELT) (($ $ (-583 (-484))) 64 T ELT)) (-3258 (((-583 $) $) 27 T ELT)) (-3973 (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ (-583 $)) 52 T ELT)) (-3947 (((-772) $) 28 T ELT)) (-3252 (($ $) 26 T ELT)) (-3253 (($ $) 58 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3265 (((-85) $) 23 T ELT)) (-3057 (((-85) $ $) 40 T ELT)) (-3958 (((-484) $) 60 T ELT))) 
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-NIL 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-3998 #1="*"))) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-555 (-350 (-484))) |has| |#2| (-950 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#2|) . T) ((-552 (-772)) . T) ((-186 $) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-184 |#2|) . T) ((-190) |has| |#2| (-190)) ((-189) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-225 |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-318 |#2|) . T) ((-329 |#2|) . T) ((-355 |#2|) . T) ((-429 |#2|) . T) ((-455 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-588 (-484)) . T) ((-588 |#2|) . T) ((-588 $) . T) ((-590 (-484)) |has| |#2| (-580 (-484))) ((-590 |#2|) . T) ((-590 $) . T) ((-582 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3998 #1#)))) ((-580 (-484)) |has| |#2| (-580 (-484))) ((-580 |#2|) . T) ((-654 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3998 #1#)))) ((-663) . T) ((-806 $ (-1090)) OR (|has| |#2| (-811 (-1090))) (|has| |#2| (-809 (-1090)))) ((-809 (-1090)) |has| |#2| (-809 (-1090))) ((-811 (-1090)) OR (|has| |#2| (-811 (-1090))) (|has| |#2| (-809 (-1090)))) ((-965 |#1| |#1| |#2| |#3| |#4|) . T) ((-950 (-350 (-484))) |has| |#2| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#2| (-950 (-484))) ((-950 |#2|) . T) ((-963 |#2|) . T) ((-968 |#2|) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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-NIL 
-(-13 (-1020 |t#1| |t#2| |t#3| |t#4|) (-707 |t#1| |t#2| |t#3| |t#4|)) 
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-NIL 
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-NIL 
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+NIL 
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+(((-72) . T) ((-553 (-773)) . T) ((-558 (-584 $)) . T) ((-558 |#1|) . T) ((-558 |#2|) . T) ((-558 |#3|) . T) ((-558 |#4|) . T) ((-558 |#5|) . T) ((-241 (-485) $) . T) ((-241 (-584 (-485)) $) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
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+NIL 
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|#3| (-25)) ELT)) (** (($ $ (-695)) NIL (|has| |#3| (-962)) ELT) (($ $ (-831)) NIL (|has| |#3| (-962)) ELT)) (* (($ $ $) NIL (|has| |#3| (-962)) ELT) (($ $ |#3|) NIL (|has| |#3| (-664)) ELT) (($ |#3| $) NIL (|has| |#3| (-664)) ELT) (($ (-485) $) NIL (|has| |#3| (-21)) ELT) (($ (-695) $) NIL (|has| |#3| (-23)) ELT) (($ (-831) $) NIL (|has| |#3| (-25)) ELT)) (-3959 (((-695) $) NIL T ELT))) 
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+NIL 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-3999 #1="*"))) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-556 (-350 (-485))) |has| |#2| (-951 (-350 (-485)))) ((-556 (-485)) . T) ((-556 |#2|) . T) ((-553 (-773)) . T) ((-186 $) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-184 |#2|) . T) ((-190) |has| |#2| (-190)) ((-189) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-225 |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-318 |#2|) . T) ((-329 |#2|) . T) ((-355 |#2|) . T) ((-429 |#2|) . T) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-589 (-485)) . T) ((-589 |#2|) . T) ((-589 $) . T) ((-591 (-485)) |has| |#2| (-581 (-485))) ((-591 |#2|) . T) ((-591 $) . T) ((-583 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3999 #1#)))) ((-581 (-485)) |has| |#2| (-581 (-485))) ((-581 |#2|) . T) ((-655 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3999 #1#)))) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-810 (-1091)) |has| |#2| (-810 (-1091))) ((-812 (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-966 |#1| |#1| |#2| |#3| |#4|) . T) ((-951 (-350 (-485))) |has| |#2| (-951 (-350 (-485)))) ((-951 (-485)) |has| |#2| (-951 (-485))) ((-951 |#2|) . T) ((-964 |#2|) . T) ((-969 |#2|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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+(((-1042 |#1| |#2| |#3| |#4|) (-113) (-392) (-718) (-757) (-978 |t#1| |t#2| |t#3|)) (T -1042)) 
+NIL 
+(-13 (-1021 |t#1| |t#2| |t#3| |t#4|) (-708 |t#1| |t#2| |t#3| |t#4|)) 
+(((-34) . T) ((-72) . T) ((-553 (-584 |#4|)) . T) ((-553 (-773)) . T) ((-124 |#4|) . T) ((-554 (-474)) |has| |#4| (-554 (-474))) ((-260 |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1014))) ((-318 |#4|) . T) ((-429 |#4|) . T) ((-456 |#4| |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1014))) ((-13) . 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) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) 56 T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) 58 T ELT)) (-3959 (((-695) $) NIL T ELT))) 
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 NIL 
 (-13) 
 (((-13) . T)) 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-484)) . T) ((-25) . T) ((-38 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-350 (-484)))) ((-66) |has| |#1| (-38 (-350 (-484)))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-740))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-555 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-555 (-484)) . T) ((-555 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1090)))) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . 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T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-553 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-473)) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-473)))) ((-553 (-800 (-330))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-330))))) ((-553 (-800 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-484))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-312)) ((-190) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-312)) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-350 (-484)))) ((-241 (-484) |#1|) . T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-484) (-1025)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-455 (-1090) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-455 (-1090) |#2|))) ((-455 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-588 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 |#2|) |has| |#1| (-312)) ((-588 $) . T) ((-590 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-590 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-582 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 |#2|) |has| |#1| (-312)) ((-582 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-580 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-580 |#2|) |has| |#1| (-312)) ((-654 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 |#2|) |has| |#1| (-312)) ((-654 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-663) . T) ((-714) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-716) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-718) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-721) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-740) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-755) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-756) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-759) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-806 $ (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-809 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-811 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-796 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-330)))) ((-796 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-484)))) ((-794 |#2|) |has| |#1| (-312)) ((-821) -12 (|has| |#1| (-312)) (|has| |#2| (-821))) ((-886 |#1| (-484) (-994)) . T) ((-832) |has| |#1| (-312)) ((-904 |#2|) |has| |#1| (-312)) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-933) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-950 (-350 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1090)))) ((-950 |#2|) . T) ((-963 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-963 |#1|) . T) ((-963 |#2|) |has| |#1| (-312)) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-968 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-968 |#1|) . T) ((-968 |#2|) |has| |#1| (-312)) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1066) -12 (|has| |#1| (-312)) (|has| |#2| (-1066))) ((-1115) |has| |#1| (-38 (-350 (-484)))) ((-1118) |has| |#1| (-38 (-350 (-484)))) ((-1129) . T) ((-1134) |has| |#1| (-312)) ((-1141 |#1|) . T) ((-1158 |#1| (-484)) . T)) 
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-NIL 
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-((-3819 (*1 *1 *2) (-12 (-5 *2 (-1069 (-2 (|:| |k| (-694)) (|:| |c| *3)))) (-4 *3 (-961)) (-4 *1 (-1172 *3)))) (-3818 (*1 *2 *1) (-12 (-4 *1 (-1172 *3)) (-4 *3 (-961)) (-5 *2 (-1069 *3)))) (-3819 (*1 *1 *2) (-12 (-5 *2 (-1069 *3)) (-4 *3 (-961)) (-4 *1 (-1172 *3)))) (-3817 (*1 *1 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-961)))) (-3816 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-484))) (-4 *1 (-1172 *3)) (-4 *3 (-961)))) (-3815 (*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1172 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (-3815 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1172 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-961)) (-4 *2 (-312)))) (-3813 (*1 *1 *1) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-961)) (-4 *2 (-38 (-350 (-484)))))) (-3813 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1090)) (-4 *1 (-1172 *3)) (-4 *3 (-961)) (-12 (-4 *3 (-29 (-484))) (-4 *3 (-871)) (-4 *3 (-1115)) (-4 *3 (-38 (-350 (-484)))))) (-12 (-5 *2 (-1090)) (-4 *1 (-1172 *3)) (-4 *3 (-961)) (-12 (|has| *3 (-15 -3082 ((-583 *2) *3))) (|has| *3 (-15 -3813 (*3 *3 *2))) (-4 *3 (-38 (-350 (-484))))))))) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-694)) . T) ((-25) . T) ((-38 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-35) |has| |#1| (-38 (-350 (-484)))) ((-66) |has| |#1| (-38 (-350 (-484)))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#1|) |has| |#1| (-146)) ((-555 $) |has| |#1| (-495)) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-239) |has| |#1| (-38 (-350 (-484)))) ((-241 (-694) |#1|) . T) ((-241 $ $) |has| (-694) (-1025)) ((-246) |has| |#1| (-495)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-495) |has| |#1| (-495)) ((-13) . T) ((-588 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) |has| |#1| (-495)) ((-654 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) |has| |#1| (-495)) ((-663) . T) ((-806 $ (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-809 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-811 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-886 |#1| (-694) (-994)) . T) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-963 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-968 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1115) |has| |#1| (-38 (-350 (-484)))) ((-1118) |has| |#1| (-38 (-350 (-484)))) ((-1129) . T) ((-1158 |#1| (-694)) . T)) 
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-((-3829 ((|#2| |#4| (-694)) 31 T ELT)) (-3828 ((|#4| |#2|) 26 T ELT)) (-3831 ((|#4| (-350 |#2|)) 49 (|has| |#1| (-495)) ELT)) (-3830 (((-1 |#4| (-583 |#4|)) |#3|) 43 T ELT))) 
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-NIL 
-(((-1175) (-113)) (T -1175)) 
-NIL 
-(-13 (-10 -7 (-6 -2287))) 
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-((-3947 (*1 *2 *1) (-12 (-5 *2 (-1090)) (-5 *1 (-1176 *3)) (-14 *3 *2))) (-3832 (*1 *2) (-12 (-5 *2 (-1090)) (-5 *1 (-1176 *3)) (-14 *3 *2)))) 
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-NIL 
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-NIL 
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-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-((-3 2789145 2789150 2789155 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2789130 2789135 2789140 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2789115 2789120 2789125 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2789100 2789105 2789110 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1209 2788079 2789018 2789095 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1208 2787294 2787473 2787692 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1207 2778453 2780322 2782256 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1206 2777841 2777994 2778183 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1205 2777303 2777606 2777719 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1204 2774863 2776765 2776968 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1203 2771627 2773280 2773851 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1202 2768884 2770614 2770668 "XPOLYC" 2770953 XPOLYC (NIL T T) -9 NIL 2771066 NIL) (-1201 2766403 2768388 2768591 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1200 2762651 2765262 2765650 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1199 2757498 2759131 2759185 "XFALG" 2761330 XFALG (NIL T T) -9 NIL 2762114 NIL) (-1198 2752654 2755387 2755429 "XF" 2756047 XF (NIL T) -9 NIL 2756443 NIL) (-1197 2752372 2752482 2752649 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1196 2751599 2751721 2751925 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1195 2749341 2751499 2751594 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1194 2747922 2748717 2748759 "XALG" 2748764 XALG (NIL T) -9 NIL 2748873 NIL) (-1193 2741773 2746332 2746810 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1192 2740016 2741018 2741339 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1191 2739615 2739887 2739956 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1190 2739102 2739405 2739498 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1189 2738179 2738389 2738684 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1188 2736475 2736938 2737400 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1187 2735364 2735949 2735991 "VSPACE" 2736127 VSPACE (NIL T) -9 NIL 2736201 NIL) (-1186 2735235 2735268 2735359 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1185 2735078 2735132 2735200 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1184 2732061 2732856 2733593 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1183 2723159 2725760 2727933 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1182 2716736 2718627 2720206 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1181 2715220 2715615 2716021 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1180 2714047 2714328 2714644 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1179 2709444 2713874 2713966 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1178 2702789 2707117 2707160 "VECTCAT" 2708148 VECTCAT (NIL T) -9 NIL 2708732 NIL) (-1177 2702068 2702394 2702784 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1176 2701562 2701804 2701924 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1175 2701495 2701500 2701530 "UTYPE" 2701535 UTYPE (NIL) -9 NIL NIL NIL) (-1174 2700482 2700658 2700919 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1173 2698333 2698841 2699365 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1172 2688215 2694185 2694227 "UTSCAT" 2695325 UTSCAT (NIL T) -9 NIL 2696082 NIL) (-1171 2686280 2687223 2688210 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1170 2685954 2686003 2686134 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1169 2677665 2684150 2684629 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1168 2672227 2674500 2674543 "URAGG" 2676583 URAGG (NIL T) -9 NIL 2677308 NIL) (-1167 2670298 2671230 2672222 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1166 2666005 2669274 2669736 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1165 2658434 2665929 2666000 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1164 2647085 2654572 2654633 "UPXSCCA" 2655201 UPXSCCA (NIL T T) -9 NIL 2655433 NIL) (-1163 2646806 2646908 2647080 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1162 2635358 2642570 2642612 "UPXSCAT" 2643252 UPXSCAT (NIL T) -9 NIL 2643860 NIL) (-1161 2634871 2634956 2635133 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1160 2626557 2634462 2634724 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2625452 2625722 2626072 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1158 2618155 2621640 2621694 "UPSCAT" 2622763 UPSCAT (NIL T T) -9 NIL 2623527 NIL) (-1157 2617575 2617827 2618150 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1156 2617249 2617298 2617429 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1155 2601379 2610333 2610375 "UPOLYC" 2612453 UPOLYC (NIL T) -9 NIL 2613673 NIL) (-1154 2595434 2598282 2601374 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1153 2594870 2594995 2595158 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1152 2594504 2594591 2594730 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1151 2593317 2593584 2593888 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1150 2592650 2592780 2592965 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1149 2592242 2592317 2592464 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1148 2583006 2592008 2592136 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1147 2582368 2582505 2582710 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1146 2580969 2581816 2582092 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1145 2580198 2580395 2580620 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1144 2567008 2580122 2580193 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1143 2546814 2560049 2560110 "ULSCCAT" 2560741 ULSCCAT (NIL T T) -9 NIL 2561028 NIL) (-1142 2546149 2546435 2546809 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1141 2534521 2541655 2541697 "ULSCAT" 2542550 ULSCAT (NIL T) -9 NIL 2543280 NIL) (-1140 2534034 2534119 2534296 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1139 2516151 2533533 2533774 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1138 2515185 2515878 2515992 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2516103) (-1137 2514218 2514911 2515025 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2515136) (-1136 2513251 2513944 2514058 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2514169) (-1135 2512284 2512977 2513091 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2513202) (-1134 2510291 2511512 2511542 "UFD" 2511753 UFD (NIL) -9 NIL 2511866 NIL) (-1133 2510135 2510192 2510286 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1132 2509387 2509594 2509810 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1131 2507607 2508060 2508525 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1130 2507332 2507572 2507602 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1129 2507270 2507275 2507305 "TYPE" 2507310 TYPE (NIL) -9 NIL 2507317 NIL) (-1128 2506429 2506649 2506889 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1127 2505607 2506038 2506273 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1126 2503761 2504334 2504873 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1125 2502795 2503031 2503267 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1124 2491412 2495588 2495684 "TSETCAT" 2500899 TSETCAT (NIL T T T T) -9 NIL 2502403 NIL) (-1123 2487749 2489565 2491407 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1122 2482141 2486975 2487257 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1121 2477478 2478491 2479420 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1120 2476975 2477050 2477213 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1119 2475051 2475341 2475696 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1118 2474535 2474684 2474714 "TRIGCAT" 2474927 TRIGCAT (NIL) -9 NIL NIL NIL) (-1117 2474286 2474389 2474530 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1116 2471341 2473392 2473673 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1115 2470447 2471143 2471173 "TRANFUN" 2471208 TRANFUN (NIL) -9 NIL 2471274 NIL) (-1114 2469911 2470162 2470442 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1113 2469748 2469786 2469847 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1112 2469205 2469336 2469487 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1111 2467946 2468603 2468839 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1110 2467758 2467795 2467867 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1109 2465972 2466618 2467047 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1108 2464352 2464689 2465011 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1107 2454413 2462113 2462169 "TBAGG" 2462486 TBAGG (NIL T T) -9 NIL 2462696 NIL) (-1106 2451949 2453138 2454408 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1105 2451426 2451551 2451696 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1104 2450936 2451256 2451346 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1103 2450433 2450550 2450688 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1102 2442937 2450361 2450428 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1101 2438690 2439985 2441230 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1100 2438059 2438218 2438399 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1099 2435213 2435966 2436749 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1098 2434987 2435177 2435208 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1097 2433941 2434626 2434752 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2434938) (-1096 2433205 2433753 2433832 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2433892) (-1095 2430028 2431187 2431887 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1094 2427711 2428394 2429028 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1093 2423789 2424835 2425812 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1092 2420888 2423444 2423673 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1091 2420484 2420571 2420693 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1090 2417108 2418582 2419401 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1089 2410068 2416305 2416598 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2401754 2409659 2409921 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2401033 2401172 2401389 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1086 2400717 2400782 2400893 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1085 2391440 2400429 2400554 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1084 2390170 2390468 2390823 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1083 2389575 2389653 2389844 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1082 2371727 2389074 2389315 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1081 2371326 2371598 2371667 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1080 2370662 2370943 2371083 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1079 2365264 2366523 2367476 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1078 2364796 2364896 2365060 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1077 2359907 2361189 2362336 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1076 2354365 2355836 2357147 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1075 2347280 2349344 2351135 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1074 2339449 2347218 2347275 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1073 2334398 2339163 2339278 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1072 2333985 2334068 2334212 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1071 2333136 2333337 2333572 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1070 2332876 2332934 2333027 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1069 2326343 2331079 2331687 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1068 2325519 2325724 2325955 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1067 2324764 2325135 2325282 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1066 2324252 2324494 2324524 "STEP" 2324618 STEP (NIL) -9 NIL 2324689 NIL) (-1065 2316746 2324170 2324247 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1064 2311731 2315544 2315587 "STAGG" 2316014 STAGG (NIL T) -9 NIL 2316188 NIL) (-1063 2310189 2310897 2311726 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1062 2308410 2310016 2310108 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1061 2307690 2308229 2308259 "SRING" 2308264 SRING (NIL) -9 NIL 2308284 NIL) (-1060 2300605 2306228 2306667 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1059 2294379 2295818 2297322 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1058 2287017 2291674 2291704 "SRAGG" 2293003 SRAGG (NIL) -9 NIL 2293607 NIL) (-1057 2286314 2286634 2287012 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1056 2280474 2285636 2286059 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1055 2274486 2277827 2278578 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1054 2270915 2271734 2272371 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1053 2269890 2270195 2270225 "SPFCAT" 2270669 SPFCAT (NIL) -9 NIL NIL NIL) (-1052 2268827 2269079 2269343 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1051 2259585 2261859 2261889 "SPADXPT" 2266526 SPADXPT (NIL) -9 NIL 2268650 NIL) (-1050 2259387 2259433 2259502 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1049 2257043 2259351 2259382 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1048 2248717 2250806 2250848 "SPACEC" 2255163 SPACEC (NIL T) -9 NIL 2256968 NIL) (-1047 2246546 2248664 2248712 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1046 2245525 2245714 2245997 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1045 2243929 2244262 2244673 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1044 2243194 2243428 2243689 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1043 2239374 2240334 2241329 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1042 2235732 2236431 2237160 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1041 2229773 2235035 2235131 "SNTSCAT" 2235136 SNTSCAT (NIL T T T T) -9 NIL 2235206 NIL) (-1040 2223594 2228414 2228804 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1039 2217366 2223513 2223589 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1038 2215798 2216129 2216527 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1037 2207490 2212364 2212466 "SMATCAT" 2213809 SMATCAT (NIL NIL T T T) -9 NIL 2214357 NIL) (-1036 2205331 2206315 2207485 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1035 2203937 2204789 2204832 "SMAGG" 2204917 SMAGG (NIL T) -9 NIL 2204992 NIL) (-1034 2201556 2203104 2203147 "SKAGG" 2203408 SKAGG (NIL T) -9 NIL 2203544 NIL) (-1033 2197602 2201376 2201487 "SINT" NIL SINT (NIL) -8 NIL NIL 2201528) (-1032 2197412 2197456 2197522 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2196487 2196719 2196987 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2195491 2195653 2195929 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2194837 2195177 2195300 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2194183 2194490 2194630 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2192294 2192786 2193292 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2185832 2192213 2192289 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2185335 2185572 2185602 "SGROUP" 2185695 SGROUP (NIL) -9 NIL 2185757 NIL) (-1024 2185225 2185257 2185330 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2184863 2184903 2184944 "SGPOPC" 2184949 SGPOPC (NIL T) -9 NIL 2185150 NIL) (-1022 2184397 2184674 2184780 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2181820 2182589 2183311 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2175960 2181222 2181318 "SFRTCAT" 2181323 SFRTCAT (NIL T T T T) -9 NIL 2181361 NIL) (-1019 2170352 2171465 2172592 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2164528 2165689 2166853 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2163500 2164402 2164523 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2159108 2160003 2160098 "SEXCAT" 2162711 SEXCAT (NIL T T T T T) -9 NIL 2163262 NIL) (-1015 2158081 2159035 2159103 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2156472 2157057 2157359 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2155995 2156180 2156210 "SETCAT" 2156327 SETCAT (NIL) -9 NIL 2156411 NIL) (-1012 2155827 2155891 2155990 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2152839 2154281 2154324 "SETAGG" 2155192 SETAGG (NIL T) -9 NIL 2155530 NIL) (-1010 2152445 2152597 2152834 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2149690 2152392 2152440 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2149156 2149466 2149566 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2148283 2148649 2148710 "SEGXCAT" 2148996 SEGXCAT (NIL T T) -9 NIL 2149116 NIL) (-1006 2147208 2147476 2147519 "SEGCAT" 2148041 SEGCAT (NIL T) -9 NIL 2148262 NIL) (-1005 2146888 2146953 2147066 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2145954 2146424 2146632 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2145532 2145811 2145887 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2144897 2145033 2145237 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2143963 2144710 2144892 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2143216 2143911 2143958 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2134703 2143085 2143211 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2133563 2133853 2134170 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2132869 2133081 2133269 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2132219 2132376 2132552 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2131792 2132023 2132051 "SASTCAT" 2132056 SASTCAT (NIL) -9 NIL 2132069 NIL) (-994 2131259 2131684 2131758 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2130862 2130903 2131074 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2130493 2130534 2130691 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2123574 2130410 2130488 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2122224 2122553 2122949 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2120985 2121346 2121646 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2120609 2120830 2120911 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2118069 2118703 2119156 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2117908 2117941 2118009 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2117399 2117702 2117793 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2113027 2113895 2114806 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2102101 2107363 2107457 "RSETCAT" 2111513 RSETCAT (NIL T T T T) -9 NIL 2112601 NIL) (-982 2100639 2101281 2102096 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2094413 2095858 2097365 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2092295 2092852 2092924 "RRCC" 2093997 RRCC (NIL T T) -9 NIL 2094338 NIL) (-979 2091820 2092019 2092290 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2091290 2091600 2091698 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2063842 2074555 2074619 "RPOLCAT" 2085093 RPOLCAT (NIL T T T) -9 NIL 2088238 NIL) (-976 2057941 2060764 2063837 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2054108 2057689 2057827 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2052436 2053175 2053431 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2048079 2050891 2050919 "RNS" 2051181 RNS (NIL) -9 NIL 2051433 NIL) (-972 2046982 2047469 2048006 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2046100 2046501 2046701 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2045238 2045800 2045828 "RNG" 2045888 RNG (NIL) -9 NIL 2045942 NIL) (-969 2045127 2045161 2045233 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-968 2044389 2044894 2044934 "RMODULE" 2044939 RMODULE (NIL T) -9 NIL 2044965 NIL) (-967 2043328 2043434 2043764 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2040279 2042918 2043211 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2033027 2035413 2035525 "RMATCAT" 2038830 RMATCAT (NIL NIL NIL T T T) -9 NIL 2039796 NIL) (-964 2032544 2032723 2033022 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2032112 2032323 2032364 "RLINSET" 2032425 RLINSET (NIL T) -9 NIL 2032469 NIL) (-962 2031757 2031838 2031964 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2030603 2031334 2031362 "RING" 2031417 RING (NIL) -9 NIL 2031509 NIL) (-960 2030448 2030504 2030598 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2029502 2029769 2030025 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2020726 2029130 2029331 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2019951 2020462 2020501 "RGBCSPC" 2020558 RGBCSPC (NIL T) -9 NIL 2020609 NIL) (-956 2018985 2019471 2019510 "RGBCMDL" 2019738 RGBCMDL (NIL T) -9 NIL 2019852 NIL) (-955 2018697 2018766 2018867 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2018460 2018501 2018596 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2016884 2017314 2017694 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2014471 2015139 2015807 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2014021 2014119 2014279 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2013643 2013741 2013782 "RETRACT" 2013913 RETRACT (NIL T) -9 NIL 2014000 NIL) (-949 2013523 2013554 2013638 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2013125 2013397 2013464 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2011605 2012496 2012693 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2011296 2011357 2011453 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2011039 2011080 2011185 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2010774 2010815 2010924 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2005845 2007296 2008511 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2002944 2003702 2004510 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2000913 2001535 2002135 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 1993841 1999464 1999900 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 1993153 1993433 1993582 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 1992638 1992753 1992918 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 1988231 1992041 1992262 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 1987463 1987662 1987875 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 1984753 1985591 1986473 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 1981335 1982371 1983430 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 1981171 1981224 1981252 "REAL" 1981257 REAL (NIL) -9 NIL 1981292 NIL) (-932 1980661 1980965 1981056 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 1980141 1980219 1980424 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 1979374 1979566 1979777 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 1978262 1978559 1978926 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1976529 1976999 1977532 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1975451 1975728 1976115 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1974278 1974587 1975006 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1967626 1971138 1971166 "RCFIELD" 1972443 RCFIELD (NIL) -9 NIL 1973173 NIL) (-924 1966244 1966856 1967553 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1963016 1964348 1964389 "RCAGG" 1965443 RCAGG (NIL T) -9 NIL 1965905 NIL) (-922 1962743 1962853 1963011 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1962188 1962317 1962478 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1961805 1961884 1962003 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1961220 1961370 1961520 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1961002 1961052 1961123 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1953444 1960120 1960428 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1943146 1953311 1953439 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1942780 1942873 1942901 "RADCAT" 1943058 RADCAT (NIL) -9 NIL NIL NIL) (-914 1942618 1942678 1942775 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1940782 1942449 1942538 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1940463 1940512 1940639 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1932750 1936834 1936874 "QUATCAT" 1937652 QUATCAT (NIL T) -9 NIL 1938416 NIL) (-910 1930000 1931280 1932656 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1925840 1929950 1929995 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1923254 1924855 1924896 "QUAGG" 1925271 QUAGG (NIL T) -9 NIL 1925447 NIL) (-907 1922856 1923128 1923195 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1921862 1922492 1922655 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1921543 1921592 1921719 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1911143 1917312 1917352 "QFCAT" 1918010 QFCAT (NIL T) -9 NIL 1919003 NIL) (-903 1908027 1909466 1911049 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1907573 1907707 1907837 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1901769 1902930 1904092 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1901188 1901368 1901600 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1899010 1899538 1899961 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1897909 1898151 1898468 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1896270 1896468 1896821 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1892026 1893242 1893283 "PTRANFN" 1895167 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1890673 1891018 1891339 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1890366 1890429 1890536 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1884682 1889125 1889165 "PTCAT" 1889457 PTCAT (NIL T) -9 NIL 1889610 NIL) (-892 1884375 1884416 1884540 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1883254 1883570 1883904 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1872133 1874694 1877003 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1865353 1867916 1868010 "PSETCAT" 1870984 PSETCAT (NIL T T T T) -9 NIL 1871793 NIL) (-888 1863803 1864537 1865348 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1863122 1863317 1863345 "PSCURVE" 1863613 PSCURVE (NIL) -9 NIL 1863780 NIL) (-886 1858724 1860544 1860608 "PSCAT" 1861443 PSCAT (NIL T T T) -9 NIL 1861682 NIL) (-885 1858038 1858320 1858719 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1856435 1857350 1857613 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1855926 1856229 1856320 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1846946 1849368 1851556 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1844716 1846227 1846267 "PRQAGG" 1846450 PRQAGG (NIL T) -9 NIL 1846553 NIL) (-880 1843889 1844335 1844363 "PROPLOG" 1844502 PROPLOG (NIL) -9 NIL 1844616 NIL) (-879 1843564 1843627 1843750 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1843000 1843139 1843311 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1841248 1842011 1842308 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1840800 1840932 1841060 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1835241 1839740 1840560 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1835070 1835108 1835167 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1834509 1834649 1834800 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1832977 1833396 1833862 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1832694 1832755 1832783 "PRIMCAT" 1832907 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1831865 1832061 1832289 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1828026 1831815 1831860 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1827725 1827787 1827898 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1824861 1827374 1827607 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1824312 1824469 1824497 "PPCURVE" 1824702 PPCURVE (NIL) -9 NIL 1824838 NIL) (-865 1823925 1824170 1824253 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1821681 1822102 1822694 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1821124 1821188 1821421 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1817844 1818330 1818941 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1803435 1809564 1809628 "POLYCAT" 1813113 POLYCAT (NIL T T T) -9 NIL 1814990 NIL) (-860 1798945 1801092 1803430 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1798602 1798676 1798795 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1798295 1798358 1798465 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1791658 1798028 1798187 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1790545 1790808 1791084 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1789149 1789462 1789792 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1784592 1789099 1789144 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1783080 1783491 1783866 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1781837 1782146 1782542 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1781508 1781592 1781709 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1781087 1781162 1781336 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1780573 1780669 1780829 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1780045 1780165 1780319 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1778940 1779158 1779535 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1778551 1778636 1778788 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1778102 1778184 1778365 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1777794 1777875 1777988 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1777307 1777382 1777590 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1776655 1776783 1776985 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1776017 1776151 1776314 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1775321 1775503 1775684 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1775044 1775118 1775212 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1771612 1772801 1773717 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1770696 1770897 1771132 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1766261 1767645 1768787 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1746182 1751069 1755916 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1745922 1745975 1746078 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1745363 1745497 1745677 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1743372 1744593 1744621 "PID" 1744818 PID (NIL) -9 NIL 1744945 NIL) (-831 1743160 1743203 1743278 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1742347 1743007 1743094 "PI" NIL PI (NIL) -8 NIL NIL 1743134) (-829 1741799 1741950 1742126 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1738127 1739085 1739990 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1736491 1736780 1737146 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1735933 1736048 1736209 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1732474 1734802 1735155 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1731080 1731360 1731685 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1729845 1730099 1730447 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1728555 1728782 1729134 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1725565 1727125 1727153 "PFECAT" 1727746 PFECAT (NIL) -9 NIL 1728123 NIL) (-820 1725188 1725353 1725560 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1724012 1724294 1724595 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1722194 1722581 1723011 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1718164 1722120 1722189 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1714067 1715214 1716081 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1711999 1713088 1713129 "PERMCAT" 1713528 PERMCAT (NIL T) -9 NIL 1713825 NIL) (-814 1711695 1711742 1711865 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1708144 1709825 1710470 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1706170 1707899 1708020 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1705039 1705302 1705343 "PDSPC" 1705876 PDSPC (NIL T) -9 NIL 1706121 NIL) (-810 1704406 1704672 1705034 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1703041 1704034 1704075 "PDRING" 1704080 PDRING (NIL T) -9 NIL 1704107 NIL) (-808 1701751 1702540 1702593 "PDMOD" 1702598 PDMOD (NIL T T) -9 NIL 1702701 NIL) (-807 1700844 1701056 1701305 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1700449 1700516 1700570 "PDDOM" 1700735 PDDOM (NIL T T) -9 NIL 1700815 NIL) (-805 1700301 1700337 1700444 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1700087 1700126 1700215 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1698404 1699158 1699457 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1698093 1698156 1698265 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1696231 1696661 1697112 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1689851 1691680 1692972 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1689482 1689555 1689687 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1687184 1687864 1688345 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1685388 1685816 1686219 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1684834 1685082 1685123 "PATMAB" 1685230 PATMAB (NIL T) -9 NIL 1685313 NIL) (-795 1683481 1683885 1684142 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1683019 1683150 1683191 "PATAB" 1683196 PATAB (NIL T) -9 NIL 1683368 NIL) (-793 1681562 1681999 1682422 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1681240 1681315 1681417 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1680929 1680992 1681101 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1680734 1680780 1680847 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1680412 1680487 1680589 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1680101 1680164 1680273 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1679792 1679862 1679959 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1679481 1679544 1679653 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1678642 1679021 1679200 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1678249 1678347 1678466 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1677217 1677642 1677861 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1675882 1676536 1676896 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1668972 1675286 1675480 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1661393 1668470 1668654 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1658118 1660033 1660073 "PADICCT" 1660654 PADICCT (NIL NIL) -9 NIL 1660936 NIL) (-778 1656108 1658068 1658113 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1655270 1655480 1655746 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1654612 1654755 1654959 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1652993 1654020 1654298 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1652517 1652776 1652873 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1651576 1652254 1652426 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1641998 1644867 1647066 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1641390 1641704 1641830 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1640667 1640862 1640890 "OUTBCON" 1641208 OUTBCON (NIL) -9 NIL 1641374 NIL) (-769 1640375 1640505 1640662 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1639756 1639901 1640062 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1639127 1639554 1639643 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1638542 1638957 1638985 "OSGROUP" 1638990 OSGROUP (NIL) -9 NIL 1639012 NIL) (-765 1637506 1637767 1638052 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1634775 1637381 1637501 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1631916 1634526 1634652 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1629934 1630462 1631022 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1623276 1625816 1625856 "OREPCAT" 1628177 OREPCAT (NIL T) -9 NIL 1629279 NIL) (-760 1621302 1622236 1623271 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1620499 1620770 1620798 "ORDTYPE" 1621103 ORDTYPE (NIL) -9 NIL 1621261 NIL) (-758 1620033 1620244 1620494 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1619495 1619871 1620028 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1618989 1619352 1619380 "ORDSET" 1619385 ORDSET (NIL) -9 NIL 1619407 NIL) (-755 1617554 1618576 1618604 "ORDRING" 1618609 ORDRING (NIL) -9 NIL 1618637 NIL) (-754 1616802 1617359 1617387 "ORDMON" 1617392 ORDMON (NIL) -9 NIL 1617413 NIL) (-753 1616106 1616268 1616460 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1615317 1615825 1615853 "ORDFIN" 1615918 ORDFIN (NIL) -9 NIL 1615992 NIL) (-751 1614711 1614850 1615036 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1611386 1613679 1614085 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1610793 1611148 1611253 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1610601 1610646 1610712 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1609902 1610178 1610219 "OPERCAT" 1610430 OPERCAT (NIL T) -9 NIL 1610526 NIL) (-746 1609714 1609781 1609897 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1607080 1608516 1609012 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1606501 1606628 1606802 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1603402 1605640 1606006 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1600286 1602795 1602835 "OMSAGG" 1602896 OMSAGG (NIL T) -9 NIL 1602960 NIL) (-741 1598698 1599957 1600125 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1596894 1598135 1598163 "OINTDOM" 1598168 OINTDOM (NIL) -9 NIL 1598189 NIL) (-739 1594324 1595896 1596225 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1593578 1594274 1594319 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1590780 1593419 1593573 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1582317 1590651 1590775 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1575826 1582208 1582312 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1574798 1575035 1575308 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1572432 1573102 1573806 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1568209 1569169 1570192 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1567717 1567805 1567999 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1565166 1565748 1566421 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1562561 1563069 1563665 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1559558 1560097 1560743 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1558913 1559021 1559279 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1558071 1558196 1558417 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1554355 1555151 1556064 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1553795 1553890 1554112 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1553476 1553525 1553652 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1550079 1553275 1553394 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1549239 1549861 1549889 "OCAMON" 1549894 OCAMON (NIL) -9 NIL 1549915 NIL) (-720 1543451 1546265 1546305 "OC" 1547400 OC (NIL T) -9 NIL 1548256 NIL) (-719 1541451 1542377 1543357 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1540867 1541285 1541313 "OASGP" 1541318 OASGP (NIL) -9 NIL 1541338 NIL) (-717 1539930 1540579 1540607 "OAMONS" 1540647 OAMONS (NIL) -9 NIL 1540690 NIL) (-716 1539075 1539656 1539684 "OAMON" 1539741 OAMON (NIL) -9 NIL 1539792 NIL) (-715 1538971 1539003 1539070 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1537722 1538496 1538524 "OAGROUP" 1538670 OAGROUP (NIL) -9 NIL 1538762 NIL) (-713 1537513 1537600 1537717 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1537253 1537309 1537397 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1532315 1533878 1535405 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1529010 1530044 1531079 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1528120 1528353 1528571 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1516981 1520009 1522457 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1511123 1516385 1516479 "NTSCAT" 1516484 NTSCAT (NIL T T T T) -9 NIL 1516522 NIL) (-706 1510464 1510643 1510836 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1510157 1510220 1510327 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1497824 1507777 1508587 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1486833 1497689 1497819 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1485553 1485878 1486235 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1484389 1484653 1485011 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1483556 1483689 1483905 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1481874 1482193 1482599 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1481587 1481621 1481745 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1481406 1481441 1481510 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1481182 1481372 1481401 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1480746 1480813 1480990 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1479032 1480109 1480364 "NNI" NIL NNI (NIL) -8 NIL NIL 1480711) (-693 1477760 1478097 1478461 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1476737 1476989 1477291 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1475824 1476389 1476430 "NETCLT" 1476601 NETCLT (NIL T) -9 NIL 1476682 NIL) (-690 1474728 1474995 1475276 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1474527 1474570 1474645 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1473058 1473446 1473866 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1471691 1472657 1472685 "NASRING" 1472795 NASRING (NIL) -9 NIL 1472875 NIL) (-686 1471536 1471592 1471686 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1470465 1471143 1471171 "NARNG" 1471288 NARNG (NIL) -9 NIL 1471379 NIL) (-684 1470241 1470326 1470460 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1469007 1469761 1469801 "NAALG" 1469880 NAALG (NIL T) -9 NIL 1469941 NIL) (-682 1468877 1468912 1469002 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1463856 1465041 1466227 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1463251 1463338 1463522 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1455261 1459755 1459807 "MTSCAT" 1460867 MTSCAT (NIL T T) -9 NIL 1461381 NIL) (-678 1455027 1455087 1455179 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1454853 1454892 1454952 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1452442 1454385 1454426 "MSETAGG" 1454431 MSETAGG (NIL T) -9 NIL 1454465 NIL) (-675 1448812 1451485 1451806 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1445086 1446909 1447649 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1444723 1444796 1444925 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1444376 1444417 1444561 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1442241 1442578 1443009 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1435639 1442140 1442236 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1435164 1435205 1435413 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1434723 1434772 1434955 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1433997 1434090 1434309 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1432614 1432975 1433365 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1432135 1432202 1432241 "MONOPC" 1432301 MONOPC (NIL T) -9 NIL 1432520 NIL) (-664 1431586 1431922 1432050 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1430728 1431107 1431135 "MONOID" 1431353 MONOID (NIL) -9 NIL 1431497 NIL) (-662 1430387 1430537 1430723 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1419325 1426195 1426254 "MONOGEN" 1426928 MONOGEN (NIL T T) -9 NIL 1427384 NIL) (-660 1417337 1418223 1419206 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1416051 1416595 1416623 "MONADWU" 1417014 MONADWU (NIL) -9 NIL 1417249 NIL) (-658 1415599 1415799 1416046 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1414876 1415177 1415205 "MONAD" 1415412 MONAD (NIL) -9 NIL 1415524 NIL) (-656 1414643 1414739 1414871 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1413033 1413803 1414082 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1412167 1412694 1412734 "MODULE" 1412739 MODULE (NIL T) -9 NIL 1412777 NIL) (-653 1411846 1411972 1412162 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1409557 1410443 1410757 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1406736 1408153 1408666 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1405370 1405944 1406220 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1394589 1404035 1404448 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1391545 1393589 1393858 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1390629 1390996 1391186 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1390198 1390247 1390426 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1388023 1389019 1389059 "MLO" 1389476 MLO (NIL T) -9 NIL 1389716 NIL) (-644 1385904 1386431 1387026 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1385372 1385468 1385622 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1385042 1385118 1385241 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1384254 1384440 1384668 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1383747 1383863 1384019 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1383119 1383233 1383418 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1382146 1382419 1382696 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1381579 1381667 1381838 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1378737 1379616 1380495 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1377404 1377752 1378105 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1374788 1376509 1376550 "MDAGG" 1376807 MDAGG (NIL T) -9 NIL 1376952 NIL) (-633 1374062 1374226 1374426 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1373140 1373426 1373656 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1371237 1371814 1372375 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1367035 1370827 1371074 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1363384 1364153 1364887 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1362137 1362306 1362635 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1351660 1355224 1355300 "MATCAT" 1360288 MATCAT (NIL T T T) -9 NIL 1361734 NIL) (-626 1348941 1350247 1351655 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1347342 1347702 1348086 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1346475 1346672 1346894 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1345226 1345552 1345879 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1344388 1344790 1344966 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1344057 1344121 1344244 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1343705 1343778 1343892 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1343240 1343355 1343497 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1341449 1342217 1342518 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1340943 1341245 1341335 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1335224 1339258 1339299 "LZSTAGG" 1340076 LZSTAGG (NIL T) -9 NIL 1340366 NIL) (-615 1332573 1333885 1335219 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1329960 1330926 1331409 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1329541 1329820 1329894 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1321810 1329402 1329536 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1321173 1321318 1321546 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1318657 1319355 1320067 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1316873 1317196 1317630 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1310272 1315923 1315964 "LSAGG" 1316026 LSAGG (NIL T) -9 NIL 1316104 NIL) (-607 1307966 1309065 1310267 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1305446 1307315 1307564 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1305113 1305204 1305327 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1304784 1304863 1304891 "LOGIC" 1305002 LOGIC (NIL) -9 NIL 1305084 NIL) (-603 1304679 1304708 1304779 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1303998 1304156 1304349 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1302783 1303032 1303383 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1298605 1301404 1301444 "LODOCAT" 1301876 LODOCAT (NIL T) -9 NIL 1302087 NIL) (-599 1298398 1298474 1298600 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1295398 1298275 1298393 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1292496 1295348 1295393 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1289583 1292426 1292491 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1288636 1288811 1289113 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1286768 1287898 1288151 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1282643 1284927 1284968 "LNAGG" 1285827 LNAGG (NIL T) -9 NIL 1286265 NIL) (-592 1282030 1282297 1282638 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1278602 1279543 1280180 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1277864 1278369 1278409 "LMODULE" 1278414 LMODULE (NIL T) -9 NIL 1278440 NIL) (-589 1275333 1277600 1277723 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1274901 1275112 1275153 "LLINSET" 1275214 LLINSET (NIL T) -9 NIL 1275258 NIL) (-587 1274577 1274837 1274896 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1274176 1274256 1274395 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1272627 1272975 1273374 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1271798 1271994 1272222 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1265111 1271054 1271308 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1264688 1264921 1264962 "LINSET" 1264967 LINSET (NIL T) -9 NIL 1265000 NIL) (-581 1263589 1264311 1264478 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1261855 1262610 1262650 "LINEXP" 1263136 LINEXP (NIL T) -9 NIL 1263409 NIL) (-579 1260477 1261464 1261645 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1259304 1259576 1259878 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1258517 1259106 1259216 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1256067 1256789 1257539 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1254697 1254994 1255385 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1253490 1254092 1254132 "LIECAT" 1254272 LIECAT (NIL T) -9 NIL 1254423 NIL) (-573 1253364 1253397 1253485 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1247620 1253054 1253282 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1239260 1247296 1247452 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1235712 1236661 1237596 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1234336 1235244 1235272 "LFCAT" 1235479 LFCAT (NIL) -9 NIL 1235618 NIL) (-568 1232575 1232905 1233250 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1230092 1230757 1231438 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1227104 1228082 1228585 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1226595 1226898 1226989 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1225302 1225626 1226026 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1224568 1224653 1224879 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1219571 1223136 1223672 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1219196 1219246 1219406 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1217967 1218740 1218780 "LALG" 1218841 LALG (NIL T) -9 NIL 1218899 NIL) (-559 1217750 1217827 1217962 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1215603 1217018 1217269 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1215432 1215462 1215503 "KVTFROM" 1215565 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1214248 1214963 1215152 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1214077 1214107 1214148 "KRCFROM" 1214210 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1213179 1213376 1213671 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1213008 1213038 1213079 "KONVERT" 1213141 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1212837 1212867 1212908 "KOERCE" 1212970 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1212407 1212500 1212632 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1210460 1211354 1211726 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1203389 1208211 1208265 "KDAGG" 1208641 KDAGG (NIL T T) -9 NIL 1208881 NIL) (-548 1203047 1203182 1203384 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1196351 1202839 1202985 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1196001 1196283 1196346 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1194971 1195470 1195719 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1194097 1194546 1194751 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1192961 1193453 1193753 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1192243 1192642 1192803 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1191953 1192189 1192238 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1186208 1191643 1191871 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1185626 1185959 1186079 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1182352 1183812 1183866 "IXAGG" 1184781 IXAGG (NIL T T) -9 NIL 1185241 NIL) (-537 1181637 1181968 1182347 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1180604 1180879 1181142 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1179266 1179473 1179766 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1178217 1178439 1178722 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1177892 1177955 1178078 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1177154 1177526 1177700 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1175130 1176430 1176704 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1164678 1170447 1171604 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1163923 1164075 1164311 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1163414 1163717 1163808 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1162707 1162798 1163011 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1161839 1162064 1162304 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1160252 1160633 1161061 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1160037 1160081 1160157 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1158887 1159184 1159479 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1158160 1158511 1158662 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1157363 1157494 1157707 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1155518 1156015 1156559 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1152599 1153867 1154556 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1152424 1152464 1152524 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1148422 1152350 1152419 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1146425 1148361 1148417 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1145796 1146095 1146225 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1145249 1145537 1145669 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1144330 1144955 1145081 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1143740 1144234 1144262 "IOBCON" 1144267 IOBCON (NIL) -9 NIL 1144288 NIL) (-511 1143311 1143375 1143557 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1135355 1137726 1140051 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1132466 1133249 1134113 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1132143 1132240 1132357 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1129585 1132079 1132138 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1127697 1128226 1128793 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1127199 1127313 1127453 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1125583 1125989 1126451 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1123362 1123956 1124567 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1120735 1121345 1122065 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1120139 1120297 1120505 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1119658 1119744 1119932 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1117863 1118384 1118841 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1110945 1112598 1114327 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1110311 1110473 1110646 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1108184 1108648 1109192 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1106310 1107260 1107288 "INTDOM" 1107587 INTDOM (NIL) -9 NIL 1107792 NIL) (-494 1105863 1106065 1106305 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1101670 1104142 1104196 "INTCAT" 1104992 INTCAT (NIL T) -9 NIL 1105308 NIL) (-492 1101235 1101355 1101482 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1100075 1100247 1100553 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1099648 1099744 1099901 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1092131 1099555 1099643 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1091429 1091984 1092049 "INT8" NIL INT8 (NIL) -8 NIL NIL 1092083) (-487 1090726 1091281 1091346 "INT64" NIL INT64 (NIL) -8 NIL NIL 1091380) (-486 1090023 1090578 1090643 "INT32" NIL INT32 (NIL) -8 NIL NIL 1090677) (-485 1089320 1089875 1089940 "INT16" NIL INT16 (NIL) -8 NIL NIL 1089974) (-484 1085783 1089239 1089315 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1079840 1083323 1083351 "INS" 1084281 INS (NIL) -9 NIL 1084940 NIL) (-482 1077902 1078820 1079767 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1076961 1077184 1077459 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1076175 1076316 1076513 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1075165 1075306 1075543 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1074317 1074481 1074741 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1073597 1073712 1073900 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1072336 1072605 1072929 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1071616 1071757 1071940 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1071279 1071351 1071449 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1068357 1069843 1070366 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1067956 1068063 1068177 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1067112 1067757 1067858 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1065962 1066230 1066551 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1064952 1065892 1065957 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1064577 1064657 1064774 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1063491 1064036 1064240 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1059586 1060641 1061584 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1058440 1058763 1058791 "INBCON" 1059304 INBCON (NIL) -9 NIL 1059570 NIL) (-464 1057894 1058159 1058435 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1057388 1057690 1057780 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1056845 1057154 1057259 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1055683 1055825 1056142 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1054106 1054375 1054714 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1048949 1054037 1054101 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-458 1048329 1048663 1048778 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-457 1043421 1047767 1047953 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-456 1042451 1043343 1043416 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-455 1042023 1042100 1042154 "IEVALAB" 1042361 IEVALAB (NIL T T) -9 NIL NIL NIL) (-454 1041778 1041858 1042018 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-453 1041163 1041390 1041547 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-452 1040156 1041083 1041158 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-451 1039219 1040076 1040151 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-450 1038301 1038948 1039085 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-449 1036664 1037235 1037286 "IDPC" 1037792 IDPC (NIL T T) -9 NIL 1038105 NIL) (-448 1035952 1036586 1036659 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-447 1035122 1035874 1035947 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-446 1034815 1035028 1035088 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-445 1034519 1034559 1034598 "IDEMOPC" 1034603 IDEMOPC (NIL T) -9 NIL 1034740 NIL) (-444 1031590 1032471 1033363 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-443 1025216 1026493 1027532 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-442 1024478 1024608 1024807 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-441 1023651 1024150 1024288 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-440 1022040 1022371 1022762 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-439 1019298 1019922 1020617 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1017524 1018004 1018537 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1015398 1017430 1017519 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1011540 1015336 1015393 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1005119 1010504 1010972 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1004687 1004750 1004923 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1004179 1004328 1004356 "HYPCAT" 1004563 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1003835 1003988 1004174 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1003448 1003693 1003776 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1003281 1003330 1003371 "HOMOTOP" 1003376 HOMOTOP (NIL T) -9 NIL 1003409 NIL) (-429 1001701 1002513 1002554 "HOAGG" 1002638 HOAGG (NIL T) -9 NIL 1002960 NIL) (-428 1001328 1001475 1001696 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 994528 1001053 1001201 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 993463 993721 993984 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 992398 993328 993458 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 990656 992231 992319 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 989971 990323 990456 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 983523 989904 989966 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 976662 983259 983410 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 976115 976272 976435 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 968615 976032 976110 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968106 968409 968500 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 965656 967893 968072 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 961342 965539 965651 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 953819 961239 961337 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 945756 953188 953443 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 944780 945289 945317 "GROUP" 945520 GROUP (NIL) -9 NIL 945654 NIL) (-412 944323 944524 944775 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 942995 943334 943721 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 941817 942174 942225 "GRMOD" 942754 GRMOD (NIL T T) -9 NIL 942920 NIL) (-409 941636 941684 941812 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 937759 938970 939970 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 936481 936805 937120 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936034 936162 936303 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935107 935606 935657 "GRALG" 935810 GRALG (NIL T T) -9 NIL 935900 NIL) (-404 934826 934927 935102 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 931845 934517 934684 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931258 931321 931578 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927112 928008 928533 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 926287 926489 926727 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 921290 922217 923236 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921038 921095 921184 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 920520 920609 920774 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920029 920070 920283 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 918830 919113 919417 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912105 918520 918681 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 901888 906895 907999 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 899940 901043 901071 "GCDDOM" 901326 GCDDOM (NIL) -9 NIL 901483 NIL) (-391 899563 899720 899935 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 890356 892826 895214 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 888491 888816 889234 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 887432 887621 887888 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 886303 886510 886814 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 885766 885908 886056 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 884378 884726 885039 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 882923 883244 883566 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 880549 880905 881310 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 873801 875462 877040 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 873453 873674 873742 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873077 873298 873379 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 871174 871857 872317 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 869767 870074 870466 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 868422 868781 869105 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 867725 867849 868036 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 866699 866965 867312 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 864357 864887 865369 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 863940 864000 864169 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 862240 863154 863457 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 861388 861522 861745 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 860559 860720 860947 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 856793 859454 859495 "FSAGG" 859865 FSAGG (NIL T) -9 NIL 860126 NIL) (-368 855147 855906 856698 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 853103 853399 853943 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 852150 852332 852632 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 851831 851880 852007 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 831987 841488 841529 "FS" 845399 FS (NIL T) -9 NIL 847677 NIL) (-363 824218 827711 831690 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 823752 823879 824031 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 818275 821433 821473 "FRNAALG" 822793 FRNAALG (NIL T) -9 NIL 823391 NIL) (-360 815016 816267 817525 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 814697 814746 814873 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 813184 813741 814035 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 812470 812563 812850 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 810304 811070 811386 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 809413 809856 809897 "FRETRCT" 809902 FRETRCT (NIL T) -9 NIL 810073 NIL) (-354 808786 809064 809408 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 805530 807050 807109 "FRAMALG" 807991 FRAMALG (NIL T T) -9 NIL 808283 NIL) (-352 804126 804677 805307 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 803819 803882 803989 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 797460 803624 803814 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 797153 797216 797323 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 789461 794032 795360 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 783239 786742 786770 "FPS" 787889 FPS (NIL) -9 NIL 788445 NIL) (-346 782796 782929 783093 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 779606 781649 781677 "FPC" 781902 FPC (NIL) -9 NIL 782044 NIL) (-344 779452 779504 779601 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 778229 778938 778979 "FPATMAB" 778984 FPATMAB (NIL T) -9 NIL 779136 NIL) (-342 776659 777255 777602 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 776234 776292 776465 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 774737 775632 775806 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 773352 773857 773885 "FNCAT" 774342 FNCAT (NIL) -9 NIL 774599 NIL) (-338 772809 773319 773347 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 771396 772758 772804 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 767984 769342 769383 "FMONCAT" 770600 FMONCAT (NIL T) -9 NIL 771204 NIL) (-335 764842 765920 765973 "FMCAT" 767154 FMCAT (NIL T T) -9 NIL 767646 NIL) (-334 763542 764665 764764 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 762590 763390 763537 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 760777 761229 761723 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 758712 759248 759826 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 752098 757049 757663 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 750579 751680 751720 "FLINEXP" 751725 FLINEXP (NIL T) -9 NIL 751818 NIL) (-328 749988 750247 750574 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 749237 749396 749610 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 746120 747199 747251 "FLALG" 748478 FLALG (NIL T T) -9 NIL 748945 NIL) (-325 745291 745452 745679 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 739016 742705 742746 "FLAGG" 743985 FLAGG (NIL T) -9 NIL 744633 NIL) (-323 738124 738528 739011 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 734685 735949 736008 "FINRALG" 737136 FINRALG (NIL T T) -9 NIL 737644 NIL) (-321 734076 734341 734680 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 733374 733670 733698 "FINITE" 733894 FINITE (NIL) -9 NIL 734001 NIL) (-319 733282 733308 733369 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 730275 731543 731584 "FINAGG" 732489 FINAGG (NIL T) -9 NIL 732943 NIL) (-317 729306 729771 730270 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 721267 723858 723898 "FINAALG" 727550 FINAALG (NIL T) -9 NIL 728988 NIL) (-315 717534 718779 719902 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 716086 716505 716559 "FILECAT" 717243 FILECAT (NIL T T) -9 NIL 717459 NIL) (-313 715437 715911 716014 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 712685 714563 714591 "FIELD" 714631 FIELD (NIL) -9 NIL 714711 NIL) (-311 711710 712171 712680 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 709714 710660 711006 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 708957 709138 709357 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 704227 708895 708952 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 703889 703956 704091 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 703429 703471 703680 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 700109 700986 701763 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 695393 700041 700104 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 690072 694882 695072 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 684553 689353 689611 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 678760 684004 684215 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 677783 677993 678308 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 673223 675928 675956 "FFIELDC" 676575 FFIELDC (NIL) -9 NIL 676950 NIL) (-298 672292 672732 673218 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 671907 671965 672089 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 670051 670574 671091 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 665145 669850 669951 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 660245 664934 665041 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 654911 660036 660144 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 654365 654414 654649 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 632940 643974 644060 "FFCAT" 649210 FFCAT (NIL T T T) -9 NIL 650646 NIL) (-290 629180 630406 631712 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 624023 629111 629175 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 622915 623384 623425 "FEVALAB" 623509 FEVALAB (NIL T) -9 NIL 623770 NIL) (-287 622320 622572 622910 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 619147 620058 620173 "FDIVCAT" 621740 FDIVCAT (NIL T T T T) -9 NIL 622176 NIL) (-285 618941 618973 619142 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 618248 618341 618618 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 616734 617732 617935 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 615827 616211 616413 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 614949 615438 615578 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 606536 611179 611219 "FAXF" 613020 FAXF (NIL T) -9 NIL 613710 NIL) (-279 604452 605256 606071 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 599601 603974 604148 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 594059 596482 596534 "FAMR" 597545 FAMR (NIL T T) -9 NIL 598004 NIL) (-276 593258 593623 594054 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 592279 593200 593253 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 589873 590752 590805 "FAMONC" 591746 FAMONC (NIL T T) -9 NIL 592131 NIL) (-273 588429 589731 589868 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 586509 586870 587272 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 585786 585983 586205 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 577646 585233 585432 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 575665 576235 576821 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 572567 573209 573929 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 567724 568431 569236 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 567413 567476 567585 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 552206 566462 566888 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 542733 551526 551814 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 542227 542529 542619 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 542003 542193 542222 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 541692 541760 541873 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 541209 541351 541392 "EVALAB" 541562 EVALAB (NIL T) -9 NIL 541666 NIL) (-259 540837 540983 541204 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 537880 539475 539503 "EUCDOM" 540057 EUCDOM (NIL) -9 NIL 540406 NIL) (-257 536807 537300 537875 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 536532 536588 536688 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 536220 536284 536393 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 529991 531891 531919 "ES" 534661 ES (NIL) -9 NIL 536045 NIL) (-253 526506 528038 529830 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 525854 526007 526183 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 518360 525784 525849 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 518049 518112 518221 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 511676 514801 516234 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 507979 509075 510168 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 506808 507158 507463 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 505693 506424 506452 "ENTIRER" 506457 ENTIRER (NIL) -9 NIL 506501 NIL) (-245 505582 505616 505688 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 502215 504012 504361 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 501306 501521 501575 "ELTAGG" 501949 ELTAGG (NIL T T) -9 NIL 502163 NIL) (-242 501086 501160 501301 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 500832 500867 500921 "ELTAB" 501005 ELTAB (NIL T T) -9 NIL 501057 NIL) (-240 500083 500253 500452 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 499807 499881 499909 "ELEMFUN" 500014 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 499707 499734 499802 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 494984 497732 497773 "ELAGG" 498706 ELAGG (NIL T) -9 NIL 499167 NIL) (-236 493782 494320 494979 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 493200 493367 493523 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 492113 492432 492711 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 485506 487504 488331 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 479485 481481 482291 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 477299 477705 478176 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 468299 470212 471753 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 467412 467913 468062 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 466110 466784 466824 "DVARCAT" 467107 DVARCAT (NIL T) -9 NIL 467247 NIL) (-227 465529 465793 466105 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 457596 465397 465524 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 455934 456725 456766 "DSEXT" 457129 DSEXT (NIL T) -9 NIL 457423 NIL) (-224 454739 455263 455929 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 454463 454528 454626 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 450614 451830 452961 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 446260 447615 448679 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 444935 445296 445682 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 444621 444680 444798 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 443596 443894 444184 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 443181 443256 443406 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 435594 437706 439821 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 431111 432130 433209 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 427735 429738 429779 "DQAGG" 430408 DQAGG (NIL T) -9 NIL 430681 NIL) (-213 414278 421918 422000 "DPOLCAT" 423837 DPOLCAT (NIL T T T T) -9 NIL 424380 NIL) (-212 410686 412334 414273 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 403789 410584 410681 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 396801 403618 403784 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 396394 396654 396743 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 395808 396256 396336 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 395094 395419 395570 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 388233 394830 394981 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 385982 387299 387339 "DMEXT" 387344 DMEXT (NIL T) -9 NIL 387519 NIL) (-204 385638 385700 385844 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 379230 385123 385313 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 376456 378059 378100 "DLAGG" 378641 DLAGG (NIL T) -9 NIL 378873 NIL) (-201 374807 375678 375706 "DIVRING" 375798 DIVRING (NIL) -9 NIL 375881 NIL) (-200 374258 374502 374802 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 372686 373103 373509 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 371723 371944 372209 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 365295 371655 371718 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 353693 360055 360108 "DIRPCAT" 360364 DIRPCAT (NIL NIL T) -9 NIL 361239 NIL) (-195 351699 352469 353356 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 351146 351312 351498 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 348429 350023 350064 "DIOPS" 350484 DIOPS (NIL T) -9 NIL 350712 NIL) (-192 348089 348233 348424 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 347096 347842 347870 "DIOID" 347875 DIOID (NIL) -9 NIL 347897 NIL) (-190 345924 346753 346781 "DIFRING" 346786 DIFRING (NIL) -9 NIL 346807 NIL) (-189 345560 345658 345686 "DIFFSPC" 345805 DIFFSPC (NIL) -9 NIL 345880 NIL) (-188 345301 345403 345555 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 344204 344829 344869 "DIFFMOD" 344874 DIFFMOD (NIL T) -9 NIL 344971 NIL) (-186 343888 343945 343986 "DIFFDOM" 344107 DIFFDOM (NIL T) -9 NIL 344175 NIL) (-185 343769 343799 343883 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 341442 342963 343003 "DIFEXT" 343008 DIFEXT (NIL T) -9 NIL 343160 NIL) (-183 339330 340924 340965 "DIAGG" 340970 DIAGG (NIL T) -9 NIL 340990 NIL) (-182 338886 339076 339325 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 334124 338076 338353 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 330582 331635 332645 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 325132 329736 330063 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 323698 323990 324365 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 320818 322070 322466 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 318602 320649 320738 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 317985 318130 318312 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 315303 316027 316827 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 313412 313870 314432 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 312795 313128 313242 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 305995 312520 312668 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 303915 304425 304929 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 303554 303603 303754 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 302813 303375 303466 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 300837 301279 301639 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 300129 300418 300564 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 299580 299726 299878 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 296942 297735 298462 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 296381 296527 296698 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 294453 294764 295131 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 294010 294265 294366 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 293211 293594 293622 "CTORCAT" 293803 CTORCAT (NIL) -9 NIL 293915 NIL) (-159 292914 293048 293206 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 292407 292664 292772 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 291823 292254 292327 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 291282 291399 291552 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 287676 288432 289187 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 287167 287470 287561 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 286386 286595 286823 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 285890 285995 286199 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 285643 285677 285783 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 282582 283344 284062 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 282101 282243 282382 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 277994 280564 281056 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 277868 277895 277923 "CONDUIT" 277960 CONDUIT (NIL) -9 NIL NIL NIL) (-146 276747 277478 277506 "COMRING" 277511 COMRING (NIL) -9 NIL 277561 NIL) (-145 275912 276279 276457 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 275608 275649 275777 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 275301 275364 275471 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 264143 275251 275296 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 263604 263743 263903 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 263357 263398 263496 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 244788 257038 257078 "COMPCAT" 258079 COMPCAT (NIL T) -9 NIL 259421 NIL) (-138 237326 240839 244432 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 237085 237119 237221 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236915 236954 237012 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236496 236775 236849 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 236073 236314 236401 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235268 235516 235544 "COMBOPC" 235882 COMBOPC (NIL) -9 NIL 236057 NIL) (-132 234332 234584 234826 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231264 231948 232571 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 230144 230595 230830 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229635 229938 230029 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229322 229375 229500 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228792 229102 229200 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225312 226382 227462 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223607 224592 224830 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221024 222243 222284 "CLAGG" 222847 CLAGG (NIL T) -9 NIL 223227 NIL) (-123 220582 220772 221019 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220211 220302 220442 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218148 218655 219203 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217109 217840 217868 "CHARZ" 217873 CHARZ (NIL) -9 NIL 217887 NIL) (-119 216903 216949 217027 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215742 216505 216533 "CHARNZ" 216594 CHARNZ (NIL) -9 NIL 216642 NIL) (-117 213220 214317 214840 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 212928 213007 213035 "CFCAT" 213146 CFCAT (NIL) -9 NIL NIL NIL) (-115 212271 212400 212582 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208539 211684 211964 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 207917 208104 208281 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207445 207864 207912 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 206918 207227 207324 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206409 206712 206803 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205658 205818 206039 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201758 203015 203723 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200124 201155 201406 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199705 199984 200058 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199139 199392 199420 "CACHSET" 199552 CACHSET (NIL) -9 NIL 199630 NIL) (-104 198491 198906 198934 "CABMON" 198984 CABMON (NIL) -9 NIL 199040 NIL) (-103 198021 198285 198395 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193510 197689 197850 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192480 193184 193319 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193482) (-100 190005 192247 192353 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187501 189759 189867 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184755 186903 186942 "BTCAT" 187009 BTCAT (NIL T) -9 NIL 187090 NIL) (-97 184506 184604 184750 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179843 183698 183724 "BTAGG" 183835 BTAGG (NIL) -9 NIL 183943 NIL) (-95 179474 179635 179838 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176612 178966 179156 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175882 176034 176212 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172976 174597 174636 "BRAGG" 175265 BRAGG (NIL T) -9 NIL 175525 NIL) (-91 172051 172482 172971 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164585 171556 171737 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162577 164537 164580 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162310 162346 162457 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160549 160982 161430 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156515 157931 158821 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155391 156282 156404 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154977 155134 155160 "BOOLE" 155268 BOOLE (NIL) -9 NIL 155349 NIL) (-83 154770 154851 154972 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153908 154435 154485 "BMODULE" 154490 BMODULE (NIL T T) -9 NIL 154554 NIL) (-81 149793 153765 153834 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149606 149646 149685 "BINOPC" 149690 BINOPC (NIL T) -9 NIL 149735 NIL) (-79 149148 149421 149523 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148669 148813 148951 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141875 148399 148544 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140122 141095 141134 "BGAGG" 141390 BGAGG (NIL T) -9 NIL 141517 NIL) (-75 139991 140029 140117 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138842 139043 139328 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135556 138022 138327 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 135141 135234 135260 "BASTYPE" 135431 BASTYPE (NIL) -9 NIL 135527 NIL) (-71 134911 135007 135136 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134426 134514 134664 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133325 134000 134185 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 133073 133078 133104 "ATTREG" 133109 ATTREG (NIL) -9 NIL NIL NIL) (-67 132678 132950 133015 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 132178 132327 132353 "ATRIG" 132554 ATRIG (NIL) -9 NIL NIL NIL) (-65 132033 132086 132173 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131603 131834 131860 "ASTCAT" 131865 ASTCAT (NIL) -9 NIL 131895 NIL) (-63 131402 131479 131598 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129625 131235 131323 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128432 128745 129110 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 126284 128362 128427 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125475 125666 125887 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 121343 125206 125320 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115655 117659 117734 "ARR2CAT" 120246 ARR2CAT (NIL T T T) -9 NIL 120967 NIL) (-56 114616 115098 115650 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 113984 114355 114477 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 112916 113084 113380 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112617 112671 112789 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 112000 112146 112302 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111405 111695 111815 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 108973 110134 110457 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108498 108758 108854 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102193 107560 108002 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97727 99390 99440 "AMR" 100178 AMR (NIL T T) -9 NIL 100775 NIL) (-46 97081 97361 97722 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79065 97015 97076 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75468 78741 78910 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72478 73138 73745 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71857 71970 72154 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68269 68894 69486 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57758 67962 68112 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57075 57229 57407 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55788 56583 56621 "ALGEBRA" 56626 ALGEBRA (NIL T) -9 NIL 56666 NIL) (-37 55574 55651 55783 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33879 52662 52714 "ALAGG" 52849 ALAGG (NIL T T) -9 NIL 53007 NIL) (-35 33379 33528 33554 "AHYP" 33755 AHYP (NIL) -9 NIL NIL NIL) (-34 32861 32993 33019 "AGG" 33224 AGG (NIL) -9 NIL 33350 NIL) (-33 32704 32762 32856 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30843 31303 31703 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30338 30641 30730 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29708 30003 30159 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17266 26545 26583 "ACFS" 27190 ACFS (NIL T) -9 NIL 27429 NIL) (-28 15889 16499 17261 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11441 13820 13846 "ACF" 14725 ACF (NIL) -9 NIL 15137 NIL) (-26 10537 10943 11436 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10039 10279 10305 "ABELSG" 10397 ABELSG (NIL) -9 NIL 10462 NIL) (-24 9937 9968 10034 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9092 9466 9492 "ABELMON" 9717 ABELMON (NIL) -9 NIL 9850 NIL) (-22 8774 8914 9087 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 7986 8469 8495 "ABELGRP" 8567 ABELGRP (NIL) -9 NIL 8642 NIL) (-20 7539 7735 7981 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6766 6805 "A1AGG" 6810 A1AGG (NIL T) -9 NIL 6844 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
+((-2570 (((-85) $ $) NIL T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3948 (((-773) $) 9 T ELT) (($ (-1096)) NIL T ELT) (((-1096) $) NIL T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) NIL T ELT))) 
+(((-1131) (-996)) (T -1131)) 
+NIL 
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T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-485) (-1026)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-456 (-1091) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-591 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-312)) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-312)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-581 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-312)) ((-655 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-312)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-664) . T) ((-715) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-717) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-719) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-722) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-741) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-756) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-757) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-760) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-807 $ (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-810 (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-812 (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-797 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-330)))) ((-797 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-485)))) ((-795 |#2|) |has| |#1| (-312)) ((-822) -12 (|has| |#1| (-312)) (|has| |#2| (-822))) ((-887 |#1| (-485) (-995)) . T) ((-833) |has| |#1| (-312)) ((-905 |#2|) |has| |#1| (-312)) ((-916) |has| |#1| (-38 (-350 (-485)))) ((-934) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-951 (-350 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-485)))) ((-951 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-485)))) ((-951 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-1091)))) ((-951 |#2|) . T) ((-964 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-312)) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-969 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-312)) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1067) -12 (|has| |#1| (-312)) (|has| |#2| (-1067))) ((-1116) |has| |#1| (-38 (-350 (-485)))) ((-1119) |has| |#1| (-38 (-350 (-485)))) ((-1130) . T) ((-1135) |has| |#1| (-312)) ((-1142 |#1|) . T) ((-1159 |#1| (-485)) . T)) 
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+(((-1173 |#1|) (-113) (-962)) (T -1173)) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| (-695)) . T) ((-25) . T) ((-38 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-496)) ((-35) |has| |#1| (-38 (-350 (-485)))) ((-66) |has| |#1| (-38 (-350 (-485)))) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-556 (-485)) . T) ((-556 |#1|) |has| |#1| (-146)) ((-556 $) |has| |#1| (-496)) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-239) |has| |#1| (-38 (-350 (-485)))) ((-241 (-695) |#1|) . T) ((-241 $ $) |has| (-695) (-1026)) ((-246) |has| |#1| (-496)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-496) |has| |#1| (-496)) ((-13) . T) ((-589 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) |has| |#1| (-496)) ((-655 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) |has| |#1| (-496)) ((-664) . T) ((-807 $ (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-810 (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-812 (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-887 |#1| (-695) (-995)) . T) ((-916) |has| |#1| (-38 (-350 (-485)))) ((-964 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-969 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1116) |has| |#1| (-38 (-350 (-485)))) ((-1119) |has| |#1| (-38 (-350 (-485)))) ((-1130) . T) ((-1159 |#1| (-695)) . T)) 
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+((-3830 ((|#2| |#4| (-695)) 31 T ELT)) (-3829 ((|#4| |#2|) 26 T ELT)) (-3832 ((|#4| (-350 |#2|)) 49 (|has| |#1| (-496)) ELT)) (-3831 (((-1 |#4| (-584 |#4|)) |#3|) 43 T ELT))) 
+(((-1175 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3829 (|#4| |#2|)) (-15 -3830 (|#2| |#4| (-695))) (-15 -3831 ((-1 |#4| (-584 |#4|)) |#3|)) (IF (|has| |#1| (-496)) (-15 -3832 (|#4| (-350 |#2|))) |%noBranch|)) (-962) (-1156 |#1|) (-601 |#2|) (-1173 |#1|)) (T -1175)) 
+((-3832 (*1 *2 *3) (-12 (-5 *3 (-350 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-496)) (-4 *4 (-962)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *5 *6 *2)) (-4 *6 (-601 *5)))) (-3831 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *5 (-1156 *4)) (-5 *2 (-1 *6 (-584 *6))) (-5 *1 (-1175 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-1173 *4)))) (-3830 (*1 *2 *3 *4) (-12 (-5 *4 (-695)) (-4 *5 (-962)) (-4 *2 (-1156 *5)) (-5 *1 (-1175 *5 *2 *6 *3)) (-4 *6 (-601 *2)) (-4 *3 (-1173 *5)))) (-3829 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *3 (-1156 *4)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *3 *5 *2)) (-4 *5 (-601 *3))))) 
+NIL 
+(((-1176) (-113)) (T -1176)) 
+NIL 
+(-13 (-10 -7 (-6 -2288))) 
+((-2570 (((-85) $ $) NIL T ELT)) (-3833 (((-1091)) 12 T ELT)) (-3244 (((-1074) $) 18 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3948 (((-773) $) 11 T ELT) (((-1091) $) 8 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) 15 T ELT))) 
+(((-1177 |#1|) (-13 (-1014) (-553 (-1091)) (-10 -8 (-15 -3948 ((-1091) $)) (-15 -3833 ((-1091))))) (-1091)) (T -1177)) 
+((-3948 (*1 *2 *1) (-12 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-14 *3 *2))) (-3833 (*1 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-14 *3 *2)))) 
+((-3840 (($ (-695)) 19 T ELT)) (-3837 (((-631 |#2|) $ $) 41 T ELT)) (-3834 ((|#2| $) 51 T ELT)) (-3835 ((|#2| $) 50 T ELT)) (-3838 ((|#2| $ $) 36 T ELT)) (-3836 (($ $ $) 47 T ELT)) (-3839 (($ $) 23 T ELT) (($ $ $) 29 T ELT)) (-3841 (($ $ $) 15 T ELT)) (* (($ (-485) $) 26 T ELT) (($ |#2| $) 32 T ELT) (($ $ |#2|) 31 T ELT))) 
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+NIL 
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(-258) (-120) (-934))) (-5 *2 (-584 (-2 (|:| -1751 (-1086 *5)) (|:| -3226 (-584 (-858 *5)))))) (-5 *1 (-1208 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091))))) (-3970 (*1 *2 *3) (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *5 (-584 (-1091))) (-5 *2 (-584 (-2 (|:| -1751 (-1086 *4)) (|:| -3226 (-584 (-858 *4)))))) (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-584 (-1091))))) (-3969 (*1 *2 *3) (-12 (-5 *3 (-584 (-858 *4))) (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *4 *5))) (-5 *1 (-1208 *4 *5 *6)) (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091))))) (-3969 (*1 *2 *3 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1208 *5 *6 *7)) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091))))) (-3969 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-258) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1208 *5 *6 *7)) (-14 *6 (-584 (-1091))) (-14 *7 (-584 (-1091)))))) 
+((-3977 (((-3 (-1180 (-350 (-485))) #1="failed") (-1180 |#1|) |#1|) 21 T ELT)) (-3975 (((-85) (-1180 |#1|)) 12 T ELT)) (-3976 (((-3 (-1180 (-485)) #1#) (-1180 |#1|)) 16 T ELT))) 
+(((-1209 |#1|) (-10 -7 (-15 -3975 ((-85) (-1180 |#1|))) (-15 -3976 ((-3 (-1180 (-485)) #1="failed") (-1180 |#1|))) (-15 -3977 ((-3 (-1180 (-350 (-485))) #1#) (-1180 |#1|) |#1|))) (-13 (-962) (-581 (-485)))) (T -1209)) 
+((-3977 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-1180 (-350 (-485)))) (-5 *1 (-1209 *4)))) (-3976 (*1 *2 *3) (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4)))) (-3975 (*1 *2 *3) (-12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-85)) (-5 *1 (-1209 *4))))) 
+((-2570 (((-85) $ $) NIL T ELT)) (-3190 (((-85) $) 12 T ELT)) (-1313 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3138 (((-695)) 9 T ELT)) (-3726 (($) NIL T CONST)) (-3469 (((-3 $ #1#) $) 57 T ELT)) (-2996 (($) 46 T ELT)) (-1215 (((-85) $ $) NIL T ELT)) (-2411 (((-85) $) 38 T ELT)) (-3447 (((-633 $) $) 36 T ELT)) (-2011 (((-831) $) 14 T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3448 (($) 26 T CONST)) (-2401 (($ (-831)) 47 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3974 (((-485) $) 16 T ELT)) (-3948 (((-773) $) 21 T ELT) (($ (-485)) 18 T ELT)) (-3128 (((-695)) 10 T CONST)) (-1266 (((-85) $ $) 59 T ELT)) (-3127 (((-85) $ $) NIL T ELT)) (-2662 (($) 23 T CONST)) (-2668 (($) 25 T CONST)) (-3058 (((-85) $ $) 31 T ELT)) (-3839 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3841 (($ $ $) 29 T ELT)) (** (($ $ (-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|) (-13 (-146) (-320) (-554 (-485)) (-1067)) (-831)) (T -1210)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2793098 2793103 2793108 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2793083 2793088 2793093 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2793068 2793073 2793078 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2793053 2793058 2793063 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1210 2792032 2792971 2793048 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1209 2791247 2791426 2791645 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1208 2782406 2784275 2786209 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2781794 2781947 2782136 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2781256 2781559 2781672 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2778816 2780718 2780921 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2775580 2777233 2777804 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2772837 2774567 2774621 "XPOLYC" 2774906 XPOLYC (NIL T T) -9 NIL 2775019 NIL) (-1202 2770356 2772341 2772544 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2766604 2769215 2769603 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2761451 2763084 2763138 "XFALG" 2765283 XFALG (NIL T T) -9 NIL 2766067 NIL) (-1199 2756607 2759340 2759382 "XF" 2760000 XF (NIL T) -9 NIL 2760396 NIL) (-1198 2756325 2756435 2756602 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2755552 2755674 2755878 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2753294 2755452 2755547 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2751875 2752670 2752712 "XALG" 2752717 XALG (NIL T) -9 NIL 2752826 NIL) (-1194 2745726 2750285 2750763 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2743969 2744971 2745292 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2743568 2743840 2743909 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2743055 2743358 2743451 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2742132 2742342 2742637 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2740428 2740891 2741353 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2739317 2739902 2739944 "VSPACE" 2740080 VSPACE (NIL T) -9 NIL 2740154 NIL) (-1187 2739188 2739221 2739312 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2739031 2739085 2739153 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2736014 2736809 2737546 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2727112 2729713 2731886 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2720689 2722580 2724159 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2719173 2719568 2719974 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2718000 2718281 2718597 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2713397 2717827 2717919 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2706742 2711070 2711113 "VECTCAT" 2712101 VECTCAT (NIL T) -9 NIL 2712685 NIL) (-1178 2706021 2706347 2706737 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2705515 2705757 2705877 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2705448 2705453 2705483 "UTYPE" 2705488 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2704435 2704611 2704872 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2702286 2702794 2703318 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2692168 2698138 2698180 "UTSCAT" 2699278 UTSCAT (NIL T) -9 NIL 2700035 NIL) (-1172 2690233 2691176 2692163 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2689907 2689956 2690087 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2681618 2688103 2688582 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2676180 2678453 2678496 "URAGG" 2680536 URAGG (NIL T) -9 NIL 2681261 NIL) (-1168 2674251 2675183 2676175 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2669958 2673227 2673689 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2662387 2669882 2669953 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2651038 2658525 2658586 "UPXSCCA" 2659154 UPXSCCA (NIL T T) -9 NIL 2659386 NIL) (-1164 2650759 2650861 2651033 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2639311 2646523 2646565 "UPXSCAT" 2647205 UPXSCAT (NIL T) -9 NIL 2647813 NIL) (-1162 2638824 2638909 2639086 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2630510 2638415 2638677 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2629405 2629675 2630025 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2622108 2625593 2625647 "UPSCAT" 2626716 UPSCAT (NIL T T) -9 NIL 2627480 NIL) (-1158 2621528 2621780 2622103 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2621202 2621251 2621382 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2605332 2614286 2614328 "UPOLYC" 2616406 UPOLYC (NIL T) -9 NIL 2617626 NIL) (-1155 2599387 2602235 2605327 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2598823 2598948 2599111 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2598457 2598544 2598683 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2597270 2597537 2597841 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2596603 2596733 2596918 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2596195 2596270 2596417 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2586959 2595961 2596089 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2586321 2586458 2586663 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2584922 2585769 2586045 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2584151 2584348 2584573 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2570961 2584075 2584146 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2550767 2564002 2564063 "ULSCCAT" 2564694 ULSCCAT (NIL T T) -9 NIL 2564981 NIL) (-1143 2550102 2550388 2550762 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2538474 2545608 2545650 "ULSCAT" 2546503 ULSCAT (NIL T) -9 NIL 2547233 NIL) (-1141 2537987 2538072 2538249 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2520104 2537486 2537727 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2519138 2519831 2519945 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2520056) (-1138 2518171 2518864 2518978 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2519089) (-1137 2517204 2517897 2518011 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2518122) (-1136 2516237 2516930 2517044 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2517155) (-1135 2514244 2515465 2515495 "UFD" 2515706 UFD (NIL) -9 NIL 2515819 NIL) (-1134 2514088 2514145 2514239 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2513340 2513547 2513763 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2511560 2512013 2512478 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2511285 2511525 2511555 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2511223 2511228 2511258 "TYPE" 2511263 TYPE (NIL) -9 NIL 2511270 NIL) (-1129 2510382 2510602 2510842 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2509560 2509991 2510226 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2507714 2508287 2508826 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2506748 2506984 2507220 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2495365 2499541 2499637 "TSETCAT" 2504852 TSETCAT (NIL T T T T) -9 NIL 2506356 NIL) (-1124 2491702 2493518 2495360 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2486094 2490928 2491210 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2481431 2482444 2483373 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2480928 2481003 2481166 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2479004 2479294 2479649 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2478488 2478637 2478667 "TRIGCAT" 2478880 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2478239 2478342 2478483 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2475294 2477345 2477626 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2474400 2475096 2475126 "TRANFUN" 2475161 TRANFUN (NIL) -9 NIL 2475227 NIL) (-1115 2473864 2474115 2474395 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2473701 2473739 2473800 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2473158 2473289 2473440 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2471899 2472556 2472792 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2471711 2471748 2471820 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2469925 2470571 2471000 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2468305 2468642 2468964 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2458366 2466066 2466122 "TBAGG" 2466439 TBAGG (NIL T T) -9 NIL 2466649 NIL) (-1107 2455902 2457091 2458361 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2455379 2455504 2455649 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2454889 2455209 2455299 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2454386 2454503 2454641 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2446890 2454314 2454381 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2442643 2443938 2445183 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2442012 2442171 2442352 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2439166 2439919 2440702 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2438940 2439130 2439161 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2437894 2438579 2438705 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2438891) (-1097 2437158 2437706 2437785 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2437845) (-1096 2433981 2435140 2435840 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2431664 2432347 2432981 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2427742 2428788 2429765 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2424841 2427397 2427626 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2424437 2424524 2424646 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2421061 2422535 2423354 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2414021 2420258 2420551 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2405707 2413612 2413874 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2404986 2405125 2405342 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2404670 2404735 2404846 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2395393 2404382 2404507 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2394123 2394421 2394776 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2393528 2393606 2393797 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2375680 2393027 2393268 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2375279 2375551 2375620 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2374615 2374896 2375036 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2369217 2370476 2371429 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2368749 2368849 2369013 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2363860 2365142 2366289 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2358318 2359789 2361100 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2351233 2353297 2355088 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2343402 2351171 2351228 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2338351 2343116 2343231 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2337938 2338021 2338165 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2337089 2337290 2337525 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2336829 2336887 2336980 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2330296 2335032 2335640 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2329472 2329677 2329908 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2328717 2329088 2329235 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2328205 2328447 2328477 "STEP" 2328571 STEP (NIL) -9 NIL 2328642 NIL) (-1066 2320699 2328123 2328200 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2315684 2319497 2319540 "STAGG" 2319967 STAGG (NIL T) -9 NIL 2320141 NIL) (-1064 2314142 2314850 2315679 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2312363 2313969 2314061 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2311643 2312182 2312212 "SRING" 2312217 SRING (NIL) -9 NIL 2312237 NIL) (-1061 2304558 2310181 2310620 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2298332 2299771 2301275 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2290970 2295627 2295657 "SRAGG" 2296956 SRAGG (NIL) -9 NIL 2297560 NIL) (-1058 2290267 2290587 2290965 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2284427 2289589 2290012 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2278439 2281780 2282531 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2274868 2275687 2276324 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2273843 2274148 2274178 "SPFCAT" 2274622 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2272780 2273032 2273296 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2263538 2265812 2265842 "SPADXPT" 2270479 SPADXPT (NIL) -9 NIL 2272603 NIL) (-1051 2263340 2263386 2263455 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2260996 2263304 2263335 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2252670 2254759 2254801 "SPACEC" 2259116 SPACEC (NIL T) -9 NIL 2260921 NIL) (-1048 2250499 2252617 2252665 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2249478 2249667 2249950 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2247882 2248215 2248626 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2247147 2247381 2247642 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2243327 2244287 2245282 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2239685 2240384 2241113 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2233726 2238988 2239084 "SNTSCAT" 2239089 SNTSCAT (NIL T T T T) -9 NIL 2239159 NIL) (-1041 2227547 2232367 2232757 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2221319 2227466 2227542 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2219751 2220082 2220480 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2211443 2216317 2216419 "SMATCAT" 2217762 SMATCAT (NIL NIL T T T) -9 NIL 2218310 NIL) (-1037 2209284 2210268 2211438 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2207901 2208753 2208796 "SMAGG" 2208881 SMAGG (NIL T) -9 NIL 2208945 NIL) (-1035 2205520 2207068 2207111 "SKAGG" 2207372 SKAGG (NIL T) -9 NIL 2207508 NIL) (-1034 2201566 2205340 2205451 "SINT" NIL SINT (NIL) -8 NIL NIL 2205492) (-1033 2201376 2201420 2201486 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2200451 2200683 2200951 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2199455 2199617 2199893 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2198801 2199141 2199264 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2198147 2198454 2198594 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2196258 2196750 2197256 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2189796 2196177 2196253 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2189299 2189536 2189566 "SGROUP" 2189659 SGROUP (NIL) -9 NIL 2189721 NIL) (-1025 2189189 2189221 2189294 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2188827 2188867 2188908 "SGPOPC" 2188913 SGPOPC (NIL T) -9 NIL 2189114 NIL) (-1023 2188361 2188638 2188744 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2185784 2186553 2187275 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2179924 2185186 2185282 "SFRTCAT" 2185287 SFRTCAT (NIL T T T T) -9 NIL 2185325 NIL) (-1020 2174316 2175429 2176556 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2168492 2169653 2170817 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2167464 2168366 2168487 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2163072 2163967 2164062 "SEXCAT" 2166675 SEXCAT (NIL T T T T T) -9 NIL 2167226 NIL) (-1016 2162045 2162999 2163067 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2160436 2161021 2161323 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2159959 2160144 2160174 "SETCAT" 2160291 SETCAT (NIL) -9 NIL 2160375 NIL) (-1013 2159791 2159855 2159954 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2156803 2158245 2158288 "SETAGG" 2159156 SETAGG (NIL T) -9 NIL 2159494 NIL) (-1011 2156409 2156561 2156798 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2153654 2156356 2156404 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2153120 2153430 2153530 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2152247 2152613 2152674 "SEGXCAT" 2152960 SEGXCAT (NIL T T) -9 NIL 2153080 NIL) (-1007 2151172 2151440 2151483 "SEGCAT" 2152005 SEGCAT (NIL T) -9 NIL 2152226 NIL) (-1006 2150852 2150917 2151030 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2149918 2150388 2150596 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2149496 2149775 2149851 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2148861 2148997 2149201 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2147927 2148674 2148856 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2147180 2147875 2147922 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2138665 2147047 2147175 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2137525 2137815 2138132 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2136831 2137043 2137231 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2136181 2136338 2136514 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2135754 2135985 2136013 "SASTCAT" 2136018 SASTCAT (NIL) -9 NIL 2136031 NIL) (-995 2135221 2135646 2135720 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2134824 2134865 2135036 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2134455 2134496 2134653 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2127536 2134372 2134450 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2126186 2126515 2126911 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2124947 2125308 2125608 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2124571 2124792 2124873 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2122031 2122665 2123118 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2121870 2121903 2121971 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2121361 2121664 2121755 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2116989 2117857 2118768 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2106063 2111325 2111419 "RSETCAT" 2115475 RSETCAT (NIL T T T T) -9 NIL 2116563 NIL) (-983 2104601 2105243 2106058 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2098375 2099820 2101327 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2096257 2096814 2096886 "RRCC" 2097959 RRCC (NIL T T) -9 NIL 2098300 NIL) (-980 2095782 2095981 2096252 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2095252 2095562 2095660 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2067804 2078517 2078581 "RPOLCAT" 2089055 RPOLCAT (NIL T T T) -9 NIL 2092200 NIL) (-977 2061903 2064726 2067799 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2058070 2061651 2061789 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2056398 2057137 2057393 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2052041 2054853 2054881 "RNS" 2055143 RNS (NIL) -9 NIL 2055395 NIL) (-973 2050944 2051431 2051968 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2050062 2050463 2050663 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2049200 2049762 2049790 "RNG" 2049850 RNG (NIL) -9 NIL 2049904 NIL) (-970 2049089 2049123 2049195 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2048351 2048856 2048896 "RMODULE" 2048901 RMODULE (NIL T) -9 NIL 2048927 NIL) (-968 2047290 2047396 2047726 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2044241 2046880 2047173 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2036989 2039375 2039487 "RMATCAT" 2042792 RMATCAT (NIL NIL NIL T T T) -9 NIL 2043758 NIL) (-965 2036506 2036685 2036984 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2036074 2036285 2036326 "RLINSET" 2036387 RLINSET (NIL T) -9 NIL 2036431 NIL) (-963 2035719 2035800 2035926 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2034565 2035296 2035324 "RING" 2035379 RING (NIL) -9 NIL 2035471 NIL) (-961 2034410 2034466 2034560 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2033464 2033731 2033987 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2024688 2033092 2033293 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2023913 2024424 2024463 "RGBCSPC" 2024520 RGBCSPC (NIL T) -9 NIL 2024571 NIL) (-957 2022947 2023433 2023472 "RGBCMDL" 2023700 RGBCMDL (NIL T) -9 NIL 2023814 NIL) (-956 2022659 2022728 2022829 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2022422 2022463 2022558 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2020846 2021276 2021656 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2018433 2019101 2019769 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2017983 2018081 2018241 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2017605 2017703 2017744 "RETRACT" 2017875 RETRACT (NIL T) -9 NIL 2017962 NIL) (-950 2017485 2017516 2017600 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2017087 2017359 2017426 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2015567 2016458 2016655 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2015258 2015319 2015415 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2015001 2015042 2015147 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2014736 2014777 2014886 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2009807 2011258 2012473 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2006906 2007664 2008472 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2004875 2005497 2006097 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 1997803 2003426 2003862 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 1997115 1997395 1997544 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 1996600 1996715 1996880 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 1992193 1996003 1996224 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 1991425 1991624 1991837 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 1988715 1989553 1990435 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1985297 1986333 1987392 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1985133 1985186 1985214 "REAL" 1985219 REAL (NIL) -9 NIL 1985254 NIL) (-933 1984623 1984927 1985018 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1984103 1984181 1984386 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1983336 1983528 1983739 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1982224 1982521 1982888 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1980491 1980961 1981494 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1979413 1979690 1980077 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1978240 1978549 1978968 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1971588 1975100 1975128 "RCFIELD" 1976405 RCFIELD (NIL) -9 NIL 1977135 NIL) (-925 1970206 1970818 1971515 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1966978 1968310 1968351 "RCAGG" 1969405 RCAGG (NIL T) -9 NIL 1969867 NIL) (-923 1966705 1966815 1966973 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1966150 1966279 1966440 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1965767 1965846 1965965 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1965182 1965332 1965482 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1964964 1965014 1965085 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1957406 1964082 1964390 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1947108 1957273 1957401 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1946742 1946835 1946863 "RADCAT" 1947020 RADCAT (NIL) -9 NIL NIL NIL) (-915 1946580 1946640 1946737 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1944744 1946411 1946500 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1944425 1944474 1944601 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1936712 1940796 1940836 "QUATCAT" 1941614 QUATCAT (NIL T) -9 NIL 1942378 NIL) (-911 1933962 1935242 1936618 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1929802 1933912 1933957 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1927216 1928817 1928858 "QUAGG" 1929233 QUAGG (NIL T) -9 NIL 1929409 NIL) (-908 1926818 1927090 1927157 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1925824 1926454 1926617 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1925505 1925554 1925681 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1915105 1921274 1921314 "QFCAT" 1921972 QFCAT (NIL T) -9 NIL 1922965 NIL) (-904 1911989 1913428 1915011 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1911535 1911669 1911799 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1905731 1906892 1908054 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1905150 1905330 1905562 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1902972 1903500 1903923 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1901871 1902113 1902430 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1900232 1900430 1900783 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1895988 1897204 1897245 "PTRANFN" 1899129 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1894635 1894980 1895301 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1894328 1894391 1894498 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1888644 1893087 1893127 "PTCAT" 1893419 PTCAT (NIL T) -9 NIL 1893572 NIL) (-893 1888337 1888378 1888502 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1887216 1887532 1887866 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1876095 1878656 1880965 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1869315 1871878 1871972 "PSETCAT" 1874946 PSETCAT (NIL T T T T) -9 NIL 1875755 NIL) (-889 1867765 1868499 1869310 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1867084 1867279 1867307 "PSCURVE" 1867575 PSCURVE (NIL) -9 NIL 1867742 NIL) (-887 1862686 1864506 1864570 "PSCAT" 1865405 PSCAT (NIL T T T) -9 NIL 1865644 NIL) (-886 1862000 1862282 1862681 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1860397 1861312 1861575 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1859888 1860191 1860282 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1850908 1853330 1855518 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1848678 1850189 1850229 "PRQAGG" 1850412 PRQAGG (NIL T) -9 NIL 1850515 NIL) (-881 1847851 1848297 1848325 "PROPLOG" 1848464 PROPLOG (NIL) -9 NIL 1848578 NIL) (-880 1847526 1847589 1847712 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1846962 1847101 1847273 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1845210 1845973 1846270 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1844762 1844894 1845022 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1839203 1843702 1844522 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1839032 1839070 1839129 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1838471 1838611 1838762 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1836939 1837358 1837824 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1836656 1836717 1836745 "PRIMCAT" 1836869 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1835827 1836023 1836251 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1831988 1835777 1835822 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1831687 1831749 1831860 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1828823 1831336 1831569 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1828274 1828431 1828459 "PPCURVE" 1828664 PPCURVE (NIL) -9 NIL 1828800 NIL) (-866 1827887 1828132 1828215 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1825643 1826064 1826656 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1825086 1825150 1825383 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1821806 1822292 1822903 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1807397 1813526 1813590 "POLYCAT" 1817075 POLYCAT (NIL T T T) -9 NIL 1818952 NIL) (-861 1802907 1805054 1807392 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1802564 1802638 1802757 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1802257 1802320 1802427 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1795620 1801990 1802149 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1794507 1794770 1795046 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1793111 1793424 1793754 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1788554 1793061 1793106 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1787042 1787453 1787828 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1785799 1786108 1786504 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1785470 1785554 1785671 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1785049 1785124 1785298 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1784535 1784631 1784791 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1784007 1784127 1784281 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1782902 1783120 1783497 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1782513 1782598 1782750 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1782064 1782146 1782327 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1781756 1781837 1781950 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1781269 1781344 1781552 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1780617 1780745 1780947 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1779979 1780113 1780276 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1779283 1779465 1779646 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1779006 1779080 1779174 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1775574 1776763 1777679 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1774658 1774859 1775094 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1770223 1771607 1772749 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1750144 1755031 1759878 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1749884 1749937 1750040 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1749325 1749459 1749639 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1747334 1748555 1748583 "PID" 1748780 PID (NIL) -9 NIL 1748907 NIL) (-832 1747122 1747165 1747240 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1746309 1746969 1747056 "PI" NIL PI (NIL) -8 NIL NIL 1747096) (-830 1745761 1745912 1746088 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1742089 1743047 1743952 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1740453 1740742 1741108 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1739895 1740010 1740171 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1736436 1738764 1739117 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1735042 1735322 1735647 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1733807 1734061 1734409 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1732517 1732744 1733096 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1729527 1731087 1731115 "PFECAT" 1731708 PFECAT (NIL) -9 NIL 1732085 NIL) (-821 1729150 1729315 1729522 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1727974 1728256 1728557 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1726156 1726543 1726973 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1722126 1726082 1726151 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1718029 1719176 1720043 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1715961 1717050 1717091 "PERMCAT" 1717490 PERMCAT (NIL T) -9 NIL 1717787 NIL) (-815 1715657 1715704 1715827 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1712106 1713787 1714432 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1710132 1711861 1711982 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1709001 1709264 1709305 "PDSPC" 1709838 PDSPC (NIL T) -9 NIL 1710083 NIL) (-811 1708368 1708634 1708996 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1707003 1707996 1708037 "PDRING" 1708042 PDRING (NIL T) -9 NIL 1708069 NIL) (-809 1705713 1706502 1706555 "PDMOD" 1706560 PDMOD (NIL T T) -9 NIL 1706663 NIL) (-808 1704806 1705018 1705267 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1704411 1704478 1704532 "PDDOM" 1704697 PDDOM (NIL T T) -9 NIL 1704777 NIL) (-806 1704263 1704299 1704406 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1704049 1704088 1704177 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1702366 1703120 1703419 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1702055 1702118 1702227 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1700193 1700623 1701074 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1693813 1695642 1696934 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1693444 1693517 1693649 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1691146 1691826 1692307 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1689350 1689778 1690181 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1688796 1689044 1689085 "PATMAB" 1689192 PATMAB (NIL T) -9 NIL 1689275 NIL) (-796 1687443 1687847 1688104 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1686981 1687112 1687153 "PATAB" 1687158 PATAB (NIL T) -9 NIL 1687330 NIL) (-794 1685524 1685961 1686384 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1685202 1685277 1685379 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1684891 1684954 1685063 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1684696 1684742 1684809 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1684374 1684449 1684551 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1684063 1684126 1684235 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1683754 1683824 1683921 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1683443 1683506 1683615 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1682604 1682983 1683162 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1682211 1682309 1682428 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1681179 1681604 1681823 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1679844 1680498 1680858 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1672934 1679248 1679442 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1665355 1672432 1672616 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1662080 1663995 1664035 "PADICCT" 1664616 PADICCT (NIL NIL) -9 NIL 1664898 NIL) (-779 1660070 1662030 1662075 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1659232 1659442 1659708 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1658574 1658717 1658921 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1656955 1657982 1658260 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1656479 1656738 1656835 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1655538 1656216 1656388 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1645960 1648829 1651028 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1645352 1645666 1645792 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1644629 1644824 1644852 "OUTBCON" 1645170 OUTBCON (NIL) -9 NIL 1645336 NIL) (-770 1644337 1644467 1644624 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1643718 1643863 1644024 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1643089 1643516 1643605 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1642504 1642919 1642947 "OSGROUP" 1642952 OSGROUP (NIL) -9 NIL 1642974 NIL) (-766 1641468 1641729 1642014 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1638737 1641343 1641463 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1635878 1638488 1638614 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1633896 1634424 1634984 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1627238 1629778 1629818 "OREPCAT" 1632139 OREPCAT (NIL T) -9 NIL 1633241 NIL) (-761 1625264 1626198 1627233 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1624461 1624732 1624760 "ORDTYPE" 1625065 ORDTYPE (NIL) -9 NIL 1625223 NIL) (-759 1623995 1624206 1624456 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1623457 1623833 1623990 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1622951 1623314 1623342 "ORDSET" 1623347 ORDSET (NIL) -9 NIL 1623369 NIL) (-756 1621516 1622538 1622566 "ORDRING" 1622571 ORDRING (NIL) -9 NIL 1622599 NIL) (-755 1620764 1621321 1621349 "ORDMON" 1621354 ORDMON (NIL) -9 NIL 1621375 NIL) (-754 1620068 1620230 1620422 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1619279 1619787 1619815 "ORDFIN" 1619880 ORDFIN (NIL) -9 NIL 1619954 NIL) (-752 1618673 1618812 1618998 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1615348 1617641 1618047 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1614755 1615110 1615215 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1614563 1614608 1614674 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1613864 1614140 1614181 "OPERCAT" 1614392 OPERCAT (NIL T) -9 NIL 1614488 NIL) (-747 1613676 1613743 1613859 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1611042 1612478 1612974 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1610463 1610590 1610764 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1607364 1609602 1609968 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1604248 1606757 1606797 "OMSAGG" 1606858 OMSAGG (NIL T) -9 NIL 1606922 NIL) (-742 1602660 1603919 1604087 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1600856 1602097 1602125 "OINTDOM" 1602130 OINTDOM (NIL) -9 NIL 1602151 NIL) (-740 1598286 1599858 1600187 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1597540 1598236 1598281 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1594742 1597381 1597535 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1586279 1594613 1594737 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1579788 1586170 1586274 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1578760 1578997 1579270 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1576394 1577064 1577768 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1572171 1573131 1574154 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1571679 1571767 1571961 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1569128 1569710 1570383 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1566523 1567031 1567627 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1563520 1564059 1564705 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1562875 1562983 1563241 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1562033 1562158 1562379 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1558317 1559113 1560026 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1557757 1557852 1558074 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1557438 1557487 1557614 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1554041 1557237 1557356 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1553201 1553823 1553851 "OCAMON" 1553856 OCAMON (NIL) -9 NIL 1553877 NIL) (-721 1547413 1550227 1550267 "OC" 1551362 OC (NIL T) -9 NIL 1552218 NIL) (-720 1545413 1546339 1547319 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1544829 1545247 1545275 "OASGP" 1545280 OASGP (NIL) -9 NIL 1545300 NIL) (-718 1543892 1544541 1544569 "OAMONS" 1544609 OAMONS (NIL) -9 NIL 1544652 NIL) (-717 1543037 1543618 1543646 "OAMON" 1543703 OAMON (NIL) -9 NIL 1543754 NIL) (-716 1542933 1542965 1543032 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1541684 1542458 1542486 "OAGROUP" 1542632 OAGROUP (NIL) -9 NIL 1542724 NIL) (-714 1541475 1541562 1541679 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1541215 1541271 1541359 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1536277 1537840 1539367 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1532972 1534006 1535041 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1532082 1532315 1532533 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1520943 1523971 1526419 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1515085 1520347 1520441 "NTSCAT" 1520446 NTSCAT (NIL T T T T) -9 NIL 1520484 NIL) (-707 1514426 1514605 1514798 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1514119 1514182 1514289 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1501786 1511739 1512549 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1490795 1501651 1501781 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1489515 1489840 1490197 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1488351 1488615 1488973 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1487518 1487651 1487867 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1485836 1486155 1486561 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1485549 1485583 1485707 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1485368 1485403 1485472 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1485144 1485334 1485363 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1484708 1484775 1484952 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1482994 1484071 1484326 "NNI" NIL NNI (NIL) -8 NIL NIL 1484673) (-694 1481722 1482059 1482423 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1480699 1480951 1481253 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1479786 1480351 1480392 "NETCLT" 1480563 NETCLT (NIL T) -9 NIL 1480644 NIL) (-691 1478690 1478957 1479238 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1478489 1478532 1478607 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1477020 1477408 1477828 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1475653 1476619 1476647 "NASRING" 1476757 NASRING (NIL) -9 NIL 1476837 NIL) (-687 1475498 1475554 1475648 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1474427 1475105 1475133 "NARNG" 1475250 NARNG (NIL) -9 NIL 1475341 NIL) (-685 1474203 1474288 1474422 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1472969 1473723 1473763 "NAALG" 1473842 NAALG (NIL T) -9 NIL 1473903 NIL) (-683 1472839 1472874 1472964 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1467818 1469003 1470189 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1467213 1467300 1467484 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1459223 1463717 1463769 "MTSCAT" 1464829 MTSCAT (NIL T T) -9 NIL 1465343 NIL) (-679 1458989 1459049 1459141 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1458815 1458854 1458914 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1456404 1458347 1458388 "MSETAGG" 1458393 MSETAGG (NIL T) -9 NIL 1458427 NIL) (-676 1452774 1455447 1455768 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1449048 1450871 1451611 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1448685 1448758 1448887 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1448338 1448379 1448523 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1446203 1446540 1446971 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1439601 1446102 1446198 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1439126 1439167 1439375 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1438685 1438734 1438917 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1437959 1438052 1438271 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1436576 1436937 1437327 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1436097 1436164 1436203 "MONOPC" 1436263 MONOPC (NIL T) -9 NIL 1436482 NIL) (-665 1435548 1435884 1436012 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1434690 1435069 1435097 "MONOID" 1435315 MONOID (NIL) -9 NIL 1435459 NIL) (-663 1434349 1434499 1434685 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1423287 1430157 1430216 "MONOGEN" 1430890 MONOGEN (NIL T T) -9 NIL 1431346 NIL) (-661 1421299 1422185 1423168 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1420013 1420557 1420585 "MONADWU" 1420976 MONADWU (NIL) -9 NIL 1421211 NIL) (-659 1419561 1419761 1420008 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1418838 1419139 1419167 "MONAD" 1419374 MONAD (NIL) -9 NIL 1419486 NIL) (-657 1418605 1418701 1418833 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1416995 1417765 1418044 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1416129 1416656 1416696 "MODULE" 1416701 MODULE (NIL T) -9 NIL 1416739 NIL) (-654 1415808 1415934 1416124 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1413519 1414405 1414719 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1410698 1412115 1412628 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1409332 1409906 1410182 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1398551 1407997 1408410 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1395507 1397551 1397820 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1394591 1394958 1395148 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1394160 1394209 1394388 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1391985 1392981 1393021 "MLO" 1393438 MLO (NIL T) -9 NIL 1393678 NIL) (-645 1389866 1390393 1390988 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1389334 1389430 1389584 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1389004 1389080 1389203 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1388216 1388402 1388630 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1387709 1387825 1387981 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1387081 1387195 1387380 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1386108 1386381 1386658 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1385541 1385629 1385800 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1382699 1383578 1384457 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1381366 1381714 1382067 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1378750 1380471 1380512 "MDAGG" 1380769 MDAGG (NIL T) -9 NIL 1380914 NIL) (-634 1378024 1378188 1378388 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1377102 1377388 1377618 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1375199 1375776 1376337 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1370997 1374789 1375036 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1367346 1368115 1368849 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1366099 1366268 1366597 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1355622 1359186 1359262 "MATCAT" 1364250 MATCAT (NIL T T T) -9 NIL 1365696 NIL) (-627 1352903 1354209 1355617 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1351304 1351664 1352048 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1350437 1350634 1350856 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1349188 1349514 1349841 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1348350 1348752 1348928 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1348019 1348083 1348206 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1347667 1347740 1347854 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1347202 1347317 1347459 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1345411 1346179 1346480 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1344905 1345207 1345297 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1339186 1343220 1343261 "LZSTAGG" 1344038 LZSTAGG (NIL T) -9 NIL 1344328 NIL) (-616 1336535 1337847 1339181 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1333922 1334888 1335371 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1333503 1333782 1333856 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1325772 1333364 1333498 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1325135 1325280 1325508 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1322619 1323317 1324029 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1320835 1321158 1321592 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1314234 1319885 1319926 "LSAGG" 1319988 LSAGG (NIL T) -9 NIL 1320066 NIL) (-608 1311928 1313027 1314229 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1309408 1311277 1311526 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1309075 1309166 1309289 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1308746 1308825 1308853 "LOGIC" 1308964 LOGIC (NIL) -9 NIL 1309046 NIL) (-604 1308641 1308670 1308741 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1307960 1308118 1308311 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1306745 1306994 1307345 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1302567 1305366 1305406 "LODOCAT" 1305838 LODOCAT (NIL T) -9 NIL 1306049 NIL) (-600 1302360 1302436 1302562 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1299360 1302237 1302355 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1296458 1299310 1299355 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1293545 1296388 1296453 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1292598 1292773 1293075 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1290730 1291860 1292113 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1286605 1288889 1288930 "LNAGG" 1289789 LNAGG (NIL T) -9 NIL 1290227 NIL) (-593 1285992 1286259 1286600 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1282564 1283505 1284142 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1281826 1282331 1282371 "LMODULE" 1282376 LMODULE (NIL T) -9 NIL 1282402 NIL) (-590 1279295 1281562 1281685 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1278863 1279074 1279115 "LLINSET" 1279176 LLINSET (NIL T) -9 NIL 1279220 NIL) (-588 1278539 1278799 1278858 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1278138 1278218 1278357 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1276589 1276937 1277336 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1275760 1275956 1276184 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1269073 1275016 1275270 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1268650 1268883 1268924 "LINSET" 1268929 LINSET (NIL T) -9 NIL 1268962 NIL) (-582 1267551 1268273 1268440 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1265817 1266572 1266612 "LINEXP" 1267098 LINEXP (NIL T) -9 NIL 1267371 NIL) (-580 1264439 1265426 1265607 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1263266 1263538 1263840 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1262479 1263068 1263178 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1260029 1260751 1261501 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1258659 1258956 1259347 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1257452 1258054 1258094 "LIECAT" 1258234 LIECAT (NIL T) -9 NIL 1258385 NIL) (-574 1257326 1257359 1257447 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1251582 1257016 1257244 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1243222 1251258 1251414 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1239674 1240623 1241558 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1238298 1239206 1239234 "LFCAT" 1239441 LFCAT (NIL) -9 NIL 1239580 NIL) (-569 1236537 1236867 1237212 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1234054 1234719 1235400 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1231066 1232044 1232547 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1230557 1230860 1230951 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1229264 1229588 1229988 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1228530 1228615 1228841 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1223533 1227098 1227634 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1223158 1223208 1223368 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1221929 1222702 1222742 "LALG" 1222803 LALG (NIL T) -9 NIL 1222861 NIL) (-560 1221712 1221789 1221924 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1219565 1220980 1221231 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1219394 1219424 1219465 "KVTFROM" 1219527 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1218210 1218925 1219114 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1218039 1218069 1218110 "KRCFROM" 1218172 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1217141 1217338 1217633 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1216970 1217000 1217041 "KONVERT" 1217103 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1216799 1216829 1216870 "KOERCE" 1216932 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1216369 1216462 1216594 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1214422 1215316 1215688 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1207351 1212173 1212227 "KDAGG" 1212603 KDAGG (NIL T T) -9 NIL 1212843 NIL) (-549 1207009 1207144 1207346 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1200313 1206801 1206947 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1199963 1200245 1200308 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1198933 1199432 1199681 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1198059 1198508 1198713 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1196923 1197415 1197715 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1196205 1196604 1196765 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1195915 1196151 1196200 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1190170 1195605 1195833 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1189588 1189921 1190041 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1186314 1187774 1187828 "IXAGG" 1188743 IXAGG (NIL T T) -9 NIL 1189203 NIL) (-538 1185599 1185930 1186309 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1184566 1184841 1185104 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1183228 1183435 1183728 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1182179 1182401 1182684 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1181854 1181917 1182040 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1181116 1181488 1181662 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1179092 1180392 1180666 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1168640 1174409 1175566 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1167885 1168037 1168273 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1167376 1167679 1167770 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1166669 1166760 1166973 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1165801 1166026 1166266 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1164214 1164595 1165023 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1163999 1164043 1164119 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1162849 1163146 1163441 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1162122 1162473 1162624 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1161325 1161456 1161669 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1159480 1159977 1160521 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1156561 1157829 1158518 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1156386 1156426 1156486 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1152384 1156312 1156381 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1150387 1152323 1152379 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1149758 1150057 1150187 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1149211 1149499 1149631 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1148292 1148917 1149043 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1147702 1148196 1148224 "IOBCON" 1148229 IOBCON (NIL) -9 NIL 1148250 NIL) (-512 1147273 1147337 1147519 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1139317 1141688 1144013 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1136428 1137211 1138075 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1136105 1136202 1136319 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1133547 1136041 1136100 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1131659 1132188 1132755 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1131161 1131275 1131415 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1129545 1129951 1130413 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1127324 1127918 1128529 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1124697 1125307 1126027 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1124101 1124259 1124467 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1123620 1123706 1123894 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1121825 1122346 1122803 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1114907 1116560 1118289 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1114273 1114435 1114608 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1112146 1112610 1113154 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1110272 1111222 1111250 "INTDOM" 1111549 INTDOM (NIL) -9 NIL 1111754 NIL) (-495 1109825 1110027 1110267 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1105632 1108104 1108158 "INTCAT" 1108954 INTCAT (NIL T) -9 NIL 1109270 NIL) (-493 1105197 1105317 1105444 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1104037 1104209 1104515 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1103610 1103706 1103863 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1096093 1103517 1103605 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1095391 1095946 1096011 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096045) (-488 1094688 1095243 1095308 "INT64" NIL INT64 (NIL) -8 NIL NIL 1095342) (-487 1093985 1094540 1094605 "INT32" NIL INT32 (NIL) -8 NIL NIL 1094639) (-486 1093282 1093837 1093902 "INT16" NIL INT16 (NIL) -8 NIL NIL 1093936) (-485 1089745 1093201 1093277 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1083802 1087285 1087313 "INS" 1088243 INS (NIL) -9 NIL 1088902 NIL) (-483 1081864 1082782 1083729 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1080923 1081146 1081421 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1080137 1080278 1080475 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1079127 1079268 1079505 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1078279 1078443 1078703 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1077559 1077674 1077862 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1076298 1076567 1076891 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1075578 1075719 1075902 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1075241 1075313 1075411 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1072319 1073805 1074328 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1071918 1072025 1072139 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1071074 1071719 1071820 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1069924 1070192 1070513 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1068914 1069854 1069919 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1068539 1068619 1068736 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1067453 1067998 1068202 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1063548 1064603 1065546 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1062402 1062725 1062753 "INBCON" 1063266 INBCON (NIL) -9 NIL 1063532 NIL) (-465 1061856 1062121 1062397 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1061350 1061652 1061742 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1060807 1061116 1061221 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1059646 1059787 1060104 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1058069 1058338 1058677 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1052912 1058000 1058064 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1052292 1052626 1052741 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1047384 1051730 1051916 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1046414 1047306 1047379 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1045986 1046063 1046117 "IEVALAB" 1046324 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1045741 1045821 1045981 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1045126 1045353 1045510 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1044119 1045046 1045121 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1043182 1044039 1044114 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1042264 1042911 1043048 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1040627 1041198 1041249 "IDPC" 1041755 IDPC (NIL T T) -9 NIL 1042068 NIL) (-449 1039915 1040549 1040622 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1039085 1039837 1039910 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1038778 1038991 1039051 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1038482 1038522 1038561 "IDEMOPC" 1038566 IDEMOPC (NIL T) -9 NIL 1038703 NIL) (-445 1035553 1036434 1037326 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1029179 1030456 1031495 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1028441 1028571 1028770 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1027614 1028113 1028251 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1026003 1026334 1026725 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1022040 1025959 1025998 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1019298 1019922 1020617 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1017524 1018004 1018537 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1015398 1017430 1017519 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1011540 1015336 1015393 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1005119 1010504 1010972 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1004687 1004750 1004923 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1004179 1004328 1004356 "HYPCAT" 1004563 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1003835 1003988 1004174 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1003448 1003693 1003776 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1003281 1003330 1003371 "HOMOTOP" 1003376 HOMOTOP (NIL T) -9 NIL 1003409 NIL) (-429 1001701 1002513 1002554 "HOAGG" 1002638 HOAGG (NIL T) -9 NIL 1002960 NIL) (-428 1001328 1001475 1001696 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 994528 1001053 1001201 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 993463 993721 993984 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 992398 993328 993458 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 990656 992231 992319 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 989971 990323 990456 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 983523 989904 989966 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 976662 983259 983410 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 976115 976272 976435 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 968615 976032 976110 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968106 968409 968500 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 965656 967893 968072 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 961342 965539 965651 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 953819 961239 961337 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 945756 953188 953443 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 944780 945289 945317 "GROUP" 945520 GROUP (NIL) -9 NIL 945654 NIL) (-412 944323 944524 944775 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 942995 943334 943721 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 941817 942174 942225 "GRMOD" 942754 GRMOD (NIL T T) -9 NIL 942920 NIL) (-409 941636 941684 941812 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 937759 938970 939970 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 936481 936805 937120 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936034 936162 936303 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935107 935606 935657 "GRALG" 935810 GRALG (NIL T T) -9 NIL 935900 NIL) (-404 934826 934927 935102 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 931845 934517 934684 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931258 931321 931578 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927112 928008 928533 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 926287 926489 926727 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 921290 922217 923236 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921038 921095 921184 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 920520 920609 920774 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920029 920070 920283 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 918830 919113 919417 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912105 918520 918681 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 901888 906895 907999 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 899940 901043 901071 "GCDDOM" 901326 GCDDOM (NIL) -9 NIL 901483 NIL) (-391 899563 899720 899935 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 890356 892826 895214 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 888491 888816 889234 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 887432 887621 887888 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 886303 886510 886814 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 885766 885908 886056 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 884378 884726 885039 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 882923 883244 883566 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 880549 880905 881310 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 873801 875462 877040 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 873453 873674 873742 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873077 873298 873379 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 871174 871857 872317 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 869767 870074 870466 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 868422 868781 869105 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 867725 867849 868036 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 866699 866965 867312 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 864357 864887 865369 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 863940 864000 864169 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 862240 863154 863457 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 861388 861522 861745 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 860559 860720 860947 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 856793 859454 859495 "FSAGG" 859865 FSAGG (NIL T) -9 NIL 860126 NIL) (-368 855147 855906 856698 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 853103 853399 853943 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 852150 852332 852632 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 851831 851880 852007 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 831987 841488 841529 "FS" 845399 FS (NIL T) -9 NIL 847677 NIL) (-363 824218 827711 831690 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 823752 823879 824031 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 818275 821433 821473 "FRNAALG" 822793 FRNAALG (NIL T) -9 NIL 823391 NIL) (-360 815016 816267 817525 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 814697 814746 814873 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 813184 813741 814035 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 812470 812563 812850 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 810304 811070 811386 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 809413 809856 809897 "FRETRCT" 809902 FRETRCT (NIL T) -9 NIL 810073 NIL) (-354 808786 809064 809408 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 805530 807050 807109 "FRAMALG" 807991 FRAMALG (NIL T T) -9 NIL 808283 NIL) (-352 804126 804677 805307 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 803819 803882 803989 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 797460 803624 803814 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 797153 797216 797323 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 789461 794032 795360 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 783239 786742 786770 "FPS" 787889 FPS (NIL) -9 NIL 788445 NIL) (-346 782796 782929 783093 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 779606 781649 781677 "FPC" 781902 FPC (NIL) -9 NIL 782044 NIL) (-344 779452 779504 779601 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 778229 778938 778979 "FPATMAB" 778984 FPATMAB (NIL T) -9 NIL 779136 NIL) (-342 776659 777255 777602 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 776234 776292 776465 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 774737 775632 775806 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 773352 773857 773885 "FNCAT" 774342 FNCAT (NIL) -9 NIL 774599 NIL) (-338 772809 773319 773347 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 771396 772758 772804 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 767984 769342 769383 "FMONCAT" 770600 FMONCAT (NIL T) -9 NIL 771204 NIL) (-335 764842 765920 765973 "FMCAT" 767154 FMCAT (NIL T T) -9 NIL 767646 NIL) (-334 763542 764665 764764 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 762590 763390 763537 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 760777 761229 761723 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 758712 759248 759826 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 752098 757049 757663 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 750579 751680 751720 "FLINEXP" 751725 FLINEXP (NIL T) -9 NIL 751818 NIL) (-328 749988 750247 750574 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 749237 749396 749610 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 746120 747199 747251 "FLALG" 748478 FLALG (NIL T T) -9 NIL 748945 NIL) (-325 745291 745452 745679 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 739016 742705 742746 "FLAGG" 743985 FLAGG (NIL T) -9 NIL 744633 NIL) (-323 738124 738528 739011 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 734685 735949 736008 "FINRALG" 737136 FINRALG (NIL T T) -9 NIL 737644 NIL) (-321 734076 734341 734680 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 733374 733670 733698 "FINITE" 733894 FINITE (NIL) -9 NIL 734001 NIL) (-319 733282 733308 733369 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 730275 731543 731584 "FINAGG" 732489 FINAGG (NIL T) -9 NIL 732943 NIL) (-317 729306 729771 730270 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 721267 723858 723898 "FINAALG" 727550 FINAALG (NIL T) -9 NIL 728988 NIL) (-315 717534 718779 719902 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 716086 716505 716559 "FILECAT" 717243 FILECAT (NIL T T) -9 NIL 717459 NIL) (-313 715437 715911 716014 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 712685 714563 714591 "FIELD" 714631 FIELD (NIL) -9 NIL 714711 NIL) (-311 711710 712171 712680 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 709714 710660 711006 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 708957 709138 709357 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 704227 708895 708952 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 703889 703956 704091 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 703429 703471 703680 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 700109 700986 701763 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 695393 700041 700104 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 690072 694882 695072 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 684553 689353 689611 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 678760 684004 684215 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 677783 677993 678308 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 673223 675928 675956 "FFIELDC" 676575 FFIELDC (NIL) -9 NIL 676950 NIL) (-298 672292 672732 673218 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 671907 671965 672089 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 670051 670574 671091 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 665145 669850 669951 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 660245 664934 665041 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 654911 660036 660144 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 654365 654414 654649 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 632940 643974 644060 "FFCAT" 649210 FFCAT (NIL T T T) -9 NIL 650646 NIL) (-290 629180 630406 631712 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 624023 629111 629175 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 622915 623384 623425 "FEVALAB" 623509 FEVALAB (NIL T) -9 NIL 623770 NIL) (-287 622320 622572 622910 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 619147 620058 620173 "FDIVCAT" 621740 FDIVCAT (NIL T T T T) -9 NIL 622176 NIL) (-285 618941 618973 619142 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 618248 618341 618618 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 616734 617732 617935 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 615827 616211 616413 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 614949 615438 615578 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 606536 611179 611219 "FAXF" 613020 FAXF (NIL T) -9 NIL 613710 NIL) (-279 604452 605256 606071 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 599601 603974 604148 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 594059 596482 596534 "FAMR" 597545 FAMR (NIL T T) -9 NIL 598004 NIL) (-276 593258 593623 594054 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 592279 593200 593253 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 589873 590752 590805 "FAMONC" 591746 FAMONC (NIL T T) -9 NIL 592131 NIL) (-273 588429 589731 589868 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 586509 586870 587272 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 585786 585983 586205 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 577646 585233 585432 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 575665 576235 576821 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 572567 573209 573929 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 567724 568431 569236 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 567413 567476 567585 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 552206 566462 566888 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 542733 551526 551814 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 542227 542529 542619 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 542003 542193 542222 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 541692 541760 541873 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 541209 541351 541392 "EVALAB" 541562 EVALAB (NIL T) -9 NIL 541666 NIL) (-259 540837 540983 541204 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 537880 539475 539503 "EUCDOM" 540057 EUCDOM (NIL) -9 NIL 540406 NIL) (-257 536807 537300 537875 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 536532 536588 536688 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 536220 536284 536393 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 529991 531891 531919 "ES" 534661 ES (NIL) -9 NIL 536045 NIL) (-253 526506 528038 529830 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 525854 526007 526183 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 518360 525784 525849 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 518049 518112 518221 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 511676 514801 516234 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 507979 509075 510168 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 506808 507158 507463 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 505693 506424 506452 "ENTIRER" 506457 ENTIRER (NIL) -9 NIL 506501 NIL) (-245 505582 505616 505688 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 502215 504012 504361 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 501306 501521 501575 "ELTAGG" 501949 ELTAGG (NIL T T) -9 NIL 502163 NIL) (-242 501086 501160 501301 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 500832 500867 500921 "ELTAB" 501005 ELTAB (NIL T T) -9 NIL 501057 NIL) (-240 500083 500253 500452 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 499807 499881 499909 "ELEMFUN" 500014 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 499707 499734 499802 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 494984 497732 497773 "ELAGG" 498706 ELAGG (NIL T) -9 NIL 499167 NIL) (-236 493782 494320 494979 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 493200 493367 493523 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 492113 492432 492711 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 485506 487504 488331 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 479485 481481 482291 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 477299 477705 478176 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 468299 470212 471753 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 467412 467913 468062 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 466110 466784 466824 "DVARCAT" 467107 DVARCAT (NIL T) -9 NIL 467247 NIL) (-227 465529 465793 466105 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 457596 465397 465524 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 455934 456725 456766 "DSEXT" 457129 DSEXT (NIL T) -9 NIL 457423 NIL) (-224 454739 455263 455929 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 454463 454528 454626 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 450614 451830 452961 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 446260 447615 448679 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 444935 445296 445682 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 444621 444680 444798 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 443596 443894 444184 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 443181 443256 443406 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 435594 437706 439821 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 431111 432130 433209 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 427735 429738 429779 "DQAGG" 430408 DQAGG (NIL T) -9 NIL 430681 NIL) (-213 414278 421918 422000 "DPOLCAT" 423837 DPOLCAT (NIL T T T T) -9 NIL 424380 NIL) (-212 410686 412334 414273 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 403789 410584 410681 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 396801 403618 403784 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 396394 396654 396743 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 395808 396256 396336 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 395094 395419 395570 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 388233 394830 394981 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 385982 387299 387339 "DMEXT" 387344 DMEXT (NIL T) -9 NIL 387519 NIL) (-204 385638 385700 385844 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 379230 385123 385313 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 376456 378059 378100 "DLAGG" 378641 DLAGG (NIL T) -9 NIL 378873 NIL) (-201 374807 375678 375706 "DIVRING" 375798 DIVRING (NIL) -9 NIL 375881 NIL) (-200 374258 374502 374802 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 372686 373103 373509 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 371723 371944 372209 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 365295 371655 371718 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 353693 360055 360108 "DIRPCAT" 360364 DIRPCAT (NIL NIL T) -9 NIL 361239 NIL) (-195 351699 352469 353356 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 351146 351312 351498 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 348429 350023 350064 "DIOPS" 350484 DIOPS (NIL T) -9 NIL 350712 NIL) (-192 348089 348233 348424 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 347096 347842 347870 "DIOID" 347875 DIOID (NIL) -9 NIL 347897 NIL) (-190 345924 346753 346781 "DIFRING" 346786 DIFRING (NIL) -9 NIL 346807 NIL) (-189 345560 345658 345686 "DIFFSPC" 345805 DIFFSPC (NIL) -9 NIL 345880 NIL) (-188 345301 345403 345555 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 344204 344829 344869 "DIFFMOD" 344874 DIFFMOD (NIL T) -9 NIL 344971 NIL) (-186 343888 343945 343986 "DIFFDOM" 344107 DIFFDOM (NIL T) -9 NIL 344175 NIL) (-185 343769 343799 343883 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 341442 342963 343003 "DIFEXT" 343008 DIFEXT (NIL T) -9 NIL 343160 NIL) (-183 339330 340924 340965 "DIAGG" 340970 DIAGG (NIL T) -9 NIL 340990 NIL) (-182 338886 339076 339325 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 334124 338076 338353 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 330582 331635 332645 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 325132 329736 330063 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 323698 323990 324365 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 320818 322070 322466 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 318602 320649 320738 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 317985 318130 318312 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 315303 316027 316827 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 313412 313870 314432 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 312795 313128 313242 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 305995 312520 312668 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 303915 304425 304929 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 303554 303603 303754 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 302813 303375 303466 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 300837 301279 301639 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 300129 300418 300564 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 299580 299726 299878 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 296942 297735 298462 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 296381 296527 296698 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 294453 294764 295131 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 294010 294265 294366 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 293211 293594 293622 "CTORCAT" 293803 CTORCAT (NIL) -9 NIL 293915 NIL) (-159 292914 293048 293206 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 292407 292664 292772 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 291823 292254 292327 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 291282 291399 291552 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 287676 288432 289187 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 287167 287470 287561 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 286386 286595 286823 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 285890 285995 286199 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 285643 285677 285783 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 282582 283344 284062 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 282101 282243 282382 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 277994 280564 281056 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 277868 277895 277923 "CONDUIT" 277960 CONDUIT (NIL) -9 NIL NIL NIL) (-146 276747 277478 277506 "COMRING" 277511 COMRING (NIL) -9 NIL 277561 NIL) (-145 275912 276279 276457 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 275608 275649 275777 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 275301 275364 275471 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 264143 275251 275296 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 263604 263743 263903 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 263357 263398 263496 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 244788 257038 257078 "COMPCAT" 258079 COMPCAT (NIL T) -9 NIL 259421 NIL) (-138 237326 240839 244432 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 237085 237119 237221 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236915 236954 237012 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236496 236775 236849 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 236073 236314 236401 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235268 235516 235544 "COMBOPC" 235882 COMBOPC (NIL) -9 NIL 236057 NIL) (-132 234332 234584 234826 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231264 231948 232571 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 230144 230595 230830 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229635 229938 230029 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229322 229375 229500 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228792 229102 229200 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225312 226382 227462 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223607 224592 224830 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221024 222243 222284 "CLAGG" 222847 CLAGG (NIL T) -9 NIL 223227 NIL) (-123 220582 220772 221019 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220211 220302 220442 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218148 218655 219203 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217109 217840 217868 "CHARZ" 217873 CHARZ (NIL) -9 NIL 217887 NIL) (-119 216903 216949 217027 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215742 216505 216533 "CHARNZ" 216594 CHARNZ (NIL) -9 NIL 216642 NIL) (-117 213220 214317 214840 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 212928 213007 213035 "CFCAT" 213146 CFCAT (NIL) -9 NIL NIL NIL) (-115 212271 212400 212582 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208539 211684 211964 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 207917 208104 208281 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207445 207864 207912 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 206918 207227 207324 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206409 206712 206803 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205658 205818 206039 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201758 203015 203723 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200124 201155 201406 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199705 199984 200058 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199139 199392 199420 "CACHSET" 199552 CACHSET (NIL) -9 NIL 199630 NIL) (-104 198491 198906 198934 "CABMON" 198984 CABMON (NIL) -9 NIL 199040 NIL) (-103 198021 198285 198395 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193510 197689 197850 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192480 193184 193319 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193482) (-100 190005 192247 192353 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187501 189759 189867 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184755 186903 186942 "BTCAT" 187009 BTCAT (NIL T) -9 NIL 187090 NIL) (-97 184506 184604 184750 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179843 183698 183724 "BTAGG" 183835 BTAGG (NIL) -9 NIL 183943 NIL) (-95 179474 179635 179838 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176612 178966 179156 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175882 176034 176212 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172976 174597 174636 "BRAGG" 175265 BRAGG (NIL T) -9 NIL 175525 NIL) (-91 172051 172482 172971 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164585 171556 171737 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162577 164537 164580 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162310 162346 162457 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160549 160982 161430 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156515 157931 158821 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155391 156282 156404 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154977 155134 155160 "BOOLE" 155268 BOOLE (NIL) -9 NIL 155349 NIL) (-83 154770 154851 154972 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153908 154435 154485 "BMODULE" 154490 BMODULE (NIL T T) -9 NIL 154554 NIL) (-81 149793 153765 153834 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149606 149646 149685 "BINOPC" 149690 BINOPC (NIL T) -9 NIL 149735 NIL) (-79 149148 149421 149523 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148669 148813 148951 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141875 148399 148544 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140122 141095 141134 "BGAGG" 141390 BGAGG (NIL T) -9 NIL 141517 NIL) (-75 139991 140029 140117 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138842 139043 139328 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135556 138022 138327 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 135141 135234 135260 "BASTYPE" 135431 BASTYPE (NIL) -9 NIL 135527 NIL) (-71 134911 135007 135136 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134426 134514 134664 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133325 134000 134185 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 133073 133078 133104 "ATTREG" 133109 ATTREG (NIL) -9 NIL NIL NIL) (-67 132678 132950 133015 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 132178 132327 132353 "ATRIG" 132554 ATRIG (NIL) -9 NIL NIL NIL) (-65 132033 132086 132173 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131603 131834 131860 "ASTCAT" 131865 ASTCAT (NIL) -9 NIL 131895 NIL) (-63 131402 131479 131598 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129625 131235 131323 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128432 128745 129110 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 126284 128362 128427 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125475 125666 125887 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 121343 125206 125320 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115655 117659 117734 "ARR2CAT" 120246 ARR2CAT (NIL T T T) -9 NIL 120967 NIL) (-56 114616 115098 115650 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 113984 114355 114477 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 112916 113084 113380 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112617 112671 112789 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 112000 112146 112302 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111405 111695 111815 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 108973 110134 110457 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108498 108758 108854 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102193 107560 108002 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97727 99390 99440 "AMR" 100178 AMR (NIL T T) -9 NIL 100775 NIL) (-46 97081 97361 97722 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79065 97015 97076 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75468 78741 78910 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72478 73138 73745 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71857 71970 72154 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68269 68894 69486 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57758 67962 68112 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57075 57229 57407 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55788 56583 56621 "ALGEBRA" 56626 ALGEBRA (NIL T) -9 NIL 56666 NIL) (-37 55574 55651 55783 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33879 52662 52714 "ALAGG" 52849 ALAGG (NIL T T) -9 NIL 53007 NIL) (-35 33379 33528 33554 "AHYP" 33755 AHYP (NIL) -9 NIL NIL NIL) (-34 32861 32993 33019 "AGG" 33224 AGG (NIL) -9 NIL 33350 NIL) (-33 32704 32762 32856 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30843 31303 31703 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30338 30641 30730 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29708 30003 30159 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17266 26545 26583 "ACFS" 27190 ACFS (NIL T) -9 NIL 27429 NIL) (-28 15889 16499 17261 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11441 13820 13846 "ACF" 14725 ACF (NIL) -9 NIL 15137 NIL) (-26 10537 10943 11436 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10039 10279 10305 "ABELSG" 10397 ABELSG (NIL) -9 NIL 10462 NIL) (-24 9937 9968 10034 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9092 9466 9492 "ABELMON" 9717 ABELMON (NIL) -9 NIL 9850 NIL) (-22 8774 8914 9087 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 7986 8469 8495 "ABELGRP" 8567 ABELGRP (NIL) -9 NIL 8642 NIL) (-20 7539 7735 7981 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6766 6805 "A1AGG" 6810 A1AGG (NIL T) -9 NIL 6844 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index dd769966..5c288fd2 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,793 +1,793 @@
 
-(630173 . 3578003925)        
+(630173 . 3578007597)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
-   (-5 *2 (-1179 (-350 (-484)))) (-5 *1 (-1208 *4))))) 
+  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485))))
+   (-5 *2 (-1180 (-350 (-485)))) (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
-   (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4))))) 
+  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485))))
+   (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-85))
-   (-5 *1 (-1208 *4))))) 
+  (-12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-85))
+   (-5 *1 (-1209 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-553 *2) (-146))) (-5 *2 (-800 *4)) (-5 *1 (-144 *4 *5 *3))
-   (-4 *4 (-1013)) (-4 *3 (-139 *5))))
+  (-12 (-4 *5 (-13 (-554 *2) (-146))) (-5 *2 (-801 *4)) (-5 *1 (-144 *4 *5 *3))
+   (-4 *4 (-1014)) (-4 *3 (-139 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-353 *3 *4))
-   (-4 *4 (-1155 *3))))
+  (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-353 *3 *4))
+   (-4 *4 (-1156 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-353 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1155 *3))
-   (-5 *2 (-1179 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-361 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-146)) (-5 *2 (-1179 *3))))
+  (-12 (-4 *1 (-353 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1156 *3))
+   (-5 *2 (-1180 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-361 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-146)) (-5 *2 (-1180 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-348 *1)) (-4 *1 (-364 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))
+  (-12 (-5 *2 (-348 *1)) (-4 *1 (-364 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717))
-   (-4 *5 (-756)) (-5 *1 (-403 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-473))))
- ((*1 *2 *1) (-12 (-4 *1 (-553 *2)) (-4 *2 (-1129))))
- ((*1 *1 *2) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1129))))
- ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-661 *3 *2)) (-4 *2 (-1155 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-403 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1016)) (-5 *1 (-474))))
+ ((*1 *2 *1) (-12 (-4 *1 (-554 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2) (-12 (-4 *1 (-558 *2)) (-4 *2 (-1130))))
+ ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-662 *3 *2)) (-4 *2 (-1156 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-857 *3)) (-4 *3 (-961)) (-4 *1 (-977 *3 *4 *5))
-   (-4 *5 (-553 (-1090))) (-4 *4 (-717)) (-4 *5 (-756))))
+  (-12 (-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 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
-    (-12 (-2561 (-4 *3 (-38 (-350 (-484))))) (-4 *3 (-38 (-484)))
-     (-4 *5 (-553 (-1090))))
-    (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756)))
-   (-12 (-5 *2 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-350 (-484)))) (-4 *5 (-553 (-1090)))) (-4 *3 (-961))
-    (-4 *4 (-717)) (-4 *5 (-756)))))
+   (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
+    (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485)))
+     (-4 *5 (-554 (-1091))))
+    (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
+   (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
+    (-12 (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962))
+    (-4 *4 (-718)) (-4 *5 (-757)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-857 (-350 (-484)))) (-4 *1 (-977 *3 *4 *5))
-   (-4 *3 (-38 (-350 (-484)))) (-4 *5 (-553 (-1090))) (-4 *3 (-961))
-   (-4 *4 (-717)) (-4 *5 (-756))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
-   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1073))
-   (-5 *1 (-981 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
-   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-1020 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1073))
-   (-5 *1 (-1059 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-1095))))
- ((*1 *2 *1) (-12 (-5 *2 (-1015)) (-5 *1 (-1095))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1109))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1109))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-703 *4 (-773 *5))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-14 *5 (-583 (-1090))) (-5 *2 (-703 *4 (-773 *6))) (-5 *1 (-1207 *4 *5 *6))
-   (-14 *6 (-583 (-1090)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-857 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-5 *2 (-857 (-937 (-350 *4)))) (-5 *1 (-1207 *4 *5 *6))
-   (-14 *5 (-583 (-1090))) (-14 *6 (-583 (-1090)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-703 *4 (-773 *6))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-14 *6 (-583 (-1090))) (-5 *2 (-857 (-937 (-350 *4))))
-   (-5 *1 (-1207 *4 *5 *6)) (-14 *5 (-583 (-1090)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-5 *2 (-1085 (-937 (-350 *4)))) (-5 *1 (-1207 *4 *5 *6))
-   (-14 *5 (-583 (-1090))) (-14 *6 (-583 (-1090)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1060 *4 (-469 (-773 *6)) (-773 *6) (-703 *4 (-773 *6))))
-   (-4 *4 (-13 (-755) (-258) (-120) (-933))) (-14 *6 (-583 (-1090)))
-   (-5 *2 (-583 (-703 *4 (-773 *6)))) (-5 *1 (-1207 *4 *5 *6))
-   (-14 *5 (-583 (-1090)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-348 *3)) (-5 *1 (-497 *3)) (-4 *3 (-483))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-258)) (-5 *2 (-348 *3))
-   (-5 *1 (-681 *4 *5 *6 *3)) (-4 *3 (-861 *6 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-258)) (-4 *7 (-861 *6 *4 *5))
-   (-5 *2 (-348 (-1085 *7))) (-5 *1 (-681 *4 *5 *6 *7)) (-5 *3 (-1085 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-392)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-5 *2 (-348 *1)) (-4 *1 (-861 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-756)) (-4 *5 (-717)) (-4 *6 (-392)) (-5 *2 (-348 *3))
-   (-5 *1 (-892 *4 *5 *6 *3)) (-4 *3 (-861 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-392)) (-4 *7 (-861 *6 *4 *5))
-   (-5 *2 (-348 (-1085 (-350 *7)))) (-5 *1 (-1087 *4 *5 *6 *7))
-   (-5 *3 (-1085 (-350 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-348 *1)) (-4 *1 (-1134))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-495)) (-5 *2 (-348 *3)) (-5 *1 (-1159 *4 *3))
-   (-4 *3 (-13 (-1155 *4) (-495) (-10 -8 (-15 -3145 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-14 *5 (-583 (-1090)))
-   (-5 *2 (-583 (-1060 *4 (-469 (-773 *6)) (-773 *6) (-703 *4 (-773 *6)))))
-   (-5 *1 (-1207 *4 *5 *6)) (-14 *6 (-583 (-1090)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
-   (-14 *5 (-583 (-1090))) (-5 *2 (-583 (-583 (-937 (-350 *4)))))
-   (-5 *1 (-1207 *4 *5 *6)) (-14 *6 (-583 (-1090)))))
+  (-12 (-5 *2 (-858 (-350 (-485)))) (-4 *1 (-978 *3 *4 *5))
+   (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091))) (-4 *3 (-962))
+   (-4 *4 (-718)) (-4 *5 (-757))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1074))
+   (-5 *1 (-982 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-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) (-12 (-5 *2 (-1016)) (-5 *1 (-1096))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1016)) (-5 *1 (-1096))))
+ ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *5))) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-14 *5 (-584 (-1091))) (-5 *2 (-704 *4 (-774 *6))) (-5 *1 (-1208 *4 *5 *6))
+   (-14 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-858 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-5 *2 (-858 (-938 (-350 *4)))) (-5 *1 (-1208 *4 *5 *6))
+   (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *6))) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-14 *6 (-584 (-1091))) (-5 *2 (-858 (-938 (-350 *4))))
+   (-5 *1 (-1208 *4 *5 *6)) (-14 *5 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1086 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
+   (-5 *2 (-1086 (-938 (-350 *4)))) (-5 *1 (-1208 *4 *5 *6))
+   (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1061 *4 (-470 (-774 *6)) (-774 *6) (-704 *4 (-774 *6))))
+   (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *6 (-584 (-1091)))
+   (-5 *2 (-584 (-704 *4 (-774 *6)))) (-5 *1 (-1208 *4 *5 *6))
+   (-14 *5 (-584 (-1091)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-348 *3)) (-5 *1 (-498 *3)) (-4 *3 (-484))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-258)) (-5 *2 (-348 *3))
+   (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-862 *6 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-258)) (-4 *7 (-862 *6 *4 *5))
+   (-5 *2 (-348 (-1086 *7))) (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1086 *7))))
+ ((*1 *2 *1)
+  (-12 (-4 *3 (-392)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
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@@ -796,10355 +796,10355 @@
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- ((*1 *2 *1) (-12 (-5 *2 (-583 (-221))) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-694)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))
- ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
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- ((*1 *2 *3 *2) (-12 (-5 *2 (-1073)) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
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+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1183))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1184))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1184))))) 
+(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
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+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1074)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
 (((*1 *2 *1 *3 *3 *4 *4)
-  (-12 (-5 *3 (-694)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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-  (-12 (-5 *3 (-694)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
    (-5 *1 (-221))))
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
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+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1186)) (-5 *1 (-1184))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1186)) (-5 *1 (-1184))))
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-  (-12 (-5 *3 (-484)) (-5 *4 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))
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   (-12
    (-5 *3
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *2 (-1185)) (-5 *1 (-1183))))
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  ((*1 *2 *1)
   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *1 (-1183))))
+   (-5 *1 (-1184))))
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-  (-12 (-5 *3 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-783)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-484)) (-5 *2 (-1185)) (-5 *1 (-1183))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1185)) (-5 *1 (-1182))))
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-130)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
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 (((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-583 (-1073))) (-5 *2 (-1073)) (-5 *1 (-1182))))
- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1182))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1182))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1183))))
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- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1183))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1184))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-1184))))) 
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-(((*1 *1 *2 *3) (-12 (-5 *2 (-408)) (-5 *3 (-583 (-221))) (-5 *1 (-1182))))
- ((*1 *1 *1) (-5 *1 (-1182)))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1183))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1186)) (-5 *1 (-1184))))) 
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+ ((*1 *1 *1) (-5 *1 (-1183)))) 
 (((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5)
-  (-12 (-5 *3 (-830)) (-5 *4 (-179)) (-5 *5 (-484)) (-5 *6 (-783))
-   (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-179)) (-5 *5 (-485)) (-5 *6 (-784))
+   (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-1179
+    (-1180
      (-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179))
-      (|:| |deltaY| (-179)) (|:| -3851 (-484)) (|:| -3849 (-484))
-      (|:| |spline| (-484)) (|:| -3880 (-484)) (|:| |axesColor| (-783))
-      (|:| -3852 (-484)) (|:| |unitsColor| (-783)) (|:| |showing| (-484)))))
-   (-5 *1 (-1182))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1092 (-350 (-484)))) (-5 *1 (-164))))
- ((*1 *2 *1) (-12 (-5 *2 (-1179 (-3 (-408) "undefined"))) (-5 *1 (-1182))))) 
+      (|:| |deltaY| (-179)) (|:| -3852 (-485)) (|:| -3850 (-485))
+      (|:| |spline| (-485)) (|:| -3881 (-485)) (|:| |axesColor| (-784))
+      (|:| -3853 (-485)) (|:| |unitsColor| (-784)) (|:| |showing| (-485)))))
+   (-5 *1 (-1183))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1093 (-350 (-485)))) (-5 *1 (-164))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1180 (-3 (-408) "undefined"))) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-408)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-830)) (-5 *2 (-408)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-408)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-831)) (-5 *2 (-408)) (-5 *1 (-1183))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-583 (-330))) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-330))) (-5 *1 (-408))))
- ((*1 *2 *1) (-12 (-5 *2 (-583 (-330))) (-5 *1 (-408))))
+  (-12 (-5 *2 (-584 (-330))) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-330))) (-5 *1 (-408))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-330))) (-5 *1 (-408))))
  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-783)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1186)) (-5 *1 (-1183))))
  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
-(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-181 *2)) (-4 *2 (-13 (-312) (-1115)))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-312))))
- ((*1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-312))))
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+ ((*1 *1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
+ ((*1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
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-  (-12 (-5 *3 (-830)) (-5 *4 (-330)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-330)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-408)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-408)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
 (((*1 *2 *3 *4 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-783)) (-5 *5 (-830))
-   (-5 *6 (-583 (-221))) (-5 *2 (-1182)) (-5 *1 (-1181))))
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+   (-5 *6 (-584 (-221))) (-5 *2 (-1183)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-583 (-221)))
-   (-5 *2 (-1182)) (-5 *1 (-1181))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221)))
+   (-5 *2 (-1183)) (-5 *1 (-1182))))) 
 (((*1 *2 *3 *4 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-783)) (-5 *5 (-830))
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+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-784)) (-5 *5 (-831))
+   (-5 *6 (-584 (-221))) (-5 *2 (-408)) (-5 *1 (-1182))))
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+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-408)) (-5 *1 (-1182))))
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-   (-5 *1 (-1181))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221))) (-5 *2 (-408))
+   (-5 *1 (-1182))))) 
 (((*1 *1 *1) (-5 *1 (-48)))
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-  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1129)) (-4 *2 (-1129))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1130)) (-4 *2 (-1130))
    (-5 *1 (-59 *5 *2))))
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-  (-12 (-4 *4 (-961)) (-5 *2 (-2 (|:| -2004 (-1085 *4)) (|:| |deg| (-830))))
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+  (-12 (-5 *3 (-485)) (-4 *1 (-1142 *4)) (-4 *4 (-962)) (-4 *4 (-496))
+   (-5 *2 (-350 (-858 *4)))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-484)) (-4 *1 (-1141 *4)) (-4 *4 (-961)) (-4 *4 (-495))
-   (-5 *2 (-350 (-857 *4)))))) 
+  (-12 (-5 *3 (-485)) (-4 *1 (-1142 *4)) (-4 *4 (-962)) (-4 *4 (-496))
+   (-5 *2 (-350 (-858 *4)))))) 
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- ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))
- ((*1 *1 *1 *1) (-5 *1 (-1137))) ((*1 *1 *1 *1) (-5 *1 (-1138)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))
+ ((*1 *1 *1 *1) (-5 *1 (-1138))) ((*1 *1 *1 *1) (-5 *1 (-1139)))) 
 (((*1 *1 *1 *1) (-5 *1 (-101)))
- ((*1 *1 *1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-830))))
- ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))
- ((*1 *1 *1 *1) (-5 *1 (-1137))) ((*1 *1 *1 *1) (-5 *1 (-1138)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))
+ ((*1 *1 *1 *1) (-5 *1 (-1138))) ((*1 *1 *1 *1) (-5 *1 (-1139)))) 
 (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-101)))
  ((*1 *1)
-  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-484)) (-14 *3 (-694)) (-4 *4 (-146))))
- ((*1 *1) (-5 *1 (-485))) ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487)))
- ((*1 *1) (-5 *1 (-488))) ((*1 *1) (-4 *1 (-663))) ((*1 *1) (-5 *1 (-1090)))
- ((*1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-830))))
- ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-830)))) ((*1 *1) (-5 *1 (-1135)))
- ((*1 *1) (-5 *1 (-1136))) ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-142 (-484))) (-5 *2 (-85)) (-5 *1 (-386))))
+  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-485)) (-14 *3 (-695)) (-4 *4 (-146))))
+ ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487))) ((*1 *1) (-5 *1 (-488)))
+ ((*1 *1) (-5 *1 (-489))) ((*1 *1) (-4 *1 (-664))) ((*1 *1) (-5 *1 (-1091)))
+ ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-831))))
+ ((*1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-831)))) ((*1 *1) (-5 *1 (-1136)))
+ ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138))) ((*1 *1) (-5 *1 (-1139)))) 
+(((*1 *2 *3) (-12 (-5 *3 (-142 (-485))) (-5 *2 (-85)) (-5 *1 (-386))))
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   (-12
    (-5 *3
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- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-873 *3)) (-4 *3 (-483))))
- ((*1 *2 *1) (-12 (-4 *1 (-1134)) (-5 *2 (-85))))) 
-(((*1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-1132))))) 
+    (-444 (-350 (-485)) (-197 *5 (-695)) (-774 *4) (-206 *4 (-350 (-485)))))
+   (-14 *4 (-584 (-1091))) (-14 *5 (-695)) (-5 *2 (-85)) (-5 *1 (-445 *4 *5))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-874 *3)) (-4 *3 (-484))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1135)) (-5 *2 (-85))))) 
+(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1133))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3229 (-583 (-1090))) (|:| -3230 (-583 (-1090)))))
-   (-5 *1 (-1132))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-583 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-583 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))) 
+  (-12 (-5 *2 (-2 (|:| -3230 (-584 (-1091))) (|:| -3231 (-584 (-1091)))))
+   (-5 *1 (-1133))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-694)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-756)) (-4 *3 (-1013))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-757)) (-4 *3 (-1014))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1131 *2))
-   (-4 *2 (-1013))))
+  (-12 (-5 *3 (-584 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1132 *2))
+   (-4 *2 (-1014))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-1013)) (-4 *2 (-756)) (-5 *1 (-1131 *2))))) 
-(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1013))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-1014)) (-4 *2 (-757)) (-5 *1 (-1132 *2))))) 
+(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1014))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-694)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1013))))
+  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1014))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1013)) (-5 *2 (-85))
-   (-5 *1 (-1131 *3))))) 
+  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1014)) (-5 *2 (-85))
+   (-5 *1 (-1132 *3))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3230 (-583 *3)) (|:| -3229 (-583 *3))))
-   (-5 *1 (-1131 *3)) (-4 *3 (-1013))))) 
+  (-12 (-5 *2 (-2 (|:| -3231 (-584 *3)) (|:| -3230 (-584 *3))))
+   (-5 *1 (-1132 *3)) (-4 *3 (-1014))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 *4)) (-4 *4 (-1013)) (-5 *2 (-1185)) (-5 *1 (-1131 *4))))
+  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *4)) (-4 *4 (-1013)) (-5 *2 (-1185)) (-5 *1 (-1131 *4))))) 
+  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-484)) (-4 *5 (-299)) (-5 *2 (-348 (-1085 (-1085 *5))))
-   (-5 *1 (-1128 *5)) (-5 *3 (-1085 (-1085 *5)))))) 
+  (-12 (-5 *4 (-485)) (-4 *5 (-299)) (-5 *2 (-348 (-1086 (-1086 *5))))
+   (-5 *1 (-1129 *5)) (-5 *3 (-1086 (-1086 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
-   (-5 *3 (-1085 (-1085 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
+   (-5 *3 (-1086 (-1086 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
-   (-5 *3 (-1085 (-1085 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
+   (-5 *3 (-1086 (-1086 *4)))))) 
 (((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-318 *3)) (-4 *1 (-124 *3))
-   (-4 *3 (-1129))))
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- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-616 *3)) (-4 *3 (-1129))))
+   (-4 *3 (-1130))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1130)) (-5 *1 (-537 *3))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1130))))
  ((*1 *2 *1 *3)
-  (|partial| -12 (-4 *1 (-1124 *4 *5 *3 *2)) (-4 *4 (-495)) (-4 *5 (-717))
-   (-4 *3 (-756)) (-4 *2 (-977 *4 *5 *3))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-5 *1 (-1127 *2)) (-4 *2 (-1129))))) 
+  (|partial| -12 (-4 *1 (-1125 *4 *5 *3 *2)) (-4 *4 (-496)) (-4 *5 (-718))
+   (-4 *3 (-757)) (-4 *2 (-978 *4 *5 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-5 *1 (-1128 *2)) (-4 *2 (-1130))))) 
 (((*1 *2 *3 *3 *3 *4 *5)
-  (-12 (-5 *5 (-583 (-583 (-179)))) (-5 *4 (-179)) (-5 *2 (-583 (-854 *4)))
-   (-5 *1 (-1126)) (-5 *3 (-854 *4))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-484)) (-5 *2 (-583 (-583 (-179)))) (-5 *1 (-1126))))) 
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+   (-5 *1 (-1127)) (-5 *3 (-855 *4))))) 
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 (((*1 *1 *2)
-  (-12 (-5 *2 (-830)) (-4 *1 (-196 *3 *4)) (-4 *4 (-961)) (-4 *4 (-1129))))
+  (-12 (-5 *2 (-831)) (-4 *1 (-196 *3 *4)) (-4 *4 (-962)) (-4 *4 (-1130))))
  ((*1 *1 *2)
-  (-12 (-14 *3 (-583 (-1090))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-694)))
+  (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3959 *3) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2400 *2) (|:| -2401 *5))
-     (-2 (|:| -2400 *2) (|:| -2401 *5))))
-   (-5 *1 (-401 *3 *4 *2 *5 *6 *7)) (-4 *2 (-756))
-   (-4 *7 (-861 *4 *5 (-773 *3)))))
- ((*1 *2 *2) (-12 (-5 *2 (-854 (-179))) (-5 *1 (-1126))))) 
+    (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5))
+     (-2 (|:| -2401 *2) (|:| -2402 *5))))
+   (-5 *1 (-401 *3 *4 *2 *5 *6 *7)) (-4 *2 (-757))
+   (-4 *7 (-862 *4 *5 (-774 *3)))))
+ ((*1 *2 *2) (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1127))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-854 (-179))) (-5 *4 (-783)) (-5 *2 (-1185)) (-5 *1 (-408))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-961)) (-4 *1 (-893 *3))))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-961))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-854 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-961))))
+  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *2 (-1186)) (-5 *1 (-408))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-962)) (-4 *1 (-894 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1049 *3)) (-4 *3 (-962)) (-5 *2 (-855 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *3 (-962)) (-4 *1 (-1049 *3))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1049 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *1 (-1049 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *1 (-1049 *3)) (-4 *3 (-962))))
  ((*1 *2 *3 *3 *3 *3)
-  (-12 (-5 *2 (-854 (-179))) (-5 *1 (-1126)) (-5 *3 (-179))))) 
+  (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1127)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *5)
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-   (-4 *3 (-887))))
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+   (-4 *3 (-888))))
  ((*1 *1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-85)) (-5 *1 (-1125 *2))
-   (-4 *2 (-887))))) 
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-85)) (-5 *1 (-1126 *2))
+   (-4 *2 (-888))))) 
+(((*1 *2 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-145))))
- ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-1125 *2)) (-4 *2 (-887))))) 
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
+(((*1 *2 *1) (-12 (-5 *1 (-1126 *2)) (-4 *2 (-888))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
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-  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *4 *5)
   (|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9))
-   (-4 *9 (-977 *6 *7 *8)) (-4 *6 (-495)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-583 *9)))) (-5 *3 (-583 *9))
-   (-4 *1 (-1124 *6 *7 *8 *9))))
+   (-4 *9 (-978 *6 *7 *8)) (-4 *6 (-496)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *9)))) (-5 *3 (-584 *9))
+   (-4 *1 (-1125 *6 *7 *8 *9))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-977 *5 *6 *7))
-   (-4 *5 (-495)) (-4 *6 (-717)) (-4 *7 (-756))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-583 *8)))) (-5 *3 (-583 *8))
-   (-4 *1 (-1124 *5 *6 *7 *8))))) 
+  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-978 *5 *6 *7))
+   (-4 *5 (-496)) (-4 *6 (-718)) (-4 *7 (-757))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *8)))) (-5 *3 (-584 *8))
+   (-4 *1 (-1125 *5 *6 *7 *8))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-583 *6))))) 
+  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-584 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-2 (|:| -3862 (-583 *6)) (|:| -1702 (-583 *6))))))) 
+  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-2 (|:| -3863 (-584 *6)) (|:| -1703 (-584 *6))))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-583 *1)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-961)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-584 *1)) (-4 *1 (-978 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-85))))
+  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
  ((*1 *2 *3 *1)
-  (-12 (-4 *1 (-1124 *4 *5 *6 *3)) (-4 *4 (-495)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *3 (-977 *4 *5 *6)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1125 *4 *5 *6 *3)) (-4 *4 (-496)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-583 *1)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-961)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-584 *1)) (-4 *1 (-978 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
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    (-5 *2 (-85))))
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-   (-4 *8 (-977 *5 *6 *7))))) 
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 (((*1 *2 *3 *1)
   (-12
-   (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2596 (-694)) (|:| |period| (-694))))
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- ((*1 *2 *3 *4)
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 (((*1 *2)
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 (((*1 *2 *3 *3)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *1 *3)
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 (((*1 *2 *3 *4 *4 *4)
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 (((*1 *2 *3 *4 *4)
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+ ((*1 *2 *3 *4)
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   (-12
    (-5 *5
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   (-12
    (-5 *5
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-   (-5 *1 (-1059 *7 *8 *9 *10 *11))))) 
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 (((*1 *2 *1)
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-   (-4 *5 (-1155 (-350 *4))) (-4 *6 (-291 *3 *4 *5))
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    (-5 *2
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-   (-5 *1 (-1027 *4 *5))))) 
+  (-12 (-5 *3 (-1149 *5 *4)) (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 *4))
+   (-5 *1 (-1028 *4 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-583 (-1148 *5 *4)))
-   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1148 *5 *4))))) 
+  (-12 (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 (-1149 *5 *4)))
+   (-5 *1 (-1028 *4 *5)) (-5 *3 (-1149 *5 *4))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-583 (-1148 *5 *4)))
-   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1148 *5 *4))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1022 *3))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-1021))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1179 (-484))) (-5 *3 (-484)) (-5 *1 (-1021))))
+  (-12 (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 (-1149 *5 *4)))
+   (-5 *1 (-1028 *4 *5)) (-5 *3 (-1149 *5 *4))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1023 *3))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *1 (-1022))))) 
+(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1180 (-485))) (-5 *3 (-485)) (-5 *1 (-1022))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-1179 (-484))) (-5 *3 (-583 (-484))) (-5 *4 (-484))
-   (-5 *1 (-1021))))) 
+  (-12 (-5 *2 (-1180 (-485))) (-5 *3 (-584 (-485))) (-5 *4 (-485))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-583 (-830))) (-5 *4 (-85))
-   (-5 *1 (-1021))))) 
+  (-12 (-5 *2 (-584 (-485))) (-5 *3 (-584 (-831))) (-5 *4 (-85))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-630 (-484))) (-5 *3 (-583 (-484))) (-5 *1 (-1021))))) 
+  (-12 (-5 *2 (-631 (-485))) (-5 *3 (-584 (-485))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-830))) (-5 *4 (-583 (-484))) (-5 *2 (-630 (-484)))
-   (-5 *1 (-1021))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *4 (-584 (-485))) (-5 *2 (-631 (-485)))
+   (-5 *1 (-1022))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-830))) (-5 *2 (-583 (-630 (-484)))) (-5 *1 (-1021))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *2 (-584 (-631 (-485)))) (-5 *1 (-1022))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-630 (-484))) (-5 *1 (-1021))))) 
+  (-12 (-5 *2 (-584 (-485))) (-5 *3 (-631 (-485))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-583 (-484))) (-5 *2 (-630 (-484))) (-5 *1 (-1021))))) 
+  (-12 (-5 *3 (-584 (-485))) (-5 *2 (-631 (-485))) (-5 *1 (-1022))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
-   (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-85)) (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-85)) (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
-   (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
-   (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
+   (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4 *5 *5)
-  (-12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-4 *3 (-977 *6 *7 *8)) (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
-   (-5 *1 (-1019 *6 *7 *8 *3 *4)) (-4 *4 (-983 *6 *7 *8 *3))))
+  (-12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *3 (-978 *6 *7 *8)) (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
+   (-5 *1 (-1020 *6 *7 *8 *3 *4)) (-4 *4 (-984 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-583 (-2 (|:| |val| (-583 *8)) (|:| -1600 *9)))) (-5 *5 (-85))
-   (-4 *8 (-977 *6 *7 *4)) (-4 *9 (-983 *6 *7 *4 *8)) (-4 *6 (-392))
-   (-4 *7 (-717)) (-4 *4 (-756))
-   (-5 *2 (-583 (-2 (|:| |val| *8) (|:| -1600 *9))))
-   (-5 *1 (-1019 *6 *7 *4 *8 *9))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| |val| (-584 *8)) (|:| -1601 *9)))) (-5 *5 (-85))
+   (-4 *8 (-978 *6 *7 *4)) (-4 *9 (-984 *6 *7 *4 *8)) (-4 *6 (-392))
+   (-4 *7 (-718)) (-4 *4 (-757))
+   (-5 *2 (-584 (-2 (|:| |val| *8) (|:| -1601 *9))))
+   (-5 *1 (-1020 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-583 *3)) (|:| -1600 *4))))
-   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-584 *3)) (|:| -1601 *4))))
+   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-984 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-984 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-4 *9 (-977 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *4) (|:| |ineq| (-583 *9))))
-   (-5 *1 (-901 *6 *7 *8 *9 *4)) (-5 *3 (-583 *9)) (-4 *4 (-983 *6 *7 *8 *9))))
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9))))
  ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-4 *9 (-977 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *4) (|:| |ineq| (-583 *9))))
-   (-5 *1 (-1018 *6 *7 *8 *9 *4)) (-5 *3 (-583 *9))
-   (-4 *4 (-983 *6 *7 *8 *9))))) 
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *9 (-978 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
+   (-5 *1 (-1019 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9))
+   (-4 *4 (-984 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
-   (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
+  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-583 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *10) (|:| |ineq| (-583 *9)))))
-   (-5 *1 (-901 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))
+    (-584 (-2 (|:| -3268 (-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 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
-   (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
+  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
    (-5 *2
-    (-583 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *10) (|:| |ineq| (-583 *9)))))
-   (-5 *1 (-1018 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))) 
+    (-584 (-2 (|:| -3268 (-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 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1600 *7))))
-   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1600 *7))))
-   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
+   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
-   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
-   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
+   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-392))
-   (-4 *6 (-717)) (-4 *7 (-756)) (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-901 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-902 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-392))
-   (-4 *6 (-717)) (-4 *7 (-756)) (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1018 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-1019 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3))
-   (-4 *3 (-983 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3))
-   (-4 *3 (-983 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3))
+   (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-901 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-902 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
-   (-5 *2 (-1185)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
+   (-5 *2 (-1186)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-983 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-986))))
+  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-984 *4 *5 *6 *7))))) 
+(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-987))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-377))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-505 *3)) (-4 *3 (-950 (-484)))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-506 *3)) (-4 *3 (-951 (-485)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-2 (|:| -3861 (-1090)) (|:| |entry| *4))))
-   (-5 *1 (-798 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))
+  (-12 (-5 *2 (-584 (-2 (|:| -3862 (-1091)) (|:| |entry| *4))))
+   (-5 *1 (-799 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-1013)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
-   (-4 *7 (-1013)) (-5 *2 (-583 *1)) (-4 *1 (-1016 *3 *4 *5 *6 *7))))) 
+  (-12 (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-4 *7 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-1017 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *2 *4 *5 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-484)) (-5 *1 (-505 *3)) (-4 *3 (-950 *2))))
+  (-12 (-4 *1 (-1017 *3 *2 *4 *5 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-485)) (-5 *1 (-506 *3)) (-4 *3 (-951 *2))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *2 *5 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-484)) (-5 *3 (-830)) (-4 *1 (-347))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-484)) (-4 *1 (-347))))
+  (-12 (-4 *1 (-1017 *3 *4 *2 *5 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
+   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
+(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-485)) (-5 *3 (-831)) (-4 *1 (-347))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-485)) (-4 *1 (-347))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1016 *3 *4 *5 *2 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
-   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
+  (-12 (-4 *1 (-1017 *3 *4 *5 *2 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
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 (((*1 *2 *1)
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+(((*1 *2 *3) (-12 (-5 *3 (-773)) (-5 *2 (-1074)) (-5 *1 (-648))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-773)) (-5 *2 (-1074)) (-5 *1 (-648))))) 
 (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
-  (|partial| -12 (-5 *2 (-583 (-1085 *13))) (-5 *3 (-1085 *13))
-   (-5 *4 (-583 *12)) (-5 *5 (-583 *10)) (-5 *6 (-583 *13))
-   (-5 *7 (-583 (-583 (-2 (|:| -3079 (-694)) (|:| |pcoef| *13)))))
-   (-5 *8 (-583 (-694))) (-5 *9 (-1179 (-583 (-1085 *10)))) (-4 *12 (-756))
-   (-4 *10 (-258)) (-4 *13 (-861 *10 *11 *12)) (-4 *11 (-717))
-   (-5 *1 (-644 *11 *12 *10 *13))))) 
+  (|partial| -12 (-5 *2 (-584 (-1086 *13))) (-5 *3 (-1086 *13))
+   (-5 *4 (-584 *12)) (-5 *5 (-584 *10)) (-5 *6 (-584 *13))
+   (-5 *7 (-584 (-584 (-2 (|:| -3080 (-695)) (|:| |pcoef| *13)))))
+   (-5 *8 (-584 (-695))) (-5 *9 (-1180 (-584 (-1086 *10)))) (-4 *12 (-757))
+   (-4 *10 (-258)) (-4 *13 (-862 *10 *11 *12)) (-4 *11 (-718))
+   (-5 *1 (-645 *11 *12 *10 *13))))) 
 (((*1 *2 *3 *4 *5 *6 *7 *8 *9)
-  (|partial| -12 (-5 *4 (-583 *11)) (-5 *5 (-583 (-1085 *9))) (-5 *6 (-583 *9))
-   (-5 *7 (-583 *12)) (-5 *8 (-583 (-694))) (-4 *11 (-756)) (-4 *9 (-258))
-   (-4 *12 (-861 *9 *10 *11)) (-4 *10 (-717)) (-5 *2 (-583 (-1085 *12)))
-   (-5 *1 (-644 *10 *11 *9 *12)) (-5 *3 (-1085 *12))))) 
+  (|partial| -12 (-5 *4 (-584 *11)) (-5 *5 (-584 (-1086 *9))) (-5 *6 (-584 *9))
+   (-5 *7 (-584 *12)) (-5 *8 (-584 (-695))) (-4 *11 (-757)) (-4 *9 (-258))
+   (-4 *12 (-862 *9 *10 *11)) (-4 *10 (-718)) (-5 *2 (-584 (-1086 *12)))
+   (-5 *1 (-645 *10 *11 *9 *12)) (-5 *3 (-1086 *12))))) 
 (((*1 *2 *3 *4 *5 *6 *2 *7 *8)
-  (|partial| -12 (-5 *2 (-583 (-1085 *11))) (-5 *3 (-1085 *11))
-   (-5 *4 (-583 *10)) (-5 *5 (-583 *8)) (-5 *6 (-583 (-694)))
-   (-5 *7 (-1179 (-583 (-1085 *8)))) (-4 *10 (-756)) (-4 *8 (-258))
-   (-4 *11 (-861 *8 *9 *10)) (-4 *9 (-717)) (-5 *1 (-644 *9 *10 *8 *11))))) 
+  (|partial| -12 (-5 *2 (-584 (-1086 *11))) (-5 *3 (-1086 *11))
+   (-5 *4 (-584 *10)) (-5 *5 (-584 *8)) (-5 *6 (-584 (-695)))
+   (-5 *7 (-1180 (-584 (-1086 *8)))) (-4 *10 (-757)) (-4 *8 (-258))
+   (-4 *11 (-862 *8 *9 *10)) (-4 *9 (-718)) (-5 *1 (-645 *9 *10 *8 *11))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *3 *5 *6 *7))
-   (-4 *3 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))
+  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *3 *5 *6 *7))
+   (-4 *3 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *3 *5 *6))
-   (-4 *3 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
+  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *3 *5 *6))
+   (-4 *3 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *4 *5 *6))
-   (-4 *4 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
+  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *4 *5 *6))
+   (-4 *4 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-642 *3 *4))
-   (-4 *3 (-1129)) (-4 *4 (-1129))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 (-1090))) (-5 *3 (-1090)) (-5 *1 (-473))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
+  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-643 *3 *4))
+   (-4 *3 (-1130)) (-4 *4 (-1130))))) 
+(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-584 (-1091))) (-5 *3 (-1091)) (-5 *1 (-474))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
  ((*1 *2 *3 *2 *2)
-  (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
+  (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
  ((*1 *2 *3 *2 *2 *2)
-  (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
+  (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *4 (-583 (-1090))) (-5 *2 (-1090)) (-5 *1 (-641 *3))
-   (-4 *3 (-553 (-473)))))) 
+  (-12 (-5 *4 (-584 (-1091))) (-5 *2 (-1091)) (-5 *1 (-642 *3))
+   (-4 *3 (-554 (-474)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-640 *3))
-   (-4 *3 (-553 (-473)))))
+  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-474)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-640 *3))
-   (-4 *3 (-553 (-473)))))) 
+  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-474)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *4 *5 *6 *7))
-   (-4 *4 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))) 
+  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *4 *5 *6 *7))
+   (-4 *4 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))) 
 (((*1 *2 *3 *3)
   (-12 (-4 *3 (-258)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3))
-   (-5 *2 (-2 (|:| -1972 *3) (|:| -2903 *3))) (-5 *1 (-629 *3 *4 *5 *6))
-   (-4 *6 (-627 *3 *4 *5))))
+   (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-630 *3 *4 *5 *6))
+   (-4 *6 (-628 *3 *4 *5))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-2 (|:| -1972 *3) (|:| -2903 *3))) (-5 *1 (-638 *3))
+  (-12 (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-639 *3))
    (-4 *3 (-258))))) 
-(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
+(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) 
+(((*1 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) 
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 (((*1 *2 *3 *3 *3 *4)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-1 (-179) (-179) (-179) (-179)))
-   (-5 *2 (-1 (-854 (-179)) (-179) (-179))) (-5 *1 (-636))))) 
+   (-5 *2 (-1 (-855 (-179)) (-179) (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *6)
-  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
-   (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-636))))) 
+  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
-   (-5 *5 (-1001 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179)))
-   (-5 *1 (-636))))) 
+   (-5 *5 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179)))
+   (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
-   (-5 *5 (-1001 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179)))
-   (-5 *1 (-636))))
+   (-5 *5 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179)))
+   (-5 *1 (-637))))
  ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *3 (-1 (-854 (-179)) (-179) (-179))) (-5 *4 (-1001 (-179)))
-   (-5 *5 (-583 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-636))))
+  (-12 (-5 *3 (-1 (-855 (-179)) (-179) (-179))) (-5 *4 (-1002 (-179)))
+   (-5 *5 (-584 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-637))))
  ((*1 *2 *2 *3 *4 *4 *5)
-  (-12 (-5 *2 (-1047 (-179))) (-5 *3 (-1 (-854 (-179)) (-179) (-179)))
-   (-5 *4 (-1001 (-179))) (-5 *5 (-583 (-221))) (-5 *1 (-636))))) 
+  (-12 (-5 *2 (-1048 (-179))) (-5 *3 (-1 (-855 (-179)) (-179) (-179)))
+   (-5 *4 (-1002 (-179))) (-5 *5 (-584 (-221))) (-5 *1 (-637))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-694)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1155 *4))))
+  (-12 (-5 *3 (-695)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1156 *4))))
  ((*1 *2 *2 *3 *2 *3)
-  (-12 (-5 *3 (-484)) (-5 *1 (-635 *2)) (-4 *2 (-1155 *3))))) 
+  (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-2 (|:| |deg| (-694)) (|:| -2576 *5)))) (-4 *5 (-1155 *4))
-   (-4 *4 (-299)) (-5 *2 (-583 *5)) (-5 *1 (-170 *4 *5))))
+  (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2577 *5)))) (-4 *5 (-1156 *4))
+   (-4 *4 (-299)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-2 (|:| -3733 *5) (|:| -3949 (-484))))) (-5 *4 (-484))
-   (-4 *5 (-1155 *4)) (-5 *2 (-583 *5)) (-5 *1 (-635 *5))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| -3734 *5) (|:| -3950 (-485))))) (-5 *4 (-485))
+   (-4 *5 (-1156 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-484)) (-5 *2 (-583 (-2 (|:| -3733 *3) (|:| -3949 *4))))
-   (-5 *1 (-635 *3)) (-4 *3 (-1155 *4))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-635 *2)) (-4 *2 (-1155 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1129)) (-4 *2 (-72))))
- ((*1 *1 *1) (-12 (-4 *1 (-634 *2)) (-4 *2 (-1013))))) 
+  (-12 (-5 *4 (-485)) (-5 *2 (-584 (-2 (|:| -3734 *3) (|:| -3950 *4))))
+   (-5 *1 (-636 *3)) (-4 *3 (-1156 *4))))) 
+(((*1 *2 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)) (-4 *2 (-72))))
+ ((*1 *1 *1) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1014))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-634 *3)) (-4 *3 (-1013))
-   (-5 *2 (-583 (-2 (|:| |entry| *3) (|:| -1730 (-694)))))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
-(((*1 *1) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
+  (-12 (-4 *1 (-635 *3)) (-4 *3 (-1014))
+   (-5 *2 (-584 (-2 (|:| |entry| *3) (|:| -1731 (-695)))))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-633 *2)) (-4 *2 (-553 (-773)))))) 
+(((*1 *1) (-12 (-5 *1 (-633 *2)) (-4 *2 (-553 (-773)))))) 
 (((*1 *2 *2 *2 *2 *2 *3)
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-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))
- ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2)
-  (|partial| -12 (-4 *3 (-495)) (-4 *3 (-146)) (-4 *4 (-324 *3))
-   (-4 *5 (-324 *3)) (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
-(((*1 *2 *2)
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-   (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
+  (-12 (-5 *2 (-631 *4)) (-5 *3 (-695)) (-4 *4 (-962)) (-5 *1 (-632 *4))))) 
+(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))
+ ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
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+(((*1 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2)
+  (|partial| -12 (-4 *3 (-496)) (-4 *3 (-146)) (-4 *4 (-324 *3))
+   (-4 *5 (-324 *3)) (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-496)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3))
+   (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
-   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
+  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
-   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
+  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-484)) (-4 *4 (-146)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4))
-   (-5 *1 (-629 *4 *5 *6 *2)) (-4 *2 (-627 *4 *5 *6))))) 
+  (-12 (-5 *3 (-485)) (-4 *4 (-146)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4))
+   (-5 *1 (-630 *4 *5 *6 *2)) (-4 *2 (-628 *4 *5 *6))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2 *2 *2)
-  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
-   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-625 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-626 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1013)) (-4 *6 (-1013)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-625 *4 *5 *6)) (-4 *4 (-1013))))) 
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-626 *4 *5 *6)) (-4 *4 (-1014))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1013)) (-4 *6 (-1013)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-625 *4 *5 *6)) (-4 *5 (-1013))))) 
+  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-626 *4 *5 *6)) (-4 *5 (-1014))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
-   (-5 *2 (-1 *6 *5)) (-5 *1 (-625 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
+   (-5 *2 (-1 *6 *5)) (-5 *1 (-626 *4 *5 *6))))) 
 (((*1 *2 *3 *4)
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 (((*1 *2 *1 *3 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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-   (-4 *6 (-1155 *2))))) 
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 (((*1 *2 *3 *4)
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-   (-5 *2 (-1085 *7)) (-5 *1 (-440 *5 *4 *6 *7)) (-4 *6 (-1155 *4))))) 
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 (((*1 *2 *2 *2)
   (-12
    (-5 *2
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-   (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) (-4 *4 (-1155 *3))
+    (-2 (|:| -2013 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+   (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3))
    (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) 
 (((*1 *2 *2 *2)
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-   (-4 *4 (-1155 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) 
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 (((*1 *2 *2 *2)
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-   (-4 *4 (-1155 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))
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+  (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $)))))
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 (((*1 *2 *2 *2)
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 (((*1 *2 *3 *3 *2 *4)
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    (-5 *1 (-439 *2 *5 *6)) (-4 *6 (-353 *2 *5))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *3 (-630 *2)) (-5 *4 (-694))
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+  (-12 (-5 *3 (-631 *2)) (-5 *4 (-695))
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    (-5 *1 (-439 *2 *5 *6)) (-4 *6 (-353 *2 *5))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-694)) (-4 *5 (-299)) (-4 *6 (-1155 *5))
+  (-12 (-5 *4 (-695)) (-4 *5 (-299)) (-4 *6 (-1156 *5))
    (-5 *2
-    (-583
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-      (|:| |basisInv| (-630 *6)))))
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    (-5 *3
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-   (-4 *7 (-1155 *6))))) 
+    (-2 (|:| -2013 (-631 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-631 *6))))
+   (-4 *7 (-1156 *6))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-583
+    (-584
      (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3)
-      (|:| |xpnt| (-484)))))
-   (-5 *1 (-348 *3)) (-4 *3 (-495))))
+      (|:| |xpnt| (-485)))))
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-   (-5 *2 (-583 (-1085 *3))) (-5 *1 (-438 *3 *5 *6)) (-4 *6 (-1155 *5))))) 
+  (-12 (-5 *4 (-695)) (-4 *3 (-299)) (-4 *5 (-1156 *3))
+   (-5 *2 (-584 (-1086 *3))) (-5 *1 (-438 *3 *5 *6)) (-4 *6 (-1156 *5))))) 
 (((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-435))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-431))))) 
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+(((*1 *2 *3)
+  (-12 (-5 *3 (-584 (-485))) (-5 *2 (-485)) (-5 *1 (-426 *4))
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 (((*1 *1 *1 *2)
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-   (-4 *4 (-961))))
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+   (-4 *4 (-962))))
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-   (-4 *4 (-961)) (-4 *5 (-196 (-3958 *3) (-694)))))
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  ((*1 *1 *1 *2)
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-(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-420))))) 
-(((*1 *2 *3 *4)
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-   (-5 *1 (-411 *5 *6 *7)) (-5 *3 (-583 (-206 *5 *6))) (-4 *7 (-392))))) 
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+(((*1 *2 *3 *3 *3 *3) (-12 (-5 *3 (-485)) (-5 *2 (-85)) (-5 *1 (-420))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *1 (-420))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-584 (-774 *5))) (-14 *5 (-584 (-1091))) (-4 *6 (-392))
+   (-5 *2 (-2 (|:| |dpolys| (-584 (-206 *5 *6))) (|:| |coords| (-584 (-485)))))
+   (-5 *1 (-411 *5 *6 *7)) (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-392))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-583 (-421 *4 *5))) (-5 *3 (-583 (-773 *4)))
-   (-14 *4 (-583 (-1090))) (-4 *5 (-392)) (-5 *1 (-411 *4 *5 *6))
+  (|partial| -12 (-5 *2 (-584 (-421 *4 *5))) (-5 *3 (-584 (-774 *4)))
+   (-14 *4 (-584 (-1091))) (-4 *5 (-392)) (-5 *1 (-411 *4 *5 *6))
    (-4 *6 (-392))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 (-773 *5))) (-14 *5 (-583 (-1090))) (-4 *6 (-392))
-   (-5 *2 (-583 (-583 (-206 *5 *6)))) (-5 *1 (-411 *5 *6 *7))
-   (-5 *3 (-583 (-206 *5 *6))) (-4 *7 (-392))))) 
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+   (-5 *2 (-584 (-584 (-206 *5 *6)))) (-5 *1 (-411 *5 *6 *7))
+   (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-392))))) 
 (((*1 *1) (-5 *1 (-408)))) 
 (((*1 *1 *2 *3 *3 *4 *5)
-  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *3 (-583 (-783)))
-   (-5 *4 (-583 (-830))) (-5 *5 (-583 (-221))) (-5 *1 (-408))))
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+   (-5 *4 (-584 (-831))) (-5 *5 (-584 (-221))) (-5 *1 (-408))))
  ((*1 *1 *2 *3 *3 *4)
-  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *3 (-583 (-783)))
-   (-5 *4 (-583 (-830))) (-5 *1 (-408))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-408))))
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
+   (-5 *4 (-584 (-831))) (-5 *1 (-408))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-408))))
  ((*1 *1 *1) (-5 *1 (-408)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-408))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-221))))
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+(((*1 *1 *2) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-221))))
  ((*1 *2 *3 *2)
-  (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-408))))
- ((*1 *2 *1) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-408))))) 
+  (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-408))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-408))))) 
 (((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-854 (-179))) (-5 *4 (-783)) (-5 *5 (-830)) (-5 *2 (-1185))
+  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *5 (-831)) (-5 *2 (-1186))
    (-5 *1 (-408))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-854 (-179))) (-5 *2 (-1185)) (-5 *1 (-408))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1186)) (-5 *1 (-408))))
  ((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-583 (-854 (-179)))) (-5 *4 (-783)) (-5 *5 (-830))
-   (-5 *2 (-1185)) (-5 *1 (-408))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-854 (-179))) (-5 *2 (-1185)) (-5 *1 (-408))))) 
+  (-12 (-5 *3 (-584 (-855 (-179)))) (-5 *4 (-784)) (-5 *5 (-831))
+   (-5 *2 (-1186)) (-5 *1 (-408))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1186)) (-5 *1 (-408))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *3 (-583 (-783)))
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
    (-5 *1 (-408))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *2 (-583 (-179)))
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-584 (-179)))
    (-5 *1 (-408))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
  ((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))) 
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
@@ -11152,440 +11152,440 @@
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-830)) (-5 *2 (-1179 (-1179 (-484)))) (-5 *1 (-406))))) 
+  (-12 (-5 *3 (-831)) (-5 *2 (-1180 (-1180 (-485)))) (-5 *1 (-406))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1179 (-1179 (-484)))) (-5 *3 (-830)) (-5 *1 (-406))))) 
+  (-12 (-5 *2 (-1180 (-1180 (-485)))) (-5 *3 (-831)) (-5 *1 (-406))))) 
 (((*1 *2 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-756)) (-4 *5 (-717)) (-4 *6 (-495))
-   (-4 *7 (-861 *6 *5 *3)) (-5 *1 (-402 *5 *3 *6 *7 *2))
+  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-757)) (-4 *5 (-718)) (-4 *6 (-496))
+   (-4 *7 (-862 *6 *5 *3)) (-5 *1 (-402 *5 *3 *6 *7 *2))
    (-4 *2
-    (-13 (-950 (-350 (-484))) (-312)
-     (-10 -8 (-15 -3947 ($ *7)) (-15 -2999 (*7 $)) (-15 -2998 (*7 $)))))))) 
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+  (-12 (-5 *2 (-485))
    (-5 *3
-    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4)
+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756))
+   (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757))
    (-5 *1 (-390 *5 *6 *7 *4))))) 
 (((*1 *2 *3 *4 *4 *2 *2 *2)
-  (-12 (-5 *2 (-484))
+  (-12 (-5 *2 (-485))
    (-5 *3
-    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4)
+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756))
+   (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757))
    (-5 *1 (-390 *5 *6 *7 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1185))
-   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1186))
+   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-484))
-   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-485))
+   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-583 *6)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-717))
-   (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
+    (-584
+     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756))
+   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757))
    (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *2)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *2)
      (|:| |polj| *2)))
-   (-4 *5 (-717)) (-4 *2 (-861 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2))
-   (-4 *4 (-392)) (-4 *6 (-756))))) 
+   (-4 *5 (-718)) (-4 *2 (-862 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2))
+   (-4 *4 (-392)) (-4 *6 (-757))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-583 (-2 (|:| |totdeg| (-694)) (|:| -2004 *3)))) (-5 *4 (-694))
-   (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756))
+  (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2005 *3)))) (-5 *4 (-695))
+   (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757))
    (-5 *1 (-390 *5 *6 *7 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *2))
-   (-4 *2 (-861 *3 *4 *5))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *2))
+   (-4 *2 (-862 *3 *4 *5))))) 
 (((*1 *2 *3 *4)
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-   (-4 *7 (-756)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718))
+   (-4 *7 (-757)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
    (-5 *1 (-390 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-694)) (|:| |poli| *6)
+    (-584
+     (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-695)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *3 (-717)) (-4 *6 (-861 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-756))
+   (-4 *3 (-718)) (-4 *6 (-862 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-757))
    (-5 *1 (-390 *4 *3 *5 *6))))) 
 (((*1 *2 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
+    (-584
+     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756))
+   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757))
    (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *3)
+    (-584
+     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *3)
       (|:| |polj| *3))))
-   (-4 *5 (-717)) (-4 *3 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756))
+   (-4 *5 (-718)) (-4 *3 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757))
    (-5 *1 (-390 *4 *5 *6 *3))))) 
 (((*1 *2 *3 *3 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85))
-   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
+  (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
+   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85))
-   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
+  (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
+   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756))
+   (-4 *5 (-718)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757))
    (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-583 *7)) (-5 *3 (-484)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-5 *3 (-485)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-583 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-584 *7))))
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-   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-583 *8))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
+   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-584 *8))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-583 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-584 *7))))
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-   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-583 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
+   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-584 *8))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-583 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-584 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-717)) (-4 *7 (-756))
-   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-583 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
+   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-584 *8))))) 
 (((*1 *2 *2)
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-   (-4 *5 (-756)) (-5 *1 (-388 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-258)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-388 *3 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-583 *7)) (-5 *3 (-1073)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-258))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-5 *3 (-1074)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-258))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *7))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-583 *7)) (-5 *3 (-1073)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-258))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-5 *3 (-1074)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-258))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-258)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *2))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-386)) (-5 *3 (-484))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-258)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *2))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-386)) (-5 *3 (-485))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))
- ((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
+  (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))
+ ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-484)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
+  (-12 (-5 *2 (-485)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-484)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
-(((*1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
-(((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))
- ((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
+  (-12 (-5 *2 (-485)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
+(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
+(((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))
+ ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-694)) (-5 *4 (-484)) (-5 *1 (-385 *2)) (-4 *2 (-961))))) 
+  (-12 (-5 *3 (-695)) (-5 *4 (-485)) (-5 *1 (-385 *2)) (-4 *2 (-962))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-348 *6)) (-4 *6 (-1155 *5)) (-4 *5 (-961))
-   (-5 *2 (-583 *6)) (-5 *1 (-384 *5 *6))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-348 *6)) (-4 *6 (-1156 *5)) (-4 *5 (-962))
+   (-5 *2 (-584 *6)) (-5 *1 (-384 *5 *6))))) 
 (((*1 *2 *3 *2)
-  (|partial| -12 (-5 *3 (-830)) (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-694)) (-5 *1 (-382 *2))
-   (-4 *2 (-1155 (-484)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-695)) (-5 *1 (-382 *2))
+   (-4 *2 (-1156 (-485)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *1 (-382 *2))
-   (-4 *2 (-1155 (-484)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *1 (-382 *2))
+   (-4 *2 (-1156 (-485)))))
  ((*1 *2 *3 *2 *4 *5)
-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *5 (-694))
-   (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
+   (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
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-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *5 (-694))
-   (-5 *6 (-85)) (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
+   (-5 *6 (-85)) (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-348 *2)) (-4 *2 (-1155 *5)) (-5 *1 (-384 *5 *2))
-   (-4 *5 (-961))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-348 *2)) (-4 *2 (-1156 *5)) (-5 *1 (-384 *5 *2))
+   (-4 *5 (-962))))) 
 (((*1 *2 *3)
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-   (-4 *4 (-1155 (-484))) (-5 *2 (-675 (-694))) (-5 *1 (-382 *4))))
+  (-12 (-5 *3 (-584 (-2 (|:| -3734 *4) (|:| -3950 (-485)))))
+   (-4 *4 (-1156 (-485))) (-5 *2 (-676 (-695))) (-5 *1 (-382 *4))))
  ((*1 *2 *3)
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-   (-5 *2 (-675 (-694))) (-5 *1 (-384 *4 *5))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-961)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1155 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-961)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1155 *3))))) 
+  (-12 (-5 *3 (-348 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-962))
+   (-5 *2 (-676 (-695))) (-5 *1 (-384 *4 *5))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-962)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1156 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-962)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1156 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-961)) (-4 *2 (-13 (-347) (-950 *4) (-312) (-1115) (-239)))
-   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1155 *4))))) 
+  (-12 (-4 *4 (-962)) (-4 *2 (-13 (-347) (-951 *4) (-312) (-1116) (-239)))
+   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1156 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-961)) (-4 *2 (-13 (-347) (-950 *4) (-312) (-1115) (-239)))
-   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1155 *4))))) 
+  (-12 (-4 *4 (-962)) (-4 *2 (-13 (-347) (-951 *4) (-312) (-1116) (-239)))
+   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1156 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-694)) (-4 *5 (-961)) (-5 *2 (-484)) (-5 *1 (-383 *5 *3 *6))
-   (-4 *3 (-1155 *5)) (-4 *6 (-13 (-347) (-950 *5) (-312) (-1115) (-239)))))
+  (-12 (-5 *4 (-695)) (-4 *5 (-962)) (-5 *2 (-485)) (-5 *1 (-383 *5 *3 *6))
+   (-4 *3 (-1156 *5)) (-4 *6 (-13 (-347) (-951 *5) (-312) (-1116) (-239)))))
  ((*1 *2 *3)
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-   (-4 *5 (-13 (-347) (-950 *4) (-312) (-1115) (-239)))))) 
+  (-12 (-4 *4 (-962)) (-5 *2 (-485)) (-5 *1 (-383 *4 *3 *5)) (-4 *3 (-1156 *4))
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 (((*1 *2 *3)
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 (((*1 *1 *2 *3)
   (-12
    (-5 *3
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+    (-584
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-379))))) 
 (((*1 *1) (-5 *1 (-379)))) 
 (((*1 *1) (-5 *1 (-379)))) 
@@ -11595,327 +11595,327 @@
 (((*1 *1) (-5 *1 (-379)))) 
 (((*1 *1) (-5 *1 (-379)))) 
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 (((*1 *1 *2)
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 (((*1 *2 *1)
-  (-12 (-4 *1 (-324 *3)) (-4 *3 (-1129)) (-4 *3 (-756)) (-5 *2 (-85))))
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  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-324 *4)) (-4 *4 (-1129))
+  (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-324 *4)) (-4 *4 (-1130))
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 (((*1 *1 *1 *1 *2)
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 (((*1 *1 *1)
-  (-12 (-4 *1 (-1035 *2)) (-4 *1 (-324 *2)) (-4 *2 (-1129)) (-4 *2 (-756))))
+  (-12 (-4 *1 (-1036 *2)) (-4 *1 (-324 *2)) (-4 *2 (-1130)) (-4 *2 (-757))))
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-  (-12 (-5 *2 (-1 (-85) *3 *3)) (-4 *1 (-1035 *3)) (-4 *1 (-324 *3))
-   (-4 *3 (-1129))))) 
+  (-12 (-5 *2 (-1 (-85) *3 *3)) (-4 *1 (-1036 *3)) (-4 *1 (-324 *3))
+   (-4 *3 (-1130))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *1)
-  (-12 (-4 *1 (-318 *3)) (-4 *3 (-1129)) (-4 *3 (-72)) (-5 *2 (-694))))
+  (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-695))))
  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1129)) (-5 *2 (-694))))) 
-(((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1179 *1)) (-4 *1 (-316 *3))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-695))))) 
+(((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1180 *1)) (-4 *1 (-316 *3))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1085 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1085 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
 (((*1 *2)
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
@@ -11960,1175 +11960,1175 @@
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-583 (-1179 *4))) (-5 *1 (-315 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-584 (-1180 *4))) (-5 *1 (-315 *3 *4))
    (-4 *3 (-316 *4))))
  ((*1 *2)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495))
-   (-5 *2 (-583 (-1179 *3)))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496))
+   (-5 *2 (-584 (-1180 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495)) (-5 *2 (-1085 *3))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496)) (-5 *2 (-1086 *3))))) 
 (((*1 *2 *1)
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-(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-495)) (-4 *2 (-146))))) 
-(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-495)) (-4 *2 (-146))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496)) (-5 *2 (-1086 *3))))) 
+(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-496)) (-4 *2 (-146))))) 
+(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-496)) (-4 *2 (-146))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *3 (-1073)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1013)) (-4 *4 (-1013))))
- ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1013)) (-4 *3 (-1013))))) 
+  (-12 (-5 *3 (-1074)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1014)) (-4 *4 (-1014))))
+ ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1073)) (-4 *1 (-314 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))) 
+  (-12 (-5 *2 (-1074)) (-4 *1 (-314 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))) 
 (((*1 *1 *1) (-4 *1 (-147)))
- ((*1 *1 *1) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1013)) (-4 *3 (-1013))))) 
+ ((*1 *1 *1) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) 
 (((*1 *2 *1)
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-(((*1 *2 *1 *2) (-12 (-4 *1 (-314 *3 *2)) (-4 *3 (-1013)) (-4 *2 (-1013))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-299))
+  (-12 (-5 *3 (-1086 *4)) (-4 *4 (-299))
    (-4 *2
     (-13 (-345)
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-      (-15 -2012 ((-1179 *2) (-830))) (-15 -3929 (*2 *2)))))
+     (-10 -7 (-15 -3948 (*2 *4)) (-15 -2011 ((-831) *2))
+      (-15 -2013 ((-1180 *2) (-831))) (-15 -3930 (*2 *2)))))
    (-5 *1 (-306 *2 *4))))) 
 (((*1 *2 *3)
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-   (-5 *3 (-1085 *4))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-870 (-1086 *4))) (-5 *1 (-305 *4))
+   (-5 *3 (-1086 *4))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-830)) (-5 *2 (-1085 *4)) (-5 *1 (-305 *4)) (-4 *4 (-299))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *1) (-12 (-4 *1 (-299)) (-5 *2 (-85))))
  ((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *2)
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-    (-3 (-1085 *3) (-1179 (-583 (-2 (|:| -3403 *3) (|:| -2400 (-1033)))))))))
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 (((*1 *2 *3)
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-    (-3 (-1085 *3) (-1179 (-583 (-2 (|:| -3403 *3) (|:| -2400 (-1033)))))))))
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 (((*1 *2)
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 (((*1 *1) (-4 *1 (-299)))) 
 (((*1 *2)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-830))
-   (-5 *2 (-1179 (-583 (-2 (|:| -3403 *4) (|:| -2400 (-1033))))))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-299))
-   (-5 *2 (-1179 (-583 (-2 (|:| -3403 *4) (|:| -2400 (-1033))))))
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    (-5 *1 (-296 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-299)) (-5 *2 (-869 (-1033)))
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 (((*1 *2)
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 (((*1 *2)
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 (((*1 *2)
-  (-12 (-4 *4 (-1134)) (-4 *5 (-1155 *4)) (-4 *6 (-1155 (-350 *5)))
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-   (-4 *5 (-1155 (-350 *4))) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *3)
-  (-12 (-4 *3 (-1134)) (-4 *5 (-1155 *3)) (-4 *6 (-1155 (-350 *5)))
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-   (-4 *5 (-1155 (-350 *4))) (-5 *2 (-85))))) 
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 (((*1 *2)
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-   (-4 *5 (-1155 (-350 *4))) (-5 *2 (-85))))) 
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 (((*1 *2 *3)
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-   (-4 *5 (-1155 (-350 *3))) (-5 *2 (-85))))
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  ((*1 *2 *3)
-  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1134)) (-4 *4 (-1155 *3))
-   (-4 *5 (-1155 (-350 *4))) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-291 *3 *4 *5)) (-4 *3 (-1135)) (-4 *4 (-1156 *3))
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 (((*1 *2)
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-   (-5 *6 (-484)) (-5 *7 (-1073)) (-5 *2 (-1125 (-838))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-485)) (-5 *7 (-1074)) (-5 *2 (-1126 (-839))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *2 (-1125 (-838))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *2 (-1126 (-839))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *8 (-1073)) (-5 *2 (-1125 (-838)))
+  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *8 (-1074)) (-5 *2 (-1126 (-839)))
    (-5 *1 (-269))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-1 (-179) (-179))) (-5 *1 (-269)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *3 *3)
   (-12 (-5 *3 (-249 *6)) (-5 *4 (-86)) (-4 *6 (-364 *5))
-   (-4 *5 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
+   (-4 *5 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
  ((*1 *2 *3 *4 *3 *5)
-  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-583 *7)) (-4 *7 (-364 *6))
-   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
+  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-584 *7)) (-4 *7 (-364 *6))
+   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-583 (-249 *7))) (-5 *4 (-583 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-364 *6)) (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-584 (-249 *7))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *7))
+   (-4 *7 (-364 *6)) (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51))
    (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-249 *8))) (-5 *4 (-583 (-86))) (-5 *5 (-249 *8))
-   (-5 *6 (-583 *8)) (-4 *8 (-364 *7)) (-4 *7 (-13 (-495) (-553 (-473))))
+  (-12 (-5 *3 (-584 (-249 *8))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *8))
+   (-5 *6 (-584 *8)) (-4 *8 (-364 *7)) (-4 *7 (-13 (-496) (-554 (-474))))
    (-5 *2 (-51)) (-5 *1 (-268 *7 *8))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-583 *7)) (-5 *4 (-583 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-364 *6)) (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-584 *7)) (-5 *4 (-584 (-86))) (-5 *5 (-249 *7))
+   (-4 *7 (-364 *6)) (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51))
    (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-583 *8)) (-5 *4 (-583 (-86))) (-5 *6 (-583 (-249 *8)))
-   (-4 *8 (-364 *7)) (-5 *5 (-249 *8)) (-4 *7 (-13 (-495) (-553 (-473))))
+  (-12 (-5 *3 (-584 *8)) (-5 *4 (-584 (-86))) (-5 *6 (-584 (-249 *8)))
+   (-4 *8 (-364 *7)) (-5 *5 (-249 *8)) (-4 *7 (-13 (-496) (-554 (-474))))
    (-5 *2 (-51)) (-5 *1 (-268 *7 *8))))
  ((*1 *2 *3 *4 *3 *5)
   (-12 (-5 *3 (-249 *5)) (-5 *4 (-86)) (-4 *5 (-364 *6))
-   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *5))))
+   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *5))))
  ((*1 *2 *3 *4 *5 *3)
   (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-4 *3 (-364 *6))
-   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
+   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
  ((*1 *2 *3 *4 *5 *5)
   (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-4 *3 (-364 *6))
-   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
+   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-5 *6 (-583 *3)) (-4 *3 (-364 *7))
-   (-4 *7 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *7 *3))))) 
+  (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-5 *6 (-584 *3)) (-4 *3 (-364 *7))
+   (-4 *7 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *7 *3))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-85)) (-5 *1 (-265 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-265 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-484)) (-5 *1 (-265 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))) 
+  (-12 (-5 *2 (-485)) (-5 *1 (-265 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-258)) (-5 *2 (-85))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-258)) (-5 *2 (-694))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-258)) (-5 *2 (-695))))) 
 (((*1 *2 *1 *1 *1)
   (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
    (-4 *1 (-258))))
  ((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2409 *1)))
+  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2410 *1)))
    (-4 *1 (-258))))) 
-(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-583 *1)) (-4 *1 (-258))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-254)) (-4 *2 (-1129))))
+(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-584 *1)) (-4 *1 (-258))))) 
+(((*1 *1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-254)) (-4 *2 (-1130))))
  ((*1 *1 *1 *2 *3)
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-249 *1))) (-4 *1 (-254))))
+  (-12 (-5 *2 (-584 (-551 *1))) (-5 *3 (-584 *1)) (-4 *1 (-254))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-249 *1))) (-4 *1 (-254))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-249 *1)) (-4 *1 (-254))))) 
 (((*1 *1 *1 *1) (-4 *1 (-254))) ((*1 *1 *1) (-4 *1 (-254)))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-550 *1)) (-4 *1 (-254))))) 
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-(((*1 *2 *1) (-12 (-5 *2 (-583 (-550 *1))) (-4 *1 (-254))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-254)) (-5 *2 (-583 (-86)))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-1090)) (-5 *2 (-85))))
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-551 *1)) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-551 *1))) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-584 (-551 *1))) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-254)) (-5 *2 (-584 (-86)))))) 
+(((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-1091)) (-5 *2 (-85))))
  ((*1 *2 *1 *1) (-12 (-4 *1 (-254)) (-5 *2 (-85))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-550 *5)) (-4 *5 (-364 *4)) (-4 *4 (-950 (-484))) (-4 *4 (-495))
-   (-5 *2 (-1085 *5)) (-5 *1 (-32 *4 *5))))
+  (-12 (-5 *3 (-551 *5)) (-4 *5 (-364 *4)) (-4 *4 (-951 (-485))) (-4 *4 (-496))
+   (-5 *2 (-1086 *5)) (-5 *1 (-32 *4 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-550 *1)) (-4 *1 (-961)) (-4 *1 (-254)) (-5 *2 (-1085 *1))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))
- ((*1 *2 *3) (-12 (-5 *3 (-583 (-1073))) (-5 *2 (-262)) (-5 *1 (-252))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))
+  (-12 (-5 *3 (-551 *1)) (-4 *1 (-962)) (-4 *1 (-254)) (-5 *2 (-1086 *1))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))
+ ((*1 *2 *3) (-12 (-5 *3 (-584 (-1074))) (-5 *2 (-262)) (-5 *1 (-252))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 (-1073))) (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))) 
+  (-12 (-5 *4 (-584 (-1074))) (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-961)) (-4 *4 (-1155 *3)) (-5 *1 (-137 *3 *4 *2))
-   (-4 *2 (-1155 *4))))
- ((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-1129))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1129))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1129))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-663)) (-4 *2 (-1129))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-663)) (-4 *2 (-1129))))) 
+  (-12 (-4 *3 (-962)) (-4 *4 (-1156 *3)) (-5 *1 (-137 *3 *4 *2))
+   (-4 *2 (-1156 *4))))
+ ((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-1130))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-664)) (-4 *2 (-1130))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-664)) (-4 *2 (-1130))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-249 *3))) (-5 *1 (-249 *3)) (-4 *3 (-495))
-   (-4 *3 (-1129))))) 
+  (-12 (-5 *2 (-584 (-249 *3))) (-5 *1 (-249 *3)) (-4 *3 (-496))
+   (-4 *3 (-1130))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-392))
    (-5 *2
-    (-583
-     (-2 (|:| |eigval| (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4))))
-      (|:| |eigmult| (-694)) (|:| |eigvec| (-583 (-630 (-350 (-857 *4))))))))
-   (-5 *1 (-248 *4)) (-5 *3 (-630 (-350 (-857 *4))))))) 
+    (-584
+     (-2 (|:| |eigval| (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4))))
+      (|:| |eigmult| (-695)) (|:| |eigvec| (-584 (-631 (-350 (-858 *4))))))))
+   (-5 *1 (-248 *4)) (-5 *3 (-631 (-350 (-858 *4))))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-392))
    (-5 *2
-    (-583
-     (-2 (|:| |eigval| (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4))))
-      (|:| |geneigvec| (-583 (-630 (-350 (-857 *4))))))))
-   (-5 *1 (-248 *4)) (-5 *3 (-630 (-350 (-857 *4))))))) 
+    (-584
+     (-2 (|:| |eigval| (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4))))
+      (|:| |geneigvec| (-584 (-631 (-350 (-858 *4))))))))
+   (-5 *1 (-248 *4)) (-5 *3 (-631 (-350 (-858 *4))))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *3 (-3 (-350 (-857 *6)) (-1080 (-1090) (-857 *6)))) (-5 *5 (-694))
-   (-4 *6 (-392)) (-5 *2 (-583 (-630 (-350 (-857 *6))))) (-5 *1 (-248 *6))
-   (-5 *4 (-630 (-350 (-857 *6))))))
+  (-12 (-5 *3 (-3 (-350 (-858 *6)) (-1081 (-1091) (-858 *6)))) (-5 *5 (-695))
+   (-4 *6 (-392)) (-5 *2 (-584 (-631 (-350 (-858 *6))))) (-5 *1 (-248 *6))
+   (-5 *4 (-631 (-350 (-858 *6))))))
  ((*1 *2 *3 *4)
   (-12
    (-5 *3
-    (-2 (|:| |eigval| (-3 (-350 (-857 *5)) (-1080 (-1090) (-857 *5))))
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-   (-4 *5 (-392)) (-5 *2 (-583 (-630 (-350 (-857 *5))))) (-5 *1 (-248 *5))
-   (-5 *4 (-630 (-350 (-857 *5))))))) 
+    (-2 (|:| |eigval| (-3 (-350 (-858 *5)) (-1081 (-1091) (-858 *5))))
+     (|:| |eigmult| (-695)) (|:| |eigvec| (-584 *4))))
+   (-4 *5 (-392)) (-5 *2 (-584 (-631 (-350 (-858 *5))))) (-5 *1 (-248 *5))
+   (-5 *4 (-631 (-350 (-858 *5))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-3 (-350 (-857 *5)) (-1080 (-1090) (-857 *5)))) (-4 *5 (-392))
-   (-5 *2 (-583 (-630 (-350 (-857 *5))))) (-5 *1 (-248 *5))
-   (-5 *4 (-630 (-350 (-857 *5))))))) 
+  (-12 (-5 *3 (-3 (-350 (-858 *5)) (-1081 (-1091) (-858 *5)))) (-4 *5 (-392))
+   (-5 *2 (-584 (-631 (-350 (-858 *5))))) (-5 *1 (-248 *5))
+   (-5 *4 (-631 (-350 (-858 *5))))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-630 (-350 (-857 *4)))) (-4 *4 (-392))
-   (-5 *2 (-583 (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4)))))
+  (-12 (-5 *3 (-631 (-350 (-858 *4)))) (-4 *4 (-392))
+   (-5 *2 (-584 (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4)))))
    (-5 *1 (-248 *4))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-583 (-997))) (-5 *1 (-247))))) 
-(((*1 *2 *3 *3 *1) (-12 (-5 *3 (-446)) (-5 *2 (-632 (-1015))) (-5 *1 (-247))))) 
-(((*1 *1 *2 *2 *3 *1) (-12 (-5 *2 (-446)) (-5 *3 (-1015)) (-5 *1 (-247))))) 
-(((*1 *2 *3 *1) (-12 (-5 *3 (-446)) (-5 *2 (-583 (-876))) (-5 *1 (-247))))) 
-(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-446)) (-5 *3 (-583 (-876))) (-5 *1 (-247))))) 
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+(((*1 *2 *3 *1) (-12 (-5 *3 (-447)) (-5 *2 (-584 (-877))) (-5 *1 (-247))))) 
+(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-447)) (-5 *3 (-584 (-877))) (-5 *1 (-247))))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-484)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1129)) (-4 *4 (-324 *2))
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    (-4 *5 (-324 *2))))
  ((*1 *2 *1 *3 *2)
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-   (-4 *2 (-1129))))) 
-(((*1 *2 *3 *4)
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-(((*1 *2 *2 *3) (-12 (-4 *3 (-312)) (-5 *1 (-240 *3 *2)) (-4 *2 (-1172 *3))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-1146 (-484))) (-4 *1 (-237 *3)) (-4 *3 (-1129))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-237 *3)) (-4 *3 (-1129))))) 
+  (-12 (-4 *1 (-1036 *2)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014))
+   (-4 *2 (-1130))))) 
+(((*1 *2 *3 *4)
+  (-12 (-4 *4 (-312)) (-5 *2 (-584 (-1070 *4))) (-5 *1 (-240 *4 *5))
+   (-5 *3 (-1070 *4)) (-4 *5 (-1173 *4))))) 
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) 
 (((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-318 *3)) (-4 *1 (-193 *3))
-   (-4 *3 (-1013))))
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+   (-4 *3 (-1014))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) 
 (((*1 *1 *2 *3 *4)
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-(((*1 *2 *1) (-12 (-5 *2 (-532)) (-5 *1 (-235))))) 
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 (((*1 *2 *1) (-12 (-5 *2 (-247)) (-5 *1 (-235))))) 
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-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1015)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1096)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1016)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-446)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-447)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-350 (-484))) (-4 *4 (-13 (-495) (-950 (-484)) (-580 (-484))))
-   (-5 *1 (-231 *4 *2)) (-4 *2 (-13 (-27) (-1115) (-364 *4)))))) 
+  (-12 (-5 *3 (-350 (-485))) (-4 *4 (-13 (-496) (-951 (-485)) (-581 (-485))))
+   (-5 *1 (-231 *4 *2)) (-4 *2 (-13 (-27) (-1116) (-364 *4)))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-550 *2)) (-4 *2 (-13 (-27) (-1115) (-364 *4)))
-   (-4 *4 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *4 *2))))) 
+  (-12 (-5 *3 (-551 *2)) (-4 *2 (-13 (-27) (-1116) (-364 *4)))
+   (-4 *4 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *4 *2))))) 
 (((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-583 (-550 *2))) (-5 *4 (-1090))
-   (-4 *2 (-13 (-27) (-1115) (-364 *5)))
-   (-4 *5 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *5 *2))))) 
+  (|partial| -12 (-5 *3 (-584 (-551 *2))) (-5 *4 (-1091))
+   (-4 *2 (-13 (-27) (-1116) (-364 *5)))
+   (-4 *5 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *5 *2))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *3 *2))
-   (-4 *2 (-13 (-27) (-1115) (-364 *3)))))
+  (-12 (-4 *3 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *3 *2))
+   (-4 *2 (-13 (-27) (-1116) (-364 *3)))))
  ((*1 *2 *2 *3)
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-    (-2 (|:| |func| *3) (|:| |kers| (-583 (-550 *3))) (|:| |vals| (-583 *3))))
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *3 *4)
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 (((*1 *1 *2) (-12 (-5 *2 (-330)) (-5 *1 (-221))))
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 (((*1 *1) (-5 *1 (-117)))
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 (((*1 *1 *2) (-12 (-5 *2 (-1 (-179) (-179) (-179) (-179))) (-5 *1 (-221))))
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\ No newline at end of file