* algebra/prtition.spad.pamphlet (parts$Partition): New.

(partitions$Partition): Likewise.
author: dos-reis <gdr@axiomatics.org> 2010-04-23 13:47:59 +0000
committer: dos-reis <gdr@axiomatics.org> 2010-04-23 13:47:59 +0000
commit: 2e76a77847facaa29b9c0f7c26ea2ba511dc285e (patch)
tree: d66199443e28ff789421e9363758442c7b1f0cee /src/share/algebra/browse.daase
parent: 308aa20f031e73d86801a36eeda29424e65077b2 (diff)
download: open-axiom-2e76a77847facaa29b9c0f7c26ea2ba511dc285e.tar.gz
1 files changed, 198 insertions, 198 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index d57c53bf..8138a230 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2268689 . 3480912610)       
+(2269076 . 3480995946)       
 (-18 A S) 
 ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) 
 NIL 
@@ -88,10 +88,10 @@ NIL
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -1709 UP UPUP -1574) 
+(-40 -1709 UP UPUP -4299) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2895 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2895 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2895 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) 
+((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) 
 (-41 R -1709) 
 ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
@@ -111,7 +111,7 @@ NIL
 (-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."))) 
 ((-4452 . T) (-4453 . T)) 
-((-2895 (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) 
+((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
@@ -167,64 +167,64 @@ NIL
 (-59 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-60 R) 
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
-(-61 -3602) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+(-61 -3599) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-62 -3602) 
+(-62 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim}      SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO)      DOUBLE PRECISION ELAM,FINFO(15)      INTEGER MAXIT,IFLAG      IF(MAXIT.EQ.-1)THEN        PRINT*,\"Output from Monit\"      ENDIF      PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) 
 NIL 
 NIL 
-(-63 -3602) 
+(-63 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim}      SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC)      DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N)      INTEGER M,N,LJC      INTEGER I,J      DO 25003 I=1,LJC        DO 25004 J=1,N          FJACC(I,J)=0.0D025004   CONTINUE25003 CONTINUE      FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/(     &XC(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/(     &XC(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)*     &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333     &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)*     &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+     &XC(2))      FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714     &286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666     &6667D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3)     &+XC(2))      FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      FJACC(1,1)=1.0D0      FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2)      FJACC(2,1)=1.0D0      FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2)      FJACC(3,1)=1.0D0      FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/(     &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)     &**2)      FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666     &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2)      FJACC(4,1)=1.0D0      FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2)      FJACC(5,1)=1.0D0      FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399     &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999     &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2)      FJACC(6,1)=1.0D0      FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/(     &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)     &**2)      FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333     &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2)      FJACC(7,1)=1.0D0      FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/(     &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)     &**2)      FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428     &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2)      FJACC(8,1)=1.0D0      FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(9,1)=1.0D0      FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)*     &*2)      FJACC(10,1)=1.0D0      FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(11,1)=1.0D0      FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,1)=1.0D0      FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(13,1)=1.0D0      FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)     &**2)      FJACC(14,1)=1.0D0      FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,1)=1.0D0      FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-64 -3602) 
+(-64 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim}      DOUBLE PRECISION FUNCTION F(X)      DOUBLE PRECISION X      F=DSIN(X)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-65 -3602) 
+(-65 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim}      SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX)      DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH)      INTEGER JTHCOL,N,NROWH,NCOLH      HX(1)=2.0D0*X(1)      HX(2)=2.0D0*X(2)      HX(3)=2.0D0*X(4)+2.0D0*X(3)      HX(4)=2.0D0*X(4)+2.0D0*X(3)      HX(5)=2.0D0*X(5)      HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6))      HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6))      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-66 -3602) 
+(-66 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim}      SUBROUTINE FUNCT1(N,XC,FC)      DOUBLE PRECISION FC,XC(N)      INTEGER N      FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5     &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X     &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+     &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC(     &2)+10.0D0*XC(1)**4+XC(1)**2      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-67 -3602) 
+(-67 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim}      FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1     &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W(     &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1     &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W(     &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8))     &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7)     &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0.     &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3     &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W(     &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-68 -3602) 
+(-68 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK)      INTEGER N,LIWORK,IFLAG,LRWORK      W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00     &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554     &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365     &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z(     &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0.     &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050     &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z     &(1)      W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010     &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136     &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D     &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8)     &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532     &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056     &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1     &))      W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0     &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033     &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502     &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D     &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(-     &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961     &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917     &D0*Z(1))      W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0.     &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688     &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315     &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z     &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0     &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802     &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0*     &Z(1)      W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+(     &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014     &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966     &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352     &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6))     &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718     &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851     &6D0*Z(1)      W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048     &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323     &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730     &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z(     &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583     &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700     &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1)      W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0     &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843     &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017     &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z(     &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136     &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015     &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1     &)      W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05     &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338     &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869     &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8)     &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056     &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544     &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z(     &1)      W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(-     &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173     &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441     &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8     &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23     &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773     &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z(     &1)      W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0     &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246     &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609     &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8     &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032     &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688     &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z(     &1)      W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0     &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830     &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D     &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8)     &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493     &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054     &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1)      W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(-     &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162     &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889     &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8     &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0.     &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226     &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763     &75D0*Z(1)      W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+(     &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169     &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453     &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z(     &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05     &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277     &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0     &*Z(1)      W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15))     &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236     &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278     &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D     &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0     &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660     &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903     &02D0*Z(1)      W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0     &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325     &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556     &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D     &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0.     &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122     &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z     &(1)      W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0.     &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669     &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114     &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z     &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0     &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739     &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0*     &Z(1)      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-69 -3602) 
+(-69 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim}      SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      DOUBLE PRECISION D(K),F(K)      INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE      CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D)      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) 
 NIL 
 NIL 
-(-70 -3602) 
+(-70 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK)      INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE      DOUBLE PRECISION A(5,5)      EXTERNAL F06PAF      A(1,1)=1.0D0      A(1,2)=0.0D0      A(1,3)=0.0D0      A(1,4)=-1.0D0      A(1,5)=0.0D0      A(2,1)=0.0D0      A(2,2)=1.0D0      A(2,3)=0.0D0      A(2,4)=0.0D0      A(2,5)=-1.0D0      A(3,1)=0.0D0      A(3,2)=0.0D0      A(3,3)=1.0D0      A(3,4)=-1.0D0      A(3,5)=0.0D0      A(4,1)=-1.0D0      A(4,2)=0.0D0      A(4,3)=-1.0D0      A(4,4)=4.0D0      A(4,5)=-1.0D0      A(5,1)=0.0D0      A(5,2)=-1.0D0      A(5,3)=0.0D0      A(5,4)=-1.0D0      A(5,5)=4.0D0      IF(MODE.EQ.1)THEN        CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1)      ELSEIF(MODE.EQ.2)THEN        CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1)      ENDIF      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-71 -3602) 
+(-71 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE PEDERV(X,Y,PW)      DOUBLE PRECISION X,Y(*)      DOUBLE PRECISION PW(3,3)      PW(1,1)=-0.03999999999999999D0      PW(1,2)=10000.0D0*Y(3)      PW(1,3)=10000.0D0*Y(2)      PW(2,1)=0.03999999999999999D0      PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2))      PW(2,3)=-10000.0D0*Y(2)      PW(3,1)=0.0D0      PW(3,2)=60000000.0D0*Y(2)      PW(3,3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-72 -3602) 
+(-72 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim}      SUBROUTINE REPORT(X,V,JINT)      DOUBLE PRECISION V(3),X      INTEGER JINT      RETURN      END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) 
 NIL 
 NIL 
-(-73 -3602) 
+(-73 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim}      SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK)      DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N)      INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK)      DOUBLE PRECISION W1(3),W2(3),MS(3,3)      IFLAG=-1      MS(1,1)=2.0D0      MS(1,2)=1.0D0      MS(1,3)=0.0D0      MS(2,1)=1.0D0      MS(2,2)=2.0D0      MS(2,3)=1.0D0      MS(3,1)=0.0D0      MS(3,2)=1.0D0      MS(3,3)=2.0D0      CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG)      IFLAG=-IFLAG      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-74 -3602) 
+(-74 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N)      INTEGER LDFJAC,N,IFLAG      IF(IFLAG.EQ.1)THEN        FVEC(1)=(-1.0D0*X(2))+X(1)        FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2)        FVEC(3)=3.0D0*X(3)      ELSEIF(IFLAG.EQ.2)THEN        FJAC(1,1)=1.0D0        FJAC(1,2)=-1.0D0        FJAC(1,3)=0.0D0        FJAC(2,1)=0.0D0        FJAC(2,2)=2.0D0        FJAC(2,3)=-1.0D0        FJAC(3,1)=0.0D0        FJAC(3,2)=0.0D0        FJAC(3,3)=3.0D0      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
@@ -236,55 +236,55 @@ NIL
 ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim}      SUBROUTINE G(EPS,YA,YB,BC,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BC(N)      INTEGER N      BC(1)=YA(1)      BC(2)=YA(2)      BC(3)=YB(2)-1.0D0      RETURN      END      SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N)      DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N)      INTEGER N      AJ(1,1)=1.0D0      AJ(1,2)=0.0D0      AJ(1,3)=0.0D0      AJ(2,1)=0.0D0      AJ(2,2)=1.0D0      AJ(2,3)=0.0D0      AJ(3,1)=0.0D0      AJ(3,2)=0.0D0      AJ(3,3)=0.0D0      BJ(1,1)=0.0D0      BJ(1,2)=0.0D0      BJ(1,3)=0.0D0      BJ(2,1)=0.0D0      BJ(2,2)=0.0D0      BJ(2,3)=0.0D0      BJ(3,1)=0.0D0      BJ(3,2)=1.0D0      BJ(3,3)=0.0D0      RETURN      END      SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N)      DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N)      INTEGER N      BCEP(1)=0.0D0      BCEP(2)=0.0D0      BCEP(3)=0.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-77 -3602) 
+(-77 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER)      DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*)      INTEGER N,IUSER(*),MODE,NSTATE      OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7)     &+(-1.0D0*X(2)*X(6))      OBJGRD(1)=X(7)      OBJGRD(2)=-1.0D0*X(6)      OBJGRD(3)=X(8)+(-1.0D0*X(7))      OBJGRD(4)=X(9)      OBJGRD(5)=-1.0D0*X(8)      OBJGRD(6)=-1.0D0*X(2)      OBJGRD(7)=(-1.0D0*X(3))+X(1)      OBJGRD(8)=(-1.0D0*X(5))+X(3)      OBJGRD(9)=X(4)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-78 -3602) 
+(-78 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim}      DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X)      DOUBLE PRECISION X(NDIM)      INTEGER NDIM      FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0*     &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
-(-79 -3602) 
+(-79 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE LSFUN1(M,N,XC,FVECC)      DOUBLE PRECISION FVECC(M),XC(N)      INTEGER I,M,N      FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/(     &XC(3)+15.0D0*XC(2))      FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X     &C(3)+7.0D0*XC(2))      FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666     &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2))      FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X     &C(3)+3.0D0*XC(2))      FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC     &(2)+1.0D0)/(XC(3)+2.2D0*XC(2))      FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X     &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2))      FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142     &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2))      FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999     &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2))      FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999     &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2))      FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666     &67D0)/(XC(3)+XC(2))      FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999     &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2))      FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3)     &+XC(2))      FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333     &3333D0)/(XC(3)+XC(2))      FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X     &C(2))      FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3     &)+XC(2))      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-80 -3602) 
+(-80 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim}      SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER     &,USER)      DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*)      INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE      IF(NEEDC(1).GT.0)THEN        C(1)=X(6)**2+X(1)**2        CJAC(1,1)=2.0D0*X(1)        CJAC(1,2)=0.0D0        CJAC(1,3)=0.0D0        CJAC(1,4)=0.0D0        CJAC(1,5)=0.0D0        CJAC(1,6)=2.0D0*X(6)      ENDIF      IF(NEEDC(2).GT.0)THEN        C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2        CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1)        CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1))        CJAC(2,3)=0.0D0        CJAC(2,4)=0.0D0        CJAC(2,5)=0.0D0        CJAC(2,6)=0.0D0      ENDIF      IF(NEEDC(3).GT.0)THEN        C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2        CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1)        CJAC(3,2)=2.0D0*X(2)        CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1))        CJAC(3,4)=0.0D0        CJAC(3,5)=0.0D0        CJAC(3,6)=0.0D0      ENDIF      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-81 -3602) 
+(-81 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim}      SUBROUTINE FCN(N,X,FVEC,IFLAG)      DOUBLE PRECISION X(N),FVEC(N)      INTEGER N,IFLAG      FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0      FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1.     &0D0      FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1.     &0D0      FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1.     &0D0      FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1.     &0D0      FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1.     &0D0      FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1.     &0D0      FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1.     &0D0      FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0      RETURN      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-82 -3602) 
+(-82 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI)      DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI      ALPHA=DSIN(X)      BETA=Y      GAMMA=X*Y      DELTA=DCOS(X)*DSIN(Y)      EPSOLN=Y+X      PHI=X      PSI=Y      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-83 -3602) 
+(-83 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim}      SUBROUTINE BNDY(X,Y,A,B,C,IBND)      DOUBLE PRECISION A,B,C,X,Y      INTEGER IBND      IF(IBND.EQ.0)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(X)      ELSEIF(IBND.EQ.1)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.2)THEN        A=1.0D0        B=0.0D0        C=DSIN(X)*DSIN(Y)      ELSEIF(IBND.EQ.3)THEN        A=0.0D0        B=1.0D0        C=-1.0D0*DSIN(Y)      ENDIF      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-84 -3602) 
+(-84 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNF(X,F)      DOUBLE PRECISION X      DOUBLE PRECISION F(2,2)      F(1,1)=0.0D0      F(1,2)=1.0D0      F(2,1)=0.0D0      F(2,2)=-10.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-85 -3602) 
+(-85 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE FCNG(X,G)      DOUBLE PRECISION G(*),X      G(1)=0.0D0      G(2)=0.0D0      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-86 -3602) 
+(-86 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim}      SUBROUTINE FCN(X,Z,F)      DOUBLE PRECISION F(*),X,Z(*)      F(1)=DTAN(Z(3))      F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2)     &**2))/(Z(2)*DCOS(Z(3)))      F(3)=-0.03199999999999999D0/(X*Z(2)**2)      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-87 -3602) 
+(-87 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim}      SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR)      DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3)      YL(1)=XL      YL(2)=2.0D0      YR(1)=1.0D0      YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM))      RETURN      END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) 
 NIL 
 NIL 
-(-88 -3602) 
+(-88 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim}      SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD)      DOUBLE PRECISION Y(N),RESULT(M,N),XSOL      INTEGER M,N,COUNT      LOGICAL FORWRD      DOUBLE PRECISION X02ALF,POINTS(8)      EXTERNAL X02ALF      INTEGER I      POINTS(1)=1.0D0      POINTS(2)=2.0D0      POINTS(3)=3.0D0      POINTS(4)=4.0D0      POINTS(5)=5.0D0      POINTS(6)=6.0D0      POINTS(7)=7.0D0      POINTS(8)=8.0D0      COUNT=COUNT+1      DO 25001 I=1,N        RESULT(COUNT,I)=Y(I)25001 CONTINUE      IF(COUNT.EQ.M)THEN        IF(FORWRD)THEN          XSOL=X02ALF()        ELSE          XSOL=-X02ALF()        ENDIF      ELSE        XSOL=POINTS(COUNT)      ENDIF      END\\end{verbatim}"))) 
 NIL 
 NIL 
-(-89 -3602) 
+(-89 -3599) 
 ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim}      DOUBLE PRECISION FUNCTION G(X,Y)      DOUBLE PRECISION X,Y(*)      G=X+Y(1)      RETURN      END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) 
 NIL 
 NIL 
@@ -295,7 +295,7 @@ NIL
 (-91 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-92 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -343,7 +343,7 @@ NIL
 (-103 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-104 R UP M |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
@@ -363,7 +363,7 @@ NIL
 (-108) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
+((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
 (-109) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -403,7 +403,7 @@ NIL
 (-118 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2895 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
+((|HasCategory| (-117 |#1|) (QUOTE (-916))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-117 |#1|) (QUOTE (-1031))) (|HasCategory| (-117 |#1|) (QUOTE (-826))) (-2892 (|HasCategory| (-117 |#1|) (QUOTE (-826))) (|HasCategory| (-117 |#1|) (QUOTE (-856)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-1161))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-117 |#1|) (QUOTE (-235))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-311))) (|HasCategory| (-117 |#1|) (QUOTE (-551))) (|HasCategory| (-117 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-916)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) 
 (-119 A S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -419,7 +419,7 @@ NIL
 (-122 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-123 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
@@ -439,15 +439,15 @@ NIL
 (-127 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-128 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-129) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2895 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) 
+((-2892 (-12 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) (-2892 (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-130) (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109)))) (|HasCategory| (-130) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-130) (QUOTE (-1109))) (|HasCategory| (-130) (LIST (QUOTE -313) (QUOTE (-130)))))) 
 (-130) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) 
 NIL 
@@ -472,11 +472,11 @@ NIL
 ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
 (((-4454 "*") . T)) 
 NIL 
-(-136 |minix| -2550 S T$) 
+(-136 |minix| -2549 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -2550 R) 
+(-137 |minix| -2549 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
@@ -499,7 +499,7 @@ NIL
 (-142) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
 ((-4452 . T) (-4442 . T) (-4453 . T)) 
-((-2895 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
+((-2892 (-12 (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-373))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
 (-143 R Q A) 
 ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) 
 NIL 
@@ -598,7 +598,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-1011))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4448)) (|HasAttribute| |#2| (QUOTE -4451)) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562)))) 
 (-167 R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
-((-4445 -2895 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3178 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-4445 -2892 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3175 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-168 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -614,8 +614,8 @@ NIL
 NIL 
 (-171 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-4445 -2895 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3178 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1212)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) 
+((-4445 -2892 (|has| |#1| (-562)) (-12 (|has| |#1| (-311)) (|has| |#1| (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4448 |has| |#1| (-6 -4448)) (-4451 |has| |#1| (-6 -4451)) (-3175 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-834)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1212)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-916))))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-235))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasAttribute| |#1| (QUOTE -4448)) (|HasAttribute| |#1| (QUOTE -4451)) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-354))))) 
 (-172 R S CS) 
 ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) 
 NIL 
@@ -807,7 +807,7 @@ NIL
 (-219) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
+((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
 (-220) 
 ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -827,7 +827,7 @@ NIL
 (-224 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-225 |CoefRing| |listIndVar|) 
 ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) 
 ((-4449 . T)) 
@@ -838,7 +838,7 @@ NIL
 NIL 
 (-227) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-3167 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-228) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -847,7 +847,7 @@ NIL
 (-229 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-230 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
@@ -884,22 +884,22 @@ NIL
 ((|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 
-(-239 S -2550 R) 
+(-239 S -2549 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) 
-(-240 -2550 R) 
+(-240 -2549 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) 
 NIL 
-(-241 -2550 A B) 
+(-241 -2549 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 
-(-242 -2550 R) 
+(-242 -2549 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."))) 
 ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2895 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
+((-2892 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2892 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
 (-243) 
 ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) 
 NIL 
@@ -919,7 +919,7 @@ NIL
 (-247 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}"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-248 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
@@ -927,7 +927,7 @@ NIL
 (-249 |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"))) 
 (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
 (-250) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 
 NIL 
@@ -942,12 +942,12 @@ NIL
 NIL 
 (-253 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-4449 -2895 (-1810 (|has| |#4| (-1058)) (|has| |#4| (-235))) (-1810 (|has| |#4| (-1058)) (|has| |#4| (-907 (-1186)))) (|has| |#4| (-6 -4449)) (-1810 (|has| |#4| (-1058)) (|has| |#4| (-645 (-570))))) (-4446 |has| |#4| (-1058)) (-4447 |has| |#4| (-1058)) ((-4454 "*") |has| |#4| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#4| (QUOTE (-368))) (-2895 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (QUOTE (-1058)))) (-2895 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-368)))) (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-799))) (-2895 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (QUOTE (-854)))) (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (QUOTE (-732))) (-2895 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-174)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-235)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-368)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-373)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-732)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-799)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-854)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1058)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1058))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (-2895 (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-732))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2895 (|HasCategory| |#4| (QUOTE (-1058))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1109)))) (-2895 (|HasAttribute| |#4| (QUOTE -4449)) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#4| (QUOTE (-132))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))))) 
+((-4449 -2892 (-1809 (|has| |#4| (-1058)) (|has| |#4| (-235))) (-1809 (|has| |#4| (-1058)) (|has| |#4| (-907 (-1186)))) (|has| |#4| (-6 -4449)) (-1809 (|has| |#4| (-1058)) (|has| |#4| (-645 (-570))))) (-4446 |has| |#4| (-1058)) (-4447 |has| |#4| (-1058)) ((-4454 "*") |has| |#4| (-174)) (-4452 . T)) 
+((-2892 (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#4| (QUOTE (-368))) (-2892 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (QUOTE (-1058)))) (-2892 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-368)))) (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-799))) (-2892 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (QUOTE (-854)))) (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (QUOTE (-732))) (-2892 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-174)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-235)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-368)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-373)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-732)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-799)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-854)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1058)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1058))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-373))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-732))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-799))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-854))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (-2892 (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (|HasCategory| |#4| (QUOTE (-732))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2892 (|HasCategory| |#4| (QUOTE (-1058))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#4| (QUOTE (-1109)))) (-2892 (|HasAttribute| |#4| (QUOTE -4449)) (-12 (|HasCategory| |#4| (QUOTE (-235))) (|HasCategory| |#4| (QUOTE (-1058)))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#4| (QUOTE (-1058))) (|HasCategory| |#4| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#4| (QUOTE (-132))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#4| (QUOTE (-1109))) (|HasCategory| |#4| (LIST (QUOTE -313) (|devaluate| |#4|))))) 
 (-254 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
-((-4449 -2895 (-1810 (|has| |#3| (-1058)) (|has| |#3| (-235))) (-1810 (|has| |#3| (-1058)) (|has| |#3| (-907 (-1186)))) (|has| |#3| (-6 -4449)) (-1810 (|has| |#3| (-1058)) (|has| |#3| (-645 (-570))))) (-4446 |has| |#3| (-1058)) (-4447 |has| |#3| (-1058)) ((-4454 "*") |has| |#3| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-368))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-799))) (-2895 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854)))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-732))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-235)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-373)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-732)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-799)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-854)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2895 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-2895 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) 
+((-4449 -2892 (-1809 (|has| |#3| (-1058)) (|has| |#3| (-235))) (-1809 (|has| |#3| (-1058)) (|has| |#3| (-907 (-1186)))) (|has| |#3| (-6 -4449)) (-1809 (|has| |#3| (-1058)) (|has| |#3| (-645 (-570))))) (-4446 |has| |#3| (-1058)) (-4447 |has| |#3| (-1058)) ((-4454 "*") |has| |#3| (-174)) (-4452 . T)) 
+((-2892 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-368))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-799))) (-2892 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854)))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-732))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-235)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-373)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-732)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-799)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-854)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-732))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2892 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-2892 (|HasAttribute| |#3| (QUOTE -4449)) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) 
 (-255 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
@@ -999,7 +999,7 @@ NIL
 (-267 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"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-268 A S) 
 ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) 
 NIL 
@@ -1100,7 +1100,7 @@ NIL
 ((|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 
-(-293 S R |Mod| -3547 -3183 |exactQuo|) 
+(-293 S R |Mod| -2077 -2948 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
@@ -1122,12 +1122,12 @@ NIL
 NIL 
 (-298 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-4449 -2895 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4446 |has| |#1| (-1058)) (-4447 |has| |#1| (-1058))) 
-((|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732)))) (|HasCategory| |#1| (QUOTE (-479))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-306))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479)))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732)))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-732)))) 
+((-4449 -2892 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4446 |has| |#1| (-1058)) (-4447 |has| |#1| (-1058))) 
+((|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732)))) (|HasCategory| |#1| (QUOTE (-479))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-306))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-479)))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-732)))) 
 (-299 |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."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-300) 
 ((|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 
@@ -1199,7 +1199,7 @@ NIL
 (-317 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))}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2895 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2895 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) 
+((|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1031))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (-2892 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-826))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-1161))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-235))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -313) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (LIST (QUOTE -290) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1263) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-551))) (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-856))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))) (-2892 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1263 |#1| |#2| |#3| |#4|) (QUOTE (-916))) (|HasCategory| $ (QUOTE (-146)))))) 
 (-318 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 
@@ -1210,8 +1210,8 @@ NIL
 NIL 
 (-320 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."))) 
-((-4449 -2895 (-1810 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2895 (-1810 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) 
-((-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-21))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2895 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2895 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2895 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) 
+((-4449 -2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2892 (-1809 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (|has| |#1| (-1058)) (|has| |#1| (-479)))) (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) 
+((-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-1058)))) (-12 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2892 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2892 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))))) (-2892 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#1| (QUOTE (-1058)))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| $ (QUOTE (-1058))) (|HasCategory| $ (LIST (QUOTE -1047) (QUOTE (-570))))) 
 (-321 R -1709) 
 ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) 
 NIL 
@@ -1223,7 +1223,7 @@ NIL
 (-323 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."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-324 M) 
 ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) 
 NIL 
@@ -1255,7 +1255,7 @@ NIL
 (-331 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."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-332 S -1709) 
 ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) 
 NIL 
@@ -1323,15 +1323,15 @@ NIL
 (-348 |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."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
+((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
 (-349 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-350 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-351 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
 NIL 
@@ -1355,23 +1355,23 @@ NIL
 (-356 |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."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
+((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
 (-357 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-358 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-359 |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}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
+((-2892 (|HasCategory| (-917 |#1|) (QUOTE (-146))) (|HasCategory| (-917 |#1|) (QUOTE (-373)))) (|HasCategory| (-917 |#1|) (QUOTE (-148))) (|HasCategory| (-917 |#1|) (QUOTE (-373))) (|HasCategory| (-917 |#1|) (QUOTE (-146)))) 
 (-360 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-361 -1709 GF) 
 ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) 
 NIL 
@@ -1387,7 +1387,7 @@ NIL
 (-364 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-146)))) 
 (-365 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) 
 NIL 
@@ -1466,7 +1466,7 @@ NIL
 NIL 
 (-384) 
 ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-4435 . T) (-4443 . T) (-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-4435 . T) (-4443 . T) (-3167 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-385 |Par|) 
 ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) 
@@ -1544,7 +1544,7 @@ NIL
 ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) 
 NIL 
 NIL 
-(-404 -3602 |returnType| -3931 |symbols|) 
+(-404 -3599 |returnType| -3931 |symbols|) 
 ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) 
 NIL 
 NIL 
@@ -1570,7 +1570,7 @@ NIL
 ((|HasAttribute| |#1| (QUOTE -4435)) (|HasAttribute| |#1| (QUOTE -4443))) 
 (-410) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) 
-((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-3167 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-411 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."))) 
@@ -1583,7 +1583,7 @@ NIL
 (-413 S) 
 ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) 
 ((-4439 -12 (|has| |#1| (-6 -4450)) (|has| |#1| (-458)) (|has| |#1| (-6 -4439))) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2895 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-826))) (-2892 (|HasCategory| |#1| (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-856)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-834)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-551))) (-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#1| (QUOTE -4439)) (|HasCategory| |#1| (QUOTE (-458)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-414 S R UP) 
 ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
@@ -1627,7 +1627,7 @@ NIL
 (-424 R) 
 ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
 ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) 
+((|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -313) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -290) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-1231))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-1231)))) (|HasCategory| |#1| (QUOTE (-1031))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-458)))) 
 (-425 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
 NIL 
@@ -1674,7 +1674,7 @@ NIL
 ((|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) 
 (-436 R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
-((-4449 -2895 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) 
+((-4449 -2892 (|has| |#1| (-1058)) (|has| |#1| (-479))) (-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) ((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-562)) (-4444 |has| |#1| (-562))) 
 NIL 
 (-437 R -1709) 
 ((|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."))) 
@@ -1771,7 +1771,7 @@ NIL
 (-460 |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"))) 
 (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
 (-461 R BP) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) 
 NIL 
@@ -1851,11 +1851,11 @@ NIL
 (-480 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-481 |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."))) 
 ((-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) 
 (-482 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)}"))) 
 ((-4453 . T) (-4452 . T)) 
@@ -1871,7 +1871,7 @@ NIL
 (-485 |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."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-486) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) 
 NIL 
@@ -1879,11 +1879,11 @@ NIL
 (-487 |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"))) 
 (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
-(-488 -2550 S) 
+((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+(-488 -2549 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}."))) 
 ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2895 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
+((-2892 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2892 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
 (-489) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
@@ -1891,7 +1891,7 @@ NIL
 (-490 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}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-491 -1709 UP UPUP R) 
 ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) 
 NIL 
@@ -1903,7 +1903,7 @@ NIL
 (-493) 
 ((|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."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
+((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
 (-494 A S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1939,11 +1939,11 @@ NIL
 (-502 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-503 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-504 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 
@@ -2019,7 +2019,7 @@ NIL
 (-522 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-523) 
 ((|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 
@@ -2027,15 +2027,15 @@ NIL
 (-524 |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}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) 
+((-2892 (|HasCategory| (-587 |#1|) (QUOTE (-146))) (|HasCategory| (-587 |#1|) (QUOTE (-373)))) (|HasCategory| (-587 |#1|) (QUOTE (-148))) (|HasCategory| (-587 |#1|) (QUOTE (-373))) (|HasCategory| (-587 |#1|) (QUOTE (-146)))) 
 (-525 R |mnRow| |mnCol| |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-526 S |mn|) 
 ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-527 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
@@ -2047,7 +2047,7 @@ NIL
 (-529 R |mnRow| |mnCol|) 
 ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-530) 
 ((|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 
@@ -2155,7 +2155,7 @@ NIL
 (-556 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-557 R -1709) 
 ((|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 
@@ -2170,7 +2170,7 @@ NIL
 NIL 
 (-560 R) 
 ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) 
-((-3170 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-3167 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-561 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."))) 
@@ -2238,7 +2238,7 @@ NIL
 NIL 
 (-577 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."))) 
-((-3170 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-3167 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-578) 
 ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) 
@@ -2327,7 +2327,7 @@ NIL
 (-599 |mn|) 
 ((|constructor| (NIL "This domain implements low-level strings"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2895 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
+((-2892 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (-2892 (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
 (-600 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 
@@ -2335,7 +2335,7 @@ NIL
 (-601 |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}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))) (|HasCategory| (-570) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570)))))) 
 (-602 |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.}"))) 
 (((-4454 "*") |has| |#1| (-562)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
@@ -2363,7 +2363,7 @@ NIL
 (-608 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-609 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
@@ -2382,12 +2382,12 @@ NIL
 NIL 
 (-613 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4449 -2895 (-1810 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
-((-2895 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) 
+((-4449 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
+((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) 
 (-614 |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."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-615 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 
@@ -2483,7 +2483,7 @@ NIL
 (-638) 
 ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109)))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-1168) (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 (-52))) (QUOTE (-1109)))) 
 (-639 S R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2494,8 +2494,8 @@ NIL
 NIL 
 (-641 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4449 -2895 (-1810 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
-((-2895 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) 
+((-4449 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
+((-2892 (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -372) (|devaluate| |#1|)))) 
 (-642 R FE) 
 ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) 
 NIL 
@@ -2507,7 +2507,7 @@ NIL
 (-644 S R) 
 ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) 
 NIL 
-((-1796 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) 
+((-1795 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) 
 (-645 R) 
 ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) 
 ((-4449 . T)) 
@@ -2531,7 +2531,7 @@ NIL
 (-650 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-834))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-651 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
@@ -2543,7 +2543,7 @@ NIL
 (-653 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-654 R) 
 ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) 
 NIL 
@@ -2584,7 +2584,7 @@ NIL
 ((|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)))) 
-(-664 A -1444) 
+(-664 A -1596) 
 ((|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}}"))) 
 ((-4446 . T) (-4447 . T) (-4449 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) 
@@ -2635,7 +2635,7 @@ NIL
 (-676 |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."))) 
 ((-4449 . T) (-4452 . T) (-4446 . T) (-4447 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2895 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-562))) (-2892 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
 (-677) 
 ((|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 
@@ -2655,7 +2655,7 @@ NIL
 (-681 R) 
 ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) 
 NIL 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (QUOTE (-1058))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-682) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
@@ -2711,7 +2711,7 @@ NIL
 (-695 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."))) 
 ((-4452 . T) (-4453 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-562))) (|HasAttribute| |#1| (QUOTE (-4454 "*"))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-696 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
@@ -2730,8 +2730,8 @@ NIL
 NIL 
 (-700) 
 ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) 
-((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3178 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2895 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2895 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2895 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2895 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) 
+((-4445 . T) (-4450 |has| (-705) (-368)) (-4444 |has| (-705) (-368)) (-3175 . T) (-4451 |has| (-705) (-6 -4451)) (-4448 |has| (-705) (-6 -4448)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((|HasCategory| (-705) (QUOTE (-148))) (|HasCategory| (-705) (QUOTE (-146))) (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-373))) (|HasCategory| (-705) (QUOTE (-368))) (-2892 (|HasCategory| (-705) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-235))) (-2892 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (LIST (QUOTE -290) (QUOTE (-705)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -313) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-705)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-705) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-705) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (-2892 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-354)))) (|HasCategory| (-705) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-705) (QUOTE (-1031))) (|HasCategory| (-705) (QUOTE (-1212))) (-12 (|HasCategory| (-705) (QUOTE (-1011))) (|HasCategory| (-705) (QUOTE (-1212)))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-368))) (|HasCategory| (-705) (QUOTE (-916)))) (-12 (|HasCategory| (-705) (QUOTE (-354))) (|HasCategory| (-705) (QUOTE (-916))))) (|HasCategory| (-705) (QUOTE (-551))) (-12 (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-1212)))) (|HasCategory| (-705) (QUOTE (-1069))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-368)))) (-2892 (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-562)))) (-12 (|HasCategory| (-705) (QUOTE (-235))) (|HasCategory| (-705) (QUOTE (-368)))) (-12 (|HasCategory| (-705) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-705) (QUOTE (-368)))) (|HasCategory| (-705) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-705) (QUOTE (-562))) (|HasAttribute| (-705) (QUOTE -4451)) (|HasAttribute| (-705) (QUOTE -4448)) (-12 (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-146)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-705) (QUOTE (-311))) (|HasCategory| (-705) (QUOTE (-916)))) (|HasCategory| (-705) (QUOTE (-354))))) 
 (-701 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}."))) 
 ((-4453 . T)) 
@@ -2750,7 +2750,7 @@ NIL
 NIL 
 (-705) 
 ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) 
-((-3170 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-3167 . T) (-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-706 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."))) 
@@ -2776,7 +2776,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-712 S -2945 I) 
+(-712 S -2942 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 
@@ -2796,14 +2796,14 @@ NIL
 ((|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 
-(-717 R |Mod| -3547 -3183 |exactQuo|) 
+(-717 R |Mod| -2077 -2948 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-718 R |Rep|) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-719 IS E |ff|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
@@ -2812,7 +2812,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-721 R |Mod| -3547 -3183 |exactQuo|) 
+(-721 R |Mod| -2077 -2948 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
 ((-4449 . T)) 
 NIL 
@@ -2879,7 +2879,7 @@ NIL
 (-737 |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."))) 
 (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+((|HasCategory| |#2| (QUOTE (-916))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-870 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
 (-738 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 
@@ -3075,7 +3075,7 @@ NIL
 (-786 R |VarSet|) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (QUOTE (-551)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1796 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (QUOTE (-551)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-570))))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-1186)))) (-1795 (|HasCategory| |#1| (LIST (QUOTE -1001) (QUOTE (-570))))))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-787 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 
@@ -3083,7 +3083,7 @@ NIL
 (-788 R) 
 ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-789 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 
@@ -3144,14 +3144,14 @@ NIL
 ((|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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 ((-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
-(-804 -2895 R OS S) 
+(-804 -2892 R OS S) 
 ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
 (-805 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
 ((-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2895 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (-2892 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1008 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) 
 (-806) 
 ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) 
 NIL 
@@ -3212,14 +3212,14 @@ NIL
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-821 -2550 S |f|) 
+(-821 -2549 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
 ((-4446 |has| |#2| (-1058)) (-4447 |has| |#2| (-1058)) (-4449 |has| |#2| (-6 -4449)) ((-4454 "*") |has| |#2| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2895 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
+((-2892 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-368))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-799))) (-2892 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854)))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-732))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1058)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (|HasCategory| |#2| (QUOTE (-235))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-174)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-235)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-373)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-854)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-732))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-799))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-854))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (QUOTE (-1058)))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (|HasCategory| |#2| (QUOTE (-1058))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasAttribute| |#2| (QUOTE -4449)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))))) 
 (-822 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"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-824 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-823 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
 (((-4454 "*") |has| |#2| (-368)) (-4445 |has| |#2| (-368)) (-4450 |has| |#2| (-368)) (-4444 |has| |#2| (-368)) (-4449 . T) (-4447 . T) (-4446 . T)) 
@@ -3287,7 +3287,7 @@ NIL
 (-839 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."))) 
 ((-4449 |has| |#1| (-854))) 
-((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) 
+((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) 
 (-840 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 
@@ -3327,12 +3327,12 @@ NIL
 (-849 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
 ((-4449 |has| |#1| (-854))) 
-((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2895 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) 
+((|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (QUOTE (-21))) (-2892 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-854)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-854))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-551)))) 
 (-850) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-851 -2550 S) 
+(-851 -2549 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 
@@ -3368,11 +3368,11 @@ NIL
 ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) 
-(-860 R |sigma| -3229) 
+(-860 R |sigma| -3226) 
 ((|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."))) 
 ((-4446 . T) (-4447 . T) (-4449 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-368)))) 
-(-861 |x| R |sigma| -3229) 
+(-861 |x| R |sigma| -3226) 
 ((|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}."))) 
 ((-4446 . T) (-4447 . T) (-4449 . T)) 
 ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-368)))) 
@@ -3439,15 +3439,15 @@ NIL
 (-877 |p|) 
 ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2895 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) 
+((|HasCategory| (-876 |#1|) (QUOTE (-916))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-148))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-876 |#1|) (QUOTE (-1031))) (|HasCategory| (-876 |#1|) (QUOTE (-826))) (-2892 (|HasCategory| (-876 |#1|) (QUOTE (-826))) (|HasCategory| (-876 |#1|) (QUOTE (-856)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-1161))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| (-876 |#1|) (QUOTE (-235))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -313) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (LIST (QUOTE -290) (LIST (QUOTE -876) (|devaluate| |#1|)) (LIST (QUOTE -876) (|devaluate| |#1|)))) (|HasCategory| (-876 |#1|) (QUOTE (-311))) (|HasCategory| (-876 |#1|) (QUOTE (-551))) (|HasCategory| (-876 |#1|) (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-876 |#1|) (QUOTE (-916)))) (|HasCategory| (-876 |#1|) (QUOTE (-146))))) 
 (-878 |p| PADIC) 
 ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2895 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-1031))) (|HasCategory| |#2| (QUOTE (-826))) (-2892 (|HasCategory| |#2| (QUOTE (-826))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-551))) (|HasCategory| |#2| (QUOTE (-856))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
 (-879 S T$) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))))) 
 (-880) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) 
 NIL 
@@ -3507,7 +3507,7 @@ NIL
 (-894 |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 (-1796 (|HasCategory| |#2| (QUOTE (-1058)))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1796 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) 
+((-12 (-1795 (|HasCategory| |#2| (QUOTE (-1058)))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#2| (QUOTE (-1058))) (-1795 (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) 
 (-895 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) 
 NIL 
@@ -3516,7 +3516,7 @@ NIL
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-897 R -2945) 
+(-897 R -2942) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
@@ -3563,7 +3563,7 @@ NIL
 (-908 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-909 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
@@ -3579,7 +3579,7 @@ NIL
 (-912 S) 
 ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
 ((-4449 . T)) 
-((-2895 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) 
+((-2892 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-856)))) 
 (-913 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 
@@ -3704,11 +3704,11 @@ NIL
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -893) (|devaluate| |#1|)))) 
-(-944 R -1709 -2945) 
+(-944 R -1709 -2942) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-945 -2945) 
+(-945 -2942) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
@@ -3731,7 +3731,7 @@ NIL
 (-950 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-951 |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 
@@ -3767,7 +3767,7 @@ NIL
 (-959 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}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1186) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-960 E V R P -1709) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
@@ -3791,7 +3791,7 @@ NIL
 (-965 S) 
 ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-966) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) 
 NIL 
@@ -3811,11 +3811,11 @@ NIL
 (-970 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}"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4450))) 
 (-971 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"))) 
 ((-4449 -12 (|has| |#2| (-479)) (|has| |#1| (-479)))) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-373)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-479))) (|HasCategory| |#2| (QUOTE (-479)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-799))) (|HasCategory| |#2| (QUOTE (-799))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-856))))) 
 (-972) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
@@ -3849,7 +3849,7 @@ NIL
 NIL 
 NIL 
 (-980) 
-((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\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|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
+((|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 
 (-981 S |Coef| |Expon| |Var|) 
@@ -3963,11 +3963,11 @@ NIL
 (-1008 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.}"))) 
 ((-4445 |has| |#1| (-294)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-294))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -290) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-551)))) 
 (-1009 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}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1010 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 
@@ -3979,11 +3979,11 @@ NIL
 (-1012 -1709 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
 ((-4445 |has| (-413 |#2|) (-368)) (-4450 |has| (-413 |#2|) (-368)) (-4444 |has| (-413 |#2|) (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2895 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2895 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2895 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) 
+((|HasCategory| (-413 |#2|) (QUOTE (-146))) (|HasCategory| (-413 |#2|) (QUOTE (-148))) (|HasCategory| (-413 |#2|) (QUOTE (-354))) (-2892 (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (|HasCategory| (-413 |#2|) (QUOTE (-368))) (|HasCategory| (-413 |#2|) (QUOTE (-373))) (-2892 (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (QUOTE (-354)))) (-2892 (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-354))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 |#2|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasCategory| (-413 |#2|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-413 |#2|) (QUOTE (-368)))) (-12 (|HasCategory| (-413 |#2|) (QUOTE (-235))) (|HasCategory| (-413 |#2|) (QUOTE (-368))))) 
 (-1013 |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."))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2895 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
+((|HasCategory| (-570) (QUOTE (-916))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| (-570) (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-148))) (|HasCategory| (-570) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-1031))) (|HasCategory| (-570) (QUOTE (-826))) (-2892 (|HasCategory| (-570) (QUOTE (-826))) (|HasCategory| (-570) (QUOTE (-856)))) (|HasCategory| (-570) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-1161))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| (-570) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| (-570) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| (-570) (QUOTE (-235))) (|HasCategory| (-570) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| (-570) (LIST (QUOTE -520) (QUOTE (-1186)) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -313) (QUOTE (-570)))) (|HasCategory| (-570) (LIST (QUOTE -290) (QUOTE (-570)) (QUOTE (-570)))) (|HasCategory| (-570) (QUOTE (-311))) (|HasCategory| (-570) (QUOTE (-551))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-570) (LIST (QUOTE -645) (QUOTE (-570)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-570) (QUOTE (-916)))) (|HasCategory| (-570) (QUOTE (-146))))) 
 (-1014) 
 ((|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 
@@ -4063,7 +4063,7 @@ NIL
 (-1033 |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"))) 
 ((-4445 . T) (-4450 . T) (-4444 . T) (-4447 . T) (-4446 . T) ((-4454 "*") . T) (-4449 . T)) 
-((-2895 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) 
+((-2892 (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-413 (-570)) (LIST (QUOTE -1047) (QUOTE (-570))))) 
 (-1034 -1709 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 
@@ -4107,7 +4107,7 @@ NIL
 (-1044) 
 ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1045) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4183,7 +4183,7 @@ NIL
 (-1063 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
 ((-4452 . T) (-4447 . T) (-4446 . T)) 
-((|HasCategory| |#3| (QUOTE (-174))) (-2895 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((|HasCategory| |#3| (QUOTE (-174))) (-2892 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-562))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1064 |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 
@@ -4219,7 +4219,7 @@ NIL
 (-1072) 
 ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2340) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2340 (-52))) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1073 S R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
@@ -4287,7 +4287,7 @@ NIL
 (-1089 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."))) 
 ((-4445 |has| |#1| (-368)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-354))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-373))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-354)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368))))) 
 (-1090 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 
@@ -4315,7 +4315,7 @@ NIL
 (-1096 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"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1097 (-1186)) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-235))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1097 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 
@@ -4375,7 +4375,7 @@ NIL
 (-1111 S) 
 ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) 
 ((-4452 . T) (-4442 . T) (-4453 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-1112 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
@@ -4419,7 +4419,7 @@ NIL
 (-1122 |dimtot| |dim1| S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
 ((-4446 |has| |#3| (-1058)) (-4447 |has| |#3| (-1058)) (-4449 |has| |#3| (-6 -4449)) ((-4454 "*") |has| |#3| (-174)) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#3| (QUOTE (-368))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-799))) (-2895 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854)))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-732))) (-2895 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-235))) (-2895 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasCategory| |#3| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-25)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-132)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-235)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-373)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-732)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-799)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-854)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109))))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2895 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) 
+((-2892 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#3| (QUOTE (-368))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-368)))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-799))) (-2892 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854)))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-732))) (-2892 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-1058)))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (|HasCategory| |#3| (QUOTE (-235))) (-2892 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasCategory| |#3| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-25)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-132)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-235)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-368)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-373)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-732)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-799)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-854)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109))))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-799))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-854))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (|HasCategory| (-570) (QUOTE (-856))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (QUOTE (-235))) (|HasCategory| |#3| (QUOTE (-1058)))) (-12 (|HasCategory| |#3| (QUOTE (-1058))) (|HasCategory| |#3| (LIST (QUOTE -907) (QUOTE (-1186))))) (-2892 (|HasCategory| |#3| (QUOTE (-1058))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570)))))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#3| (QUOTE (-1109)))) (|HasAttribute| |#3| (QUOTE -4449)) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#3| (QUOTE (-1109))) (|HasCategory| |#3| (LIST (QUOTE -313) (|devaluate| |#3|))))) 
 (-1123 R |x|) 
 ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) 
 NIL 
@@ -4467,11 +4467,11 @@ NIL
 (-1134 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."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1135 |Coef| |Var| SMP) 
 ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) 
 (-1136 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}"))) 
 ((-4453 . T) (-4452 . T)) 
@@ -4531,11 +4531,11 @@ NIL
 (-1150 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2895 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))) (-2892 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -313) (LIST (QUOTE -1149) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1149 |#1| |#2|) (QUOTE (-1109))))) (|HasCategory| (-1149 |#1| |#2|) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1151 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
 ((-4449 . T) (-4441 |has| |#2| (-6 (-4454 "*"))) (-4452 . T) (-4446 . T) (-4447 . T)) 
-((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2895 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
+((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (-12 (|HasCategory| |#2| (QUOTE (-235))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-368))) (-2892 (|HasAttribute| |#2| (QUOTE (-4454 "*"))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) 
 (-1152 S) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
@@ -4555,7 +4555,7 @@ NIL
 (-1156 S) 
 ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1157 A S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
@@ -4567,7 +4567,7 @@ NIL
 (-1159 |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."))) 
 ((-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-856))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109)))) 
 (-1160) 
 ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
@@ -4595,7 +4595,7 @@ NIL
 (-1166 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) 
 ((-4453 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1167) 
 ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) 
 ((-4453 . T) (-4452 . T)) 
@@ -4603,11 +4603,11 @@ NIL
 (-1168) 
 NIL 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
+((-2892 (-12 (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| (-145) (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-145) (QUOTE (-1109))) (|HasCategory| (-145) (LIST (QUOTE -313) (QUOTE (-145)))))) 
 (-1169 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2340 |#1|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1170 A) 
 ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) 
 NIL 
@@ -4638,8 +4638,8 @@ NIL
 NIL 
 (-1177 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-4454 "*") -2895 (-1810 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1810 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4445 -2895 (-1810 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1810 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-148)))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368))))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(((-4454 "*") -2892 (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4445 -2892 (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1809 (|has| |#1| (-368)) (|has| (-1184 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-148)))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368))))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1184) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1184 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1178 R -1709) 
 ((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) 
 NIL 
@@ -4659,15 +4659,15 @@ NIL
 (-1182 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."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4448 |has| |#1| (-368)) (-4450 |has| |#1| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+((|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#1| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1161))) (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-235))) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1183 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-1184 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-1185) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
@@ -4683,7 +4683,7 @@ NIL
 (-1188 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-6 -4450)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4450))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-458))) (-12 (|HasCategory| (-980) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasAttribute| |#1| (QUOTE -4450))) 
 (-1189) 
 ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) 
 NIL 
@@ -4727,7 +4727,7 @@ NIL
 (-1199 |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}"))) 
 ((-4452 . T) (-4453 . T)) 
-((-12 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2107) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2895 (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2107 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2340) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2340 |#2|)) (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1200 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 
@@ -4783,7 +4783,7 @@ NIL
 (-1213 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
 ((-4453 . T) (-4452 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
 (-1214 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
@@ -4815,7 +4815,7 @@ NIL
 (-1221 |Coef|) 
 ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-368)))) 
 (-1222 |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 
@@ -4891,11 +4891,11 @@ NIL
 (-1240 |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)}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-146))))) (-2895 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-148))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856))))) (-2895 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-916))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-146)))))) 
+((-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-146))))) (-2892 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-148))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-235)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856))))) (-2892 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-826)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1031)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-1186)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -290) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -520) (QUOTE (-1186)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-916))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-551)))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-146)))))) 
 (-1241 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
-(((-4454 "*") -2895 (-1810 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1810 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-916)))) (-4445 -2895 (-1810 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1810 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-148)))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368))))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) 
+(((-4454 "*") -2892 (-1809 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-826))) (|has| |#1| (-174)) (-1809 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-916)))) (-4445 -2892 (-1809 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-826))) (|has| |#1| (-562)) (-1809 (|has| |#1| (-368)) (|has| (-1269 |#1| |#2| |#3|) (-916)))) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
+((-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-148)))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|)))))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-235))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-570)) (|devaluate| |#1|))))) (|HasCategory| (-570) (QUOTE (-1121))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1031))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368))))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-1161))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -290) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -313) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -520) (QUOTE (-1186)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-570))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-551))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-146))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-826))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1242 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 
@@ -4931,7 +4931,7 @@ NIL
 (-1250 |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}"))) 
 (((-4454 "*") |has| |#2| (-174)) (-4445 |has| |#2| (-562)) (-4448 |has| |#2| (-368)) (-4450 |has| |#2| (-6 -4450)) (-4447 . T) (-4446 . T) (-4449 . T)) 
-((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2895 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2895 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2895 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
+((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-174))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-562)))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-384)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-384))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -893) (QUOTE (-570)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-570))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-384)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -620) (LIST (QUOTE -899) (QUOTE (-570)))))) (-12 (|HasCategory| (-1091) (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#2| (LIST (QUOTE -620) (QUOTE (-542))))) (|HasCategory| |#2| (LIST (QUOTE -645) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (QUOTE (-570)))) (-2892 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| |#2| (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (-2892 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-562))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-458))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-1161))) (|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasCategory| |#2| (QUOTE (-235))) (|HasAttribute| |#2| (QUOTE -4450)) (|HasCategory| |#2| (QUOTE (-458))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (-2892 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-916)))) (|HasCategory| |#2| (QUOTE (-146))))) 
 (-1251 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 
@@ -4975,15 +4975,15 @@ NIL
 (-1261 |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)}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) 
+((|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) 
 (-1262 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4450 |has| |#1| (-368)) (-4444 |has| |#1| (-368)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2895 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (|HasCategory| |#1| (QUOTE (-174))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570))) (|devaluate| |#1|)))) (|HasCategory| (-413 (-570)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-2892 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-562)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -413) (QUOTE (-570)))))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-1263 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))}."))) 
 (((-4454 "*") |has| (-1262 |#2| |#3| |#4|) (-174)) (-4445 |has| (-1262 |#2| |#3| |#4|) (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2895 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) 
+((|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-174))) (-2892 (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570)))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| (-1262 |#2| |#3| |#4|) (LIST (QUOTE -1047) (QUOTE (-570)))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-368))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-458))) (|HasCategory| (-1262 |#2| |#3| |#4|) (QUOTE (-562)))) 
 (-1264 A S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
@@ -4999,7 +4999,7 @@ NIL
 (-1267 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2023) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#2| (QUOTE (-966))) (|HasCategory| |#2| (QUOTE (-1212))) (|HasSignature| |#2| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3170) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1186))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#2| (QUOTE (-368)))) 
 (-1268 |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."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
@@ -5007,7 +5007,7 @@ NIL
 (-1269 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2895 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2895 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -2023) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasCategory| |#1| (QUOTE (-562))) (-2892 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-777)) (|devaluate| |#1|)))) (|HasCategory| (-777) (QUOTE (-1121))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasSignature| |#1| (LIST (QUOTE -3802) (LIST (|devaluate| |#1|) (QUOTE (-1186)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-777))))) (|HasCategory| |#1| (QUOTE (-368))) (-2892 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-570)))) (|HasCategory| |#1| (QUOTE (-966))) (|HasCategory| |#1| (QUOTE (-1212))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -413) (QUOTE (-570))))) (|HasSignature| |#1| (LIST (QUOTE -3170) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1755) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#1|))))))) 
 (-1270 |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 
@@ -5039,7 +5039,7 @@ NIL
 (-1277 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."))) 
 ((-4453 . T) (-4452 . T)) 
-((-2895 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2895 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2895 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
+((-2892 (-12 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (-2892 (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#1| (QUOTE (-1058))) (-12 (|HasCategory| |#1| (QUOTE (-1011))) (|HasCategory| |#1| (QUOTE (-1058)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-1278) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
@@ -5172,4 +5172,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2268669 2268674 2268679 2268684) (-2 NIL 2268649 2268654 2268659 2268664) (-1 NIL 2268629 2268634 2268639 2268644) (0 NIL 2268609 2268614 2268619 2268624) (-1306 "ZMOD.spad" 2268418 2268431 2268547 2268604) (-1305 "ZLINDEP.spad" 2267484 2267495 2268408 2268413) (-1304 "ZDSOLVE.spad" 2257429 2257451 2267474 2267479) (-1303 "YSTREAM.spad" 2256924 2256935 2257419 2257424) (-1302 "YDIAGRAM.spad" 2256558 2256567 2256914 2256919) (-1301 "XRPOLY.spad" 2255778 2255798 2256414 2256483) (-1300 "XPR.spad" 2253573 2253586 2255496 2255595) (-1299 "XPOLY.spad" 2253128 2253139 2253429 2253498) (-1298 "XPOLYC.spad" 2252447 2252463 2253054 2253123) (-1297 "XPBWPOLY.spad" 2250884 2250904 2252227 2252296) (-1296 "XF.spad" 2249347 2249362 2250786 2250879) (-1295 "XF.spad" 2247790 2247807 2249231 2249236) (-1294 "XFALG.spad" 2244838 2244854 2247716 2247785) (-1293 "XEXPPKG.spad" 2244089 2244115 2244828 2244833) (-1292 "XDPOLY.spad" 2243703 2243719 2243945 2244014) (-1291 "XALG.spad" 2243363 2243374 2243659 2243698) (-1290 "WUTSET.spad" 2239202 2239219 2243009 2243036) (-1289 "WP.spad" 2238401 2238445 2239060 2239127) (-1288 "WHILEAST.spad" 2238199 2238208 2238391 2238396) (-1287 "WHEREAST.spad" 2237870 2237879 2238189 2238194) (-1286 "WFFINTBS.spad" 2235533 2235555 2237860 2237865) (-1285 "WEIER.spad" 2233755 2233766 2235523 2235528) (-1284 "VSPACE.spad" 2233428 2233439 2233723 2233750) (-1283 "VSPACE.spad" 2233121 2233134 2233418 2233423) (-1282 "VOID.spad" 2232798 2232807 2233111 2233116) (-1281 "VIEW.spad" 2230478 2230487 2232788 2232793) (-1280 "VIEWDEF.spad" 2225679 2225688 2230468 2230473) (-1279 "VIEW3D.spad" 2209640 2209649 2225669 2225674) (-1278 "VIEW2D.spad" 2197531 2197540 2209630 2209635) (-1277 "VECTOR.spad" 2196205 2196216 2196456 2196483) (-1276 "VECTOR2.spad" 2194844 2194857 2196195 2196200) (-1275 "VECTCAT.spad" 2192748 2192759 2194812 2194839) (-1274 "VECTCAT.spad" 2190459 2190472 2192525 2192530) (-1273 "VARIABLE.spad" 2190239 2190254 2190449 2190454) (-1272 "UTYPE.spad" 2189883 2189892 2190229 2190234) (-1271 "UTSODETL.spad" 2189178 2189202 2189839 2189844) (-1270 "UTSODE.spad" 2187394 2187414 2189168 2189173) (-1269 "UTS.spad" 2182198 2182226 2185861 2185958) (-1268 "UTSCAT.spad" 2179677 2179693 2182096 2182193) (-1267 "UTSCAT.spad" 2176800 2176818 2179221 2179226) (-1266 "UTS2.spad" 2176395 2176430 2176790 2176795) (-1265 "URAGG.spad" 2171068 2171079 2176385 2176390) (-1264 "URAGG.spad" 2165705 2165718 2171024 2171029) (-1263 "UPXSSING.spad" 2163350 2163376 2164786 2164919) (-1262 "UPXS.spad" 2160504 2160532 2161482 2161631) (-1261 "UPXSCONS.spad" 2158263 2158283 2158636 2158785) (-1260 "UPXSCCA.spad" 2156834 2156854 2158109 2158258) (-1259 "UPXSCCA.spad" 2155547 2155569 2156824 2156829) (-1258 "UPXSCAT.spad" 2154136 2154152 2155393 2155542) (-1257 "UPXS2.spad" 2153679 2153732 2154126 2154131) (-1256 "UPSQFREE.spad" 2152093 2152107 2153669 2153674) (-1255 "UPSCAT.spad" 2149704 2149728 2151991 2152088) (-1254 "UPSCAT.spad" 2147021 2147047 2149310 2149315) (-1253 "UPOLYC.spad" 2142061 2142072 2146863 2147016) (-1252 "UPOLYC.spad" 2136993 2137006 2141797 2141802) (-1251 "UPOLYC2.spad" 2136464 2136483 2136983 2136988) (-1250 "UP.spad" 2133663 2133678 2134050 2134203) (-1249 "UPMP.spad" 2132563 2132576 2133653 2133658) (-1248 "UPDIVP.spad" 2132128 2132142 2132553 2132558) (-1247 "UPDECOMP.spad" 2130373 2130387 2132118 2132123) (-1246 "UPCDEN.spad" 2129582 2129598 2130363 2130368) (-1245 "UP2.spad" 2128946 2128967 2129572 2129577) (-1244 "UNISEG.spad" 2128299 2128310 2128865 2128870) (-1243 "UNISEG2.spad" 2127796 2127809 2128255 2128260) (-1242 "UNIFACT.spad" 2126899 2126911 2127786 2127791) (-1241 "ULS.spad" 2117457 2117485 2118544 2118973) (-1240 "ULSCONS.spad" 2109853 2109873 2110223 2110372) (-1239 "ULSCCAT.spad" 2107590 2107610 2109699 2109848) (-1238 "ULSCCAT.spad" 2105435 2105457 2107546 2107551) (-1237 "ULSCAT.spad" 2103667 2103683 2105281 2105430) (-1236 "ULS2.spad" 2103181 2103234 2103657 2103662) (-1235 "UINT8.spad" 2103058 2103067 2103171 2103176) (-1234 "UINT64.spad" 2102934 2102943 2103048 2103053) (-1233 "UINT32.spad" 2102810 2102819 2102924 2102929) (-1232 "UINT16.spad" 2102686 2102695 2102800 2102805) (-1231 "UFD.spad" 2101751 2101760 2102612 2102681) (-1230 "UFD.spad" 2100878 2100889 2101741 2101746) (-1229 "UDVO.spad" 2099759 2099768 2100868 2100873) (-1228 "UDPO.spad" 2097252 2097263 2099715 2099720) (-1227 "TYPE.spad" 2097184 2097193 2097242 2097247) (-1226 "TYPEAST.spad" 2097103 2097112 2097174 2097179) (-1225 "TWOFACT.spad" 2095755 2095770 2097093 2097098) (-1224 "TUPLE.spad" 2095241 2095252 2095654 2095659) (-1223 "TUBETOOL.spad" 2092108 2092117 2095231 2095236) (-1222 "TUBE.spad" 2090755 2090772 2092098 2092103) (-1221 "TS.spad" 2089354 2089370 2090320 2090417) (-1220 "TSETCAT.spad" 2076481 2076498 2089322 2089349) (-1219 "TSETCAT.spad" 2063594 2063613 2076437 2076442) (-1218 "TRMANIP.spad" 2057960 2057977 2063300 2063305) (-1217 "TRIMAT.spad" 2056923 2056948 2057950 2057955) (-1216 "TRIGMNIP.spad" 2055450 2055467 2056913 2056918) (-1215 "TRIGCAT.spad" 2054962 2054971 2055440 2055445) (-1214 "TRIGCAT.spad" 2054472 2054483 2054952 2054957) (-1213 "TREE.spad" 2053047 2053058 2054079 2054106) (-1212 "TRANFUN.spad" 2052886 2052895 2053037 2053042) (-1211 "TRANFUN.spad" 2052723 2052734 2052876 2052881) (-1210 "TOPSP.spad" 2052397 2052406 2052713 2052718) (-1209 "TOOLSIGN.spad" 2052060 2052071 2052387 2052392) (-1208 "TEXTFILE.spad" 2050621 2050630 2052050 2052055) (-1207 "TEX.spad" 2047767 2047776 2050611 2050616) (-1206 "TEX1.spad" 2047323 2047334 2047757 2047762) (-1205 "TEMUTL.spad" 2046878 2046887 2047313 2047318) (-1204 "TBCMPPK.spad" 2044971 2044994 2046868 2046873) (-1203 "TBAGG.spad" 2044021 2044044 2044951 2044966) (-1202 "TBAGG.spad" 2043079 2043104 2044011 2044016) (-1201 "TANEXP.spad" 2042487 2042498 2043069 2043074) (-1200 "TALGOP.spad" 2042211 2042222 2042477 2042482) (-1199 "TABLE.spad" 2040622 2040645 2040892 2040919) (-1198 "TABLEAU.spad" 2040103 2040114 2040612 2040617) (-1197 "TABLBUMP.spad" 2036906 2036917 2040093 2040098) (-1196 "SYSTEM.spad" 2036134 2036143 2036896 2036901) (-1195 "SYSSOLP.spad" 2033617 2033628 2036124 2036129) (-1194 "SYSPTR.spad" 2033516 2033525 2033607 2033612) (-1193 "SYSNNI.spad" 2032698 2032709 2033506 2033511) (-1192 "SYSINT.spad" 2032102 2032113 2032688 2032693) (-1191 "SYNTAX.spad" 2028308 2028317 2032092 2032097) (-1190 "SYMTAB.spad" 2026376 2026385 2028298 2028303) (-1189 "SYMS.spad" 2022399 2022408 2026366 2026371) (-1188 "SYMPOLY.spad" 2021406 2021417 2021488 2021615) (-1187 "SYMFUNC.spad" 2020907 2020918 2021396 2021401) (-1186 "SYMBOL.spad" 2018410 2018419 2020897 2020902) (-1185 "SWITCH.spad" 2015181 2015190 2018400 2018405) (-1184 "SUTS.spad" 2012086 2012114 2013648 2013745) (-1183 "SUPXS.spad" 2009227 2009255 2010218 2010367) (-1182 "SUP.spad" 2006040 2006051 2006813 2006966) (-1181 "SUPFRACF.spad" 2005145 2005163 2006030 2006035) (-1180 "SUP2.spad" 2004537 2004550 2005135 2005140) (-1179 "SUMRF.spad" 2003511 2003522 2004527 2004532) (-1178 "SUMFS.spad" 2003148 2003165 2003501 2003506) (-1177 "SULS.spad" 1993693 1993721 1994793 1995222) (-1176 "SUCHTAST.spad" 1993462 1993471 1993683 1993688) (-1175 "SUCH.spad" 1993144 1993159 1993452 1993457) (-1174 "SUBSPACE.spad" 1985259 1985274 1993134 1993139) (-1173 "SUBRESP.spad" 1984429 1984443 1985215 1985220) (-1172 "STTF.spad" 1980528 1980544 1984419 1984424) (-1171 "STTFNC.spad" 1976996 1977012 1980518 1980523) (-1170 "STTAYLOR.spad" 1969631 1969642 1976877 1976882) (-1169 "STRTBL.spad" 1968136 1968153 1968285 1968312) (-1168 "STRING.spad" 1967545 1967554 1967559 1967586) (-1167 "STRICAT.spad" 1967333 1967342 1967513 1967540) (-1166 "STREAM.spad" 1964251 1964262 1966858 1966873) (-1165 "STREAM3.spad" 1963824 1963839 1964241 1964246) (-1164 "STREAM2.spad" 1962952 1962965 1963814 1963819) (-1163 "STREAM1.spad" 1962658 1962669 1962942 1962947) (-1162 "STINPROD.spad" 1961594 1961610 1962648 1962653) (-1161 "STEP.spad" 1960795 1960804 1961584 1961589) (-1160 "STEPAST.spad" 1960029 1960038 1960785 1960790) (-1159 "STBL.spad" 1958555 1958583 1958722 1958737) (-1158 "STAGG.spad" 1957630 1957641 1958545 1958550) (-1157 "STAGG.spad" 1956703 1956716 1957620 1957625) (-1156 "STACK.spad" 1956060 1956071 1956310 1956337) (-1155 "SREGSET.spad" 1953764 1953781 1955706 1955733) (-1154 "SRDCMPK.spad" 1952325 1952345 1953754 1953759) (-1153 "SRAGG.spad" 1947468 1947477 1952293 1952320) (-1152 "SRAGG.spad" 1942631 1942642 1947458 1947463) (-1151 "SQMATRIX.spad" 1940247 1940265 1941163 1941250) (-1150 "SPLTREE.spad" 1934799 1934812 1939683 1939710) (-1149 "SPLNODE.spad" 1931387 1931400 1934789 1934794) (-1148 "SPFCAT.spad" 1930196 1930205 1931377 1931382) (-1147 "SPECOUT.spad" 1928748 1928757 1930186 1930191) (-1146 "SPADXPT.spad" 1920343 1920352 1928738 1928743) (-1145 "spad-parser.spad" 1919808 1919817 1920333 1920338) (-1144 "SPADAST.spad" 1919509 1919518 1919798 1919803) (-1143 "SPACEC.spad" 1903708 1903719 1919499 1919504) (-1142 "SPACE3.spad" 1903484 1903495 1903698 1903703) (-1141 "SORTPAK.spad" 1903033 1903046 1903440 1903445) (-1140 "SOLVETRA.spad" 1900796 1900807 1903023 1903028) (-1139 "SOLVESER.spad" 1899324 1899335 1900786 1900791) (-1138 "SOLVERAD.spad" 1895350 1895361 1899314 1899319) (-1137 "SOLVEFOR.spad" 1893812 1893830 1895340 1895345) (-1136 "SNTSCAT.spad" 1893412 1893429 1893780 1893807) (-1135 "SMTS.spad" 1891684 1891710 1892977 1893074) (-1134 "SMP.spad" 1889159 1889179 1889549 1889676) (-1133 "SMITH.spad" 1888004 1888029 1889149 1889154) (-1132 "SMATCAT.spad" 1886114 1886144 1887948 1887999) (-1131 "SMATCAT.spad" 1884156 1884188 1885992 1885997) (-1130 "SKAGG.spad" 1883119 1883130 1884124 1884151) (-1129 "SINT.spad" 1882059 1882068 1882985 1883114) (-1128 "SIMPAN.spad" 1881787 1881796 1882049 1882054) (-1127 "SIG.spad" 1881117 1881126 1881777 1881782) (-1126 "SIGNRF.spad" 1880235 1880246 1881107 1881112) (-1125 "SIGNEF.spad" 1879514 1879531 1880225 1880230) (-1124 "SIGAST.spad" 1878899 1878908 1879504 1879509) (-1123 "SHP.spad" 1876827 1876842 1878855 1878860) (-1122 "SHDP.spad" 1866538 1866565 1867047 1867178) (-1121 "SGROUP.spad" 1866146 1866155 1866528 1866533) (-1120 "SGROUP.spad" 1865752 1865763 1866136 1866141) (-1119 "SGCF.spad" 1858891 1858900 1865742 1865747) (-1118 "SFRTCAT.spad" 1857821 1857838 1858859 1858886) (-1117 "SFRGCD.spad" 1856884 1856904 1857811 1857816) (-1116 "SFQCMPK.spad" 1851521 1851541 1856874 1856879) (-1115 "SFORT.spad" 1850960 1850974 1851511 1851516) (-1114 "SEXOF.spad" 1850803 1850843 1850950 1850955) (-1113 "SEX.spad" 1850695 1850704 1850793 1850798) (-1112 "SEXCAT.spad" 1848296 1848336 1850685 1850690) (-1111 "SET.spad" 1846620 1846631 1847717 1847756) (-1110 "SETMN.spad" 1845070 1845087 1846610 1846615) (-1109 "SETCAT.spad" 1844392 1844401 1845060 1845065) (-1108 "SETCAT.spad" 1843712 1843723 1844382 1844387) (-1107 "SETAGG.spad" 1840261 1840272 1843692 1843707) (-1106 "SETAGG.spad" 1836818 1836831 1840251 1840256) (-1105 "SEQAST.spad" 1836521 1836530 1836808 1836813) (-1104 "SEGXCAT.spad" 1835677 1835690 1836511 1836516) (-1103 "SEG.spad" 1835490 1835501 1835596 1835601) (-1102 "SEGCAT.spad" 1834415 1834426 1835480 1835485) (-1101 "SEGBIND.spad" 1834173 1834184 1834362 1834367) (-1100 "SEGBIND2.spad" 1833871 1833884 1834163 1834168) (-1099 "SEGAST.spad" 1833585 1833594 1833861 1833866) (-1098 "SEG2.spad" 1833020 1833033 1833541 1833546) (-1097 "SDVAR.spad" 1832296 1832307 1833010 1833015) (-1096 "SDPOL.spad" 1829722 1829733 1830013 1830140) (-1095 "SCPKG.spad" 1827811 1827822 1829712 1829717) (-1094 "SCOPE.spad" 1826964 1826973 1827801 1827806) (-1093 "SCACHE.spad" 1825660 1825671 1826954 1826959) (-1092 "SASTCAT.spad" 1825569 1825578 1825650 1825655) (-1091 "SAOS.spad" 1825441 1825450 1825559 1825564) (-1090 "SAERFFC.spad" 1825154 1825174 1825431 1825436) (-1089 "SAE.spad" 1823329 1823345 1823940 1824075) (-1088 "SAEFACT.spad" 1823030 1823050 1823319 1823324) (-1087 "RURPK.spad" 1820689 1820705 1823020 1823025) (-1086 "RULESET.spad" 1820142 1820166 1820679 1820684) (-1085 "RULE.spad" 1818382 1818406 1820132 1820137) (-1084 "RULECOLD.spad" 1818234 1818247 1818372 1818377) (-1083 "RTVALUE.spad" 1817969 1817978 1818224 1818229) (-1082 "RSTRCAST.spad" 1817686 1817695 1817959 1817964) (-1081 "RSETGCD.spad" 1814064 1814084 1817676 1817681) (-1080 "RSETCAT.spad" 1804000 1804017 1814032 1814059) (-1079 "RSETCAT.spad" 1793956 1793975 1803990 1803995) (-1078 "RSDCMPK.spad" 1792408 1792428 1793946 1793951) (-1077 "RRCC.spad" 1790792 1790822 1792398 1792403) (-1076 "RRCC.spad" 1789174 1789206 1790782 1790787) (-1075 "RPTAST.spad" 1788876 1788885 1789164 1789169) (-1074 "RPOLCAT.spad" 1768236 1768251 1788744 1788871) (-1073 "RPOLCAT.spad" 1747309 1747326 1767819 1767824) (-1072 "ROUTINE.spad" 1743192 1743201 1745956 1745983) (-1071 "ROMAN.spad" 1742520 1742529 1743058 1743187) (-1070 "ROIRC.spad" 1741600 1741632 1742510 1742515) (-1069 "RNS.spad" 1740503 1740512 1741502 1741595) (-1068 "RNS.spad" 1739492 1739503 1740493 1740498) (-1067 "RNG.spad" 1739227 1739236 1739482 1739487) (-1066 "RNGBIND.spad" 1738387 1738401 1739182 1739187) (-1065 "RMODULE.spad" 1738152 1738163 1738377 1738382) (-1064 "RMCAT2.spad" 1737572 1737629 1738142 1738147) (-1063 "RMATRIX.spad" 1736396 1736415 1736739 1736778) (-1062 "RMATCAT.spad" 1731975 1732006 1736352 1736391) (-1061 "RMATCAT.spad" 1727444 1727477 1731823 1731828) (-1060 "RLINSET.spad" 1726838 1726849 1727434 1727439) (-1059 "RINTERP.spad" 1726726 1726746 1726828 1726833) (-1058 "RING.spad" 1726196 1726205 1726706 1726721) (-1057 "RING.spad" 1725674 1725685 1726186 1726191) (-1056 "RIDIST.spad" 1725066 1725075 1725664 1725669) (-1055 "RGCHAIN.spad" 1723649 1723665 1724551 1724578) (-1054 "RGBCSPC.spad" 1723430 1723442 1723639 1723644) (-1053 "RGBCMDL.spad" 1722960 1722972 1723420 1723425) (-1052 "RF.spad" 1720602 1720613 1722950 1722955) (-1051 "RFFACTOR.spad" 1720064 1720075 1720592 1720597) (-1050 "RFFACT.spad" 1719799 1719811 1720054 1720059) (-1049 "RFDIST.spad" 1718795 1718804 1719789 1719794) (-1048 "RETSOL.spad" 1718214 1718227 1718785 1718790) (-1047 "RETRACT.spad" 1717642 1717653 1718204 1718209) (-1046 "RETRACT.spad" 1717068 1717081 1717632 1717637) (-1045 "RETAST.spad" 1716880 1716889 1717058 1717063) (-1044 "RESULT.spad" 1714940 1714949 1715527 1715554) (-1043 "RESRING.spad" 1714287 1714334 1714878 1714935) (-1042 "RESLATC.spad" 1713611 1713622 1714277 1714282) (-1041 "REPSQ.spad" 1713342 1713353 1713601 1713606) (-1040 "REP.spad" 1710896 1710905 1713332 1713337) (-1039 "REPDB.spad" 1710603 1710614 1710886 1710891) (-1038 "REP2.spad" 1700261 1700272 1710445 1710450) (-1037 "REP1.spad" 1694457 1694468 1700211 1700216) (-1036 "REGSET.spad" 1692254 1692271 1694103 1694130) (-1035 "REF.spad" 1691589 1691600 1692209 1692214) (-1034 "REDORDER.spad" 1690795 1690812 1691579 1691584) (-1033 "RECLOS.spad" 1689578 1689598 1690282 1690375) (-1032 "REALSOLV.spad" 1688718 1688727 1689568 1689573) (-1031 "REAL.spad" 1688590 1688599 1688708 1688713) (-1030 "REAL0Q.spad" 1685888 1685903 1688580 1688585) (-1029 "REAL0.spad" 1682732 1682747 1685878 1685883) (-1028 "RDUCEAST.spad" 1682453 1682462 1682722 1682727) (-1027 "RDIV.spad" 1682108 1682133 1682443 1682448) (-1026 "RDIST.spad" 1681675 1681686 1682098 1682103) (-1025 "RDETRS.spad" 1680539 1680557 1681665 1681670) (-1024 "RDETR.spad" 1678678 1678696 1680529 1680534) (-1023 "RDEEFS.spad" 1677777 1677794 1678668 1678673) (-1022 "RDEEF.spad" 1676787 1676804 1677767 1677772) (-1021 "RCFIELD.spad" 1673973 1673982 1676689 1676782) (-1020 "RCFIELD.spad" 1671245 1671256 1673963 1673968) (-1019 "RCAGG.spad" 1669173 1669184 1671235 1671240) (-1018 "RCAGG.spad" 1667028 1667041 1669092 1669097) (-1017 "RATRET.spad" 1666388 1666399 1667018 1667023) (-1016 "RATFACT.spad" 1666080 1666092 1666378 1666383) (-1015 "RANDSRC.spad" 1665399 1665408 1666070 1666075) (-1014 "RADUTIL.spad" 1665155 1665164 1665389 1665394) (-1013 "RADIX.spad" 1662076 1662090 1663622 1663715) (-1012 "RADFF.spad" 1660489 1660526 1660608 1660764) (-1011 "RADCAT.spad" 1660084 1660093 1660479 1660484) (-1010 "RADCAT.spad" 1659677 1659688 1660074 1660079) (-1009 "QUEUE.spad" 1659025 1659036 1659284 1659311) (-1008 "QUAT.spad" 1657606 1657617 1657949 1658014) (-1007 "QUATCT2.spad" 1657226 1657245 1657596 1657601) (-1006 "QUATCAT.spad" 1655396 1655407 1657156 1657221) (-1005 "QUATCAT.spad" 1653317 1653330 1655079 1655084) (-1004 "QUAGG.spad" 1652144 1652155 1653285 1653312) (-1003 "QQUTAST.spad" 1651912 1651921 1652134 1652139) (-1002 "QFORM.spad" 1651376 1651391 1651902 1651907) (-1001 "QFCAT.spad" 1650078 1650089 1651278 1651371) (-1000 "QFCAT.spad" 1648371 1648384 1649573 1649578) (-999 "QFCAT2.spad" 1648064 1648080 1648361 1648366) (-998 "QEQUAT.spad" 1647623 1647631 1648054 1648059) (-997 "QCMPACK.spad" 1642370 1642389 1647613 1647618) (-996 "QALGSET.spad" 1638449 1638481 1642284 1642289) (-995 "QALGSET2.spad" 1636445 1636463 1638439 1638444) (-994 "PWFFINTB.spad" 1633861 1633882 1636435 1636440) (-993 "PUSHVAR.spad" 1633200 1633219 1633851 1633856) (-992 "PTRANFN.spad" 1629328 1629338 1633190 1633195) (-991 "PTPACK.spad" 1626416 1626426 1629318 1629323) (-990 "PTFUNC2.spad" 1626239 1626253 1626406 1626411) (-989 "PTCAT.spad" 1625494 1625504 1626207 1626234) (-988 "PSQFR.spad" 1624801 1624825 1625484 1625489) (-987 "PSEUDLIN.spad" 1623687 1623697 1624791 1624796) (-986 "PSETPK.spad" 1609120 1609136 1623565 1623570) (-985 "PSETCAT.spad" 1603040 1603063 1609100 1609115) (-984 "PSETCAT.spad" 1596934 1596959 1602996 1603001) (-983 "PSCURVE.spad" 1595917 1595925 1596924 1596929) (-982 "PSCAT.spad" 1594700 1594729 1595815 1595912) (-981 "PSCAT.spad" 1593573 1593604 1594690 1594695) (-980 "PRTITION.spad" 1592658 1592666 1593563 1593568) (-979 "PRTDAST.spad" 1592377 1592385 1592648 1592653) (-978 "PRS.spad" 1581939 1581956 1592333 1592338) (-977 "PRQAGG.spad" 1581374 1581384 1581907 1581934) (-976 "PROPLOG.spad" 1580946 1580954 1581364 1581369) (-975 "PROPFUN2.spad" 1580569 1580582 1580936 1580941) (-974 "PROPFUN1.spad" 1579967 1579978 1580559 1580564) (-973 "PROPFRML.spad" 1578535 1578546 1579957 1579962) (-972 "PROPERTY.spad" 1578023 1578031 1578525 1578530) (-971 "PRODUCT.spad" 1575705 1575717 1575989 1576044) (-970 "PR.spad" 1574097 1574109 1574796 1574923) (-969 "PRINT.spad" 1573849 1573857 1574087 1574092) (-968 "PRIMES.spad" 1572102 1572112 1573839 1573844) (-967 "PRIMELT.spad" 1570183 1570197 1572092 1572097) (-966 "PRIMCAT.spad" 1569810 1569818 1570173 1570178) (-965 "PRIMARR.spad" 1568815 1568825 1568993 1569020) (-964 "PRIMARR2.spad" 1567582 1567594 1568805 1568810) (-963 "PREASSOC.spad" 1566964 1566976 1567572 1567577) (-962 "PPCURVE.spad" 1566101 1566109 1566954 1566959) (-961 "PORTNUM.spad" 1565876 1565884 1566091 1566096) (-960 "POLYROOT.spad" 1564725 1564747 1565832 1565837) (-959 "POLY.spad" 1562060 1562070 1562575 1562702) (-958 "POLYLIFT.spad" 1561325 1561348 1562050 1562055) (-957 "POLYCATQ.spad" 1559443 1559465 1561315 1561320) (-956 "POLYCAT.spad" 1552913 1552934 1559311 1559438) (-955 "POLYCAT.spad" 1545721 1545744 1552121 1552126) (-954 "POLY2UP.spad" 1545173 1545187 1545711 1545716) (-953 "POLY2.spad" 1544770 1544782 1545163 1545168) (-952 "POLUTIL.spad" 1543711 1543740 1544726 1544731) (-951 "POLTOPOL.spad" 1542459 1542474 1543701 1543706) (-950 "POINT.spad" 1541297 1541307 1541384 1541411) (-949 "PNTHEORY.spad" 1537999 1538007 1541287 1541292) (-948 "PMTOOLS.spad" 1536774 1536788 1537989 1537994) (-947 "PMSYM.spad" 1536323 1536333 1536764 1536769) (-946 "PMQFCAT.spad" 1535914 1535928 1536313 1536318) (-945 "PMPRED.spad" 1535393 1535407 1535904 1535909) (-944 "PMPREDFS.spad" 1534847 1534869 1535383 1535388) (-943 "PMPLCAT.spad" 1533927 1533945 1534779 1534784) (-942 "PMLSAGG.spad" 1533512 1533526 1533917 1533922) (-941 "PMKERNEL.spad" 1533091 1533103 1533502 1533507) (-940 "PMINS.spad" 1532671 1532681 1533081 1533086) (-939 "PMFS.spad" 1532248 1532266 1532661 1532666) (-938 "PMDOWN.spad" 1531538 1531552 1532238 1532243) (-937 "PMASS.spad" 1530548 1530556 1531528 1531533) (-936 "PMASSFS.spad" 1529515 1529531 1530538 1530543) (-935 "PLOTTOOL.spad" 1529295 1529303 1529505 1529510) (-934 "PLOT.spad" 1524218 1524226 1529285 1529290) (-933 "PLOT3D.spad" 1520682 1520690 1524208 1524213) (-932 "PLOT1.spad" 1519839 1519849 1520672 1520677) (-931 "PLEQN.spad" 1507129 1507156 1519829 1519834) (-930 "PINTERP.spad" 1506751 1506770 1507119 1507124) (-929 "PINTERPA.spad" 1506535 1506551 1506741 1506746) (-928 "PI.spad" 1506144 1506152 1506509 1506530) (-927 "PID.spad" 1505114 1505122 1506070 1506139) (-926 "PICOERCE.spad" 1504771 1504781 1505104 1505109) (-925 "PGROEB.spad" 1503372 1503386 1504761 1504766) (-924 "PGE.spad" 1494989 1494997 1503362 1503367) (-923 "PGCD.spad" 1493879 1493896 1494979 1494984) (-922 "PFRPAC.spad" 1493028 1493038 1493869 1493874) (-921 "PFR.spad" 1489691 1489701 1492930 1493023) (-920 "PFOTOOLS.spad" 1488949 1488965 1489681 1489686) (-919 "PFOQ.spad" 1488319 1488337 1488939 1488944) (-918 "PFO.spad" 1487738 1487765 1488309 1488314) (-917 "PF.spad" 1487312 1487324 1487543 1487636) (-916 "PFECAT.spad" 1484994 1485002 1487238 1487307) (-915 "PFECAT.spad" 1482704 1482714 1484950 1484955) (-914 "PFBRU.spad" 1480592 1480604 1482694 1482699) (-913 "PFBR.spad" 1478152 1478175 1480582 1480587) (-912 "PERM.spad" 1473837 1473847 1477982 1477997) (-911 "PERMGRP.spad" 1468599 1468609 1473827 1473832) (-910 "PERMCAT.spad" 1467157 1467167 1468579 1468594) (-909 "PERMAN.spad" 1465689 1465703 1467147 1467152) (-908 "PENDTREE.spad" 1465030 1465040 1465318 1465323) (-907 "PDRING.spad" 1463581 1463591 1465010 1465025) (-906 "PDRING.spad" 1462140 1462152 1463571 1463576) (-905 "PDEPROB.spad" 1461155 1461163 1462130 1462135) (-904 "PDEPACK.spad" 1455195 1455203 1461145 1461150) (-903 "PDECOMP.spad" 1454665 1454682 1455185 1455190) (-902 "PDECAT.spad" 1453021 1453029 1454655 1454660) (-901 "PCOMP.spad" 1452874 1452887 1453011 1453016) (-900 "PBWLB.spad" 1451462 1451479 1452864 1452869) (-899 "PATTERN.spad" 1446001 1446011 1451452 1451457) (-898 "PATTERN2.spad" 1445739 1445751 1445991 1445996) (-897 "PATTERN1.spad" 1444075 1444091 1445729 1445734) (-896 "PATRES.spad" 1441650 1441662 1444065 1444070) (-895 "PATRES2.spad" 1441322 1441336 1441640 1441645) (-894 "PATMATCH.spad" 1439519 1439550 1441030 1441035) (-893 "PATMAB.spad" 1438948 1438958 1439509 1439514) (-892 "PATLRES.spad" 1438034 1438048 1438938 1438943) (-891 "PATAB.spad" 1437798 1437808 1438024 1438029) (-890 "PARTPERM.spad" 1435076 1435084 1437788 1437793) (-889 "PARSURF.spad" 1434510 1434538 1435066 1435071) (-888 "PARSU2.spad" 1434307 1434323 1434500 1434505) (-887 "script-parser.spad" 1433827 1433835 1434297 1434302) (-886 "PARSCURV.spad" 1433261 1433289 1433817 1433822) (-885 "PARSC2.spad" 1433052 1433068 1433251 1433256) (-884 "PARPCURV.spad" 1432514 1432542 1433042 1433047) (-883 "PARPC2.spad" 1432305 1432321 1432504 1432509) (-882 "PARAMAST.spad" 1431433 1431441 1432295 1432300) (-881 "PAN2EXPR.spad" 1430845 1430853 1431423 1431428) (-880 "PALETTE.spad" 1429815 1429823 1430835 1430840) (-879 "PAIR.spad" 1428802 1428815 1429403 1429408) (-878 "PADICRC.spad" 1426136 1426154 1427307 1427400) (-877 "PADICRAT.spad" 1424151 1424163 1424372 1424465) (-876 "PADIC.spad" 1423846 1423858 1424077 1424146) (-875 "PADICCT.spad" 1422395 1422407 1423772 1423841) (-874 "PADEPAC.spad" 1421084 1421103 1422385 1422390) (-873 "PADE.spad" 1419836 1419852 1421074 1421079) (-872 "OWP.spad" 1419076 1419106 1419694 1419761) (-871 "OVERSET.spad" 1418649 1418657 1419066 1419071) (-870 "OVAR.spad" 1418430 1418453 1418639 1418644) (-869 "OUT.spad" 1417516 1417524 1418420 1418425) (-868 "OUTFORM.spad" 1406908 1406916 1417506 1417511) (-867 "OUTBFILE.spad" 1406326 1406334 1406898 1406903) (-866 "OUTBCON.spad" 1405332 1405340 1406316 1406321) (-865 "OUTBCON.spad" 1404336 1404346 1405322 1405327) (-864 "OSI.spad" 1403811 1403819 1404326 1404331) (-863 "OSGROUP.spad" 1403729 1403737 1403801 1403806) (-862 "ORTHPOL.spad" 1402214 1402224 1403646 1403651) (-861 "OREUP.spad" 1401667 1401695 1401894 1401933) (-860 "ORESUP.spad" 1400968 1400992 1401347 1401386) (-859 "OREPCTO.spad" 1398825 1398837 1400888 1400893) (-858 "OREPCAT.spad" 1392972 1392982 1398781 1398820) (-857 "OREPCAT.spad" 1387009 1387021 1392820 1392825) (-856 "ORDSET.spad" 1386181 1386189 1386999 1387004) (-855 "ORDSET.spad" 1385351 1385361 1386171 1386176) (-854 "ORDRING.spad" 1384741 1384749 1385331 1385346) (-853 "ORDRING.spad" 1384139 1384149 1384731 1384736) (-852 "ORDMON.spad" 1383994 1384002 1384129 1384134) (-851 "ORDFUNS.spad" 1383126 1383142 1383984 1383989) (-850 "ORDFIN.spad" 1382946 1382954 1383116 1383121) (-849 "ORDCOMP.spad" 1381411 1381421 1382493 1382522) (-848 "ORDCOMP2.spad" 1380704 1380716 1381401 1381406) (-847 "OPTPROB.spad" 1379342 1379350 1380694 1380699) (-846 "OPTPACK.spad" 1371751 1371759 1379332 1379337) (-845 "OPTCAT.spad" 1369430 1369438 1371741 1371746) (-844 "OPSIG.spad" 1369084 1369092 1369420 1369425) (-843 "OPQUERY.spad" 1368633 1368641 1369074 1369079) (-842 "OP.spad" 1368375 1368385 1368455 1368522) (-841 "OPERCAT.spad" 1367841 1367851 1368365 1368370) (-840 "OPERCAT.spad" 1367305 1367317 1367831 1367836) (-839 "ONECOMP.spad" 1366050 1366060 1366852 1366881) (-838 "ONECOMP2.spad" 1365474 1365486 1366040 1366045) (-837 "OMSERVER.spad" 1364480 1364488 1365464 1365469) (-836 "OMSAGG.spad" 1364268 1364278 1364436 1364475) (-835 "OMPKG.spad" 1362884 1362892 1364258 1364263) (-834 "OM.spad" 1361857 1361865 1362874 1362879) (-833 "OMLO.spad" 1361282 1361294 1361743 1361782) (-832 "OMEXPR.spad" 1361116 1361126 1361272 1361277) (-831 "OMERR.spad" 1360661 1360669 1361106 1361111) (-830 "OMERRK.spad" 1359695 1359703 1360651 1360656) (-829 "OMENC.spad" 1359039 1359047 1359685 1359690) (-828 "OMDEV.spad" 1353348 1353356 1359029 1359034) (-827 "OMCONN.spad" 1352757 1352765 1353338 1353343) (-826 "OINTDOM.spad" 1352520 1352528 1352683 1352752) (-825 "OFMONOID.spad" 1350643 1350653 1352476 1352481) (-824 "ODVAR.spad" 1349904 1349914 1350633 1350638) (-823 "ODR.spad" 1349548 1349574 1349716 1349865) (-822 "ODPOL.spad" 1346930 1346940 1347270 1347397) (-821 "ODP.spad" 1336777 1336797 1337150 1337281) (-820 "ODETOOLS.spad" 1335426 1335445 1336767 1336772) (-819 "ODESYS.spad" 1333120 1333137 1335416 1335421) (-818 "ODERTRIC.spad" 1329129 1329146 1333077 1333082) (-817 "ODERED.spad" 1328528 1328552 1329119 1329124) (-816 "ODERAT.spad" 1326143 1326160 1328518 1328523) (-815 "ODEPRRIC.spad" 1323180 1323202 1326133 1326138) (-814 "ODEPROB.spad" 1322437 1322445 1323170 1323175) (-813 "ODEPRIM.spad" 1319771 1319793 1322427 1322432) (-812 "ODEPAL.spad" 1319157 1319181 1319761 1319766) (-811 "ODEPACK.spad" 1305823 1305831 1319147 1319152) (-810 "ODEINT.spad" 1305258 1305274 1305813 1305818) (-809 "ODEIFTBL.spad" 1302653 1302661 1305248 1305253) (-808 "ODEEF.spad" 1298144 1298160 1302643 1302648) (-807 "ODECONST.spad" 1297681 1297699 1298134 1298139) (-806 "ODECAT.spad" 1296279 1296287 1297671 1297676) (-805 "OCT.spad" 1294415 1294425 1295129 1295168) (-804 "OCTCT2.spad" 1294061 1294082 1294405 1294410) (-803 "OC.spad" 1291857 1291867 1294017 1294056) (-802 "OC.spad" 1289378 1289390 1291540 1291545) (-801 "OCAMON.spad" 1289226 1289234 1289368 1289373) (-800 "OASGP.spad" 1289041 1289049 1289216 1289221) (-799 "OAMONS.spad" 1288563 1288571 1289031 1289036) (-798 "OAMON.spad" 1288424 1288432 1288553 1288558) (-797 "OAGROUP.spad" 1288286 1288294 1288414 1288419) (-796 "NUMTUBE.spad" 1287877 1287893 1288276 1288281) (-795 "NUMQUAD.spad" 1275853 1275861 1287867 1287872) (-794 "NUMODE.spad" 1267207 1267215 1275843 1275848) (-793 "NUMINT.spad" 1264773 1264781 1267197 1267202) (-792 "NUMFMT.spad" 1263613 1263621 1264763 1264768) (-791 "NUMERIC.spad" 1255727 1255737 1263418 1263423) (-790 "NTSCAT.spad" 1254235 1254251 1255695 1255722) (-789 "NTPOLFN.spad" 1253786 1253796 1254152 1254157) (-788 "NSUP.spad" 1246832 1246842 1251372 1251525) (-787 "NSUP2.spad" 1246224 1246236 1246822 1246827) (-786 "NSMP.spad" 1242454 1242473 1242762 1242889) (-785 "NREP.spad" 1240832 1240846 1242444 1242449) (-784 "NPCOEF.spad" 1240078 1240098 1240822 1240827) (-783 "NORMRETR.spad" 1239676 1239715 1240068 1240073) (-782 "NORMPK.spad" 1237578 1237597 1239666 1239671) (-781 "NORMMA.spad" 1237266 1237292 1237568 1237573) (-780 "NONE.spad" 1237007 1237015 1237256 1237261) (-779 "NONE1.spad" 1236683 1236693 1236997 1237002) (-778 "NODE1.spad" 1236170 1236186 1236673 1236678) (-777 "NNI.spad" 1235065 1235073 1236144 1236165) (-776 "NLINSOL.spad" 1233691 1233701 1235055 1235060) (-775 "NIPROB.spad" 1232232 1232240 1233681 1233686) (-774 "NFINTBAS.spad" 1229792 1229809 1232222 1232227) (-773 "NETCLT.spad" 1229766 1229777 1229782 1229787) (-772 "NCODIV.spad" 1227982 1227998 1229756 1229761) (-771 "NCNTFRAC.spad" 1227624 1227638 1227972 1227977) (-770 "NCEP.spad" 1225790 1225804 1227614 1227619) (-769 "NASRING.spad" 1225386 1225394 1225780 1225785) (-768 "NASRING.spad" 1224980 1224990 1225376 1225381) (-767 "NARNG.spad" 1224332 1224340 1224970 1224975) (-766 "NARNG.spad" 1223682 1223692 1224322 1224327) (-765 "NAGSP.spad" 1222759 1222767 1223672 1223677) (-764 "NAGS.spad" 1212420 1212428 1222749 1222754) (-763 "NAGF07.spad" 1210851 1210859 1212410 1212415) (-762 "NAGF04.spad" 1205253 1205261 1210841 1210846) (-761 "NAGF02.spad" 1199322 1199330 1205243 1205248) (-760 "NAGF01.spad" 1195083 1195091 1199312 1199317) (-759 "NAGE04.spad" 1188783 1188791 1195073 1195078) (-758 "NAGE02.spad" 1179443 1179451 1188773 1188778) (-757 "NAGE01.spad" 1175445 1175453 1179433 1179438) (-756 "NAGD03.spad" 1173449 1173457 1175435 1175440) (-755 "NAGD02.spad" 1166196 1166204 1173439 1173444) (-754 "NAGD01.spad" 1160489 1160497 1166186 1166191) (-753 "NAGC06.spad" 1156364 1156372 1160479 1160484) (-752 "NAGC05.spad" 1154865 1154873 1156354 1156359) (-751 "NAGC02.spad" 1154132 1154140 1154855 1154860) (-750 "NAALG.spad" 1153673 1153683 1154100 1154127) (-749 "NAALG.spad" 1153234 1153246 1153663 1153668) (-748 "MULTSQFR.spad" 1150192 1150209 1153224 1153229) (-747 "MULTFACT.spad" 1149575 1149592 1150182 1150187) (-746 "MTSCAT.spad" 1147669 1147690 1149473 1149570) (-745 "MTHING.spad" 1147328 1147338 1147659 1147664) (-744 "MSYSCMD.spad" 1146762 1146770 1147318 1147323) (-743 "MSET.spad" 1144720 1144730 1146468 1146507) (-742 "MSETAGG.spad" 1144565 1144575 1144688 1144715) (-741 "MRING.spad" 1141542 1141554 1144273 1144340) (-740 "MRF2.spad" 1141112 1141126 1141532 1141537) (-739 "MRATFAC.spad" 1140658 1140675 1141102 1141107) (-738 "MPRFF.spad" 1138698 1138717 1140648 1140653) (-737 "MPOLY.spad" 1136169 1136184 1136528 1136655) (-736 "MPCPF.spad" 1135433 1135452 1136159 1136164) (-735 "MPC3.spad" 1135250 1135290 1135423 1135428) (-734 "MPC2.spad" 1134896 1134929 1135240 1135245) (-733 "MONOTOOL.spad" 1133247 1133264 1134886 1134891) (-732 "MONOID.spad" 1132566 1132574 1133237 1133242) (-731 "MONOID.spad" 1131883 1131893 1132556 1132561) (-730 "MONOGEN.spad" 1130631 1130644 1131743 1131878) (-729 "MONOGEN.spad" 1129401 1129416 1130515 1130520) (-728 "MONADWU.spad" 1127431 1127439 1129391 1129396) (-727 "MONADWU.spad" 1125459 1125469 1127421 1127426) (-726 "MONAD.spad" 1124619 1124627 1125449 1125454) (-725 "MONAD.spad" 1123777 1123787 1124609 1124614) (-724 "MOEBIUS.spad" 1122513 1122527 1123757 1123772) (-723 "MODULE.spad" 1122383 1122393 1122481 1122508) (-722 "MODULE.spad" 1122273 1122285 1122373 1122378) (-721 "MODRING.spad" 1121608 1121647 1122253 1122268) (-720 "MODOP.spad" 1120273 1120285 1121430 1121497) (-719 "MODMONOM.spad" 1120004 1120022 1120263 1120268) (-718 "MODMON.spad" 1116799 1116815 1117518 1117671) (-717 "MODFIELD.spad" 1116161 1116200 1116701 1116794) (-716 "MMLFORM.spad" 1115021 1115029 1116151 1116156) (-715 "MMAP.spad" 1114763 1114797 1115011 1115016) (-714 "MLO.spad" 1113222 1113232 1114719 1114758) (-713 "MLIFT.spad" 1111834 1111851 1113212 1113217) (-712 "MKUCFUNC.spad" 1111369 1111387 1111824 1111829) (-711 "MKRECORD.spad" 1110973 1110986 1111359 1111364) (-710 "MKFUNC.spad" 1110380 1110390 1110963 1110968) (-709 "MKFLCFN.spad" 1109348 1109358 1110370 1110375) (-708 "MKBCFUNC.spad" 1108843 1108861 1109338 1109343) (-707 "MINT.spad" 1108282 1108290 1108745 1108838) (-706 "MHROWRED.spad" 1106793 1106803 1108272 1108277) (-705 "MFLOAT.spad" 1105313 1105321 1106683 1106788) (-704 "MFINFACT.spad" 1104713 1104735 1105303 1105308) (-703 "MESH.spad" 1102495 1102503 1104703 1104708) (-702 "MDDFACT.spad" 1100706 1100716 1102485 1102490) (-701 "MDAGG.spad" 1099997 1100007 1100686 1100701) (-700 "MCMPLX.spad" 1096008 1096016 1096622 1096823) (-699 "MCDEN.spad" 1095218 1095230 1095998 1096003) (-698 "MCALCFN.spad" 1092340 1092366 1095208 1095213) (-697 "MAYBE.spad" 1091624 1091635 1092330 1092335) (-696 "MATSTOR.spad" 1088932 1088942 1091614 1091619) (-695 "MATRIX.spad" 1087636 1087646 1088120 1088147) (-694 "MATLIN.spad" 1084980 1085004 1087520 1087525) (-693 "MATCAT.spad" 1076709 1076731 1084948 1084975) (-692 "MATCAT.spad" 1068310 1068334 1076551 1076556) (-691 "MATCAT2.spad" 1067592 1067640 1068300 1068305) (-690 "MAPPKG3.spad" 1066507 1066521 1067582 1067587) (-689 "MAPPKG2.spad" 1065845 1065857 1066497 1066502) (-688 "MAPPKG1.spad" 1064673 1064683 1065835 1065840) (-687 "MAPPAST.spad" 1063988 1063996 1064663 1064668) (-686 "MAPHACK3.spad" 1063800 1063814 1063978 1063983) (-685 "MAPHACK2.spad" 1063569 1063581 1063790 1063795) (-684 "MAPHACK1.spad" 1063213 1063223 1063559 1063564) (-683 "MAGMA.spad" 1061003 1061020 1063203 1063208) (-682 "MACROAST.spad" 1060582 1060590 1060993 1060998) (-681 "M3D.spad" 1058302 1058312 1059960 1059965) (-680 "LZSTAGG.spad" 1055540 1055550 1058292 1058297) (-679 "LZSTAGG.spad" 1052776 1052788 1055530 1055535) (-678 "LWORD.spad" 1049481 1049498 1052766 1052771) (-677 "LSTAST.spad" 1049265 1049273 1049471 1049476) (-676 "LSQM.spad" 1047495 1047509 1047889 1047940) (-675 "LSPP.spad" 1047030 1047047 1047485 1047490) (-674 "LSMP.spad" 1045880 1045908 1047020 1047025) (-673 "LSMP1.spad" 1043698 1043712 1045870 1045875) (-672 "LSAGG.spad" 1043367 1043377 1043666 1043693) (-671 "LSAGG.spad" 1043056 1043068 1043357 1043362) (-670 "LPOLY.spad" 1042010 1042029 1042912 1042981) (-669 "LPEFRAC.spad" 1041281 1041291 1042000 1042005) (-668 "LO.spad" 1040682 1040696 1041215 1041242) (-667 "LOGIC.spad" 1040284 1040292 1040672 1040677) (-666 "LOGIC.spad" 1039884 1039894 1040274 1040279) (-665 "LODOOPS.spad" 1038814 1038826 1039874 1039879) (-664 "LODO.spad" 1038198 1038214 1038494 1038533) (-663 "LODOF.spad" 1037244 1037261 1038155 1038160) (-662 "LODOCAT.spad" 1035910 1035920 1037200 1037239) (-661 "LODOCAT.spad" 1034574 1034586 1035866 1035871) (-660 "LODO2.spad" 1033847 1033859 1034254 1034293) (-659 "LODO1.spad" 1033247 1033257 1033527 1033566) (-658 "LODEEF.spad" 1032049 1032067 1033237 1033242) (-657 "LNAGG.spad" 1027881 1027891 1032039 1032044) (-656 "LNAGG.spad" 1023677 1023689 1027837 1027842) (-655 "LMOPS.spad" 1020445 1020462 1023667 1023672) (-654 "LMODULE.spad" 1020213 1020223 1020435 1020440) (-653 "LMDICT.spad" 1019500 1019510 1019764 1019791) (-652 "LLINSET.spad" 1018897 1018907 1019490 1019495) (-651 "LITERAL.spad" 1018803 1018814 1018887 1018892) (-650 "LIST.spad" 1016538 1016548 1017950 1017977) (-649 "LIST3.spad" 1015849 1015863 1016528 1016533) (-648 "LIST2.spad" 1014551 1014563 1015839 1015844) (-647 "LIST2MAP.spad" 1011454 1011466 1014541 1014546) (-646 "LINSET.spad" 1011076 1011086 1011444 1011449) (-645 "LINEXP.spad" 1010510 1010520 1011056 1011071) (-644 "LINDEP.spad" 1009319 1009331 1010422 1010427) (-643 "LIMITRF.spad" 1007247 1007257 1009309 1009314) (-642 "LIMITPS.spad" 1006150 1006163 1007237 1007242) (-641 "LIE.spad" 1004166 1004178 1005440 1005585) (-640 "LIECAT.spad" 1003642 1003652 1004092 1004161) (-639 "LIECAT.spad" 1003146 1003158 1003598 1003603) (-638 "LIB.spad" 1001196 1001204 1001805 1001820) (-637 "LGROBP.spad" 998549 998568 1001186 1001191) (-636 "LF.spad" 997504 997520 998539 998544) (-635 "LFCAT.spad" 996563 996571 997494 997499) (-634 "LEXTRIPK.spad" 992066 992081 996553 996558) (-633 "LEXP.spad" 990069 990096 992046 992061) (-632 "LETAST.spad" 989768 989776 990059 990064) (-631 "LEADCDET.spad" 988166 988183 989758 989763) (-630 "LAZM3PK.spad" 986870 986892 988156 988161) (-629 "LAUPOL.spad" 985563 985576 986463 986532) (-628 "LAPLACE.spad" 985146 985162 985553 985558) (-627 "LA.spad" 984586 984600 985068 985107) (-626 "LALG.spad" 984362 984372 984566 984581) (-625 "LALG.spad" 984146 984158 984352 984357) (-624 "KVTFROM.spad" 983881 983891 984136 984141) (-623 "KTVLOGIC.spad" 983393 983401 983871 983876) (-622 "KRCFROM.spad" 983131 983141 983383 983388) (-621 "KOVACIC.spad" 981854 981871 983121 983126) (-620 "KONVERT.spad" 981576 981586 981844 981849) (-619 "KOERCE.spad" 981313 981323 981566 981571) (-618 "KERNEL.spad" 979968 979978 981097 981102) (-617 "KERNEL2.spad" 979671 979683 979958 979963) (-616 "KDAGG.spad" 978780 978802 979651 979666) (-615 "KDAGG.spad" 977897 977921 978770 978775) (-614 "KAFILE.spad" 976860 976876 977095 977122) (-613 "JORDAN.spad" 974689 974701 976150 976295) (-612 "JOINAST.spad" 974383 974391 974679 974684) (-611 "JAVACODE.spad" 974249 974257 974373 974378) (-610 "IXAGG.spad" 972382 972406 974239 974244) (-609 "IXAGG.spad" 970370 970396 972229 972234) (-608 "IVECTOR.spad" 969140 969155 969295 969322) (-607 "ITUPLE.spad" 968301 968311 969130 969135) (-606 "ITRIGMNP.spad" 967140 967159 968291 968296) (-605 "ITFUN3.spad" 966646 966660 967130 967135) (-604 "ITFUN2.spad" 966390 966402 966636 966641) (-603 "ITFORM.spad" 965745 965753 966380 966385) (-602 "ITAYLOR.spad" 963739 963754 965609 965706) (-601 "ISUPS.spad" 956176 956191 962713 962810) (-600 "ISUMP.spad" 955677 955693 956166 956171) (-599 "ISTRING.spad" 954765 954778 954846 954873) (-598 "ISAST.spad" 954484 954492 954755 954760) (-597 "IRURPK.spad" 953201 953220 954474 954479) (-596 "IRSN.spad" 951173 951181 953191 953196) (-595 "IRRF2F.spad" 949658 949668 951129 951134) (-594 "IRREDFFX.spad" 949259 949270 949648 949653) (-593 "IROOT.spad" 947598 947608 949249 949254) (-592 "IR.spad" 945399 945413 947453 947480) (-591 "IRFORM.spad" 944723 944731 945389 945394) (-590 "IR2.spad" 943751 943767 944713 944718) (-589 "IR2F.spad" 942957 942973 943741 943746) (-588 "IPRNTPK.spad" 942717 942725 942947 942952) (-587 "IPF.spad" 942282 942294 942522 942615) (-586 "IPADIC.spad" 942043 942069 942208 942277) (-585 "IP4ADDR.spad" 941600 941608 942033 942038) (-584 "IOMODE.spad" 941122 941130 941590 941595) (-583 "IOBFILE.spad" 940483 940491 941112 941117) (-582 "IOBCON.spad" 940348 940356 940473 940478) (-581 "INVLAPLA.spad" 939997 940013 940338 940343) (-580 "INTTR.spad" 933379 933396 939987 939992) (-579 "INTTOOLS.spad" 931134 931150 932953 932958) (-578 "INTSLPE.spad" 930454 930462 931124 931129) (-577 "INTRVL.spad" 930020 930030 930368 930449) (-576 "INTRF.spad" 928444 928458 930010 930015) (-575 "INTRET.spad" 927876 927886 928434 928439) (-574 "INTRAT.spad" 926603 926620 927866 927871) (-573 "INTPM.spad" 924988 925004 926246 926251) (-572 "INTPAF.spad" 922852 922870 924920 924925) (-571 "INTPACK.spad" 913226 913234 922842 922847) (-570 "INT.spad" 912674 912682 913080 913221) (-569 "INTHERTR.spad" 911948 911965 912664 912669) (-568 "INTHERAL.spad" 911618 911642 911938 911943) (-567 "INTHEORY.spad" 908057 908065 911608 911613) (-566 "INTG0.spad" 901790 901808 907989 907994) (-565 "INTFTBL.spad" 895819 895827 901780 901785) (-564 "INTFACT.spad" 894878 894888 895809 895814) (-563 "INTEF.spad" 893263 893279 894868 894873) (-562 "INTDOM.spad" 891886 891894 893189 893258) (-561 "INTDOM.spad" 890571 890581 891876 891881) (-560 "INTCAT.spad" 888830 888840 890485 890566) (-559 "INTBIT.spad" 888337 888345 888820 888825) (-558 "INTALG.spad" 887525 887552 888327 888332) (-557 "INTAF.spad" 887025 887041 887515 887520) (-556 "INTABL.spad" 885543 885574 885706 885733) (-555 "INT8.spad" 885423 885431 885533 885538) (-554 "INT64.spad" 885302 885310 885413 885418) (-553 "INT32.spad" 885181 885189 885292 885297) (-552 "INT16.spad" 885060 885068 885171 885176) (-551 "INS.spad" 882563 882571 884962 885055) (-550 "INS.spad" 880152 880162 882553 882558) (-549 "INPSIGN.spad" 879600 879613 880142 880147) (-548 "INPRODPF.spad" 878696 878715 879590 879595) (-547 "INPRODFF.spad" 877784 877808 878686 878691) (-546 "INNMFACT.spad" 876759 876776 877774 877779) (-545 "INMODGCD.spad" 876247 876277 876749 876754) (-544 "INFSP.spad" 874544 874566 876237 876242) (-543 "INFPROD0.spad" 873624 873643 874534 874539) (-542 "INFORM.spad" 870823 870831 873614 873619) (-541 "INFORM1.spad" 870448 870458 870813 870818) (-540 "INFINITY.spad" 870000 870008 870438 870443) (-539 "INETCLTS.spad" 869977 869985 869990 869995) (-538 "INEP.spad" 868515 868537 869967 869972) (-537 "INDE.spad" 868244 868261 868505 868510) (-536 "INCRMAPS.spad" 867665 867675 868234 868239) (-535 "INBFILE.spad" 866737 866745 867655 867660) (-534 "INBFF.spad" 862531 862542 866727 866732) (-533 "INBCON.spad" 860821 860829 862521 862526) (-532 "INBCON.spad" 859109 859119 860811 860816) (-531 "INAST.spad" 858770 858778 859099 859104) (-530 "IMPTAST.spad" 858478 858486 858760 858765) (-529 "IMATRIX.spad" 857423 857449 857935 857962) (-528 "IMATQF.spad" 856517 856561 857379 857384) (-527 "IMATLIN.spad" 855122 855146 856473 856478) (-526 "ILIST.spad" 853780 853795 854305 854332) (-525 "IIARRAY2.spad" 853168 853206 853387 853414) (-524 "IFF.spad" 852578 852594 852849 852942) (-523 "IFAST.spad" 852192 852200 852568 852573) (-522 "IFARRAY.spad" 849685 849700 851375 851402) (-521 "IFAMON.spad" 849547 849564 849641 849646) (-520 "IEVALAB.spad" 848952 848964 849537 849542) (-519 "IEVALAB.spad" 848355 848369 848942 848947) (-518 "IDPO.spad" 848153 848165 848345 848350) (-517 "IDPOAMS.spad" 847909 847921 848143 848148) (-516 "IDPOAM.spad" 847629 847641 847899 847904) (-515 "IDPC.spad" 846567 846579 847619 847624) (-514 "IDPAM.spad" 846312 846324 846557 846562) (-513 "IDPAG.spad" 846059 846071 846302 846307) (-512 "IDENT.spad" 845709 845717 846049 846054) (-511 "IDECOMP.spad" 842948 842966 845699 845704) (-510 "IDEAL.spad" 837897 837936 842883 842888) (-509 "ICDEN.spad" 837086 837102 837887 837892) (-508 "ICARD.spad" 836277 836285 837076 837081) (-507 "IBPTOOLS.spad" 834884 834901 836267 836272) (-506 "IBITS.spad" 834087 834100 834520 834547) (-505 "IBATOOL.spad" 831064 831083 834077 834082) (-504 "IBACHIN.spad" 829571 829586 831054 831059) (-503 "IARRAY2.spad" 828559 828585 829178 829205) (-502 "IARRAY1.spad" 827604 827619 827742 827769) (-501 "IAN.spad" 825827 825835 827420 827513) (-500 "IALGFACT.spad" 825430 825463 825817 825822) (-499 "HYPCAT.spad" 824854 824862 825420 825425) (-498 "HYPCAT.spad" 824276 824286 824844 824849) (-497 "HOSTNAME.spad" 824084 824092 824266 824271) (-496 "HOMOTOP.spad" 823827 823837 824074 824079) (-495 "HOAGG.spad" 821109 821119 823817 823822) (-494 "HOAGG.spad" 818166 818178 820876 820881) (-493 "HEXADEC.spad" 816268 816276 816633 816726) (-492 "HEUGCD.spad" 815303 815314 816258 816263) (-491 "HELLFDIV.spad" 814893 814917 815293 815298) (-490 "HEAP.spad" 814285 814295 814500 814527) (-489 "HEADAST.spad" 813818 813826 814275 814280) (-488 "HDP.spad" 803661 803677 804038 804169) (-487 "HDMP.spad" 800875 800890 801491 801618) (-486 "HB.spad" 799126 799134 800865 800870) (-485 "HASHTBL.spad" 797596 797627 797807 797834) (-484 "HASAST.spad" 797312 797320 797586 797591) (-483 "HACKPI.spad" 796803 796811 797214 797307) (-482 "GTSET.spad" 795742 795758 796449 796476) (-481 "GSTBL.spad" 794261 794296 794435 794450) (-480 "GSERIES.spad" 791432 791459 792393 792542) (-479 "GROUP.spad" 790705 790713 791412 791427) (-478 "GROUP.spad" 789986 789996 790695 790700) (-477 "GROEBSOL.spad" 788480 788501 789976 789981) (-476 "GRMOD.spad" 787051 787063 788470 788475) (-475 "GRMOD.spad" 785620 785634 787041 787046) (-474 "GRIMAGE.spad" 778509 778517 785610 785615) (-473 "GRDEF.spad" 776888 776896 778499 778504) (-472 "GRAY.spad" 775351 775359 776878 776883) (-471 "GRALG.spad" 774428 774440 775341 775346) (-470 "GRALG.spad" 773503 773517 774418 774423) (-469 "GPOLSET.spad" 772957 772980 773185 773212) (-468 "GOSPER.spad" 772226 772244 772947 772952) (-467 "GMODPOL.spad" 771374 771401 772194 772221) (-466 "GHENSEL.spad" 770457 770471 771364 771369) (-465 "GENUPS.spad" 766750 766763 770447 770452) (-464 "GENUFACT.spad" 766327 766337 766740 766745) (-463 "GENPGCD.spad" 765913 765930 766317 766322) (-462 "GENMFACT.spad" 765365 765384 765903 765908) (-461 "GENEEZ.spad" 763316 763329 765355 765360) (-460 "GDMP.spad" 760372 760389 761146 761273) (-459 "GCNAALG.spad" 754295 754322 760166 760233) (-458 "GCDDOM.spad" 753471 753479 754221 754290) (-457 "GCDDOM.spad" 752709 752719 753461 753466) (-456 "GB.spad" 750235 750273 752665 752670) (-455 "GBINTERN.spad" 746255 746293 750225 750230) (-454 "GBF.spad" 742022 742060 746245 746250) (-453 "GBEUCLID.spad" 739904 739942 742012 742017) (-452 "GAUSSFAC.spad" 739217 739225 739894 739899) (-451 "GALUTIL.spad" 737543 737553 739173 739178) (-450 "GALPOLYU.spad" 735997 736010 737533 737538) (-449 "GALFACTU.spad" 734170 734189 735987 735992) (-448 "GALFACT.spad" 724359 724370 734160 734165) (-447 "FVFUN.spad" 721382 721390 724349 724354) (-446 "FVC.spad" 720434 720442 721372 721377) (-445 "FUNDESC.spad" 720112 720120 720424 720429) (-444 "FUNCTION.spad" 719961 719973 720102 720107) (-443 "FT.spad" 718258 718266 719951 719956) (-442 "FTEM.spad" 717423 717431 718248 718253) (-441 "FSUPFACT.spad" 716323 716342 717359 717364) (-440 "FST.spad" 714409 714417 716313 716318) (-439 "FSRED.spad" 713889 713905 714399 714404) (-438 "FSPRMELT.spad" 712771 712787 713846 713851) (-437 "FSPECF.spad" 710862 710878 712761 712766) (-436 "FS.spad" 705130 705140 710637 710857) (-435 "FS.spad" 699176 699188 704685 704690) (-434 "FSINT.spad" 698836 698852 699166 699171) (-433 "FSERIES.spad" 698027 698039 698656 698755) (-432 "FSCINT.spad" 697344 697360 698017 698022) (-431 "FSAGG.spad" 696461 696471 697300 697339) (-430 "FSAGG.spad" 695540 695552 696381 696386) (-429 "FSAGG2.spad" 694283 694299 695530 695535) (-428 "FS2UPS.spad" 688774 688808 694273 694278) (-427 "FS2.spad" 688421 688437 688764 688769) (-426 "FS2EXPXP.spad" 687546 687569 688411 688416) (-425 "FRUTIL.spad" 686500 686510 687536 687541) (-424 "FR.spad" 680216 680226 685524 685593) (-423 "FRNAALG.spad" 675335 675345 680158 680211) (-422 "FRNAALG.spad" 670466 670478 675291 675296) (-421 "FRNAAF2.spad" 669922 669940 670456 670461) (-420 "FRMOD.spad" 669332 669362 669853 669858) (-419 "FRIDEAL.spad" 668557 668578 669312 669327) (-418 "FRIDEAL2.spad" 668161 668193 668547 668552) (-417 "FRETRCT.spad" 667672 667682 668151 668156) (-416 "FRETRCT.spad" 667049 667061 667530 667535) (-415 "FRAMALG.spad" 665397 665410 667005 667044) (-414 "FRAMALG.spad" 663777 663792 665387 665392) (-413 "FRAC.spad" 660876 660886 661279 661452) (-412 "FRAC2.spad" 660481 660493 660866 660871) (-411 "FR2.spad" 659817 659829 660471 660476) (-410 "FPS.spad" 656632 656640 659707 659812) (-409 "FPS.spad" 653475 653485 656552 656557) (-408 "FPC.spad" 652521 652529 653377 653470) (-407 "FPC.spad" 651653 651663 652511 652516) (-406 "FPATMAB.spad" 651415 651425 651643 651648) (-405 "FPARFRAC.spad" 649902 649919 651405 651410) (-404 "FORTRAN.spad" 648408 648451 649892 649897) (-403 "FORT.spad" 647357 647365 648398 648403) (-402 "FORTFN.spad" 644527 644535 647347 647352) (-401 "FORTCAT.spad" 644211 644219 644517 644522) (-400 "FORMULA.spad" 641685 641693 644201 644206) (-399 "FORMULA1.spad" 641164 641174 641675 641680) (-398 "FORDER.spad" 640855 640879 641154 641159) (-397 "FOP.spad" 640056 640064 640845 640850) (-396 "FNLA.spad" 639480 639502 640024 640051) (-395 "FNCAT.spad" 638075 638083 639470 639475) (-394 "FNAME.spad" 637967 637975 638065 638070) (-393 "FMTC.spad" 637765 637773 637893 637962) (-392 "FMONOID.spad" 637430 637440 637721 637726) (-391 "FMONCAT.spad" 634583 634593 637420 637425) (-390 "FM.spad" 634278 634290 634517 634544) (-389 "FMFUN.spad" 631308 631316 634268 634273) (-388 "FMC.spad" 630360 630368 631298 631303) (-387 "FMCAT.spad" 628028 628046 630328 630355) (-386 "FM1.spad" 627385 627397 627962 627989) (-385 "FLOATRP.spad" 625120 625134 627375 627380) (-384 "FLOAT.spad" 618434 618442 624986 625115) (-383 "FLOATCP.spad" 615865 615879 618424 618429) (-382 "FLINEXP.spad" 615577 615587 615845 615860) (-381 "FLINEXP.spad" 615243 615255 615513 615518) (-380 "FLASORT.spad" 614569 614581 615233 615238) (-379 "FLALG.spad" 612215 612234 614495 614564) (-378 "FLAGG.spad" 609257 609267 612195 612210) (-377 "FLAGG.spad" 606200 606212 609140 609145) (-376 "FLAGG2.spad" 604925 604941 606190 606195) (-375 "FINRALG.spad" 602986 602999 604881 604920) (-374 "FINRALG.spad" 600973 600988 602870 602875) (-373 "FINITE.spad" 600125 600133 600963 600968) (-372 "FINAALG.spad" 589246 589256 600067 600120) (-371 "FINAALG.spad" 578379 578391 589202 589207) (-370 "FILE.spad" 577962 577972 578369 578374) (-369 "FILECAT.spad" 576488 576505 577952 577957) (-368 "FIELD.spad" 575894 575902 576390 576483) (-367 "FIELD.spad" 575386 575396 575884 575889) (-366 "FGROUP.spad" 574033 574043 575366 575381) (-365 "FGLMICPK.spad" 572820 572835 574023 574028) (-364 "FFX.spad" 572195 572210 572536 572629) (-363 "FFSLPE.spad" 571698 571719 572185 572190) (-362 "FFPOLY.spad" 562960 562971 571688 571693) (-361 "FFPOLY2.spad" 562020 562037 562950 562955) (-360 "FFP.spad" 561417 561437 561736 561829) (-359 "FF.spad" 560865 560881 561098 561191) (-358 "FFNBX.spad" 559377 559397 560581 560674) (-357 "FFNBP.spad" 557890 557907 559093 559186) (-356 "FFNB.spad" 556355 556376 557571 557664) (-355 "FFINTBAS.spad" 553869 553888 556345 556350) (-354 "FFIELDC.spad" 551446 551454 553771 553864) (-353 "FFIELDC.spad" 549109 549119 551436 551441) (-352 "FFHOM.spad" 547857 547874 549099 549104) (-351 "FFF.spad" 545292 545303 547847 547852) (-350 "FFCGX.spad" 544139 544159 545008 545101) (-349 "FFCGP.spad" 543028 543048 543855 543948) (-348 "FFCG.spad" 541820 541841 542709 542802) (-347 "FFCAT.spad" 534993 535015 541659 541815) (-346 "FFCAT.spad" 528245 528269 534913 534918) (-345 "FFCAT2.spad" 527992 528032 528235 528240) (-344 "FEXPR.spad" 519709 519755 527748 527787) (-343 "FEVALAB.spad" 519417 519427 519699 519704) (-342 "FEVALAB.spad" 518910 518922 519194 519199) (-341 "FDIV.spad" 518352 518376 518900 518905) (-340 "FDIVCAT.spad" 516416 516440 518342 518347) (-339 "FDIVCAT.spad" 514478 514504 516406 516411) (-338 "FDIV2.spad" 514134 514174 514468 514473) (-337 "FCTRDATA.spad" 513142 513150 514124 514129) (-336 "FCPAK1.spad" 511709 511717 513132 513137) (-335 "FCOMP.spad" 511088 511098 511699 511704) (-334 "FC.spad" 501095 501103 511078 511083) (-333 "FAXF.spad" 494066 494080 500997 501090) (-332 "FAXF.spad" 487089 487105 494022 494027) (-331 "FARRAY.spad" 485239 485249 486272 486299) (-330 "FAMR.spad" 483375 483387 485137 485234) (-329 "FAMR.spad" 481495 481509 483259 483264) (-328 "FAMONOID.spad" 481163 481173 481449 481454) (-327 "FAMONC.spad" 479459 479471 481153 481158) (-326 "FAGROUP.spad" 479083 479093 479355 479382) (-325 "FACUTIL.spad" 477287 477304 479073 479078) (-324 "FACTFUNC.spad" 476481 476491 477277 477282) (-323 "EXPUPXS.spad" 473314 473337 474613 474762) (-322 "EXPRTUBE.spad" 470602 470610 473304 473309) (-321 "EXPRODE.spad" 467762 467778 470592 470597) (-320 "EXPR.spad" 463037 463047 463751 464158) (-319 "EXPR2UPS.spad" 459159 459172 463027 463032) (-318 "EXPR2.spad" 458864 458876 459149 459154) (-317 "EXPEXPAN.spad" 455804 455829 456436 456529) (-316 "EXIT.spad" 455475 455483 455794 455799) (-315 "EXITAST.spad" 455211 455219 455465 455470) (-314 "EVALCYC.spad" 454671 454685 455201 455206) (-313 "EVALAB.spad" 454243 454253 454661 454666) (-312 "EVALAB.spad" 453813 453825 454233 454238) (-311 "EUCDOM.spad" 451387 451395 453739 453808) (-310 "EUCDOM.spad" 449023 449033 451377 451382) (-309 "ESTOOLS.spad" 440869 440877 449013 449018) (-308 "ESTOOLS2.spad" 440472 440486 440859 440864) (-307 "ESTOOLS1.spad" 440157 440168 440462 440467) (-306 "ES.spad" 432972 432980 440147 440152) (-305 "ES.spad" 425693 425703 432870 432875) (-304 "ESCONT.spad" 422486 422494 425683 425688) (-303 "ESCONT1.spad" 422235 422247 422476 422481) (-302 "ES2.spad" 421740 421756 422225 422230) (-301 "ES1.spad" 421310 421326 421730 421735) (-300 "ERROR.spad" 418637 418645 421300 421305) (-299 "EQTBL.spad" 417109 417131 417318 417345) (-298 "EQ.spad" 411914 411924 414701 414813) (-297 "EQ2.spad" 411632 411644 411904 411909) (-296 "EP.spad" 407958 407968 411622 411627) (-295 "ENV.spad" 406636 406644 407948 407953) (-294 "ENTIRER.spad" 406304 406312 406580 406631) (-293 "EMR.spad" 405511 405552 406230 406299) (-292 "ELTAGG.spad" 403765 403784 405501 405506) (-291 "ELTAGG.spad" 401983 402004 403721 403726) (-290 "ELTAB.spad" 401432 401450 401973 401978) (-289 "ELFUTS.spad" 400819 400838 401422 401427) (-288 "ELEMFUN.spad" 400508 400516 400809 400814) (-287 "ELEMFUN.spad" 400195 400205 400498 400503) (-286 "ELAGG.spad" 398166 398176 400175 400190) (-285 "ELAGG.spad" 396074 396086 398085 398090) (-284 "ELABOR.spad" 395420 395428 396064 396069) (-283 "ELABEXPR.spad" 394352 394360 395410 395415) (-282 "EFUPXS.spad" 391128 391158 394308 394313) (-281 "EFULS.spad" 387964 387987 391084 391089) (-280 "EFSTRUC.spad" 385979 385995 387954 387959) (-279 "EF.spad" 380755 380771 385969 385974) (-278 "EAB.spad" 379031 379039 380745 380750) (-277 "E04UCFA.spad" 378567 378575 379021 379026) (-276 "E04NAFA.spad" 378144 378152 378557 378562) (-275 "E04MBFA.spad" 377724 377732 378134 378139) (-274 "E04JAFA.spad" 377260 377268 377714 377719) (-273 "E04GCFA.spad" 376796 376804 377250 377255) (-272 "E04FDFA.spad" 376332 376340 376786 376791) (-271 "E04DGFA.spad" 375868 375876 376322 376327) (-270 "E04AGNT.spad" 371718 371726 375858 375863) (-269 "DVARCAT.spad" 368407 368417 371708 371713) (-268 "DVARCAT.spad" 365094 365106 368397 368402) (-267 "DSMP.spad" 362561 362575 362866 362993) (-266 "DROPT.spad" 356520 356528 362551 362556) (-265 "DROPT1.spad" 356185 356195 356510 356515) (-264 "DROPT0.spad" 351042 351050 356175 356180) (-263 "DRAWPT.spad" 349215 349223 351032 351037) (-262 "DRAW.spad" 342091 342104 349205 349210) (-261 "DRAWHACK.spad" 341399 341409 342081 342086) (-260 "DRAWCX.spad" 338869 338877 341389 341394) (-259 "DRAWCURV.spad" 338416 338431 338859 338864) (-258 "DRAWCFUN.spad" 327948 327956 338406 338411) (-257 "DQAGG.spad" 326126 326136 327916 327943) (-256 "DPOLCAT.spad" 321475 321491 325994 326121) (-255 "DPOLCAT.spad" 316910 316928 321431 321436) (-254 "DPMO.spad" 309136 309152 309274 309575) (-253 "DPMM.spad" 301375 301393 301500 301801) (-252 "DOMTMPLT.spad" 301035 301043 301365 301370) (-251 "DOMCTOR.spad" 300790 300798 301025 301030) (-250 "DOMAIN.spad" 299877 299885 300780 300785) (-249 "DMP.spad" 297137 297152 297707 297834) (-248 "DLP.spad" 296489 296499 297127 297132) (-247 "DLIST.spad" 295068 295078 295672 295699) (-246 "DLAGG.spad" 293485 293495 295058 295063) (-245 "DIVRING.spad" 293027 293035 293429 293480) (-244 "DIVRING.spad" 292613 292623 293017 293022) (-243 "DISPLAY.spad" 290803 290811 292603 292608) (-242 "DIRPROD.spad" 280383 280399 281023 281154) (-241 "DIRPROD2.spad" 279201 279219 280373 280378) (-240 "DIRPCAT.spad" 278145 278161 279065 279196) (-239 "DIRPCAT.spad" 276818 276836 277740 277745) (-238 "DIOSP.spad" 275643 275651 276808 276813) (-237 "DIOPS.spad" 274639 274649 275623 275638) (-236 "DIOPS.spad" 273609 273621 274595 274600) (-235 "DIFRING.spad" 272905 272913 273589 273604) (-234 "DIFRING.spad" 272209 272219 272895 272900) (-233 "DIFEXT.spad" 271380 271390 272189 272204) (-232 "DIFEXT.spad" 270468 270480 271279 271284) (-231 "DIAGG.spad" 270098 270108 270448 270463) (-230 "DIAGG.spad" 269736 269748 270088 270093) (-229 "DHMATRIX.spad" 268048 268058 269193 269220) (-228 "DFSFUN.spad" 261688 261696 268038 268043) (-227 "DFLOAT.spad" 258419 258427 261578 261683) (-226 "DFINTTLS.spad" 256650 256666 258409 258414) (-225 "DERHAM.spad" 254564 254596 256630 256645) (-224 "DEQUEUE.spad" 253888 253898 254171 254198) (-223 "DEGRED.spad" 253505 253519 253878 253883) (-222 "DEFINTRF.spad" 251042 251052 253495 253500) (-221 "DEFINTEF.spad" 249552 249568 251032 251037) (-220 "DEFAST.spad" 248920 248928 249542 249547) (-219 "DECIMAL.spad" 247026 247034 247387 247480) (-218 "DDFACT.spad" 244839 244856 247016 247021) (-217 "DBLRESP.spad" 244439 244463 244829 244834) (-216 "DBASE.spad" 243103 243113 244429 244434) (-215 "DATAARY.spad" 242565 242578 243093 243098) (-214 "D03FAFA.spad" 242393 242401 242555 242560) (-213 "D03EEFA.spad" 242213 242221 242383 242388) (-212 "D03AGNT.spad" 241299 241307 242203 242208) (-211 "D02EJFA.spad" 240761 240769 241289 241294) (-210 "D02CJFA.spad" 240239 240247 240751 240756) (-209 "D02BHFA.spad" 239729 239737 240229 240234) (-208 "D02BBFA.spad" 239219 239227 239719 239724) (-207 "D02AGNT.spad" 234033 234041 239209 239214) (-206 "D01WGTS.spad" 232352 232360 234023 234028) (-205 "D01TRNS.spad" 232329 232337 232342 232347) (-204 "D01GBFA.spad" 231851 231859 232319 232324) (-203 "D01FCFA.spad" 231373 231381 231841 231846) (-202 "D01ASFA.spad" 230841 230849 231363 231368) (-201 "D01AQFA.spad" 230287 230295 230831 230836) (-200 "D01APFA.spad" 229711 229719 230277 230282) (-199 "D01ANFA.spad" 229205 229213 229701 229706) (-198 "D01AMFA.spad" 228715 228723 229195 229200) (-197 "D01ALFA.spad" 228255 228263 228705 228710) (-196 "D01AKFA.spad" 227781 227789 228245 228250) (-195 "D01AJFA.spad" 227304 227312 227771 227776) (-194 "D01AGNT.spad" 223371 223379 227294 227299) (-193 "CYCLOTOM.spad" 222877 222885 223361 223366) (-192 "CYCLES.spad" 219669 219677 222867 222872) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
-\ No newline at end of file
+((-3 NIL 2269056 2269061 2269066 2269071) (-2 NIL 2269036 2269041 2269046 2269051) (-1 NIL 2269016 2269021 2269026 2269031) (0 NIL 2268996 2269001 2269006 2269011) (-1306 "ZMOD.spad" 2268805 2268818 2268934 2268991) (-1305 "ZLINDEP.spad" 2267871 2267882 2268795 2268800) (-1304 "ZDSOLVE.spad" 2257816 2257838 2267861 2267866) (-1303 "YSTREAM.spad" 2257311 2257322 2257806 2257811) (-1302 "YDIAGRAM.spad" 2256945 2256954 2257301 2257306) (-1301 "XRPOLY.spad" 2256165 2256185 2256801 2256870) (-1300 "XPR.spad" 2253960 2253973 2255883 2255982) (-1299 "XPOLY.spad" 2253515 2253526 2253816 2253885) (-1298 "XPOLYC.spad" 2252834 2252850 2253441 2253510) (-1297 "XPBWPOLY.spad" 2251271 2251291 2252614 2252683) (-1296 "XF.spad" 2249734 2249749 2251173 2251266) (-1295 "XF.spad" 2248177 2248194 2249618 2249623) (-1294 "XFALG.spad" 2245225 2245241 2248103 2248172) (-1293 "XEXPPKG.spad" 2244476 2244502 2245215 2245220) (-1292 "XDPOLY.spad" 2244090 2244106 2244332 2244401) (-1291 "XALG.spad" 2243750 2243761 2244046 2244085) (-1290 "WUTSET.spad" 2239589 2239606 2243396 2243423) (-1289 "WP.spad" 2238788 2238832 2239447 2239514) (-1288 "WHILEAST.spad" 2238586 2238595 2238778 2238783) (-1287 "WHEREAST.spad" 2238257 2238266 2238576 2238581) (-1286 "WFFINTBS.spad" 2235920 2235942 2238247 2238252) (-1285 "WEIER.spad" 2234142 2234153 2235910 2235915) (-1284 "VSPACE.spad" 2233815 2233826 2234110 2234137) (-1283 "VSPACE.spad" 2233508 2233521 2233805 2233810) (-1282 "VOID.spad" 2233185 2233194 2233498 2233503) (-1281 "VIEW.spad" 2230865 2230874 2233175 2233180) (-1280 "VIEWDEF.spad" 2226066 2226075 2230855 2230860) (-1279 "VIEW3D.spad" 2210027 2210036 2226056 2226061) (-1278 "VIEW2D.spad" 2197918 2197927 2210017 2210022) (-1277 "VECTOR.spad" 2196592 2196603 2196843 2196870) (-1276 "VECTOR2.spad" 2195231 2195244 2196582 2196587) (-1275 "VECTCAT.spad" 2193135 2193146 2195199 2195226) (-1274 "VECTCAT.spad" 2190846 2190859 2192912 2192917) (-1273 "VARIABLE.spad" 2190626 2190641 2190836 2190841) (-1272 "UTYPE.spad" 2190270 2190279 2190616 2190621) (-1271 "UTSODETL.spad" 2189565 2189589 2190226 2190231) (-1270 "UTSODE.spad" 2187781 2187801 2189555 2189560) (-1269 "UTS.spad" 2182585 2182613 2186248 2186345) (-1268 "UTSCAT.spad" 2180064 2180080 2182483 2182580) (-1267 "UTSCAT.spad" 2177187 2177205 2179608 2179613) (-1266 "UTS2.spad" 2176782 2176817 2177177 2177182) (-1265 "URAGG.spad" 2171455 2171466 2176772 2176777) (-1264 "URAGG.spad" 2166092 2166105 2171411 2171416) (-1263 "UPXSSING.spad" 2163737 2163763 2165173 2165306) (-1262 "UPXS.spad" 2160891 2160919 2161869 2162018) (-1261 "UPXSCONS.spad" 2158650 2158670 2159023 2159172) (-1260 "UPXSCCA.spad" 2157221 2157241 2158496 2158645) (-1259 "UPXSCCA.spad" 2155934 2155956 2157211 2157216) (-1258 "UPXSCAT.spad" 2154523 2154539 2155780 2155929) (-1257 "UPXS2.spad" 2154066 2154119 2154513 2154518) (-1256 "UPSQFREE.spad" 2152480 2152494 2154056 2154061) (-1255 "UPSCAT.spad" 2150091 2150115 2152378 2152475) (-1254 "UPSCAT.spad" 2147408 2147434 2149697 2149702) (-1253 "UPOLYC.spad" 2142448 2142459 2147250 2147403) (-1252 "UPOLYC.spad" 2137380 2137393 2142184 2142189) (-1251 "UPOLYC2.spad" 2136851 2136870 2137370 2137375) (-1250 "UP.spad" 2134050 2134065 2134437 2134590) (-1249 "UPMP.spad" 2132950 2132963 2134040 2134045) (-1248 "UPDIVP.spad" 2132515 2132529 2132940 2132945) (-1247 "UPDECOMP.spad" 2130760 2130774 2132505 2132510) (-1246 "UPCDEN.spad" 2129969 2129985 2130750 2130755) (-1245 "UP2.spad" 2129333 2129354 2129959 2129964) (-1244 "UNISEG.spad" 2128686 2128697 2129252 2129257) (-1243 "UNISEG2.spad" 2128183 2128196 2128642 2128647) (-1242 "UNIFACT.spad" 2127286 2127298 2128173 2128178) (-1241 "ULS.spad" 2117844 2117872 2118931 2119360) (-1240 "ULSCONS.spad" 2110240 2110260 2110610 2110759) (-1239 "ULSCCAT.spad" 2107977 2107997 2110086 2110235) (-1238 "ULSCCAT.spad" 2105822 2105844 2107933 2107938) (-1237 "ULSCAT.spad" 2104054 2104070 2105668 2105817) (-1236 "ULS2.spad" 2103568 2103621 2104044 2104049) (-1235 "UINT8.spad" 2103445 2103454 2103558 2103563) (-1234 "UINT64.spad" 2103321 2103330 2103435 2103440) (-1233 "UINT32.spad" 2103197 2103206 2103311 2103316) (-1232 "UINT16.spad" 2103073 2103082 2103187 2103192) (-1231 "UFD.spad" 2102138 2102147 2102999 2103068) (-1230 "UFD.spad" 2101265 2101276 2102128 2102133) (-1229 "UDVO.spad" 2100146 2100155 2101255 2101260) (-1228 "UDPO.spad" 2097639 2097650 2100102 2100107) (-1227 "TYPE.spad" 2097571 2097580 2097629 2097634) (-1226 "TYPEAST.spad" 2097490 2097499 2097561 2097566) (-1225 "TWOFACT.spad" 2096142 2096157 2097480 2097485) (-1224 "TUPLE.spad" 2095628 2095639 2096041 2096046) (-1223 "TUBETOOL.spad" 2092495 2092504 2095618 2095623) (-1222 "TUBE.spad" 2091142 2091159 2092485 2092490) (-1221 "TS.spad" 2089741 2089757 2090707 2090804) (-1220 "TSETCAT.spad" 2076868 2076885 2089709 2089736) (-1219 "TSETCAT.spad" 2063981 2064000 2076824 2076829) (-1218 "TRMANIP.spad" 2058347 2058364 2063687 2063692) (-1217 "TRIMAT.spad" 2057310 2057335 2058337 2058342) (-1216 "TRIGMNIP.spad" 2055837 2055854 2057300 2057305) (-1215 "TRIGCAT.spad" 2055349 2055358 2055827 2055832) (-1214 "TRIGCAT.spad" 2054859 2054870 2055339 2055344) (-1213 "TREE.spad" 2053434 2053445 2054466 2054493) (-1212 "TRANFUN.spad" 2053273 2053282 2053424 2053429) (-1211 "TRANFUN.spad" 2053110 2053121 2053263 2053268) (-1210 "TOPSP.spad" 2052784 2052793 2053100 2053105) (-1209 "TOOLSIGN.spad" 2052447 2052458 2052774 2052779) (-1208 "TEXTFILE.spad" 2051008 2051017 2052437 2052442) (-1207 "TEX.spad" 2048154 2048163 2050998 2051003) (-1206 "TEX1.spad" 2047710 2047721 2048144 2048149) (-1205 "TEMUTL.spad" 2047265 2047274 2047700 2047705) (-1204 "TBCMPPK.spad" 2045358 2045381 2047255 2047260) (-1203 "TBAGG.spad" 2044408 2044431 2045338 2045353) (-1202 "TBAGG.spad" 2043466 2043491 2044398 2044403) (-1201 "TANEXP.spad" 2042874 2042885 2043456 2043461) (-1200 "TALGOP.spad" 2042598 2042609 2042864 2042869) (-1199 "TABLE.spad" 2041009 2041032 2041279 2041306) (-1198 "TABLEAU.spad" 2040490 2040501 2040999 2041004) (-1197 "TABLBUMP.spad" 2037293 2037304 2040480 2040485) (-1196 "SYSTEM.spad" 2036521 2036530 2037283 2037288) (-1195 "SYSSOLP.spad" 2034004 2034015 2036511 2036516) (-1194 "SYSPTR.spad" 2033903 2033912 2033994 2033999) (-1193 "SYSNNI.spad" 2033085 2033096 2033893 2033898) (-1192 "SYSINT.spad" 2032489 2032500 2033075 2033080) (-1191 "SYNTAX.spad" 2028695 2028704 2032479 2032484) (-1190 "SYMTAB.spad" 2026763 2026772 2028685 2028690) (-1189 "SYMS.spad" 2022786 2022795 2026753 2026758) (-1188 "SYMPOLY.spad" 2021793 2021804 2021875 2022002) (-1187 "SYMFUNC.spad" 2021294 2021305 2021783 2021788) (-1186 "SYMBOL.spad" 2018797 2018806 2021284 2021289) (-1185 "SWITCH.spad" 2015568 2015577 2018787 2018792) (-1184 "SUTS.spad" 2012473 2012501 2014035 2014132) (-1183 "SUPXS.spad" 2009614 2009642 2010605 2010754) (-1182 "SUP.spad" 2006427 2006438 2007200 2007353) (-1181 "SUPFRACF.spad" 2005532 2005550 2006417 2006422) (-1180 "SUP2.spad" 2004924 2004937 2005522 2005527) (-1179 "SUMRF.spad" 2003898 2003909 2004914 2004919) (-1178 "SUMFS.spad" 2003535 2003552 2003888 2003893) (-1177 "SULS.spad" 1994080 1994108 1995180 1995609) (-1176 "SUCHTAST.spad" 1993849 1993858 1994070 1994075) (-1175 "SUCH.spad" 1993531 1993546 1993839 1993844) (-1174 "SUBSPACE.spad" 1985646 1985661 1993521 1993526) (-1173 "SUBRESP.spad" 1984816 1984830 1985602 1985607) (-1172 "STTF.spad" 1980915 1980931 1984806 1984811) (-1171 "STTFNC.spad" 1977383 1977399 1980905 1980910) (-1170 "STTAYLOR.spad" 1970018 1970029 1977264 1977269) (-1169 "STRTBL.spad" 1968523 1968540 1968672 1968699) (-1168 "STRING.spad" 1967932 1967941 1967946 1967973) (-1167 "STRICAT.spad" 1967720 1967729 1967900 1967927) (-1166 "STREAM.spad" 1964638 1964649 1967245 1967260) (-1165 "STREAM3.spad" 1964211 1964226 1964628 1964633) (-1164 "STREAM2.spad" 1963339 1963352 1964201 1964206) (-1163 "STREAM1.spad" 1963045 1963056 1963329 1963334) (-1162 "STINPROD.spad" 1961981 1961997 1963035 1963040) (-1161 "STEP.spad" 1961182 1961191 1961971 1961976) (-1160 "STEPAST.spad" 1960416 1960425 1961172 1961177) (-1159 "STBL.spad" 1958942 1958970 1959109 1959124) (-1158 "STAGG.spad" 1958017 1958028 1958932 1958937) (-1157 "STAGG.spad" 1957090 1957103 1958007 1958012) (-1156 "STACK.spad" 1956447 1956458 1956697 1956724) (-1155 "SREGSET.spad" 1954151 1954168 1956093 1956120) (-1154 "SRDCMPK.spad" 1952712 1952732 1954141 1954146) (-1153 "SRAGG.spad" 1947855 1947864 1952680 1952707) (-1152 "SRAGG.spad" 1943018 1943029 1947845 1947850) (-1151 "SQMATRIX.spad" 1940634 1940652 1941550 1941637) (-1150 "SPLTREE.spad" 1935186 1935199 1940070 1940097) (-1149 "SPLNODE.spad" 1931774 1931787 1935176 1935181) (-1148 "SPFCAT.spad" 1930583 1930592 1931764 1931769) (-1147 "SPECOUT.spad" 1929135 1929144 1930573 1930578) (-1146 "SPADXPT.spad" 1920730 1920739 1929125 1929130) (-1145 "spad-parser.spad" 1920195 1920204 1920720 1920725) (-1144 "SPADAST.spad" 1919896 1919905 1920185 1920190) (-1143 "SPACEC.spad" 1904095 1904106 1919886 1919891) (-1142 "SPACE3.spad" 1903871 1903882 1904085 1904090) (-1141 "SORTPAK.spad" 1903420 1903433 1903827 1903832) (-1140 "SOLVETRA.spad" 1901183 1901194 1903410 1903415) (-1139 "SOLVESER.spad" 1899711 1899722 1901173 1901178) (-1138 "SOLVERAD.spad" 1895737 1895748 1899701 1899706) (-1137 "SOLVEFOR.spad" 1894199 1894217 1895727 1895732) (-1136 "SNTSCAT.spad" 1893799 1893816 1894167 1894194) (-1135 "SMTS.spad" 1892071 1892097 1893364 1893461) (-1134 "SMP.spad" 1889546 1889566 1889936 1890063) (-1133 "SMITH.spad" 1888391 1888416 1889536 1889541) (-1132 "SMATCAT.spad" 1886501 1886531 1888335 1888386) (-1131 "SMATCAT.spad" 1884543 1884575 1886379 1886384) (-1130 "SKAGG.spad" 1883506 1883517 1884511 1884538) (-1129 "SINT.spad" 1882446 1882455 1883372 1883501) (-1128 "SIMPAN.spad" 1882174 1882183 1882436 1882441) (-1127 "SIG.spad" 1881504 1881513 1882164 1882169) (-1126 "SIGNRF.spad" 1880622 1880633 1881494 1881499) (-1125 "SIGNEF.spad" 1879901 1879918 1880612 1880617) (-1124 "SIGAST.spad" 1879286 1879295 1879891 1879896) (-1123 "SHP.spad" 1877214 1877229 1879242 1879247) (-1122 "SHDP.spad" 1866925 1866952 1867434 1867565) (-1121 "SGROUP.spad" 1866533 1866542 1866915 1866920) (-1120 "SGROUP.spad" 1866139 1866150 1866523 1866528) (-1119 "SGCF.spad" 1859278 1859287 1866129 1866134) (-1118 "SFRTCAT.spad" 1858208 1858225 1859246 1859273) (-1117 "SFRGCD.spad" 1857271 1857291 1858198 1858203) (-1116 "SFQCMPK.spad" 1851908 1851928 1857261 1857266) (-1115 "SFORT.spad" 1851347 1851361 1851898 1851903) (-1114 "SEXOF.spad" 1851190 1851230 1851337 1851342) (-1113 "SEX.spad" 1851082 1851091 1851180 1851185) (-1112 "SEXCAT.spad" 1848683 1848723 1851072 1851077) (-1111 "SET.spad" 1847007 1847018 1848104 1848143) (-1110 "SETMN.spad" 1845457 1845474 1846997 1847002) (-1109 "SETCAT.spad" 1844779 1844788 1845447 1845452) (-1108 "SETCAT.spad" 1844099 1844110 1844769 1844774) (-1107 "SETAGG.spad" 1840648 1840659 1844079 1844094) (-1106 "SETAGG.spad" 1837205 1837218 1840638 1840643) (-1105 "SEQAST.spad" 1836908 1836917 1837195 1837200) (-1104 "SEGXCAT.spad" 1836064 1836077 1836898 1836903) (-1103 "SEG.spad" 1835877 1835888 1835983 1835988) (-1102 "SEGCAT.spad" 1834802 1834813 1835867 1835872) (-1101 "SEGBIND.spad" 1834560 1834571 1834749 1834754) (-1100 "SEGBIND2.spad" 1834258 1834271 1834550 1834555) (-1099 "SEGAST.spad" 1833972 1833981 1834248 1834253) (-1098 "SEG2.spad" 1833407 1833420 1833928 1833933) (-1097 "SDVAR.spad" 1832683 1832694 1833397 1833402) (-1096 "SDPOL.spad" 1830109 1830120 1830400 1830527) (-1095 "SCPKG.spad" 1828198 1828209 1830099 1830104) (-1094 "SCOPE.spad" 1827351 1827360 1828188 1828193) (-1093 "SCACHE.spad" 1826047 1826058 1827341 1827346) (-1092 "SASTCAT.spad" 1825956 1825965 1826037 1826042) (-1091 "SAOS.spad" 1825828 1825837 1825946 1825951) (-1090 "SAERFFC.spad" 1825541 1825561 1825818 1825823) (-1089 "SAE.spad" 1823716 1823732 1824327 1824462) (-1088 "SAEFACT.spad" 1823417 1823437 1823706 1823711) (-1087 "RURPK.spad" 1821076 1821092 1823407 1823412) (-1086 "RULESET.spad" 1820529 1820553 1821066 1821071) (-1085 "RULE.spad" 1818769 1818793 1820519 1820524) (-1084 "RULECOLD.spad" 1818621 1818634 1818759 1818764) (-1083 "RTVALUE.spad" 1818356 1818365 1818611 1818616) (-1082 "RSTRCAST.spad" 1818073 1818082 1818346 1818351) (-1081 "RSETGCD.spad" 1814451 1814471 1818063 1818068) (-1080 "RSETCAT.spad" 1804387 1804404 1814419 1814446) (-1079 "RSETCAT.spad" 1794343 1794362 1804377 1804382) (-1078 "RSDCMPK.spad" 1792795 1792815 1794333 1794338) (-1077 "RRCC.spad" 1791179 1791209 1792785 1792790) (-1076 "RRCC.spad" 1789561 1789593 1791169 1791174) (-1075 "RPTAST.spad" 1789263 1789272 1789551 1789556) (-1074 "RPOLCAT.spad" 1768623 1768638 1789131 1789258) (-1073 "RPOLCAT.spad" 1747696 1747713 1768206 1768211) (-1072 "ROUTINE.spad" 1743579 1743588 1746343 1746370) (-1071 "ROMAN.spad" 1742907 1742916 1743445 1743574) (-1070 "ROIRC.spad" 1741987 1742019 1742897 1742902) (-1069 "RNS.spad" 1740890 1740899 1741889 1741982) (-1068 "RNS.spad" 1739879 1739890 1740880 1740885) (-1067 "RNG.spad" 1739614 1739623 1739869 1739874) (-1066 "RNGBIND.spad" 1738774 1738788 1739569 1739574) (-1065 "RMODULE.spad" 1738539 1738550 1738764 1738769) (-1064 "RMCAT2.spad" 1737959 1738016 1738529 1738534) (-1063 "RMATRIX.spad" 1736783 1736802 1737126 1737165) (-1062 "RMATCAT.spad" 1732362 1732393 1736739 1736778) (-1061 "RMATCAT.spad" 1727831 1727864 1732210 1732215) (-1060 "RLINSET.spad" 1727225 1727236 1727821 1727826) (-1059 "RINTERP.spad" 1727113 1727133 1727215 1727220) (-1058 "RING.spad" 1726583 1726592 1727093 1727108) (-1057 "RING.spad" 1726061 1726072 1726573 1726578) (-1056 "RIDIST.spad" 1725453 1725462 1726051 1726056) (-1055 "RGCHAIN.spad" 1724036 1724052 1724938 1724965) (-1054 "RGBCSPC.spad" 1723817 1723829 1724026 1724031) (-1053 "RGBCMDL.spad" 1723347 1723359 1723807 1723812) (-1052 "RF.spad" 1720989 1721000 1723337 1723342) (-1051 "RFFACTOR.spad" 1720451 1720462 1720979 1720984) (-1050 "RFFACT.spad" 1720186 1720198 1720441 1720446) (-1049 "RFDIST.spad" 1719182 1719191 1720176 1720181) (-1048 "RETSOL.spad" 1718601 1718614 1719172 1719177) (-1047 "RETRACT.spad" 1718029 1718040 1718591 1718596) (-1046 "RETRACT.spad" 1717455 1717468 1718019 1718024) (-1045 "RETAST.spad" 1717267 1717276 1717445 1717450) (-1044 "RESULT.spad" 1715327 1715336 1715914 1715941) (-1043 "RESRING.spad" 1714674 1714721 1715265 1715322) (-1042 "RESLATC.spad" 1713998 1714009 1714664 1714669) (-1041 "REPSQ.spad" 1713729 1713740 1713988 1713993) (-1040 "REP.spad" 1711283 1711292 1713719 1713724) (-1039 "REPDB.spad" 1710990 1711001 1711273 1711278) (-1038 "REP2.spad" 1700648 1700659 1710832 1710837) (-1037 "REP1.spad" 1694844 1694855 1700598 1700603) (-1036 "REGSET.spad" 1692641 1692658 1694490 1694517) (-1035 "REF.spad" 1691976 1691987 1692596 1692601) (-1034 "REDORDER.spad" 1691182 1691199 1691966 1691971) (-1033 "RECLOS.spad" 1689965 1689985 1690669 1690762) (-1032 "REALSOLV.spad" 1689105 1689114 1689955 1689960) (-1031 "REAL.spad" 1688977 1688986 1689095 1689100) (-1030 "REAL0Q.spad" 1686275 1686290 1688967 1688972) (-1029 "REAL0.spad" 1683119 1683134 1686265 1686270) (-1028 "RDUCEAST.spad" 1682840 1682849 1683109 1683114) (-1027 "RDIV.spad" 1682495 1682520 1682830 1682835) (-1026 "RDIST.spad" 1682062 1682073 1682485 1682490) (-1025 "RDETRS.spad" 1680926 1680944 1682052 1682057) (-1024 "RDETR.spad" 1679065 1679083 1680916 1680921) (-1023 "RDEEFS.spad" 1678164 1678181 1679055 1679060) (-1022 "RDEEF.spad" 1677174 1677191 1678154 1678159) (-1021 "RCFIELD.spad" 1674360 1674369 1677076 1677169) (-1020 "RCFIELD.spad" 1671632 1671643 1674350 1674355) (-1019 "RCAGG.spad" 1669560 1669571 1671622 1671627) (-1018 "RCAGG.spad" 1667415 1667428 1669479 1669484) (-1017 "RATRET.spad" 1666775 1666786 1667405 1667410) (-1016 "RATFACT.spad" 1666467 1666479 1666765 1666770) (-1015 "RANDSRC.spad" 1665786 1665795 1666457 1666462) (-1014 "RADUTIL.spad" 1665542 1665551 1665776 1665781) (-1013 "RADIX.spad" 1662463 1662477 1664009 1664102) (-1012 "RADFF.spad" 1660876 1660913 1660995 1661151) (-1011 "RADCAT.spad" 1660471 1660480 1660866 1660871) (-1010 "RADCAT.spad" 1660064 1660075 1660461 1660466) (-1009 "QUEUE.spad" 1659412 1659423 1659671 1659698) (-1008 "QUAT.spad" 1657993 1658004 1658336 1658401) (-1007 "QUATCT2.spad" 1657613 1657632 1657983 1657988) (-1006 "QUATCAT.spad" 1655783 1655794 1657543 1657608) (-1005 "QUATCAT.spad" 1653704 1653717 1655466 1655471) (-1004 "QUAGG.spad" 1652531 1652542 1653672 1653699) (-1003 "QQUTAST.spad" 1652299 1652308 1652521 1652526) (-1002 "QFORM.spad" 1651763 1651778 1652289 1652294) (-1001 "QFCAT.spad" 1650465 1650476 1651665 1651758) (-1000 "QFCAT.spad" 1648758 1648771 1649960 1649965) (-999 "QFCAT2.spad" 1648451 1648467 1648748 1648753) (-998 "QEQUAT.spad" 1648010 1648018 1648441 1648446) (-997 "QCMPACK.spad" 1642757 1642776 1648000 1648005) (-996 "QALGSET.spad" 1638836 1638868 1642671 1642676) (-995 "QALGSET2.spad" 1636832 1636850 1638826 1638831) (-994 "PWFFINTB.spad" 1634248 1634269 1636822 1636827) (-993 "PUSHVAR.spad" 1633587 1633606 1634238 1634243) (-992 "PTRANFN.spad" 1629715 1629725 1633577 1633582) (-991 "PTPACK.spad" 1626803 1626813 1629705 1629710) (-990 "PTFUNC2.spad" 1626626 1626640 1626793 1626798) (-989 "PTCAT.spad" 1625881 1625891 1626594 1626621) (-988 "PSQFR.spad" 1625188 1625212 1625871 1625876) (-987 "PSEUDLIN.spad" 1624074 1624084 1625178 1625183) (-986 "PSETPK.spad" 1609507 1609523 1623952 1623957) (-985 "PSETCAT.spad" 1603427 1603450 1609487 1609502) (-984 "PSETCAT.spad" 1597321 1597346 1603383 1603388) (-983 "PSCURVE.spad" 1596304 1596312 1597311 1597316) (-982 "PSCAT.spad" 1595087 1595116 1596202 1596299) (-981 "PSCAT.spad" 1593960 1593991 1595077 1595082) (-980 "PRTITION.spad" 1592658 1592666 1593950 1593955) (-979 "PRTDAST.spad" 1592377 1592385 1592648 1592653) (-978 "PRS.spad" 1581939 1581956 1592333 1592338) (-977 "PRQAGG.spad" 1581374 1581384 1581907 1581934) (-976 "PROPLOG.spad" 1580946 1580954 1581364 1581369) (-975 "PROPFUN2.spad" 1580569 1580582 1580936 1580941) (-974 "PROPFUN1.spad" 1579967 1579978 1580559 1580564) (-973 "PROPFRML.spad" 1578535 1578546 1579957 1579962) (-972 "PROPERTY.spad" 1578023 1578031 1578525 1578530) (-971 "PRODUCT.spad" 1575705 1575717 1575989 1576044) (-970 "PR.spad" 1574097 1574109 1574796 1574923) (-969 "PRINT.spad" 1573849 1573857 1574087 1574092) (-968 "PRIMES.spad" 1572102 1572112 1573839 1573844) (-967 "PRIMELT.spad" 1570183 1570197 1572092 1572097) (-966 "PRIMCAT.spad" 1569810 1569818 1570173 1570178) (-965 "PRIMARR.spad" 1568815 1568825 1568993 1569020) (-964 "PRIMARR2.spad" 1567582 1567594 1568805 1568810) (-963 "PREASSOC.spad" 1566964 1566976 1567572 1567577) (-962 "PPCURVE.spad" 1566101 1566109 1566954 1566959) (-961 "PORTNUM.spad" 1565876 1565884 1566091 1566096) (-960 "POLYROOT.spad" 1564725 1564747 1565832 1565837) (-959 "POLY.spad" 1562060 1562070 1562575 1562702) (-958 "POLYLIFT.spad" 1561325 1561348 1562050 1562055) (-957 "POLYCATQ.spad" 1559443 1559465 1561315 1561320) (-956 "POLYCAT.spad" 1552913 1552934 1559311 1559438) (-955 "POLYCAT.spad" 1545721 1545744 1552121 1552126) (-954 "POLY2UP.spad" 1545173 1545187 1545711 1545716) (-953 "POLY2.spad" 1544770 1544782 1545163 1545168) (-952 "POLUTIL.spad" 1543711 1543740 1544726 1544731) (-951 "POLTOPOL.spad" 1542459 1542474 1543701 1543706) (-950 "POINT.spad" 1541297 1541307 1541384 1541411) (-949 "PNTHEORY.spad" 1537999 1538007 1541287 1541292) (-948 "PMTOOLS.spad" 1536774 1536788 1537989 1537994) (-947 "PMSYM.spad" 1536323 1536333 1536764 1536769) (-946 "PMQFCAT.spad" 1535914 1535928 1536313 1536318) (-945 "PMPRED.spad" 1535393 1535407 1535904 1535909) (-944 "PMPREDFS.spad" 1534847 1534869 1535383 1535388) (-943 "PMPLCAT.spad" 1533927 1533945 1534779 1534784) (-942 "PMLSAGG.spad" 1533512 1533526 1533917 1533922) (-941 "PMKERNEL.spad" 1533091 1533103 1533502 1533507) (-940 "PMINS.spad" 1532671 1532681 1533081 1533086) (-939 "PMFS.spad" 1532248 1532266 1532661 1532666) (-938 "PMDOWN.spad" 1531538 1531552 1532238 1532243) (-937 "PMASS.spad" 1530548 1530556 1531528 1531533) (-936 "PMASSFS.spad" 1529515 1529531 1530538 1530543) (-935 "PLOTTOOL.spad" 1529295 1529303 1529505 1529510) (-934 "PLOT.spad" 1524218 1524226 1529285 1529290) (-933 "PLOT3D.spad" 1520682 1520690 1524208 1524213) (-932 "PLOT1.spad" 1519839 1519849 1520672 1520677) (-931 "PLEQN.spad" 1507129 1507156 1519829 1519834) (-930 "PINTERP.spad" 1506751 1506770 1507119 1507124) (-929 "PINTERPA.spad" 1506535 1506551 1506741 1506746) (-928 "PI.spad" 1506144 1506152 1506509 1506530) (-927 "PID.spad" 1505114 1505122 1506070 1506139) (-926 "PICOERCE.spad" 1504771 1504781 1505104 1505109) (-925 "PGROEB.spad" 1503372 1503386 1504761 1504766) (-924 "PGE.spad" 1494989 1494997 1503362 1503367) (-923 "PGCD.spad" 1493879 1493896 1494979 1494984) (-922 "PFRPAC.spad" 1493028 1493038 1493869 1493874) (-921 "PFR.spad" 1489691 1489701 1492930 1493023) (-920 "PFOTOOLS.spad" 1488949 1488965 1489681 1489686) (-919 "PFOQ.spad" 1488319 1488337 1488939 1488944) (-918 "PFO.spad" 1487738 1487765 1488309 1488314) (-917 "PF.spad" 1487312 1487324 1487543 1487636) (-916 "PFECAT.spad" 1484994 1485002 1487238 1487307) (-915 "PFECAT.spad" 1482704 1482714 1484950 1484955) (-914 "PFBRU.spad" 1480592 1480604 1482694 1482699) (-913 "PFBR.spad" 1478152 1478175 1480582 1480587) (-912 "PERM.spad" 1473837 1473847 1477982 1477997) (-911 "PERMGRP.spad" 1468599 1468609 1473827 1473832) (-910 "PERMCAT.spad" 1467157 1467167 1468579 1468594) (-909 "PERMAN.spad" 1465689 1465703 1467147 1467152) (-908 "PENDTREE.spad" 1465030 1465040 1465318 1465323) (-907 "PDRING.spad" 1463581 1463591 1465010 1465025) (-906 "PDRING.spad" 1462140 1462152 1463571 1463576) (-905 "PDEPROB.spad" 1461155 1461163 1462130 1462135) (-904 "PDEPACK.spad" 1455195 1455203 1461145 1461150) (-903 "PDECOMP.spad" 1454665 1454682 1455185 1455190) (-902 "PDECAT.spad" 1453021 1453029 1454655 1454660) (-901 "PCOMP.spad" 1452874 1452887 1453011 1453016) (-900 "PBWLB.spad" 1451462 1451479 1452864 1452869) (-899 "PATTERN.spad" 1446001 1446011 1451452 1451457) (-898 "PATTERN2.spad" 1445739 1445751 1445991 1445996) (-897 "PATTERN1.spad" 1444075 1444091 1445729 1445734) (-896 "PATRES.spad" 1441650 1441662 1444065 1444070) (-895 "PATRES2.spad" 1441322 1441336 1441640 1441645) (-894 "PATMATCH.spad" 1439519 1439550 1441030 1441035) (-893 "PATMAB.spad" 1438948 1438958 1439509 1439514) (-892 "PATLRES.spad" 1438034 1438048 1438938 1438943) (-891 "PATAB.spad" 1437798 1437808 1438024 1438029) (-890 "PARTPERM.spad" 1435076 1435084 1437788 1437793) (-889 "PARSURF.spad" 1434510 1434538 1435066 1435071) (-888 "PARSU2.spad" 1434307 1434323 1434500 1434505) (-887 "script-parser.spad" 1433827 1433835 1434297 1434302) (-886 "PARSCURV.spad" 1433261 1433289 1433817 1433822) (-885 "PARSC2.spad" 1433052 1433068 1433251 1433256) (-884 "PARPCURV.spad" 1432514 1432542 1433042 1433047) (-883 "PARPC2.spad" 1432305 1432321 1432504 1432509) (-882 "PARAMAST.spad" 1431433 1431441 1432295 1432300) (-881 "PAN2EXPR.spad" 1430845 1430853 1431423 1431428) (-880 "PALETTE.spad" 1429815 1429823 1430835 1430840) (-879 "PAIR.spad" 1428802 1428815 1429403 1429408) (-878 "PADICRC.spad" 1426136 1426154 1427307 1427400) (-877 "PADICRAT.spad" 1424151 1424163 1424372 1424465) (-876 "PADIC.spad" 1423846 1423858 1424077 1424146) (-875 "PADICCT.spad" 1422395 1422407 1423772 1423841) (-874 "PADEPAC.spad" 1421084 1421103 1422385 1422390) (-873 "PADE.spad" 1419836 1419852 1421074 1421079) (-872 "OWP.spad" 1419076 1419106 1419694 1419761) (-871 "OVERSET.spad" 1418649 1418657 1419066 1419071) (-870 "OVAR.spad" 1418430 1418453 1418639 1418644) (-869 "OUT.spad" 1417516 1417524 1418420 1418425) (-868 "OUTFORM.spad" 1406908 1406916 1417506 1417511) (-867 "OUTBFILE.spad" 1406326 1406334 1406898 1406903) (-866 "OUTBCON.spad" 1405332 1405340 1406316 1406321) (-865 "OUTBCON.spad" 1404336 1404346 1405322 1405327) (-864 "OSI.spad" 1403811 1403819 1404326 1404331) (-863 "OSGROUP.spad" 1403729 1403737 1403801 1403806) (-862 "ORTHPOL.spad" 1402214 1402224 1403646 1403651) (-861 "OREUP.spad" 1401667 1401695 1401894 1401933) (-860 "ORESUP.spad" 1400968 1400992 1401347 1401386) (-859 "OREPCTO.spad" 1398825 1398837 1400888 1400893) (-858 "OREPCAT.spad" 1392972 1392982 1398781 1398820) (-857 "OREPCAT.spad" 1387009 1387021 1392820 1392825) (-856 "ORDSET.spad" 1386181 1386189 1386999 1387004) (-855 "ORDSET.spad" 1385351 1385361 1386171 1386176) (-854 "ORDRING.spad" 1384741 1384749 1385331 1385346) (-853 "ORDRING.spad" 1384139 1384149 1384731 1384736) (-852 "ORDMON.spad" 1383994 1384002 1384129 1384134) (-851 "ORDFUNS.spad" 1383126 1383142 1383984 1383989) (-850 "ORDFIN.spad" 1382946 1382954 1383116 1383121) (-849 "ORDCOMP.spad" 1381411 1381421 1382493 1382522) (-848 "ORDCOMP2.spad" 1380704 1380716 1381401 1381406) (-847 "OPTPROB.spad" 1379342 1379350 1380694 1380699) (-846 "OPTPACK.spad" 1371751 1371759 1379332 1379337) (-845 "OPTCAT.spad" 1369430 1369438 1371741 1371746) (-844 "OPSIG.spad" 1369084 1369092 1369420 1369425) (-843 "OPQUERY.spad" 1368633 1368641 1369074 1369079) (-842 "OP.spad" 1368375 1368385 1368455 1368522) (-841 "OPERCAT.spad" 1367841 1367851 1368365 1368370) (-840 "OPERCAT.spad" 1367305 1367317 1367831 1367836) (-839 "ONECOMP.spad" 1366050 1366060 1366852 1366881) (-838 "ONECOMP2.spad" 1365474 1365486 1366040 1366045) (-837 "OMSERVER.spad" 1364480 1364488 1365464 1365469) (-836 "OMSAGG.spad" 1364268 1364278 1364436 1364475) (-835 "OMPKG.spad" 1362884 1362892 1364258 1364263) (-834 "OM.spad" 1361857 1361865 1362874 1362879) (-833 "OMLO.spad" 1361282 1361294 1361743 1361782) (-832 "OMEXPR.spad" 1361116 1361126 1361272 1361277) (-831 "OMERR.spad" 1360661 1360669 1361106 1361111) (-830 "OMERRK.spad" 1359695 1359703 1360651 1360656) (-829 "OMENC.spad" 1359039 1359047 1359685 1359690) (-828 "OMDEV.spad" 1353348 1353356 1359029 1359034) (-827 "OMCONN.spad" 1352757 1352765 1353338 1353343) (-826 "OINTDOM.spad" 1352520 1352528 1352683 1352752) (-825 "OFMONOID.spad" 1350643 1350653 1352476 1352481) (-824 "ODVAR.spad" 1349904 1349914 1350633 1350638) (-823 "ODR.spad" 1349548 1349574 1349716 1349865) (-822 "ODPOL.spad" 1346930 1346940 1347270 1347397) (-821 "ODP.spad" 1336777 1336797 1337150 1337281) (-820 "ODETOOLS.spad" 1335426 1335445 1336767 1336772) (-819 "ODESYS.spad" 1333120 1333137 1335416 1335421) (-818 "ODERTRIC.spad" 1329129 1329146 1333077 1333082) (-817 "ODERED.spad" 1328528 1328552 1329119 1329124) (-816 "ODERAT.spad" 1326143 1326160 1328518 1328523) (-815 "ODEPRRIC.spad" 1323180 1323202 1326133 1326138) (-814 "ODEPROB.spad" 1322437 1322445 1323170 1323175) (-813 "ODEPRIM.spad" 1319771 1319793 1322427 1322432) (-812 "ODEPAL.spad" 1319157 1319181 1319761 1319766) (-811 "ODEPACK.spad" 1305823 1305831 1319147 1319152) (-810 "ODEINT.spad" 1305258 1305274 1305813 1305818) (-809 "ODEIFTBL.spad" 1302653 1302661 1305248 1305253) (-808 "ODEEF.spad" 1298144 1298160 1302643 1302648) (-807 "ODECONST.spad" 1297681 1297699 1298134 1298139) (-806 "ODECAT.spad" 1296279 1296287 1297671 1297676) (-805 "OCT.spad" 1294415 1294425 1295129 1295168) (-804 "OCTCT2.spad" 1294061 1294082 1294405 1294410) (-803 "OC.spad" 1291857 1291867 1294017 1294056) (-802 "OC.spad" 1289378 1289390 1291540 1291545) (-801 "OCAMON.spad" 1289226 1289234 1289368 1289373) (-800 "OASGP.spad" 1289041 1289049 1289216 1289221) (-799 "OAMONS.spad" 1288563 1288571 1289031 1289036) (-798 "OAMON.spad" 1288424 1288432 1288553 1288558) (-797 "OAGROUP.spad" 1288286 1288294 1288414 1288419) (-796 "NUMTUBE.spad" 1287877 1287893 1288276 1288281) (-795 "NUMQUAD.spad" 1275853 1275861 1287867 1287872) (-794 "NUMODE.spad" 1267207 1267215 1275843 1275848) (-793 "NUMINT.spad" 1264773 1264781 1267197 1267202) (-792 "NUMFMT.spad" 1263613 1263621 1264763 1264768) (-791 "NUMERIC.spad" 1255727 1255737 1263418 1263423) (-790 "NTSCAT.spad" 1254235 1254251 1255695 1255722) (-789 "NTPOLFN.spad" 1253786 1253796 1254152 1254157) (-788 "NSUP.spad" 1246832 1246842 1251372 1251525) (-787 "NSUP2.spad" 1246224 1246236 1246822 1246827) (-786 "NSMP.spad" 1242454 1242473 1242762 1242889) (-785 "NREP.spad" 1240832 1240846 1242444 1242449) (-784 "NPCOEF.spad" 1240078 1240098 1240822 1240827) (-783 "NORMRETR.spad" 1239676 1239715 1240068 1240073) (-782 "NORMPK.spad" 1237578 1237597 1239666 1239671) (-781 "NORMMA.spad" 1237266 1237292 1237568 1237573) (-780 "NONE.spad" 1237007 1237015 1237256 1237261) (-779 "NONE1.spad" 1236683 1236693 1236997 1237002) (-778 "NODE1.spad" 1236170 1236186 1236673 1236678) (-777 "NNI.spad" 1235065 1235073 1236144 1236165) (-776 "NLINSOL.spad" 1233691 1233701 1235055 1235060) (-775 "NIPROB.spad" 1232232 1232240 1233681 1233686) (-774 "NFINTBAS.spad" 1229792 1229809 1232222 1232227) (-773 "NETCLT.spad" 1229766 1229777 1229782 1229787) (-772 "NCODIV.spad" 1227982 1227998 1229756 1229761) (-771 "NCNTFRAC.spad" 1227624 1227638 1227972 1227977) (-770 "NCEP.spad" 1225790 1225804 1227614 1227619) (-769 "NASRING.spad" 1225386 1225394 1225780 1225785) (-768 "NASRING.spad" 1224980 1224990 1225376 1225381) (-767 "NARNG.spad" 1224332 1224340 1224970 1224975) (-766 "NARNG.spad" 1223682 1223692 1224322 1224327) (-765 "NAGSP.spad" 1222759 1222767 1223672 1223677) (-764 "NAGS.spad" 1212420 1212428 1222749 1222754) (-763 "NAGF07.spad" 1210851 1210859 1212410 1212415) (-762 "NAGF04.spad" 1205253 1205261 1210841 1210846) (-761 "NAGF02.spad" 1199322 1199330 1205243 1205248) (-760 "NAGF01.spad" 1195083 1195091 1199312 1199317) (-759 "NAGE04.spad" 1188783 1188791 1195073 1195078) (-758 "NAGE02.spad" 1179443 1179451 1188773 1188778) (-757 "NAGE01.spad" 1175445 1175453 1179433 1179438) (-756 "NAGD03.spad" 1173449 1173457 1175435 1175440) (-755 "NAGD02.spad" 1166196 1166204 1173439 1173444) (-754 "NAGD01.spad" 1160489 1160497 1166186 1166191) (-753 "NAGC06.spad" 1156364 1156372 1160479 1160484) (-752 "NAGC05.spad" 1154865 1154873 1156354 1156359) (-751 "NAGC02.spad" 1154132 1154140 1154855 1154860) (-750 "NAALG.spad" 1153673 1153683 1154100 1154127) (-749 "NAALG.spad" 1153234 1153246 1153663 1153668) (-748 "MULTSQFR.spad" 1150192 1150209 1153224 1153229) (-747 "MULTFACT.spad" 1149575 1149592 1150182 1150187) (-746 "MTSCAT.spad" 1147669 1147690 1149473 1149570) (-745 "MTHING.spad" 1147328 1147338 1147659 1147664) (-744 "MSYSCMD.spad" 1146762 1146770 1147318 1147323) (-743 "MSET.spad" 1144720 1144730 1146468 1146507) (-742 "MSETAGG.spad" 1144565 1144575 1144688 1144715) (-741 "MRING.spad" 1141542 1141554 1144273 1144340) (-740 "MRF2.spad" 1141112 1141126 1141532 1141537) (-739 "MRATFAC.spad" 1140658 1140675 1141102 1141107) (-738 "MPRFF.spad" 1138698 1138717 1140648 1140653) (-737 "MPOLY.spad" 1136169 1136184 1136528 1136655) (-736 "MPCPF.spad" 1135433 1135452 1136159 1136164) (-735 "MPC3.spad" 1135250 1135290 1135423 1135428) (-734 "MPC2.spad" 1134896 1134929 1135240 1135245) (-733 "MONOTOOL.spad" 1133247 1133264 1134886 1134891) (-732 "MONOID.spad" 1132566 1132574 1133237 1133242) (-731 "MONOID.spad" 1131883 1131893 1132556 1132561) (-730 "MONOGEN.spad" 1130631 1130644 1131743 1131878) (-729 "MONOGEN.spad" 1129401 1129416 1130515 1130520) (-728 "MONADWU.spad" 1127431 1127439 1129391 1129396) (-727 "MONADWU.spad" 1125459 1125469 1127421 1127426) (-726 "MONAD.spad" 1124619 1124627 1125449 1125454) (-725 "MONAD.spad" 1123777 1123787 1124609 1124614) (-724 "MOEBIUS.spad" 1122513 1122527 1123757 1123772) (-723 "MODULE.spad" 1122383 1122393 1122481 1122508) (-722 "MODULE.spad" 1122273 1122285 1122373 1122378) (-721 "MODRING.spad" 1121608 1121647 1122253 1122268) (-720 "MODOP.spad" 1120273 1120285 1121430 1121497) (-719 "MODMONOM.spad" 1120004 1120022 1120263 1120268) (-718 "MODMON.spad" 1116799 1116815 1117518 1117671) (-717 "MODFIELD.spad" 1116161 1116200 1116701 1116794) (-716 "MMLFORM.spad" 1115021 1115029 1116151 1116156) (-715 "MMAP.spad" 1114763 1114797 1115011 1115016) (-714 "MLO.spad" 1113222 1113232 1114719 1114758) (-713 "MLIFT.spad" 1111834 1111851 1113212 1113217) (-712 "MKUCFUNC.spad" 1111369 1111387 1111824 1111829) (-711 "MKRECORD.spad" 1110973 1110986 1111359 1111364) (-710 "MKFUNC.spad" 1110380 1110390 1110963 1110968) (-709 "MKFLCFN.spad" 1109348 1109358 1110370 1110375) (-708 "MKBCFUNC.spad" 1108843 1108861 1109338 1109343) (-707 "MINT.spad" 1108282 1108290 1108745 1108838) (-706 "MHROWRED.spad" 1106793 1106803 1108272 1108277) (-705 "MFLOAT.spad" 1105313 1105321 1106683 1106788) (-704 "MFINFACT.spad" 1104713 1104735 1105303 1105308) (-703 "MESH.spad" 1102495 1102503 1104703 1104708) (-702 "MDDFACT.spad" 1100706 1100716 1102485 1102490) (-701 "MDAGG.spad" 1099997 1100007 1100686 1100701) (-700 "MCMPLX.spad" 1096008 1096016 1096622 1096823) (-699 "MCDEN.spad" 1095218 1095230 1095998 1096003) (-698 "MCALCFN.spad" 1092340 1092366 1095208 1095213) (-697 "MAYBE.spad" 1091624 1091635 1092330 1092335) (-696 "MATSTOR.spad" 1088932 1088942 1091614 1091619) (-695 "MATRIX.spad" 1087636 1087646 1088120 1088147) (-694 "MATLIN.spad" 1084980 1085004 1087520 1087525) (-693 "MATCAT.spad" 1076709 1076731 1084948 1084975) (-692 "MATCAT.spad" 1068310 1068334 1076551 1076556) (-691 "MATCAT2.spad" 1067592 1067640 1068300 1068305) (-690 "MAPPKG3.spad" 1066507 1066521 1067582 1067587) (-689 "MAPPKG2.spad" 1065845 1065857 1066497 1066502) (-688 "MAPPKG1.spad" 1064673 1064683 1065835 1065840) (-687 "MAPPAST.spad" 1063988 1063996 1064663 1064668) (-686 "MAPHACK3.spad" 1063800 1063814 1063978 1063983) (-685 "MAPHACK2.spad" 1063569 1063581 1063790 1063795) (-684 "MAPHACK1.spad" 1063213 1063223 1063559 1063564) (-683 "MAGMA.spad" 1061003 1061020 1063203 1063208) (-682 "MACROAST.spad" 1060582 1060590 1060993 1060998) (-681 "M3D.spad" 1058302 1058312 1059960 1059965) (-680 "LZSTAGG.spad" 1055540 1055550 1058292 1058297) (-679 "LZSTAGG.spad" 1052776 1052788 1055530 1055535) (-678 "LWORD.spad" 1049481 1049498 1052766 1052771) (-677 "LSTAST.spad" 1049265 1049273 1049471 1049476) (-676 "LSQM.spad" 1047495 1047509 1047889 1047940) (-675 "LSPP.spad" 1047030 1047047 1047485 1047490) (-674 "LSMP.spad" 1045880 1045908 1047020 1047025) (-673 "LSMP1.spad" 1043698 1043712 1045870 1045875) (-672 "LSAGG.spad" 1043367 1043377 1043666 1043693) (-671 "LSAGG.spad" 1043056 1043068 1043357 1043362) (-670 "LPOLY.spad" 1042010 1042029 1042912 1042981) (-669 "LPEFRAC.spad" 1041281 1041291 1042000 1042005) (-668 "LO.spad" 1040682 1040696 1041215 1041242) (-667 "LOGIC.spad" 1040284 1040292 1040672 1040677) (-666 "LOGIC.spad" 1039884 1039894 1040274 1040279) (-665 "LODOOPS.spad" 1038814 1038826 1039874 1039879) (-664 "LODO.spad" 1038198 1038214 1038494 1038533) (-663 "LODOF.spad" 1037244 1037261 1038155 1038160) (-662 "LODOCAT.spad" 1035910 1035920 1037200 1037239) (-661 "LODOCAT.spad" 1034574 1034586 1035866 1035871) (-660 "LODO2.spad" 1033847 1033859 1034254 1034293) (-659 "LODO1.spad" 1033247 1033257 1033527 1033566) (-658 "LODEEF.spad" 1032049 1032067 1033237 1033242) (-657 "LNAGG.spad" 1027881 1027891 1032039 1032044) (-656 "LNAGG.spad" 1023677 1023689 1027837 1027842) (-655 "LMOPS.spad" 1020445 1020462 1023667 1023672) (-654 "LMODULE.spad" 1020213 1020223 1020435 1020440) (-653 "LMDICT.spad" 1019500 1019510 1019764 1019791) (-652 "LLINSET.spad" 1018897 1018907 1019490 1019495) (-651 "LITERAL.spad" 1018803 1018814 1018887 1018892) (-650 "LIST.spad" 1016538 1016548 1017950 1017977) (-649 "LIST3.spad" 1015849 1015863 1016528 1016533) (-648 "LIST2.spad" 1014551 1014563 1015839 1015844) (-647 "LIST2MAP.spad" 1011454 1011466 1014541 1014546) (-646 "LINSET.spad" 1011076 1011086 1011444 1011449) (-645 "LINEXP.spad" 1010510 1010520 1011056 1011071) (-644 "LINDEP.spad" 1009319 1009331 1010422 1010427) (-643 "LIMITRF.spad" 1007247 1007257 1009309 1009314) (-642 "LIMITPS.spad" 1006150 1006163 1007237 1007242) (-641 "LIE.spad" 1004166 1004178 1005440 1005585) (-640 "LIECAT.spad" 1003642 1003652 1004092 1004161) (-639 "LIECAT.spad" 1003146 1003158 1003598 1003603) (-638 "LIB.spad" 1001196 1001204 1001805 1001820) (-637 "LGROBP.spad" 998549 998568 1001186 1001191) (-636 "LF.spad" 997504 997520 998539 998544) (-635 "LFCAT.spad" 996563 996571 997494 997499) (-634 "LEXTRIPK.spad" 992066 992081 996553 996558) (-633 "LEXP.spad" 990069 990096 992046 992061) (-632 "LETAST.spad" 989768 989776 990059 990064) (-631 "LEADCDET.spad" 988166 988183 989758 989763) (-630 "LAZM3PK.spad" 986870 986892 988156 988161) (-629 "LAUPOL.spad" 985563 985576 986463 986532) (-628 "LAPLACE.spad" 985146 985162 985553 985558) (-627 "LA.spad" 984586 984600 985068 985107) (-626 "LALG.spad" 984362 984372 984566 984581) (-625 "LALG.spad" 984146 984158 984352 984357) (-624 "KVTFROM.spad" 983881 983891 984136 984141) (-623 "KTVLOGIC.spad" 983393 983401 983871 983876) (-622 "KRCFROM.spad" 983131 983141 983383 983388) (-621 "KOVACIC.spad" 981854 981871 983121 983126) (-620 "KONVERT.spad" 981576 981586 981844 981849) (-619 "KOERCE.spad" 981313 981323 981566 981571) (-618 "KERNEL.spad" 979968 979978 981097 981102) (-617 "KERNEL2.spad" 979671 979683 979958 979963) (-616 "KDAGG.spad" 978780 978802 979651 979666) (-615 "KDAGG.spad" 977897 977921 978770 978775) (-614 "KAFILE.spad" 976860 976876 977095 977122) (-613 "JORDAN.spad" 974689 974701 976150 976295) (-612 "JOINAST.spad" 974383 974391 974679 974684) (-611 "JAVACODE.spad" 974249 974257 974373 974378) (-610 "IXAGG.spad" 972382 972406 974239 974244) (-609 "IXAGG.spad" 970370 970396 972229 972234) (-608 "IVECTOR.spad" 969140 969155 969295 969322) (-607 "ITUPLE.spad" 968301 968311 969130 969135) (-606 "ITRIGMNP.spad" 967140 967159 968291 968296) (-605 "ITFUN3.spad" 966646 966660 967130 967135) (-604 "ITFUN2.spad" 966390 966402 966636 966641) (-603 "ITFORM.spad" 965745 965753 966380 966385) (-602 "ITAYLOR.spad" 963739 963754 965609 965706) (-601 "ISUPS.spad" 956176 956191 962713 962810) (-600 "ISUMP.spad" 955677 955693 956166 956171) (-599 "ISTRING.spad" 954765 954778 954846 954873) (-598 "ISAST.spad" 954484 954492 954755 954760) (-597 "IRURPK.spad" 953201 953220 954474 954479) (-596 "IRSN.spad" 951173 951181 953191 953196) (-595 "IRRF2F.spad" 949658 949668 951129 951134) (-594 "IRREDFFX.spad" 949259 949270 949648 949653) (-593 "IROOT.spad" 947598 947608 949249 949254) (-592 "IR.spad" 945399 945413 947453 947480) (-591 "IRFORM.spad" 944723 944731 945389 945394) (-590 "IR2.spad" 943751 943767 944713 944718) (-589 "IR2F.spad" 942957 942973 943741 943746) (-588 "IPRNTPK.spad" 942717 942725 942947 942952) (-587 "IPF.spad" 942282 942294 942522 942615) (-586 "IPADIC.spad" 942043 942069 942208 942277) (-585 "IP4ADDR.spad" 941600 941608 942033 942038) (-584 "IOMODE.spad" 941122 941130 941590 941595) (-583 "IOBFILE.spad" 940483 940491 941112 941117) (-582 "IOBCON.spad" 940348 940356 940473 940478) (-581 "INVLAPLA.spad" 939997 940013 940338 940343) (-580 "INTTR.spad" 933379 933396 939987 939992) (-579 "INTTOOLS.spad" 931134 931150 932953 932958) (-578 "INTSLPE.spad" 930454 930462 931124 931129) (-577 "INTRVL.spad" 930020 930030 930368 930449) (-576 "INTRF.spad" 928444 928458 930010 930015) (-575 "INTRET.spad" 927876 927886 928434 928439) (-574 "INTRAT.spad" 926603 926620 927866 927871) (-573 "INTPM.spad" 924988 925004 926246 926251) (-572 "INTPAF.spad" 922852 922870 924920 924925) (-571 "INTPACK.spad" 913226 913234 922842 922847) (-570 "INT.spad" 912674 912682 913080 913221) (-569 "INTHERTR.spad" 911948 911965 912664 912669) (-568 "INTHERAL.spad" 911618 911642 911938 911943) (-567 "INTHEORY.spad" 908057 908065 911608 911613) (-566 "INTG0.spad" 901790 901808 907989 907994) (-565 "INTFTBL.spad" 895819 895827 901780 901785) (-564 "INTFACT.spad" 894878 894888 895809 895814) (-563 "INTEF.spad" 893263 893279 894868 894873) (-562 "INTDOM.spad" 891886 891894 893189 893258) (-561 "INTDOM.spad" 890571 890581 891876 891881) (-560 "INTCAT.spad" 888830 888840 890485 890566) (-559 "INTBIT.spad" 888337 888345 888820 888825) (-558 "INTALG.spad" 887525 887552 888327 888332) (-557 "INTAF.spad" 887025 887041 887515 887520) (-556 "INTABL.spad" 885543 885574 885706 885733) (-555 "INT8.spad" 885423 885431 885533 885538) (-554 "INT64.spad" 885302 885310 885413 885418) (-553 "INT32.spad" 885181 885189 885292 885297) (-552 "INT16.spad" 885060 885068 885171 885176) (-551 "INS.spad" 882563 882571 884962 885055) (-550 "INS.spad" 880152 880162 882553 882558) (-549 "INPSIGN.spad" 879600 879613 880142 880147) (-548 "INPRODPF.spad" 878696 878715 879590 879595) (-547 "INPRODFF.spad" 877784 877808 878686 878691) (-546 "INNMFACT.spad" 876759 876776 877774 877779) (-545 "INMODGCD.spad" 876247 876277 876749 876754) (-544 "INFSP.spad" 874544 874566 876237 876242) (-543 "INFPROD0.spad" 873624 873643 874534 874539) (-542 "INFORM.spad" 870823 870831 873614 873619) (-541 "INFORM1.spad" 870448 870458 870813 870818) (-540 "INFINITY.spad" 870000 870008 870438 870443) (-539 "INETCLTS.spad" 869977 869985 869990 869995) (-538 "INEP.spad" 868515 868537 869967 869972) (-537 "INDE.spad" 868244 868261 868505 868510) (-536 "INCRMAPS.spad" 867665 867675 868234 868239) (-535 "INBFILE.spad" 866737 866745 867655 867660) (-534 "INBFF.spad" 862531 862542 866727 866732) (-533 "INBCON.spad" 860821 860829 862521 862526) (-532 "INBCON.spad" 859109 859119 860811 860816) (-531 "INAST.spad" 858770 858778 859099 859104) (-530 "IMPTAST.spad" 858478 858486 858760 858765) (-529 "IMATRIX.spad" 857423 857449 857935 857962) (-528 "IMATQF.spad" 856517 856561 857379 857384) (-527 "IMATLIN.spad" 855122 855146 856473 856478) (-526 "ILIST.spad" 853780 853795 854305 854332) (-525 "IIARRAY2.spad" 853168 853206 853387 853414) (-524 "IFF.spad" 852578 852594 852849 852942) (-523 "IFAST.spad" 852192 852200 852568 852573) (-522 "IFARRAY.spad" 849685 849700 851375 851402) (-521 "IFAMON.spad" 849547 849564 849641 849646) (-520 "IEVALAB.spad" 848952 848964 849537 849542) (-519 "IEVALAB.spad" 848355 848369 848942 848947) (-518 "IDPO.spad" 848153 848165 848345 848350) (-517 "IDPOAMS.spad" 847909 847921 848143 848148) (-516 "IDPOAM.spad" 847629 847641 847899 847904) (-515 "IDPC.spad" 846567 846579 847619 847624) (-514 "IDPAM.spad" 846312 846324 846557 846562) (-513 "IDPAG.spad" 846059 846071 846302 846307) (-512 "IDENT.spad" 845709 845717 846049 846054) (-511 "IDECOMP.spad" 842948 842966 845699 845704) (-510 "IDEAL.spad" 837897 837936 842883 842888) (-509 "ICDEN.spad" 837086 837102 837887 837892) (-508 "ICARD.spad" 836277 836285 837076 837081) (-507 "IBPTOOLS.spad" 834884 834901 836267 836272) (-506 "IBITS.spad" 834087 834100 834520 834547) (-505 "IBATOOL.spad" 831064 831083 834077 834082) (-504 "IBACHIN.spad" 829571 829586 831054 831059) (-503 "IARRAY2.spad" 828559 828585 829178 829205) (-502 "IARRAY1.spad" 827604 827619 827742 827769) (-501 "IAN.spad" 825827 825835 827420 827513) (-500 "IALGFACT.spad" 825430 825463 825817 825822) (-499 "HYPCAT.spad" 824854 824862 825420 825425) (-498 "HYPCAT.spad" 824276 824286 824844 824849) (-497 "HOSTNAME.spad" 824084 824092 824266 824271) (-496 "HOMOTOP.spad" 823827 823837 824074 824079) (-495 "HOAGG.spad" 821109 821119 823817 823822) (-494 "HOAGG.spad" 818166 818178 820876 820881) (-493 "HEXADEC.spad" 816268 816276 816633 816726) (-492 "HEUGCD.spad" 815303 815314 816258 816263) (-491 "HELLFDIV.spad" 814893 814917 815293 815298) (-490 "HEAP.spad" 814285 814295 814500 814527) (-489 "HEADAST.spad" 813818 813826 814275 814280) (-488 "HDP.spad" 803661 803677 804038 804169) (-487 "HDMP.spad" 800875 800890 801491 801618) (-486 "HB.spad" 799126 799134 800865 800870) (-485 "HASHTBL.spad" 797596 797627 797807 797834) (-484 "HASAST.spad" 797312 797320 797586 797591) (-483 "HACKPI.spad" 796803 796811 797214 797307) (-482 "GTSET.spad" 795742 795758 796449 796476) (-481 "GSTBL.spad" 794261 794296 794435 794450) (-480 "GSERIES.spad" 791432 791459 792393 792542) (-479 "GROUP.spad" 790705 790713 791412 791427) (-478 "GROUP.spad" 789986 789996 790695 790700) (-477 "GROEBSOL.spad" 788480 788501 789976 789981) (-476 "GRMOD.spad" 787051 787063 788470 788475) (-475 "GRMOD.spad" 785620 785634 787041 787046) (-474 "GRIMAGE.spad" 778509 778517 785610 785615) (-473 "GRDEF.spad" 776888 776896 778499 778504) (-472 "GRAY.spad" 775351 775359 776878 776883) (-471 "GRALG.spad" 774428 774440 775341 775346) (-470 "GRALG.spad" 773503 773517 774418 774423) (-469 "GPOLSET.spad" 772957 772980 773185 773212) (-468 "GOSPER.spad" 772226 772244 772947 772952) (-467 "GMODPOL.spad" 771374 771401 772194 772221) (-466 "GHENSEL.spad" 770457 770471 771364 771369) (-465 "GENUPS.spad" 766750 766763 770447 770452) (-464 "GENUFACT.spad" 766327 766337 766740 766745) (-463 "GENPGCD.spad" 765913 765930 766317 766322) (-462 "GENMFACT.spad" 765365 765384 765903 765908) (-461 "GENEEZ.spad" 763316 763329 765355 765360) (-460 "GDMP.spad" 760372 760389 761146 761273) (-459 "GCNAALG.spad" 754295 754322 760166 760233) (-458 "GCDDOM.spad" 753471 753479 754221 754290) (-457 "GCDDOM.spad" 752709 752719 753461 753466) (-456 "GB.spad" 750235 750273 752665 752670) (-455 "GBINTERN.spad" 746255 746293 750225 750230) (-454 "GBF.spad" 742022 742060 746245 746250) (-453 "GBEUCLID.spad" 739904 739942 742012 742017) (-452 "GAUSSFAC.spad" 739217 739225 739894 739899) (-451 "GALUTIL.spad" 737543 737553 739173 739178) (-450 "GALPOLYU.spad" 735997 736010 737533 737538) (-449 "GALFACTU.spad" 734170 734189 735987 735992) (-448 "GALFACT.spad" 724359 724370 734160 734165) (-447 "FVFUN.spad" 721382 721390 724349 724354) (-446 "FVC.spad" 720434 720442 721372 721377) (-445 "FUNDESC.spad" 720112 720120 720424 720429) (-444 "FUNCTION.spad" 719961 719973 720102 720107) (-443 "FT.spad" 718258 718266 719951 719956) (-442 "FTEM.spad" 717423 717431 718248 718253) (-441 "FSUPFACT.spad" 716323 716342 717359 717364) (-440 "FST.spad" 714409 714417 716313 716318) (-439 "FSRED.spad" 713889 713905 714399 714404) (-438 "FSPRMELT.spad" 712771 712787 713846 713851) (-437 "FSPECF.spad" 710862 710878 712761 712766) (-436 "FS.spad" 705130 705140 710637 710857) (-435 "FS.spad" 699176 699188 704685 704690) (-434 "FSINT.spad" 698836 698852 699166 699171) (-433 "FSERIES.spad" 698027 698039 698656 698755) (-432 "FSCINT.spad" 697344 697360 698017 698022) (-431 "FSAGG.spad" 696461 696471 697300 697339) (-430 "FSAGG.spad" 695540 695552 696381 696386) (-429 "FSAGG2.spad" 694283 694299 695530 695535) (-428 "FS2UPS.spad" 688774 688808 694273 694278) (-427 "FS2.spad" 688421 688437 688764 688769) (-426 "FS2EXPXP.spad" 687546 687569 688411 688416) (-425 "FRUTIL.spad" 686500 686510 687536 687541) (-424 "FR.spad" 680216 680226 685524 685593) (-423 "FRNAALG.spad" 675335 675345 680158 680211) (-422 "FRNAALG.spad" 670466 670478 675291 675296) (-421 "FRNAAF2.spad" 669922 669940 670456 670461) (-420 "FRMOD.spad" 669332 669362 669853 669858) (-419 "FRIDEAL.spad" 668557 668578 669312 669327) (-418 "FRIDEAL2.spad" 668161 668193 668547 668552) (-417 "FRETRCT.spad" 667672 667682 668151 668156) (-416 "FRETRCT.spad" 667049 667061 667530 667535) (-415 "FRAMALG.spad" 665397 665410 667005 667044) (-414 "FRAMALG.spad" 663777 663792 665387 665392) (-413 "FRAC.spad" 660876 660886 661279 661452) (-412 "FRAC2.spad" 660481 660493 660866 660871) (-411 "FR2.spad" 659817 659829 660471 660476) (-410 "FPS.spad" 656632 656640 659707 659812) (-409 "FPS.spad" 653475 653485 656552 656557) (-408 "FPC.spad" 652521 652529 653377 653470) (-407 "FPC.spad" 651653 651663 652511 652516) (-406 "FPATMAB.spad" 651415 651425 651643 651648) (-405 "FPARFRAC.spad" 649902 649919 651405 651410) (-404 "FORTRAN.spad" 648408 648451 649892 649897) (-403 "FORT.spad" 647357 647365 648398 648403) (-402 "FORTFN.spad" 644527 644535 647347 647352) (-401 "FORTCAT.spad" 644211 644219 644517 644522) (-400 "FORMULA.spad" 641685 641693 644201 644206) (-399 "FORMULA1.spad" 641164 641174 641675 641680) (-398 "FORDER.spad" 640855 640879 641154 641159) (-397 "FOP.spad" 640056 640064 640845 640850) (-396 "FNLA.spad" 639480 639502 640024 640051) (-395 "FNCAT.spad" 638075 638083 639470 639475) (-394 "FNAME.spad" 637967 637975 638065 638070) (-393 "FMTC.spad" 637765 637773 637893 637962) (-392 "FMONOID.spad" 637430 637440 637721 637726) (-391 "FMONCAT.spad" 634583 634593 637420 637425) (-390 "FM.spad" 634278 634290 634517 634544) (-389 "FMFUN.spad" 631308 631316 634268 634273) (-388 "FMC.spad" 630360 630368 631298 631303) (-387 "FMCAT.spad" 628028 628046 630328 630355) (-386 "FM1.spad" 627385 627397 627962 627989) (-385 "FLOATRP.spad" 625120 625134 627375 627380) (-384 "FLOAT.spad" 618434 618442 624986 625115) (-383 "FLOATCP.spad" 615865 615879 618424 618429) (-382 "FLINEXP.spad" 615577 615587 615845 615860) (-381 "FLINEXP.spad" 615243 615255 615513 615518) (-380 "FLASORT.spad" 614569 614581 615233 615238) (-379 "FLALG.spad" 612215 612234 614495 614564) (-378 "FLAGG.spad" 609257 609267 612195 612210) (-377 "FLAGG.spad" 606200 606212 609140 609145) (-376 "FLAGG2.spad" 604925 604941 606190 606195) (-375 "FINRALG.spad" 602986 602999 604881 604920) (-374 "FINRALG.spad" 600973 600988 602870 602875) (-373 "FINITE.spad" 600125 600133 600963 600968) (-372 "FINAALG.spad" 589246 589256 600067 600120) (-371 "FINAALG.spad" 578379 578391 589202 589207) (-370 "FILE.spad" 577962 577972 578369 578374) (-369 "FILECAT.spad" 576488 576505 577952 577957) (-368 "FIELD.spad" 575894 575902 576390 576483) (-367 "FIELD.spad" 575386 575396 575884 575889) (-366 "FGROUP.spad" 574033 574043 575366 575381) (-365 "FGLMICPK.spad" 572820 572835 574023 574028) (-364 "FFX.spad" 572195 572210 572536 572629) (-363 "FFSLPE.spad" 571698 571719 572185 572190) (-362 "FFPOLY.spad" 562960 562971 571688 571693) (-361 "FFPOLY2.spad" 562020 562037 562950 562955) (-360 "FFP.spad" 561417 561437 561736 561829) (-359 "FF.spad" 560865 560881 561098 561191) (-358 "FFNBX.spad" 559377 559397 560581 560674) (-357 "FFNBP.spad" 557890 557907 559093 559186) (-356 "FFNB.spad" 556355 556376 557571 557664) (-355 "FFINTBAS.spad" 553869 553888 556345 556350) (-354 "FFIELDC.spad" 551446 551454 553771 553864) (-353 "FFIELDC.spad" 549109 549119 551436 551441) (-352 "FFHOM.spad" 547857 547874 549099 549104) (-351 "FFF.spad" 545292 545303 547847 547852) (-350 "FFCGX.spad" 544139 544159 545008 545101) (-349 "FFCGP.spad" 543028 543048 543855 543948) (-348 "FFCG.spad" 541820 541841 542709 542802) (-347 "FFCAT.spad" 534993 535015 541659 541815) (-346 "FFCAT.spad" 528245 528269 534913 534918) (-345 "FFCAT2.spad" 527992 528032 528235 528240) (-344 "FEXPR.spad" 519709 519755 527748 527787) (-343 "FEVALAB.spad" 519417 519427 519699 519704) (-342 "FEVALAB.spad" 518910 518922 519194 519199) (-341 "FDIV.spad" 518352 518376 518900 518905) (-340 "FDIVCAT.spad" 516416 516440 518342 518347) (-339 "FDIVCAT.spad" 514478 514504 516406 516411) (-338 "FDIV2.spad" 514134 514174 514468 514473) (-337 "FCTRDATA.spad" 513142 513150 514124 514129) (-336 "FCPAK1.spad" 511709 511717 513132 513137) (-335 "FCOMP.spad" 511088 511098 511699 511704) (-334 "FC.spad" 501095 501103 511078 511083) (-333 "FAXF.spad" 494066 494080 500997 501090) (-332 "FAXF.spad" 487089 487105 494022 494027) (-331 "FARRAY.spad" 485239 485249 486272 486299) (-330 "FAMR.spad" 483375 483387 485137 485234) (-329 "FAMR.spad" 481495 481509 483259 483264) (-328 "FAMONOID.spad" 481163 481173 481449 481454) (-327 "FAMONC.spad" 479459 479471 481153 481158) (-326 "FAGROUP.spad" 479083 479093 479355 479382) (-325 "FACUTIL.spad" 477287 477304 479073 479078) (-324 "FACTFUNC.spad" 476481 476491 477277 477282) (-323 "EXPUPXS.spad" 473314 473337 474613 474762) (-322 "EXPRTUBE.spad" 470602 470610 473304 473309) (-321 "EXPRODE.spad" 467762 467778 470592 470597) (-320 "EXPR.spad" 463037 463047 463751 464158) (-319 "EXPR2UPS.spad" 459159 459172 463027 463032) (-318 "EXPR2.spad" 458864 458876 459149 459154) (-317 "EXPEXPAN.spad" 455804 455829 456436 456529) (-316 "EXIT.spad" 455475 455483 455794 455799) (-315 "EXITAST.spad" 455211 455219 455465 455470) (-314 "EVALCYC.spad" 454671 454685 455201 455206) (-313 "EVALAB.spad" 454243 454253 454661 454666) (-312 "EVALAB.spad" 453813 453825 454233 454238) (-311 "EUCDOM.spad" 451387 451395 453739 453808) (-310 "EUCDOM.spad" 449023 449033 451377 451382) (-309 "ESTOOLS.spad" 440869 440877 449013 449018) (-308 "ESTOOLS2.spad" 440472 440486 440859 440864) (-307 "ESTOOLS1.spad" 440157 440168 440462 440467) (-306 "ES.spad" 432972 432980 440147 440152) (-305 "ES.spad" 425693 425703 432870 432875) (-304 "ESCONT.spad" 422486 422494 425683 425688) (-303 "ESCONT1.spad" 422235 422247 422476 422481) (-302 "ES2.spad" 421740 421756 422225 422230) (-301 "ES1.spad" 421310 421326 421730 421735) (-300 "ERROR.spad" 418637 418645 421300 421305) (-299 "EQTBL.spad" 417109 417131 417318 417345) (-298 "EQ.spad" 411914 411924 414701 414813) (-297 "EQ2.spad" 411632 411644 411904 411909) (-296 "EP.spad" 407958 407968 411622 411627) (-295 "ENV.spad" 406636 406644 407948 407953) (-294 "ENTIRER.spad" 406304 406312 406580 406631) (-293 "EMR.spad" 405511 405552 406230 406299) (-292 "ELTAGG.spad" 403765 403784 405501 405506) (-291 "ELTAGG.spad" 401983 402004 403721 403726) (-290 "ELTAB.spad" 401432 401450 401973 401978) (-289 "ELFUTS.spad" 400819 400838 401422 401427) (-288 "ELEMFUN.spad" 400508 400516 400809 400814) (-287 "ELEMFUN.spad" 400195 400205 400498 400503) (-286 "ELAGG.spad" 398166 398176 400175 400190) (-285 "ELAGG.spad" 396074 396086 398085 398090) (-284 "ELABOR.spad" 395420 395428 396064 396069) (-283 "ELABEXPR.spad" 394352 394360 395410 395415) (-282 "EFUPXS.spad" 391128 391158 394308 394313) (-281 "EFULS.spad" 387964 387987 391084 391089) (-280 "EFSTRUC.spad" 385979 385995 387954 387959) (-279 "EF.spad" 380755 380771 385969 385974) (-278 "EAB.spad" 379031 379039 380745 380750) (-277 "E04UCFA.spad" 378567 378575 379021 379026) (-276 "E04NAFA.spad" 378144 378152 378557 378562) (-275 "E04MBFA.spad" 377724 377732 378134 378139) (-274 "E04JAFA.spad" 377260 377268 377714 377719) (-273 "E04GCFA.spad" 376796 376804 377250 377255) (-272 "E04FDFA.spad" 376332 376340 376786 376791) (-271 "E04DGFA.spad" 375868 375876 376322 376327) (-270 "E04AGNT.spad" 371718 371726 375858 375863) (-269 "DVARCAT.spad" 368407 368417 371708 371713) (-268 "DVARCAT.spad" 365094 365106 368397 368402) (-267 "DSMP.spad" 362561 362575 362866 362993) (-266 "DROPT.spad" 356520 356528 362551 362556) (-265 "DROPT1.spad" 356185 356195 356510 356515) (-264 "DROPT0.spad" 351042 351050 356175 356180) (-263 "DRAWPT.spad" 349215 349223 351032 351037) (-262 "DRAW.spad" 342091 342104 349205 349210) (-261 "DRAWHACK.spad" 341399 341409 342081 342086) (-260 "DRAWCX.spad" 338869 338877 341389 341394) (-259 "DRAWCURV.spad" 338416 338431 338859 338864) (-258 "DRAWCFUN.spad" 327948 327956 338406 338411) (-257 "DQAGG.spad" 326126 326136 327916 327943) (-256 "DPOLCAT.spad" 321475 321491 325994 326121) (-255 "DPOLCAT.spad" 316910 316928 321431 321436) (-254 "DPMO.spad" 309136 309152 309274 309575) (-253 "DPMM.spad" 301375 301393 301500 301801) (-252 "DOMTMPLT.spad" 301035 301043 301365 301370) (-251 "DOMCTOR.spad" 300790 300798 301025 301030) (-250 "DOMAIN.spad" 299877 299885 300780 300785) (-249 "DMP.spad" 297137 297152 297707 297834) (-248 "DLP.spad" 296489 296499 297127 297132) (-247 "DLIST.spad" 295068 295078 295672 295699) (-246 "DLAGG.spad" 293485 293495 295058 295063) (-245 "DIVRING.spad" 293027 293035 293429 293480) (-244 "DIVRING.spad" 292613 292623 293017 293022) (-243 "DISPLAY.spad" 290803 290811 292603 292608) (-242 "DIRPROD.spad" 280383 280399 281023 281154) (-241 "DIRPROD2.spad" 279201 279219 280373 280378) (-240 "DIRPCAT.spad" 278145 278161 279065 279196) (-239 "DIRPCAT.spad" 276818 276836 277740 277745) (-238 "DIOSP.spad" 275643 275651 276808 276813) (-237 "DIOPS.spad" 274639 274649 275623 275638) (-236 "DIOPS.spad" 273609 273621 274595 274600) (-235 "DIFRING.spad" 272905 272913 273589 273604) (-234 "DIFRING.spad" 272209 272219 272895 272900) (-233 "DIFEXT.spad" 271380 271390 272189 272204) (-232 "DIFEXT.spad" 270468 270480 271279 271284) (-231 "DIAGG.spad" 270098 270108 270448 270463) (-230 "DIAGG.spad" 269736 269748 270088 270093) (-229 "DHMATRIX.spad" 268048 268058 269193 269220) (-228 "DFSFUN.spad" 261688 261696 268038 268043) (-227 "DFLOAT.spad" 258419 258427 261578 261683) (-226 "DFINTTLS.spad" 256650 256666 258409 258414) (-225 "DERHAM.spad" 254564 254596 256630 256645) (-224 "DEQUEUE.spad" 253888 253898 254171 254198) (-223 "DEGRED.spad" 253505 253519 253878 253883) (-222 "DEFINTRF.spad" 251042 251052 253495 253500) (-221 "DEFINTEF.spad" 249552 249568 251032 251037) (-220 "DEFAST.spad" 248920 248928 249542 249547) (-219 "DECIMAL.spad" 247026 247034 247387 247480) (-218 "DDFACT.spad" 244839 244856 247016 247021) (-217 "DBLRESP.spad" 244439 244463 244829 244834) (-216 "DBASE.spad" 243103 243113 244429 244434) (-215 "DATAARY.spad" 242565 242578 243093 243098) (-214 "D03FAFA.spad" 242393 242401 242555 242560) (-213 "D03EEFA.spad" 242213 242221 242383 242388) (-212 "D03AGNT.spad" 241299 241307 242203 242208) (-211 "D02EJFA.spad" 240761 240769 241289 241294) (-210 "D02CJFA.spad" 240239 240247 240751 240756) (-209 "D02BHFA.spad" 239729 239737 240229 240234) (-208 "D02BBFA.spad" 239219 239227 239719 239724) (-207 "D02AGNT.spad" 234033 234041 239209 239214) (-206 "D01WGTS.spad" 232352 232360 234023 234028) (-205 "D01TRNS.spad" 232329 232337 232342 232347) (-204 "D01GBFA.spad" 231851 231859 232319 232324) (-203 "D01FCFA.spad" 231373 231381 231841 231846) (-202 "D01ASFA.spad" 230841 230849 231363 231368) (-201 "D01AQFA.spad" 230287 230295 230831 230836) (-200 "D01APFA.spad" 229711 229719 230277 230282) (-199 "D01ANFA.spad" 229205 229213 229701 229706) (-198 "D01AMFA.spad" 228715 228723 229195 229200) (-197 "D01ALFA.spad" 228255 228263 228705 228710) (-196 "D01AKFA.spad" 227781 227789 228245 228250) (-195 "D01AJFA.spad" 227304 227312 227771 227776) (-194 "D01AGNT.spad" 223371 223379 227294 227299) (-193 "CYCLOTOM.spad" 222877 222885 223361 223366) (-192 "CYCLES.spad" 219669 219677 222867 222872) (-191 "CVMP.spad" 219086 219096 219659 219664) (-190 "CTRIGMNP.spad" 217586 217602 219076 219081) (-189 "CTOR.spad" 217277 217285 217576 217581) (-188 "CTORKIND.spad" 216880 216888 217267 217272) (-187 "CTORCAT.spad" 216129 216137 216870 216875) (-186 "CTORCAT.spad" 215376 215386 216119 216124) (-185 "CTORCALL.spad" 214965 214975 215366 215371) (-184 "CSTTOOLS.spad" 214210 214223 214955 214960) (-183 "CRFP.spad" 207934 207947 214200 214205) (-182 "CRCEAST.spad" 207654 207662 207924 207929) (-181 "CRAPACK.spad" 206705 206715 207644 207649) (-180 "CPMATCH.spad" 206209 206224 206630 206635) (-179 "CPIMA.spad" 205914 205933 206199 206204) (-178 "COORDSYS.spad" 200923 200933 205904 205909) (-177 "CONTOUR.spad" 200334 200342 200913 200918) (-176 "CONTFRAC.spad" 196084 196094 200236 200329) (-175 "CONDUIT.spad" 195842 195850 196074 196079) (-174 "COMRING.spad" 195516 195524 195780 195837) (-173 "COMPPROP.spad" 195034 195042 195506 195511) (-172 "COMPLPAT.spad" 194801 194816 195024 195029) (-171 "COMPLEX.spad" 188938 188948 189182 189443) (-170 "COMPLEX2.spad" 188653 188665 188928 188933) (-169 "COMPILER.spad" 188202 188210 188643 188648) (-168 "COMPFACT.spad" 187804 187818 188192 188197) (-167 "COMPCAT.spad" 185876 185886 187538 187799) (-166 "COMPCAT.spad" 183676 183688 185340 185345) (-165 "COMMUPC.spad" 183424 183442 183666 183671) (-164 "COMMONOP.spad" 182957 182965 183414 183419) (-163 "COMM.spad" 182768 182776 182947 182952) (-162 "COMMAAST.spad" 182531 182539 182758 182763) (-161 "COMBOPC.spad" 181446 181454 182521 182526) (-160 "COMBINAT.spad" 180213 180223 181436 181441) (-159 "COMBF.spad" 177595 177611 180203 180208) (-158 "COLOR.spad" 176432 176440 177585 177590) (-157 "COLONAST.spad" 176098 176106 176422 176427) (-156 "CMPLXRT.spad" 175809 175826 176088 176093) (-155 "CLLCTAST.spad" 175471 175479 175799 175804) (-154 "CLIP.spad" 171579 171587 175461 175466) (-153 "CLIF.spad" 170234 170250 171535 171574) (-152 "CLAGG.spad" 166739 166749 170224 170229) (-151 "CLAGG.spad" 163115 163127 166602 166607) (-150 "CINTSLPE.spad" 162446 162459 163105 163110) (-149 "CHVAR.spad" 160584 160606 162436 162441) (-148 "CHARZ.spad" 160499 160507 160564 160579) (-147 "CHARPOL.spad" 160009 160019 160489 160494) (-146 "CHARNZ.spad" 159762 159770 159989 160004) (-145 "CHAR.spad" 157636 157644 159752 159757) (-144 "CFCAT.spad" 156964 156972 157626 157631) (-143 "CDEN.spad" 156160 156174 156954 156959) (-142 "CCLASS.spad" 154309 154317 155571 155610) (-141 "CATEGORY.spad" 153351 153359 154299 154304) (-140 "CATCTOR.spad" 153242 153250 153341 153346) (-139 "CATAST.spad" 152860 152868 153232 153237) (-138 "CASEAST.spad" 152574 152582 152850 152855) (-137 "CARTEN.spad" 147861 147885 152564 152569) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
+\ No newline at end of file
author	dos-reis <gdr@axiomatics.org>	2010-04-23 13:47:59 +0000
committer	dos-reis <gdr@axiomatics.org>	2010-04-23 13:47:59 +0000
commit	2e76a77847facaa29b9c0f7c26ea2ba511dc285e (patch)
tree	d66199443e28ff789421e9363758442c7b1f0cee /src/share/algebra/browse.daase
parent	308aa20f031e73d86801a36eeda29424e65077b2 (diff)
download	open-axiom-2e76a77847facaa29b9c0f7c26ea2ba511dc285e.tar.gz