From 95a8891a808572509f7449aa32022df42f8b7ab8 Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Mon, 26 Apr 2010 02:05:39 +0000
Subject: 	* algebra/carten.spad.pamphlet (CartesianTensor): Satisfy 
 instantiation of Eltable. 	* algebra/clifford.spad.pamphlet
 (QuadraticForm): Likewise. 	* algebra/domain.spad.pamphlet
 (DomainTemplate): Likewise. 	* algebra/files.spad.pamphlet (Library):
 Likewise. 	* algebra/aggcat.spad.pamphlet (LinearAggregate): Extend 
 instantiation of Eltable. 	* algebra/naalg.spad.pamphlet
 (FiniteRankNonAssociativeAlgebra): 	Likewise. 	*
 algebra/pscat.spad.pamphlet (UnivariatePowerSeriesCategory): 	Likewise. 
 * algebra/sex.spad.pamphlet (SExpressionCategory): Likewise. 	*
 algebra/Makefile.pamphlet: Update rules.

---
 src/share/algebra/browse.daase | 188 ++++++++++++++++++++---------------------
 1 file changed, 94 insertions(+), 94 deletions(-)

(limited to 'src/share/algebra/browse.daase')

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index d5c92bcf..1ff96889 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2268346 . 3481068679)       
+(2266417 . 3481235699)       
 (-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 
@@ -88,7 +88,7 @@ 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 -4299) 
+(-40 -1709 UP UPUP -1909) 
 ((|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))) (-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))))) 
@@ -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)) 
-((-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|))))))) 
+((-2892 (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|))))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| (-570) (QUOTE (-856))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
@@ -172,59 +172,59 @@ NIL
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
 ((-4452 . T) (-4453 . T)) 
 ((-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) 
-(-61 -3599) 
+(-61 -3600) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|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 -3599) 
+(-62 -3600) 
 ((|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 -3599) 
+(-63 -3600) 
 ((|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 -3599) 
+(-64 -3600) 
 ((|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 -3599) 
+(-65 -3600) 
 ((|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 -3599) 
+(-66 -3600) 
 ((|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 -3599) 
+(-67 -3600) 
 ((|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 -3599) 
+(-68 -3600) 
 ((|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 -3599) 
+(-69 -3600) 
 ((|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 -3599) 
+(-70 -3600) 
 ((|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 -3599) 
+(-71 -3600) 
 ((|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 -3599) 
+(-72 -3600) 
 ((|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 -3599) 
+(-73 -3600) 
 ((|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 -3599) 
+(-74 -3600) 
 ((|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 -3599) 
+(-77 -3600) 
 ((|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 -3599) 
+(-78 -3600) 
 ((|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 -3599) 
+(-79 -3600) 
 ((|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 -3599) 
+(-80 -3600) 
 ((|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 -3599) 
+(-81 -3600) 
 ((|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 -3599) 
+(-82 -3600) 
 ((|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 -3599) 
+(-83 -3600) 
 ((|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 -3599) 
+(-84 -3600) 
 ((|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 -3599) 
+(-85 -3600) 
 ((|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 -3599) 
+(-86 -3600) 
 ((|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 -3599) 
+(-87 -3600) 
 ((|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 -3599) 
+(-88 -3600) 
 ((|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 -3599) 
+(-89 -3600) 
 ((|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 
@@ -472,12 +472,12 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
 (((-4454 "*") . T)) 
 NIL 
-(-136 |minix| -2549 S T$) 
+(-136 |minix| -2550 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -2549 R) 
-((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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."))) 
+(-137 |minix| -2550 R) 
+((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) 
 NIL 
 NIL 
 (-138) 
@@ -884,19 +884,19 @@ 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 -2549 R) 
+(-239 S -2550 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 -2549 R) 
+(-240 -2550 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 -2549 A B) 
+(-241 -2550 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 -2549 R) 
+(-242 -2550 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)) 
 ((-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 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(|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|))))) 
@@ -937,16 +937,16 @@ NIL
 NIL 
 NIL 
 (-252) 
-((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|elt| (((|Syntax|) $ (|NonNegativeInteger|)) "\\spad{x.i} yields the entry at slot \\spad{i} in \\spad{x}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
+((|constructor| (NIL "Represntation of domain templates resulting from compiling a domain constructor")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# x} returns the length of the domain template \\spad{x}."))) 
 NIL 
 NIL 
 (-253 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
-((-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)) 
+((-4449 -2892 (-1808 (|has| |#4| (-1058)) (|has| |#4| (-235))) (-1808 (|has| |#4| (-1058)) (|has| |#4| (-907 (-1186)))) (|has| |#4| (-6 -4449)) (-1808 (|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|))) 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(|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 -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)) 
+((-4449 -2892 (-1808 (|has| |#3| (-1058)) (|has| |#3| (-235))) (-1808 (|has| |#3| (-1058)) (|has| |#3| (-907 (-1186)))) (|has| |#3| (-6 -4449)) (-1808 (|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."))) 
@@ -1088,8 +1088,8 @@ NIL
 ((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}"))) 
 NIL 
 NIL 
-(-290 S |Index|) 
-((|constructor| (NIL "An eltable over domains \\spad{D} and \\spad{I} is a structure which can be viewed as a function from \\spad{D} to \\spad{I}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,i)} (also written: \\spad{u} . \\spad{i}) returns the element of \\spad{u} indexed by \\spad{i}. Error: if \\spad{i} is not an index of \\spad{u}."))) 
+(-290 S T$) 
+((|constructor| (NIL "An eltable over domains \\spad{S} and \\spad{T} is a structure which can be viewed as a function from \\spad{S} to \\spad{T}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,s)} (also written: \\spad{u.s}) returns the value of \\spad{u} at \\spad{s}. Error: if \\spad{u} is not defined at \\spad{s}."))) 
 NIL 
 NIL 
 (-291 S |Dom| |Im|) 
@@ -1100,8 +1100,8 @@ 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| -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| $) "\\spad{modulus(x)} \\undocumented"))) 
+(-293 S R |Mod| -3733 -2483 |exactQuo|) 
+((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-294) 
@@ -1127,7 +1127,7 @@ NIL
 (-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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 
@@ -1210,7 +1210,7 @@ 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 -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))) 
+((-4449 -2892 (-1808 (|has| |#1| (-1058)) (|has| |#1| (-645 (-570)))) (-12 (|has| |#1| (-562)) (-2892 (-1808 (|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)}."))) 
@@ -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))) (-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))))) (|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 -2833) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1756) (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 
@@ -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 -3599 |returnType| -3931 |symbols|) 
+(-404 -3600 |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 
@@ -1617,17 +1617,17 @@ NIL
 NIL 
 NIL 
 (-422 S R) 
-((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
+((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-368)))) 
 (-423 R) 
-((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
+((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
 ((-4449 |has| |#1| (-562)) (-4447 . T) (-4446 . T)) 
 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| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) 
 ((-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
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 (-425 R) 
 ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) 
 NIL 
@@ -1851,11 +1851,11 @@ NIL
 (-480 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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)) 
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 (-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)) 
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+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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|) (|:| -2339 |#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|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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."))) 
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 (-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 
@@ -1880,7 +1880,7 @@ NIL
 ((|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"))) 
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-(-488 -2549 S) 
+(-488 -2550 S) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(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|))))) 
@@ -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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -313) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#2| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 
@@ -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 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
+((-4449 -2892 (-1808 (|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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#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)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#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 
@@ -2481,9 +2481,9 @@ NIL
 NIL 
 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."))) 
+((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) 
 ((-4453 . T)) 
-((-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)))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-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)) (|:| -2339 (-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)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 (-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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2494,7 +2494,7 @@ NIL
 NIL 
 (-641 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -2892 (-1809 (|has| |#2| (-372 |#1|)) (|has| |#1| (-562))) (-12 (|has| |#2| (-423 |#1|)) (|has| |#1| (-562)))) (-4447 . T) (-4446 . T)) 
+((-4449 -2892 (-1808 (|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))}."))) 
@@ -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 
-((-1795 (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-368)))) 
+((-1796 (|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)) 
@@ -2553,11 +2553,11 @@ NIL
 NIL 
 NIL 
 (-656 A S) 
-((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
+((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 ((|HasAttribute| |#1| (QUOTE -4453))) 
 (-657 S) 
-((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
+((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
 (-658 R -1709 L) 
@@ -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 -1596) 
+(-664 A -1422) 
 ((|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)))) 
@@ -2796,7 +2796,7 @@ 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| -2077 -2948 |exactQuo|) 
+(-717 R |Mod| -3733 -2483 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
@@ -2812,7 +2812,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
 ((-4447 |has| |#1| (-174)) (-4446 |has| |#1| (-174)) (-4449 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-721 R |Mod| -2077 -2948 |exactQuo|) 
+(-721 R |Mod| -3733 -2483 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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 
@@ -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)) 
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 (-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 
@@ -3212,7 +3212,7 @@ 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 -2549 S |f|) 
+(-821 -2550 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)) 
 ((-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 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(-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|))))) 
@@ -3332,7 +3332,7 @@ NIL
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-851 -2549 S) 
+(-851 -2550 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| -3226) 
+(-860 R |sigma| -3225) 
 ((|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| -3226) 
+(-861 |x| R |sigma| -3225) 
 ((|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)))) 
@@ -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 (-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))))) 
+((-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))))) 
 (-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 
@@ -3937,7 +3937,7 @@ NIL
 ((-4444 . T) (-4450 . T) (-4445 . T) ((-4454 "*") . T) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-1002 |n| K) 
-((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
+((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
 (-1003) 
@@ -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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-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 
@@ -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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1186))) (LIST (QUOTE |:|) (QUOTE -2339) (QUOTE (-52))))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-52) (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| (-52) (QUOTE (-1109))) (|HasCategory| (-52) (LIST (QUOTE -313) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (QUOTE (-1109))) (|HasCategory| (-1186) (QUOTE (-856))) (|HasCategory| (-52) (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-52))) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-52) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1186)) (|:| -2339 (-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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
@@ -4377,7 +4377,7 @@ NIL
 ((-4452 . T) (-4442 . T) (-4453 . T)) 
 ((-2892 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -620) (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-856))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|))))) 
 (-1112 |Str| |Sym| |Int| |Flt| |Expr|) 
-((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|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."))) 
+((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) 
 NIL 
 NIL 
 (-1113) 
@@ -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 (|:| -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)))) 
+((-12 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#2|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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|) (|:| -2339 |#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|) (|:| -2339 |#2|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 |#1|) (|:| -2339 |#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 
@@ -4607,7 +4607,7 @@ NIL
 (-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 (|:| -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))))) 
+((-12 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -313) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2106) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2339) (|devaluate| |#1|)))))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-1109)))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -620) (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -313) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (QUOTE (-1109))) (|HasCategory| (-1168) (QUOTE (-856))) (|HasCategory| |#1| (QUOTE (-1109))) (-2892 (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#1|)) (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-868)))) (|HasCategory| (-2 (|:| -2106 (-1168)) (|:| -2339 |#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."))) 
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 (-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 
@@ -4663,11 +4663,11 @@ NIL
 (-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}."))) 
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 (-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}."))) 
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 (-1185) 
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 NIL 
@@ -4727,7 +4727,7 @@ NIL
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 ((|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}"))) 
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 ((|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 
@@ -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)}."))) 
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(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 
@@ -4945,11 +4945,11 @@ NIL
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 NIL 
 (-1254 S |Coef| |Expon|) 
-((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
+((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
 ((|HasCategory| |#2| (LIST (QUOTE -907) (QUOTE (-1186)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3802) (LIST (|devaluate| |#2|) (QUOTE (-1186)))))) 
 (-1255 |Coef| |Expon|) 
-((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
+((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 (((-4454 "*") |has| |#1| (-174)) (-4445 |has| |#1| (-562)) (-4446 . T) (-4447 . T) (-4449 . T)) 
 NIL 
 (-1256 RC P) 
@@ -4975,11 +4975,11 @@ 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)}."))) 
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+((|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 -2833) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1756) (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))) (-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))))) (|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 -2833) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1186))))) (|HasSignature| |#1| (LIST (QUOTE -1756) (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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
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@@ -4999,7 +4999,7 @@ NIL
 (-1267 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 -3170) (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 -1756) (LIST (LIST (QUOTE -650) (QUOTE (-1186))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2833) (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)) 
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 (-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 
@@ -5172,4 +5172,4 @@ NIL
 NIL 
 NIL 
 NIL 
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(-1050 "RFFACT.spad" 1719456 1719468 1719711 1719716) (-1049 "RFDIST.spad" 1718452 1718461 1719446 1719451) (-1048 "RETSOL.spad" 1717871 1717884 1718442 1718447) (-1047 "RETRACT.spad" 1717299 1717310 1717861 1717866) (-1046 "RETRACT.spad" 1716725 1716738 1717289 1717294) (-1045 "RETAST.spad" 1716537 1716546 1716715 1716720) (-1044 "RESULT.spad" 1714597 1714606 1715184 1715211) (-1043 "RESRING.spad" 1713944 1713991 1714535 1714592) (-1042 "RESLATC.spad" 1713268 1713279 1713934 1713939) (-1041 "REPSQ.spad" 1712999 1713010 1713258 1713263) (-1040 "REP.spad" 1710553 1710562 1712989 1712994) (-1039 "REPDB.spad" 1710260 1710271 1710543 1710548) (-1038 "REP2.spad" 1699918 1699929 1710102 1710107) (-1037 "REP1.spad" 1694114 1694125 1699868 1699873) (-1036 "REGSET.spad" 1691911 1691928 1693760 1693787) (-1035 "REF.spad" 1691246 1691257 1691866 1691871) (-1034 "REDORDER.spad" 1690452 1690469 1691236 1691241) (-1033 "RECLOS.spad" 1689235 1689255 1689939 1690032) (-1032 "REALSOLV.spad" 1688375 1688384 1689225 1689230) (-1031 "REAL.spad" 1688247 1688256 1688365 1688370) (-1030 "REAL0Q.spad" 1685545 1685560 1688237 1688242) (-1029 "REAL0.spad" 1682389 1682404 1685535 1685540) (-1028 "RDUCEAST.spad" 1682110 1682119 1682379 1682384) (-1027 "RDIV.spad" 1681765 1681790 1682100 1682105) (-1026 "RDIST.spad" 1681332 1681343 1681755 1681760) (-1025 "RDETRS.spad" 1680196 1680214 1681322 1681327) (-1024 "RDETR.spad" 1678335 1678353 1680186 1680191) (-1023 "RDEEFS.spad" 1677434 1677451 1678325 1678330) (-1022 "RDEEF.spad" 1676444 1676461 1677424 1677429) (-1021 "RCFIELD.spad" 1673630 1673639 1676346 1676439) (-1020 "RCFIELD.spad" 1670902 1670913 1673620 1673625) (-1019 "RCAGG.spad" 1668830 1668841 1670892 1670897) (-1018 "RCAGG.spad" 1666685 1666698 1668749 1668754) (-1017 "RATRET.spad" 1666045 1666056 1666675 1666680) (-1016 "RATFACT.spad" 1665737 1665749 1666035 1666040) (-1015 "RANDSRC.spad" 1665056 1665065 1665727 1665732) (-1014 "RADUTIL.spad" 1664812 1664821 1665046 1665051) (-1013 "RADIX.spad" 1661733 1661747 1663279 1663372) (-1012 "RADFF.spad" 1660146 1660183 1660265 1660421) (-1011 "RADCAT.spad" 1659741 1659750 1660136 1660141) (-1010 "RADCAT.spad" 1659334 1659345 1659731 1659736) (-1009 "QUEUE.spad" 1658682 1658693 1658941 1658968) (-1008 "QUAT.spad" 1657263 1657274 1657606 1657671) (-1007 "QUATCT2.spad" 1656883 1656902 1657253 1657258) (-1006 "QUATCAT.spad" 1655053 1655064 1656813 1656878) (-1005 "QUATCAT.spad" 1652974 1652987 1654736 1654741) (-1004 "QUAGG.spad" 1651801 1651812 1652942 1652969) (-1003 "QQUTAST.spad" 1651569 1651578 1651791 1651796) (-1002 "QFORM.spad" 1651033 1651048 1651559 1651564) (-1001 "QFCAT.spad" 1649735 1649746 1650935 1651028) (-1000 "QFCAT.spad" 1648028 1648041 1649230 1649235) (-999 "QFCAT2.spad" 1647721 1647737 1648018 1648023) (-998 "QEQUAT.spad" 1647280 1647288 1647711 1647716) (-997 "QCMPACK.spad" 1642027 1642046 1647270 1647275) (-996 "QALGSET.spad" 1638106 1638138 1641941 1641946) (-995 "QALGSET2.spad" 1636102 1636120 1638096 1638101) (-994 "PWFFINTB.spad" 1633518 1633539 1636092 1636097) (-993 "PUSHVAR.spad" 1632857 1632876 1633508 1633513) (-992 "PTRANFN.spad" 1628985 1628995 1632847 1632852) (-991 "PTPACK.spad" 1626073 1626083 1628975 1628980) (-990 "PTFUNC2.spad" 1625896 1625910 1626063 1626068) (-989 "PTCAT.spad" 1625151 1625161 1625864 1625891) (-988 "PSQFR.spad" 1624458 1624482 1625141 1625146) (-987 "PSEUDLIN.spad" 1623344 1623354 1624448 1624453) (-986 "PSETPK.spad" 1608777 1608793 1623222 1623227) (-985 "PSETCAT.spad" 1602697 1602720 1608757 1608772) (-984 "PSETCAT.spad" 1596591 1596616 1602653 1602658) (-983 "PSCURVE.spad" 1595574 1595582 1596581 1596586) (-982 "PSCAT.spad" 1594357 1594386 1595472 1595569) (-981 "PSCAT.spad" 1593230 1593261 1594347 1594352) (-980 "PRTITION.spad" 1591928 1591936 1593220 1593225) (-979 "PRTDAST.spad" 1591647 1591655 1591918 1591923) (-978 "PRS.spad" 1581209 1581226 1591603 1591608) (-977 "PRQAGG.spad" 1580644 1580654 1581177 1581204) (-976 "PROPLOG.spad" 1580216 1580224 1580634 1580639) (-975 "PROPFUN2.spad" 1579839 1579852 1580206 1580211) (-974 "PROPFUN1.spad" 1579237 1579248 1579829 1579834) (-973 "PROPFRML.spad" 1577805 1577816 1579227 1579232) (-972 "PROPERTY.spad" 1577293 1577301 1577795 1577800) (-971 "PRODUCT.spad" 1574975 1574987 1575259 1575314) (-970 "PR.spad" 1573367 1573379 1574066 1574193) (-969 "PRINT.spad" 1573119 1573127 1573357 1573362) (-968 "PRIMES.spad" 1571372 1571382 1573109 1573114) (-967 "PRIMELT.spad" 1569453 1569467 1571362 1571367) (-966 "PRIMCAT.spad" 1569080 1569088 1569443 1569448) (-965 "PRIMARR.spad" 1568085 1568095 1568263 1568290) (-964 "PRIMARR2.spad" 1566852 1566864 1568075 1568080) (-963 "PREASSOC.spad" 1566234 1566246 1566842 1566847) (-962 "PPCURVE.spad" 1565371 1565379 1566224 1566229) (-961 "PORTNUM.spad" 1565146 1565154 1565361 1565366) (-960 "POLYROOT.spad" 1563995 1564017 1565102 1565107) (-959 "POLY.spad" 1561330 1561340 1561845 1561972) (-958 "POLYLIFT.spad" 1560595 1560618 1561320 1561325) (-957 "POLYCATQ.spad" 1558713 1558735 1560585 1560590) (-956 "POLYCAT.spad" 1552183 1552204 1558581 1558708) (-955 "POLYCAT.spad" 1544991 1545014 1551391 1551396) (-954 "POLY2UP.spad" 1544443 1544457 1544981 1544986) (-953 "POLY2.spad" 1544040 1544052 1544433 1544438) (-952 "POLUTIL.spad" 1542981 1543010 1543996 1544001) (-951 "POLTOPOL.spad" 1541729 1541744 1542971 1542976) (-950 "POINT.spad" 1540567 1540577 1540654 1540681) (-949 "PNTHEORY.spad" 1537269 1537277 1540557 1540562) (-948 "PMTOOLS.spad" 1536044 1536058 1537259 1537264) (-947 "PMSYM.spad" 1535593 1535603 1536034 1536039) (-946 "PMQFCAT.spad" 1535184 1535198 1535583 1535588) (-945 "PMPRED.spad" 1534663 1534677 1535174 1535179) (-944 "PMPREDFS.spad" 1534117 1534139 1534653 1534658) (-943 "PMPLCAT.spad" 1533197 1533215 1534049 1534054) (-942 "PMLSAGG.spad" 1532782 1532796 1533187 1533192) (-941 "PMKERNEL.spad" 1532361 1532373 1532772 1532777) (-940 "PMINS.spad" 1531941 1531951 1532351 1532356) (-939 "PMFS.spad" 1531518 1531536 1531931 1531936) (-938 "PMDOWN.spad" 1530808 1530822 1531508 1531513) (-937 "PMASS.spad" 1529818 1529826 1530798 1530803) (-936 "PMASSFS.spad" 1528785 1528801 1529808 1529813) (-935 "PLOTTOOL.spad" 1528565 1528573 1528775 1528780) (-934 "PLOT.spad" 1523488 1523496 1528555 1528560) (-933 "PLOT3D.spad" 1519952 1519960 1523478 1523483) (-932 "PLOT1.spad" 1519109 1519119 1519942 1519947) (-931 "PLEQN.spad" 1506399 1506426 1519099 1519104) (-930 "PINTERP.spad" 1506021 1506040 1506389 1506394) (-929 "PINTERPA.spad" 1505805 1505821 1506011 1506016) (-928 "PI.spad" 1505414 1505422 1505779 1505800) (-927 "PID.spad" 1504384 1504392 1505340 1505409) (-926 "PICOERCE.spad" 1504041 1504051 1504374 1504379) (-925 "PGROEB.spad" 1502642 1502656 1504031 1504036) (-924 "PGE.spad" 1494259 1494267 1502632 1502637) (-923 "PGCD.spad" 1493149 1493166 1494249 1494254) (-922 "PFRPAC.spad" 1492298 1492308 1493139 1493144) (-921 "PFR.spad" 1488961 1488971 1492200 1492293) (-920 "PFOTOOLS.spad" 1488219 1488235 1488951 1488956) (-919 "PFOQ.spad" 1487589 1487607 1488209 1488214) (-918 "PFO.spad" 1487008 1487035 1487579 1487584) (-917 "PF.spad" 1486582 1486594 1486813 1486906) (-916 "PFECAT.spad" 1484264 1484272 1486508 1486577) (-915 "PFECAT.spad" 1481974 1481984 1484220 1484225) (-914 "PFBRU.spad" 1479862 1479874 1481964 1481969) (-913 "PFBR.spad" 1477422 1477445 1479852 1479857) (-912 "PERM.spad" 1473107 1473117 1477252 1477267) (-911 "PERMGRP.spad" 1467869 1467879 1473097 1473102) (-910 "PERMCAT.spad" 1466427 1466437 1467849 1467864) (-909 "PERMAN.spad" 1464959 1464973 1466417 1466422) (-908 "PENDTREE.spad" 1464300 1464310 1464588 1464593) (-907 "PDRING.spad" 1462851 1462861 1464280 1464295) (-906 "PDRING.spad" 1461410 1461422 1462841 1462846) (-905 "PDEPROB.spad" 1460425 1460433 1461400 1461405) (-904 "PDEPACK.spad" 1454465 1454473 1460415 1460420) (-903 "PDECOMP.spad" 1453935 1453952 1454455 1454460) (-902 "PDECAT.spad" 1452291 1452299 1453925 1453930) (-901 "PCOMP.spad" 1452144 1452157 1452281 1452286) (-900 "PBWLB.spad" 1450732 1450749 1452134 1452139) (-899 "PATTERN.spad" 1445271 1445281 1450722 1450727) (-898 "PATTERN2.spad" 1445009 1445021 1445261 1445266) (-897 "PATTERN1.spad" 1443345 1443361 1444999 1445004) (-896 "PATRES.spad" 1440920 1440932 1443335 1443340) (-895 "PATRES2.spad" 1440592 1440606 1440910 1440915) (-894 "PATMATCH.spad" 1438789 1438820 1440300 1440305) (-893 "PATMAB.spad" 1438218 1438228 1438779 1438784) (-892 "PATLRES.spad" 1437304 1437318 1438208 1438213) (-891 "PATAB.spad" 1437068 1437078 1437294 1437299) (-890 "PARTPERM.spad" 1435076 1435084 1437058 1437063) (-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 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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 2266397 2266402 2266407 2266412) (-2 NIL 2266377 2266382 2266387 2266392) (-1 NIL 2266357 2266362 2266367 2266372) (0 NIL 2266337 2266342 2266347 2266352) (-1306 "ZMOD.spad" 2266146 2266159 2266275 2266332) (-1305 "ZLINDEP.spad" 2265212 2265223 2266136 2266141) (-1304 "ZDSOLVE.spad" 2255157 2255179 2265202 2265207) (-1303 "YSTREAM.spad" 2254652 2254663 2255147 2255152) (-1302 "YDIAGRAM.spad" 2254286 2254295 2254642 2254647) (-1301 "XRPOLY.spad" 2253506 2253526 2254142 2254211) (-1300 "XPR.spad" 2251301 2251314 2253224 2253323) (-1299 "XPOLY.spad" 2250856 2250867 2251157 2251226) (-1298 "XPOLYC.spad" 2250175 2250191 2250782 2250851) (-1297 "XPBWPOLY.spad" 2248612 2248632 2249955 2250024) (-1296 "XF.spad" 2247075 2247090 2248514 2248607) (-1295 "XF.spad" 2245518 2245535 2246959 2246964) (-1294 "XFALG.spad" 2242566 2242582 2245444 2245513) (-1293 "XEXPPKG.spad" 2241817 2241843 2242556 2242561) (-1292 "XDPOLY.spad" 2241431 2241447 2241673 2241742) (-1291 "XALG.spad" 2241091 2241102 2241387 2241426) (-1290 "WUTSET.spad" 2236930 2236947 2240737 2240764) (-1289 "WP.spad" 2236129 2236173 2236788 2236855) (-1288 "WHILEAST.spad" 2235927 2235936 2236119 2236124) (-1287 "WHEREAST.spad" 2235598 2235607 2235917 2235922) (-1286 "WFFINTBS.spad" 2233261 2233283 2235588 2235593) (-1285 "WEIER.spad" 2231483 2231494 2233251 2233256) (-1284 "VSPACE.spad" 2231156 2231167 2231451 2231478) (-1283 "VSPACE.spad" 2230849 2230862 2231146 2231151) (-1282 "VOID.spad" 2230526 2230535 2230839 2230844) (-1281 "VIEW.spad" 2228206 2228215 2230516 2230521) (-1280 "VIEWDEF.spad" 2223407 2223416 2228196 2228201) (-1279 "VIEW3D.spad" 2207368 2207377 2223397 2223402) (-1278 "VIEW2D.spad" 2195259 2195268 2207358 2207363) (-1277 "VECTOR.spad" 2193933 2193944 2194184 2194211) (-1276 "VECTOR2.spad" 2192572 2192585 2193923 2193928) (-1275 "VECTCAT.spad" 2190476 2190487 2192540 2192567) (-1274 "VECTCAT.spad" 2188187 2188200 2190253 2190258) (-1273 "VARIABLE.spad" 2187967 2187982 2188177 2188182) (-1272 "UTYPE.spad" 2187611 2187620 2187957 2187962) (-1271 "UTSODETL.spad" 2186906 2186930 2187567 2187572) (-1270 "UTSODE.spad" 2185122 2185142 2186896 2186901) (-1269 "UTS.spad" 2179926 2179954 2183589 2183686) (-1268 "UTSCAT.spad" 2177405 2177421 2179824 2179921) (-1267 "UTSCAT.spad" 2174528 2174546 2176949 2176954) (-1266 "UTS2.spad" 2174123 2174158 2174518 2174523) (-1265 "URAGG.spad" 2168796 2168807 2174113 2174118) (-1264 "URAGG.spad" 2163433 2163446 2168752 2168757) (-1263 "UPXSSING.spad" 2161078 2161104 2162514 2162647) (-1262 "UPXS.spad" 2158232 2158260 2159210 2159359) (-1261 "UPXSCONS.spad" 2155991 2156011 2156364 2156513) (-1260 "UPXSCCA.spad" 2154562 2154582 2155837 2155986) (-1259 "UPXSCCA.spad" 2153275 2153297 2154552 2154557) (-1258 "UPXSCAT.spad" 2151864 2151880 2153121 2153270) (-1257 "UPXS2.spad" 2151407 2151460 2151854 2151859) (-1256 "UPSQFREE.spad" 2149821 2149835 2151397 2151402) (-1255 "UPSCAT.spad" 2147608 2147632 2149719 2149816) (-1254 "UPSCAT.spad" 2145101 2145127 2147214 2147219) (-1253 "UPOLYC.spad" 2140141 2140152 2144943 2145096) (-1252 "UPOLYC.spad" 2135073 2135086 2139877 2139882) (-1251 "UPOLYC2.spad" 2134544 2134563 2135063 2135068) (-1250 "UP.spad" 2131743 2131758 2132130 2132283) (-1249 "UPMP.spad" 2130643 2130656 2131733 2131738) (-1248 "UPDIVP.spad" 2130208 2130222 2130633 2130638) (-1247 "UPDECOMP.spad" 2128453 2128467 2130198 2130203) (-1246 "UPCDEN.spad" 2127662 2127678 2128443 2128448) (-1245 "UP2.spad" 2127026 2127047 2127652 2127657) (-1244 "UNISEG.spad" 2126379 2126390 2126945 2126950) (-1243 "UNISEG2.spad" 2125876 2125889 2126335 2126340) (-1242 "UNIFACT.spad" 2124979 2124991 2125866 2125871) (-1241 "ULS.spad" 2115537 2115565 2116624 2117053) (-1240 "ULSCONS.spad" 2107933 2107953 2108303 2108452) (-1239 "ULSCCAT.spad" 2105670 2105690 2107779 2107928) (-1238 "ULSCCAT.spad" 2103515 2103537 2105626 2105631) (-1237 "ULSCAT.spad" 2101747 2101763 2103361 2103510) (-1236 "ULS2.spad" 2101261 2101314 2101737 2101742) (-1235 "UINT8.spad" 2101138 2101147 2101251 2101256) (-1234 "UINT64.spad" 2101014 2101023 2101128 2101133) (-1233 "UINT32.spad" 2100890 2100899 2101004 2101009) (-1232 "UINT16.spad" 2100766 2100775 2100880 2100885) (-1231 "UFD.spad" 2099831 2099840 2100692 2100761) (-1230 "UFD.spad" 2098958 2098969 2099821 2099826) (-1229 "UDVO.spad" 2097839 2097848 2098948 2098953) (-1228 "UDPO.spad" 2095332 2095343 2097795 2097800) (-1227 "TYPE.spad" 2095264 2095273 2095322 2095327) (-1226 "TYPEAST.spad" 2095183 2095192 2095254 2095259) (-1225 "TWOFACT.spad" 2093835 2093850 2095173 2095178) (-1224 "TUPLE.spad" 2093321 2093332 2093734 2093739) (-1223 "TUBETOOL.spad" 2090188 2090197 2093311 2093316) (-1222 "TUBE.spad" 2088835 2088852 2090178 2090183) (-1221 "TS.spad" 2087434 2087450 2088400 2088497) (-1220 "TSETCAT.spad" 2074561 2074578 2087402 2087429) (-1219 "TSETCAT.spad" 2061674 2061693 2074517 2074522) (-1218 "TRMANIP.spad" 2056040 2056057 2061380 2061385) (-1217 "TRIMAT.spad" 2055003 2055028 2056030 2056035) (-1216 "TRIGMNIP.spad" 2053530 2053547 2054993 2054998) (-1215 "TRIGCAT.spad" 2053042 2053051 2053520 2053525) (-1214 "TRIGCAT.spad" 2052552 2052563 2053032 2053037) (-1213 "TREE.spad" 2051127 2051138 2052159 2052186) (-1212 "TRANFUN.spad" 2050966 2050975 2051117 2051122) (-1211 "TRANFUN.spad" 2050803 2050814 2050956 2050961) (-1210 "TOPSP.spad" 2050477 2050486 2050793 2050798) (-1209 "TOOLSIGN.spad" 2050140 2050151 2050467 2050472) (-1208 "TEXTFILE.spad" 2048701 2048710 2050130 2050135) (-1207 "TEX.spad" 2045847 2045856 2048691 2048696) (-1206 "TEX1.spad" 2045403 2045414 2045837 2045842) (-1205 "TEMUTL.spad" 2044958 2044967 2045393 2045398) (-1204 "TBCMPPK.spad" 2043051 2043074 2044948 2044953) (-1203 "TBAGG.spad" 2042101 2042124 2043031 2043046) (-1202 "TBAGG.spad" 2041159 2041184 2042091 2042096) (-1201 "TANEXP.spad" 2040567 2040578 2041149 2041154) (-1200 "TALGOP.spad" 2040291 2040302 2040557 2040562) (-1199 "TABLE.spad" 2038702 2038725 2038972 2038999) (-1198 "TABLEAU.spad" 2038183 2038194 2038692 2038697) (-1197 "TABLBUMP.spad" 2034986 2034997 2038173 2038178) (-1196 "SYSTEM.spad" 2034214 2034223 2034976 2034981) (-1195 "SYSSOLP.spad" 2031697 2031708 2034204 2034209) (-1194 "SYSPTR.spad" 2031596 2031605 2031687 2031692) (-1193 "SYSNNI.spad" 2030778 2030789 2031586 2031591) (-1192 "SYSINT.spad" 2030182 2030193 2030768 2030773) (-1191 "SYNTAX.spad" 2026388 2026397 2030172 2030177) (-1190 "SYMTAB.spad" 2024456 2024465 2026378 2026383) (-1189 "SYMS.spad" 2020479 2020488 2024446 2024451) (-1188 "SYMPOLY.spad" 2019486 2019497 2019568 2019695) (-1187 "SYMFUNC.spad" 2018987 2018998 2019476 2019481) (-1186 "SYMBOL.spad" 2016490 2016499 2018977 2018982) (-1185 "SWITCH.spad" 2013261 2013270 2016480 2016485) (-1184 "SUTS.spad" 2010166 2010194 2011728 2011825) (-1183 "SUPXS.spad" 2007307 2007335 2008298 2008447) (-1182 "SUP.spad" 2004120 2004131 2004893 2005046) (-1181 "SUPFRACF.spad" 2003225 2003243 2004110 2004115) (-1180 "SUP2.spad" 2002617 2002630 2003215 2003220) (-1179 "SUMRF.spad" 2001591 2001602 2002607 2002612) (-1178 "SUMFS.spad" 2001228 2001245 2001581 2001586) (-1177 "SULS.spad" 1991773 1991801 1992873 1993302) (-1176 "SUCHTAST.spad" 1991542 1991551 1991763 1991768) (-1175 "SUCH.spad" 1991224 1991239 1991532 1991537) (-1174 "SUBSPACE.spad" 1983339 1983354 1991214 1991219) (-1173 "SUBRESP.spad" 1982509 1982523 1983295 1983300) (-1172 "STTF.spad" 1978608 1978624 1982499 1982504) (-1171 "STTFNC.spad" 1975076 1975092 1978598 1978603) (-1170 "STTAYLOR.spad" 1967711 1967722 1974957 1974962) (-1169 "STRTBL.spad" 1966216 1966233 1966365 1966392) (-1168 "STRING.spad" 1965625 1965634 1965639 1965666) (-1167 "STRICAT.spad" 1965413 1965422 1965593 1965620) (-1166 "STREAM.spad" 1962331 1962342 1964938 1964953) (-1165 "STREAM3.spad" 1961904 1961919 1962321 1962326) (-1164 "STREAM2.spad" 1961032 1961045 1961894 1961899) (-1163 "STREAM1.spad" 1960738 1960749 1961022 1961027) (-1162 "STINPROD.spad" 1959674 1959690 1960728 1960733) (-1161 "STEP.spad" 1958875 1958884 1959664 1959669) (-1160 "STEPAST.spad" 1958109 1958118 1958865 1958870) (-1159 "STBL.spad" 1956635 1956663 1956802 1956817) (-1158 "STAGG.spad" 1955710 1955721 1956625 1956630) (-1157 "STAGG.spad" 1954783 1954796 1955700 1955705) (-1156 "STACK.spad" 1954140 1954151 1954390 1954417) (-1155 "SREGSET.spad" 1951844 1951861 1953786 1953813) (-1154 "SRDCMPK.spad" 1950405 1950425 1951834 1951839) (-1153 "SRAGG.spad" 1945548 1945557 1950373 1950400) (-1152 "SRAGG.spad" 1940711 1940722 1945538 1945543) (-1151 "SQMATRIX.spad" 1938327 1938345 1939243 1939330) (-1150 "SPLTREE.spad" 1932879 1932892 1937763 1937790) (-1149 "SPLNODE.spad" 1929467 1929480 1932869 1932874) (-1148 "SPFCAT.spad" 1928276 1928285 1929457 1929462) (-1147 "SPECOUT.spad" 1926828 1926837 1928266 1928271) (-1146 "SPADXPT.spad" 1918423 1918432 1926818 1926823) (-1145 "spad-parser.spad" 1917888 1917897 1918413 1918418) (-1144 "SPADAST.spad" 1917589 1917598 1917878 1917883) (-1143 "SPACEC.spad" 1901788 1901799 1917579 1917584) (-1142 "SPACE3.spad" 1901564 1901575 1901778 1901783) (-1141 "SORTPAK.spad" 1901113 1901126 1901520 1901525) (-1140 "SOLVETRA.spad" 1898876 1898887 1901103 1901108) (-1139 "SOLVESER.spad" 1897404 1897415 1898866 1898871) (-1138 "SOLVERAD.spad" 1893430 1893441 1897394 1897399) (-1137 "SOLVEFOR.spad" 1891892 1891910 1893420 1893425) (-1136 "SNTSCAT.spad" 1891492 1891509 1891860 1891887) (-1135 "SMTS.spad" 1889764 1889790 1891057 1891154) (-1134 "SMP.spad" 1887239 1887259 1887629 1887756) (-1133 "SMITH.spad" 1886084 1886109 1887229 1887234) (-1132 "SMATCAT.spad" 1884194 1884224 1886028 1886079) (-1131 "SMATCAT.spad" 1882236 1882268 1884072 1884077) (-1130 "SKAGG.spad" 1881199 1881210 1882204 1882231) (-1129 "SINT.spad" 1880139 1880148 1881065 1881194) (-1128 "SIMPAN.spad" 1879867 1879876 1880129 1880134) (-1127 "SIG.spad" 1879197 1879206 1879857 1879862) (-1126 "SIGNRF.spad" 1878315 1878326 1879187 1879192) (-1125 "SIGNEF.spad" 1877594 1877611 1878305 1878310) (-1124 "SIGAST.spad" 1876979 1876988 1877584 1877589) (-1123 "SHP.spad" 1874907 1874922 1876935 1876940) (-1122 "SHDP.spad" 1864618 1864645 1865127 1865258) (-1121 "SGROUP.spad" 1864226 1864235 1864608 1864613) (-1120 "SGROUP.spad" 1863832 1863843 1864216 1864221) (-1119 "SGCF.spad" 1856971 1856980 1863822 1863827) (-1118 "SFRTCAT.spad" 1855901 1855918 1856939 1856966) (-1117 "SFRGCD.spad" 1854964 1854984 1855891 1855896) (-1116 "SFQCMPK.spad" 1849601 1849621 1854954 1854959) (-1115 "SFORT.spad" 1849040 1849054 1849591 1849596) (-1114 "SEXOF.spad" 1848883 1848923 1849030 1849035) (-1113 "SEX.spad" 1848775 1848784 1848873 1848878) (-1112 "SEXCAT.spad" 1846556 1846596 1848765 1848770) (-1111 "SET.spad" 1844880 1844891 1845977 1846016) (-1110 "SETMN.spad" 1843330 1843347 1844870 1844875) (-1109 "SETCAT.spad" 1842652 1842661 1843320 1843325) (-1108 "SETCAT.spad" 1841972 1841983 1842642 1842647) (-1107 "SETAGG.spad" 1838521 1838532 1841952 1841967) (-1106 "SETAGG.spad" 1835078 1835091 1838511 1838516) (-1105 "SEQAST.spad" 1834781 1834790 1835068 1835073) (-1104 "SEGXCAT.spad" 1833937 1833950 1834771 1834776) (-1103 "SEG.spad" 1833750 1833761 1833856 1833861) (-1102 "SEGCAT.spad" 1832675 1832686 1833740 1833745) (-1101 "SEGBIND.spad" 1832433 1832444 1832622 1832627) (-1100 "SEGBIND2.spad" 1832131 1832144 1832423 1832428) (-1099 "SEGAST.spad" 1831845 1831854 1832121 1832126) (-1098 "SEG2.spad" 1831280 1831293 1831801 1831806) (-1097 "SDVAR.spad" 1830556 1830567 1831270 1831275) (-1096 "SDPOL.spad" 1827982 1827993 1828273 1828400) (-1095 "SCPKG.spad" 1826071 1826082 1827972 1827977) (-1094 "SCOPE.spad" 1825224 1825233 1826061 1826066) (-1093 "SCACHE.spad" 1823920 1823931 1825214 1825219) (-1092 "SASTCAT.spad" 1823829 1823838 1823910 1823915) (-1091 "SAOS.spad" 1823701 1823710 1823819 1823824) (-1090 "SAERFFC.spad" 1823414 1823434 1823691 1823696) (-1089 "SAE.spad" 1821589 1821605 1822200 1822335) (-1088 "SAEFACT.spad" 1821290 1821310 1821579 1821584) (-1087 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1738772 1739762 1739855) (-1068 "RNS.spad" 1737752 1737763 1738753 1738758) (-1067 "RNG.spad" 1737487 1737496 1737742 1737747) (-1066 "RNGBIND.spad" 1736647 1736661 1737442 1737447) (-1065 "RMODULE.spad" 1736412 1736423 1736637 1736642) (-1064 "RMCAT2.spad" 1735832 1735889 1736402 1736407) (-1063 "RMATRIX.spad" 1734656 1734675 1734999 1735038) (-1062 "RMATCAT.spad" 1730235 1730266 1734612 1734651) (-1061 "RMATCAT.spad" 1725704 1725737 1730083 1730088) (-1060 "RLINSET.spad" 1725098 1725109 1725694 1725699) (-1059 "RINTERP.spad" 1724986 1725006 1725088 1725093) (-1058 "RING.spad" 1724456 1724465 1724966 1724981) (-1057 "RING.spad" 1723934 1723945 1724446 1724451) (-1056 "RIDIST.spad" 1723326 1723335 1723924 1723929) (-1055 "RGCHAIN.spad" 1721909 1721925 1722811 1722838) (-1054 "RGBCSPC.spad" 1721690 1721702 1721899 1721904) (-1053 "RGBCMDL.spad" 1721220 1721232 1721680 1721685) (-1052 "RF.spad" 1718862 1718873 1721210 1721215) (-1051 "RFFACTOR.spad" 1718324 1718335 1718852 1718857) (-1050 "RFFACT.spad" 1718059 1718071 1718314 1718319) (-1049 "RFDIST.spad" 1717055 1717064 1718049 1718054) (-1048 "RETSOL.spad" 1716474 1716487 1717045 1717050) (-1047 "RETRACT.spad" 1715902 1715913 1716464 1716469) (-1046 "RETRACT.spad" 1715328 1715341 1715892 1715897) (-1045 "RETAST.spad" 1715140 1715149 1715318 1715323) (-1044 "RESULT.spad" 1713200 1713209 1713787 1713814) (-1043 "RESRING.spad" 1712547 1712594 1713138 1713195) (-1042 "RESLATC.spad" 1711871 1711882 1712537 1712542) (-1041 "REPSQ.spad" 1711602 1711613 1711861 1711866) (-1040 "REP.spad" 1709156 1709165 1711592 1711597) (-1039 "REPDB.spad" 1708863 1708874 1709146 1709151) (-1038 "REP2.spad" 1698521 1698532 1708705 1708710) (-1037 "REP1.spad" 1692717 1692728 1698471 1698476) (-1036 "REGSET.spad" 1690514 1690531 1692363 1692390) (-1035 "REF.spad" 1689849 1689860 1690469 1690474) (-1034 "REDORDER.spad" 1689055 1689072 1689839 1689844) (-1033 "RECLOS.spad" 1687838 1687858 1688542 1688635) (-1032 "REALSOLV.spad" 1686978 1686987 1687828 1687833) (-1031 "REAL.spad" 1686850 1686859 1686968 1686973) (-1030 "REAL0Q.spad" 1684148 1684163 1686840 1686845) (-1029 "REAL0.spad" 1680992 1681007 1684138 1684143) (-1028 "RDUCEAST.spad" 1680713 1680722 1680982 1680987) (-1027 "RDIV.spad" 1680368 1680393 1680703 1680708) (-1026 "RDIST.spad" 1679935 1679946 1680358 1680363) (-1025 "RDETRS.spad" 1678799 1678817 1679925 1679930) (-1024 "RDETR.spad" 1676938 1676956 1678789 1678794) (-1023 "RDEEFS.spad" 1676037 1676054 1676928 1676933) (-1022 "RDEEF.spad" 1675047 1675064 1676027 1676032) (-1021 "RCFIELD.spad" 1672233 1672242 1674949 1675042) (-1020 "RCFIELD.spad" 1669505 1669516 1672223 1672228) (-1019 "RCAGG.spad" 1667433 1667444 1669495 1669500) (-1018 "RCAGG.spad" 1665288 1665301 1667352 1667357) (-1017 "RATRET.spad" 1664648 1664659 1665278 1665283) (-1016 "RATFACT.spad" 1664340 1664352 1664638 1664643) (-1015 "RANDSRC.spad" 1663659 1663668 1664330 1664335) (-1014 "RADUTIL.spad" 1663415 1663424 1663649 1663654) (-1013 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1636853 1636858) (-994 "PWFFINTB.spad" 1632275 1632296 1634849 1634854) (-993 "PUSHVAR.spad" 1631614 1631633 1632265 1632270) (-992 "PTRANFN.spad" 1627742 1627752 1631604 1631609) (-991 "PTPACK.spad" 1624830 1624840 1627732 1627737) (-990 "PTFUNC2.spad" 1624653 1624667 1624820 1624825) (-989 "PTCAT.spad" 1623908 1623918 1624621 1624648) (-988 "PSQFR.spad" 1623215 1623239 1623898 1623903) (-987 "PSEUDLIN.spad" 1622101 1622111 1623205 1623210) (-986 "PSETPK.spad" 1607534 1607550 1621979 1621984) (-985 "PSETCAT.spad" 1601454 1601477 1607514 1607529) (-984 "PSETCAT.spad" 1595348 1595373 1601410 1601415) (-983 "PSCURVE.spad" 1594331 1594339 1595338 1595343) (-982 "PSCAT.spad" 1593114 1593143 1594229 1594326) (-981 "PSCAT.spad" 1591987 1592018 1593104 1593109) (-980 "PRTITION.spad" 1590685 1590693 1591977 1591982) (-979 "PRTDAST.spad" 1590404 1590412 1590675 1590680) (-978 "PRS.spad" 1579966 1579983 1590360 1590365) (-977 "PRQAGG.spad" 1579401 1579411 1579934 1579961) (-976 "PROPLOG.spad" 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1560082) (-957 "POLYCATQ.spad" 1557470 1557492 1559342 1559347) (-956 "POLYCAT.spad" 1550940 1550961 1557338 1557465) (-955 "POLYCAT.spad" 1543748 1543771 1550148 1550153) (-954 "POLY2UP.spad" 1543200 1543214 1543738 1543743) (-953 "POLY2.spad" 1542797 1542809 1543190 1543195) (-952 "POLUTIL.spad" 1541738 1541767 1542753 1542758) (-951 "POLTOPOL.spad" 1540486 1540501 1541728 1541733) (-950 "POINT.spad" 1539324 1539334 1539411 1539438) (-949 "PNTHEORY.spad" 1536026 1536034 1539314 1539319) (-948 "PMTOOLS.spad" 1534801 1534815 1536016 1536021) (-947 "PMSYM.spad" 1534350 1534360 1534791 1534796) (-946 "PMQFCAT.spad" 1533941 1533955 1534340 1534345) (-945 "PMPRED.spad" 1533420 1533434 1533931 1533936) (-944 "PMPREDFS.spad" 1532874 1532896 1533410 1533415) (-943 "PMPLCAT.spad" 1531954 1531972 1532806 1532811) (-942 "PMLSAGG.spad" 1531539 1531553 1531944 1531949) (-941 "PMKERNEL.spad" 1531118 1531130 1531529 1531534) (-940 "PMINS.spad" 1530698 1530708 1531108 1531113) (-939 "PMFS.spad" 1530275 1530293 1530688 1530693) (-938 "PMDOWN.spad" 1529565 1529579 1530265 1530270) (-937 "PMASS.spad" 1528575 1528583 1529555 1529560) (-936 "PMASSFS.spad" 1527542 1527558 1528565 1528570) (-935 "PLOTTOOL.spad" 1527322 1527330 1527532 1527537) (-934 "PLOT.spad" 1522245 1522253 1527312 1527317) (-933 "PLOT3D.spad" 1518709 1518717 1522235 1522240) (-932 "PLOT1.spad" 1517866 1517876 1518699 1518704) (-931 "PLEQN.spad" 1505156 1505183 1517856 1517861) (-930 "PINTERP.spad" 1504778 1504797 1505146 1505151) (-929 "PINTERPA.spad" 1504562 1504578 1504768 1504773) (-928 "PI.spad" 1504171 1504179 1504536 1504557) (-927 "PID.spad" 1503141 1503149 1504097 1504166) (-926 "PICOERCE.spad" 1502798 1502808 1503131 1503136) (-925 "PGROEB.spad" 1501399 1501413 1502788 1502793) (-924 "PGE.spad" 1493016 1493024 1501389 1501394) (-923 "PGCD.spad" 1491906 1491923 1493006 1493011) (-922 "PFRPAC.spad" 1491055 1491065 1491896 1491901) (-921 "PFR.spad" 1487718 1487728 1490957 1491050) (-920 "PFOTOOLS.spad" 1486976 1486992 1487708 1487713) (-919 "PFOQ.spad" 1486346 1486364 1486966 1486971) (-918 "PFO.spad" 1485765 1485792 1486336 1486341) (-917 "PF.spad" 1485339 1485351 1485570 1485663) (-916 "PFECAT.spad" 1483021 1483029 1485265 1485334) (-915 "PFECAT.spad" 1480731 1480741 1482977 1482982) (-914 "PFBRU.spad" 1478619 1478631 1480721 1480726) (-913 "PFBR.spad" 1476179 1476202 1478609 1478614) (-912 "PERM.spad" 1471864 1471874 1476009 1476024) (-911 "PERMGRP.spad" 1466626 1466636 1471854 1471859) (-910 "PERMCAT.spad" 1465184 1465194 1466606 1466621) (-909 "PERMAN.spad" 1463716 1463730 1465174 1465179) (-908 "PENDTREE.spad" 1463057 1463067 1463345 1463350) (-907 "PDRING.spad" 1461608 1461618 1463037 1463052) (-906 "PDRING.spad" 1460167 1460179 1461598 1461603) (-905 "PDEPROB.spad" 1459182 1459190 1460157 1460162) (-904 "PDEPACK.spad" 1453222 1453230 1459172 1459177) (-903 "PDECOMP.spad" 1452692 1452709 1453212 1453217) (-902 "PDECAT.spad" 1451048 1451056 1452682 1452687) (-901 "PCOMP.spad" 1450901 1450914 1451038 1451043) (-900 "PBWLB.spad" 1449489 1449506 1450891 1450896) (-899 "PATTERN.spad" 1444028 1444038 1449479 1449484) (-898 "PATTERN2.spad" 1443766 1443778 1444018 1444023) (-897 "PATTERN1.spad" 1442102 1442118 1443756 1443761) (-896 "PATRES.spad" 1439677 1439689 1442092 1442097) (-895 "PATRES2.spad" 1439349 1439363 1439667 1439672) (-894 "PATMATCH.spad" 1437546 1437577 1439057 1439062) (-893 "PATMAB.spad" 1436975 1436985 1437536 1437541) (-892 "PATLRES.spad" 1436061 1436075 1436965 1436970) (-891 "PATAB.spad" 1435825 1435835 1436051 1436056) (-890 "PARTPERM.spad" 1433833 1433841 1435815 1435820) (-889 "PARSURF.spad" 1433267 1433295 1433823 1433828) (-888 "PARSU2.spad" 1433064 1433080 1433257 1433262) (-887 "script-parser.spad" 1432584 1432592 1433054 1433059) (-886 "PARSCURV.spad" 1432018 1432046 1432574 1432579) (-885 "PARSC2.spad" 1431809 1431825 1432008 1432013) (-884 "PARPCURV.spad" 1431271 1431299 1431799 1431804) (-883 "PARPC2.spad" 1431062 1431078 1431261 1431266) (-882 "PARAMAST.spad" 1430190 1430198 1431052 1431057) (-881 "PAN2EXPR.spad" 1429602 1429610 1430180 1430185) (-880 "PALETTE.spad" 1428572 1428580 1429592 1429597) (-879 "PAIR.spad" 1427559 1427572 1428160 1428165) (-878 "PADICRC.spad" 1424893 1424911 1426064 1426157) (-877 "PADICRAT.spad" 1422908 1422920 1423129 1423222) (-876 "PADIC.spad" 1422603 1422615 1422834 1422903) (-875 "PADICCT.spad" 1421152 1421164 1422529 1422598) (-874 "PADEPAC.spad" 1419841 1419860 1421142 1421147) (-873 "PADE.spad" 1418593 1418609 1419831 1419836) (-872 "OWP.spad" 1417833 1417863 1418451 1418518) (-871 "OVERSET.spad" 1417406 1417414 1417823 1417828) (-870 "OVAR.spad" 1417187 1417210 1417396 1417401) (-869 "OUT.spad" 1416273 1416281 1417177 1417182) (-868 "OUTFORM.spad" 1405665 1405673 1416263 1416268) (-867 "OUTBFILE.spad" 1405083 1405091 1405655 1405660) (-866 "OUTBCON.spad" 1404089 1404097 1405073 1405078) (-865 "OUTBCON.spad" 1403093 1403103 1404079 1404084) (-864 "OSI.spad" 1402568 1402576 1403083 1403088) (-863 "OSGROUP.spad" 1402486 1402494 1402558 1402563) (-862 "ORTHPOL.spad" 1400971 1400981 1402403 1402408) (-861 "OREUP.spad" 1400424 1400452 1400651 1400690) (-860 "ORESUP.spad" 1399725 1399749 1400104 1400143) (-859 "OREPCTO.spad" 1397582 1397594 1399645 1399650) (-858 "OREPCAT.spad" 1391729 1391739 1397538 1397577) (-857 "OREPCAT.spad" 1385766 1385778 1391577 1391582) (-856 "ORDSET.spad" 1384938 1384946 1385756 1385761) (-855 "ORDSET.spad" 1384108 1384118 1384928 1384933) (-854 "ORDRING.spad" 1383498 1383506 1384088 1384103) (-853 "ORDRING.spad" 1382896 1382906 1383488 1383493) (-852 "ORDMON.spad" 1382751 1382759 1382886 1382891) (-851 "ORDFUNS.spad" 1381883 1381899 1382741 1382746) (-850 "ORDFIN.spad" 1381703 1381711 1381873 1381878) (-849 "ORDCOMP.spad" 1380168 1380178 1381250 1381279) (-848 "ORDCOMP2.spad" 1379461 1379473 1380158 1380163) (-847 "OPTPROB.spad" 1378099 1378107 1379451 1379456) (-846 "OPTPACK.spad" 1370508 1370516 1378089 1378094) (-845 "OPTCAT.spad" 1368187 1368195 1370498 1370503) (-844 "OPSIG.spad" 1367841 1367849 1368177 1368182) (-843 "OPQUERY.spad" 1367390 1367398 1367831 1367836) (-842 "OP.spad" 1367132 1367142 1367212 1367279) (-841 "OPERCAT.spad" 1366598 1366608 1367122 1367127) (-840 "OPERCAT.spad" 1366062 1366074 1366588 1366593) (-839 "ONECOMP.spad" 1364807 1364817 1365609 1365638) (-838 "ONECOMP2.spad" 1364231 1364243 1364797 1364802) (-837 "OMSERVER.spad" 1363237 1363245 1364221 1364226) (-836 "OMSAGG.spad" 1363025 1363035 1363193 1363232) (-835 "OMPKG.spad" 1361641 1361649 1363015 1363020) (-834 "OM.spad" 1360614 1360622 1361631 1361636) (-833 "OMLO.spad" 1360039 1360051 1360500 1360539) (-832 "OMEXPR.spad" 1359873 1359883 1360029 1360034) (-831 "OMERR.spad" 1359418 1359426 1359863 1359868) (-830 "OMERRK.spad" 1358452 1358460 1359408 1359413) (-829 "OMENC.spad" 1357796 1357804 1358442 1358447) (-828 "OMDEV.spad" 1352105 1352113 1357786 1357791) (-827 "OMCONN.spad" 1351514 1351522 1352095 1352100) (-826 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1301405) (-807 "ODECONST.spad" 1296438 1296456 1296891 1296896) (-806 "ODECAT.spad" 1295036 1295044 1296428 1296433) (-805 "OCT.spad" 1293172 1293182 1293886 1293925) (-804 "OCTCT2.spad" 1292818 1292839 1293162 1293167) (-803 "OC.spad" 1290614 1290624 1292774 1292813) (-802 "OC.spad" 1288135 1288147 1290297 1290302) (-801 "OCAMON.spad" 1287983 1287991 1288125 1288130) (-800 "OASGP.spad" 1287798 1287806 1287973 1287978) (-799 "OAMONS.spad" 1287320 1287328 1287788 1287793) (-798 "OAMON.spad" 1287181 1287189 1287310 1287315) (-797 "OAGROUP.spad" 1287043 1287051 1287171 1287176) (-796 "NUMTUBE.spad" 1286634 1286650 1287033 1287038) (-795 "NUMQUAD.spad" 1274610 1274618 1286624 1286629) (-794 "NUMODE.spad" 1265964 1265972 1274600 1274605) (-793 "NUMINT.spad" 1263530 1263538 1265954 1265959) (-792 "NUMFMT.spad" 1262370 1262378 1263520 1263525) (-791 "NUMERIC.spad" 1254484 1254494 1262175 1262180) (-790 "NTSCAT.spad" 1252992 1253008 1254452 1254479) (-789 "NTPOLFN.spad" 1252543 1252553 1252909 1252914) (-788 "NSUP.spad" 1245589 1245599 1250129 1250282) (-787 "NSUP2.spad" 1244981 1244993 1245579 1245584) (-786 "NSMP.spad" 1241211 1241230 1241519 1241646) (-785 "NREP.spad" 1239589 1239603 1241201 1241206) (-784 "NPCOEF.spad" 1238835 1238855 1239579 1239584) (-783 "NORMRETR.spad" 1238433 1238472 1238825 1238830) (-782 "NORMPK.spad" 1236335 1236354 1238423 1238428) (-781 "NORMMA.spad" 1236023 1236049 1236325 1236330) (-780 "NONE.spad" 1235764 1235772 1236013 1236018) (-779 "NONE1.spad" 1235440 1235450 1235754 1235759) (-778 "NODE1.spad" 1234927 1234943 1235430 1235435) (-777 "NNI.spad" 1233822 1233830 1234901 1234922) (-776 "NLINSOL.spad" 1232448 1232458 1233812 1233817) (-775 "NIPROB.spad" 1230989 1230997 1232438 1232443) (-774 "NFINTBAS.spad" 1228549 1228566 1230979 1230984) (-773 "NETCLT.spad" 1228523 1228534 1228539 1228544) (-772 "NCODIV.spad" 1226739 1226755 1228513 1228518) (-771 "NCNTFRAC.spad" 1226381 1226395 1226729 1226734) (-770 "NCEP.spad" 1224547 1224561 1226371 1226376) (-769 "NASRING.spad" 1224143 1224151 1224537 1224542) (-768 "NASRING.spad" 1223737 1223747 1224133 1224138) (-767 "NARNG.spad" 1223089 1223097 1223727 1223732) (-766 "NARNG.spad" 1222439 1222449 1223079 1223084) (-765 "NAGSP.spad" 1221516 1221524 1222429 1222434) (-764 "NAGS.spad" 1211177 1211185 1221506 1221511) (-763 "NAGF07.spad" 1209608 1209616 1211167 1211172) (-762 "NAGF04.spad" 1204010 1204018 1209598 1209603) (-761 "NAGF02.spad" 1198079 1198087 1204000 1204005) (-760 "NAGF01.spad" 1193840 1193848 1198069 1198074) (-759 "NAGE04.spad" 1187540 1187548 1193830 1193835) (-758 "NAGE02.spad" 1178200 1178208 1187530 1187535) (-757 "NAGE01.spad" 1174202 1174210 1178190 1178195) (-756 "NAGD03.spad" 1172206 1172214 1174192 1174197) (-755 "NAGD02.spad" 1164953 1164961 1172196 1172201) (-754 "NAGD01.spad" 1159246 1159254 1164943 1164948) (-753 "NAGC06.spad" 1155121 1155129 1159236 1159241) (-752 "NAGC05.spad" 1153622 1153630 1155111 1155116) (-751 "NAGC02.spad" 1152889 1152897 1153612 1153617) (-750 "NAALG.spad" 1152430 1152440 1152857 1152884) (-749 "NAALG.spad" 1151991 1152003 1152420 1152425) (-748 "MULTSQFR.spad" 1148949 1148966 1151981 1151986) (-747 "MULTFACT.spad" 1148332 1148349 1148939 1148944) (-746 "MTSCAT.spad" 1146426 1146447 1148230 1148327) (-745 "MTHING.spad" 1146085 1146095 1146416 1146421) (-744 "MSYSCMD.spad" 1145519 1145527 1146075 1146080) (-743 "MSET.spad" 1143477 1143487 1145225 1145264) (-742 "MSETAGG.spad" 1143322 1143332 1143445 1143472) (-741 "MRING.spad" 1140299 1140311 1143030 1143097) (-740 "MRF2.spad" 1139869 1139883 1140289 1140294) (-739 "MRATFAC.spad" 1139415 1139432 1139859 1139864) (-738 "MPRFF.spad" 1137455 1137474 1139405 1139410) (-737 "MPOLY.spad" 1134926 1134941 1135285 1135412) (-736 "MPCPF.spad" 1134190 1134209 1134916 1134921) (-735 "MPC3.spad" 1134007 1134047 1134180 1134185) (-734 "MPC2.spad" 1133653 1133686 1133997 1134002) (-733 "MONOTOOL.spad" 1132004 1132021 1133643 1133648) (-732 "MONOID.spad" 1131323 1131331 1131994 1131999) (-731 "MONOID.spad" 1130640 1130650 1131313 1131318) (-730 "MONOGEN.spad" 1129388 1129401 1130500 1130635) (-729 "MONOGEN.spad" 1128158 1128173 1129272 1129277) (-728 "MONADWU.spad" 1126188 1126196 1128148 1128153) (-727 "MONADWU.spad" 1124216 1124226 1126178 1126183) (-726 "MONAD.spad" 1123376 1123384 1124206 1124211) (-725 "MONAD.spad" 1122534 1122544 1123366 1123371) (-724 "MOEBIUS.spad" 1121270 1121284 1122514 1122529) (-723 "MODULE.spad" 1121140 1121150 1121238 1121265) (-722 "MODULE.spad" 1121030 1121042 1121130 1121135) (-721 "MODRING.spad" 1120365 1120404 1121010 1121025) (-720 "MODOP.spad" 1119030 1119042 1120187 1120254) (-719 "MODMONOM.spad" 1118761 1118779 1119020 1119025) (-718 "MODMON.spad" 1115556 1115572 1116275 1116428) (-717 "MODFIELD.spad" 1114918 1114957 1115458 1115551) (-716 "MMLFORM.spad" 1113778 1113786 1114908 1114913) (-715 "MMAP.spad" 1113520 1113554 1113768 1113773) (-714 "MLO.spad" 1111979 1111989 1113476 1113515) (-713 "MLIFT.spad" 1110591 1110608 1111969 1111974) (-712 "MKUCFUNC.spad" 1110126 1110144 1110581 1110586) (-711 "MKRECORD.spad" 1109730 1109743 1110116 1110121) (-710 "MKFUNC.spad" 1109137 1109147 1109720 1109725) (-709 "MKFLCFN.spad" 1108105 1108115 1109127 1109132) (-708 "MKBCFUNC.spad" 1107600 1107618 1108095 1108100) (-707 "MINT.spad" 1107039 1107047 1107502 1107595) (-706 "MHROWRED.spad" 1105550 1105560 1107029 1107034) (-705 "MFLOAT.spad" 1104070 1104078 1105440 1105545) (-704 "MFINFACT.spad" 1103470 1103492 1104060 1104065) (-703 "MESH.spad" 1101252 1101260 1103460 1103465) (-702 "MDDFACT.spad" 1099463 1099473 1101242 1101247) (-701 "MDAGG.spad" 1098754 1098764 1099443 1099458) (-700 "MCMPLX.spad" 1094765 1094773 1095379 1095580) (-699 "MCDEN.spad" 1093975 1093987 1094755 1094760) (-698 "MCALCFN.spad" 1091097 1091123 1093965 1093970) (-697 "MAYBE.spad" 1090381 1090392 1091087 1091092) (-696 "MATSTOR.spad" 1087689 1087699 1090371 1090376) (-695 "MATRIX.spad" 1086393 1086403 1086877 1086904) (-694 "MATLIN.spad" 1083737 1083761 1086277 1086282) (-693 "MATCAT.spad" 1075466 1075488 1083705 1083732) (-692 "MATCAT.spad" 1067067 1067091 1075308 1075313) (-691 "MATCAT2.spad" 1066349 1066397 1067057 1067062) (-690 "MAPPKG3.spad" 1065264 1065278 1066339 1066344) (-689 "MAPPKG2.spad" 1064602 1064614 1065254 1065259) (-688 "MAPPKG1.spad" 1063430 1063440 1064592 1064597) (-687 "MAPPAST.spad" 1062745 1062753 1063420 1063425) (-686 "MAPHACK3.spad" 1062557 1062571 1062735 1062740) (-685 "MAPHACK2.spad" 1062326 1062338 1062547 1062552) (-684 "MAPHACK1.spad" 1061970 1061980 1062316 1062321) (-683 "MAGMA.spad" 1059760 1059777 1061960 1061965) (-682 "MACROAST.spad" 1059339 1059347 1059750 1059755) (-681 "M3D.spad" 1057059 1057069 1058717 1058722) (-680 "LZSTAGG.spad" 1054297 1054307 1057049 1057054) (-679 "LZSTAGG.spad" 1051533 1051545 1054287 1054292) (-678 "LWORD.spad" 1048238 1048255 1051523 1051528) (-677 "LSTAST.spad" 1048022 1048030 1048228 1048233) (-676 "LSQM.spad" 1046252 1046266 1046646 1046697) (-675 "LSPP.spad" 1045787 1045804 1046242 1046247) (-674 "LSMP.spad" 1044637 1044665 1045777 1045782) (-673 "LSMP1.spad" 1042455 1042469 1044627 1044632) (-672 "LSAGG.spad" 1042124 1042134 1042423 1042450) (-671 "LSAGG.spad" 1041813 1041825 1042114 1042119) (-670 "LPOLY.spad" 1040767 1040786 1041669 1041738) (-669 "LPEFRAC.spad" 1040038 1040048 1040757 1040762) (-668 "LO.spad" 1039439 1039453 1039972 1039999) (-667 "LOGIC.spad" 1039041 1039049 1039429 1039434) (-666 "LOGIC.spad" 1038641 1038651 1039031 1039036) (-665 "LODOOPS.spad" 1037571 1037583 1038631 1038636) (-664 "LODO.spad" 1036955 1036971 1037251 1037290) (-663 "LODOF.spad" 1036001 1036018 1036912 1036917) (-662 "LODOCAT.spad" 1034667 1034677 1035957 1035996) (-661 "LODOCAT.spad" 1033331 1033343 1034623 1034628) (-660 "LODO2.spad" 1032604 1032616 1033011 1033050) (-659 "LODO1.spad" 1032004 1032014 1032284 1032323) (-658 "LODEEF.spad" 1030806 1030824 1031994 1031999) (-657 "LNAGG.spad" 1026953 1026963 1030796 1030801) (-656 "LNAGG.spad" 1023064 1023076 1026909 1026914) (-655 "LMOPS.spad" 1019832 1019849 1023054 1023059) (-654 "LMODULE.spad" 1019600 1019610 1019822 1019827) (-653 "LMDICT.spad" 1018887 1018897 1019151 1019178) (-652 "LLINSET.spad" 1018284 1018294 1018877 1018882) (-651 "LITERAL.spad" 1018190 1018201 1018274 1018279) (-650 "LIST.spad" 1015925 1015935 1017337 1017364) (-649 "LIST3.spad" 1015236 1015250 1015915 1015920) (-648 "LIST2.spad" 1013938 1013950 1015226 1015231) (-647 "LIST2MAP.spad" 1010841 1010853 1013928 1013933) (-646 "LINSET.spad" 1010463 1010473 1010831 1010836) (-645 "LINEXP.spad" 1009897 1009907 1010443 1010458) (-644 "LINDEP.spad" 1008706 1008718 1009809 1009814) (-643 "LIMITRF.spad" 1006634 1006644 1008696 1008701) (-642 "LIMITPS.spad" 1005537 1005550 1006624 1006629) (-641 "LIE.spad" 1003553 1003565 1004827 1004972) (-640 "LIECAT.spad" 1003029 1003039 1003479 1003548) (-639 "LIECAT.spad" 1002533 1002545 1002985 1002990) (-638 "LIB.spad" 1000746 1000754 1001192 1001207) (-637 "LGROBP.spad" 998099 998118 1000736 1000741) (-636 "LF.spad" 997054 997070 998089 998094) (-635 "LFCAT.spad" 996113 996121 997044 997049) (-634 "LEXTRIPK.spad" 991616 991631 996103 996108) (-633 "LEXP.spad" 989619 989646 991596 991611) (-632 "LETAST.spad" 989318 989326 989609 989614) (-631 "LEADCDET.spad" 987716 987733 989308 989313) (-630 "LAZM3PK.spad" 986420 986442 987706 987711) (-629 "LAUPOL.spad" 985113 985126 986013 986082) (-628 "LAPLACE.spad" 984696 984712 985103 985108) (-627 "LA.spad" 984136 984150 984618 984657) (-626 "LALG.spad" 983912 983922 984116 984131) (-625 "LALG.spad" 983696 983708 983902 983907) (-624 "KVTFROM.spad" 983431 983441 983686 983691) (-623 "KTVLOGIC.spad" 982943 982951 983421 983426) (-622 "KRCFROM.spad" 982681 982691 982933 982938) (-621 "KOVACIC.spad" 981404 981421 982671 982676) (-620 "KONVERT.spad" 981126 981136 981394 981399) (-619 "KOERCE.spad" 980863 980873 981116 981121) (-618 "KERNEL.spad" 979518 979528 980647 980652) (-617 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867215 867225 867784 867789) (-535 "INBFILE.spad" 866287 866295 867205 867210) (-534 "INBFF.spad" 862081 862092 866277 866282) (-533 "INBCON.spad" 860371 860379 862071 862076) (-532 "INBCON.spad" 858659 858669 860361 860366) (-531 "INAST.spad" 858320 858328 858649 858654) (-530 "IMPTAST.spad" 858028 858036 858310 858315) (-529 "IMATRIX.spad" 856973 856999 857485 857512) (-528 "IMATQF.spad" 856067 856111 856929 856934) (-527 "IMATLIN.spad" 854672 854696 856023 856028) (-526 "ILIST.spad" 853330 853345 853855 853882) (-525 "IIARRAY2.spad" 852718 852756 852937 852964) (-524 "IFF.spad" 852128 852144 852399 852492) (-523 "IFAST.spad" 851742 851750 852118 852123) (-522 "IFARRAY.spad" 849235 849250 850925 850952) (-521 "IFAMON.spad" 849097 849114 849191 849196) (-520 "IEVALAB.spad" 848502 848514 849087 849092) (-519 "IEVALAB.spad" 847905 847919 848492 848497) (-518 "IDPO.spad" 847703 847715 847895 847900) (-517 "IDPOAMS.spad" 847459 847471 847693 847698) (-516 "IDPOAM.spad" 847179 847191 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217205 217496 217501) (-188 "CTORKIND.spad" 216800 216808 217187 217192) (-187 "CTORCAT.spad" 216049 216057 216790 216795) (-186 "CTORCAT.spad" 215296 215306 216039 216044) (-185 "CTORCALL.spad" 214885 214895 215286 215291) (-184 "CSTTOOLS.spad" 214130 214143 214875 214880) (-183 "CRFP.spad" 207854 207867 214120 214125) (-182 "CRCEAST.spad" 207574 207582 207844 207849) (-181 "CRAPACK.spad" 206625 206635 207564 207569) (-180 "CPMATCH.spad" 206129 206144 206550 206555) (-179 "CPIMA.spad" 205834 205853 206119 206124) (-178 "COORDSYS.spad" 200843 200853 205824 205829) (-177 "CONTOUR.spad" 200254 200262 200833 200838) (-176 "CONTFRAC.spad" 196004 196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) 
\ No newline at end of file
-- 
cgit v1.2.3