* algebra/catdef.spad.pamphlet (LeftLinearSet): Weaken requirement

on argument. (RightLinearSet): Likewise. (LinearSet): Likewise.
author: dos-reis <gdr@axiomatics.org> 2010-06-17 02:36:50 +0000
committer: dos-reis <gdr@axiomatics.org> 2010-06-17 02:36:50 +0000
commit: 4c62f989b0c11eb9d3e6c04d966d108fd842fe5d (patch)
tree: 58d7faf9768f563e092598279e4f19e1291dbdf4 /src/share/algebra/browse.daase
parent: 5b0bfceb3efc34578e1de66194b835bb48009466 (diff)
download: open-axiom-4c62f989b0c11eb9d3e6c04d966d108fd842fe5d.tar.gz
1 files changed, 88 insertions, 88 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index df343568..0ca16cc9 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,5 +1,5 @@
 
-(2268894 . 3485693909)       
+(2268415 . 3485728182)       
 (-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 -1395 UP UPUP -4154) 
+(-40 -1395 UP UPUP -4418) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
 ((-4451 |has| (-417 |#2|) (-372)) (-4456 |has| (-417 |#2|) (-372)) (-4450 |has| (-417 |#2|) (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) 
 ((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2832 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2832 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2832 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2832 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) 
@@ -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."))) 
 ((-4458 . T) (-4459 . T)) 
-((-2832 (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|))))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|))))))) 
+((-2832 (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|))))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
@@ -172,59 +172,59 @@ NIL
 ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) 
 ((-4458 . T) (-4459 . T)) 
 ((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) 
-(-61 -2041) 
+(-61 -2039) 
 ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim}      SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT)      DOUBLE PRECISION ELAM,P,Q,X,DQDL      INTEGER JINT      P=1.0D0      Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X)      DQDL=1.0D0      RETURN      END\\end{verbatim}")) (|coerce| (($ (|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 -2041) 
+(-62 -2039) 
 ((|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 -2041) 
+(-63 -2039) 
 ((|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 -2041) 
+(-64 -2039) 
 ((|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 -2041) 
+(-65 -2039) 
 ((|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 -2041) 
+(-66 -2039) 
 ((|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 -2041) 
+(-67 -2039) 
 ((|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 -2041) 
+(-68 -2039) 
 ((|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 -2041) 
+(-69 -2039) 
 ((|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 -2041) 
+(-70 -2039) 
 ((|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 -2041) 
+(-71 -2039) 
 ((|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 -2041) 
+(-72 -2039) 
 ((|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 -2041) 
+(-73 -2039) 
 ((|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 -2041) 
+(-74 -2039) 
 ((|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 -2041) 
+(-77 -2039) 
 ((|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 -2041) 
+(-78 -2039) 
 ((|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 -2041) 
+(-79 -2039) 
 ((|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 -2041) 
+(-80 -2039) 
 ((|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 -2041) 
+(-81 -2039) 
 ((|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 -2041) 
+(-82 -2039) 
 ((|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 -2041) 
+(-83 -2039) 
 ((|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 -2041) 
+(-84 -2039) 
 ((|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 -2041) 
+(-85 -2039) 
 ((|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 -2041) 
+(-86 -2039) 
 ((|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 -2041) 
+(-87 -2039) 
 ((|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 -2041) 
+(-88 -2039) 
 ((|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 -2041) 
+(-89 -2039) 
 ((|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 
@@ -472,11 +472,11 @@ NIL
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
 (((-4460 "*") . T)) 
 NIL 
-(-136 |minix| -4106 S T$) 
+(-136 |minix| -4105 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
-(-137 |minix| -4106 R) 
+(-137 |minix| -4105 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 
@@ -900,19 +900,19 @@ 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 
-(-243 S -4106 R) 
+(-243 S -4105 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 (-372))) (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-858))) (|HasAttribute| |#3| (QUOTE -4455)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (QUOTE (-1115)))) 
-(-244 -4106 R) 
+(-244 -4105 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"))) 
 ((-4452 |has| |#2| (-1064)) (-4453 |has| |#2| (-1064)) (-4455 |has| |#2| (-6 -4455)) ((-4460 "*") |has| |#2| (-174)) (-4458 . T)) 
 NIL 
-(-245 -4106 A B) 
+(-245 -4105 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 
-(-246 -4106 R) 
+(-246 -4105 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."))) 
 ((-4452 |has| |#2| (-1064)) (-4453 |has| |#2| (-1064)) (-4455 |has| |#2| (-6 -4455)) ((-4460 "*") |has| |#2| (-174)) (-4458 . T)) 
 ((-2832 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-372))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) 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@@ -958,11 +958,11 @@ NIL
 NIL 
 (-257 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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 (-258 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
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+((-4455 -2832 (-2096 (|has| |#3| (-1064)) (|has| |#3| (-239))) (|has| |#3| (-6 -4455)) (-2096 (|has| |#3| (-1064)) (|has| |#3| (-913 (-1192))))) (-4452 |has| |#3| (-1064)) (-4453 |has| |#3| (-1064)) ((-4460 "*") |has| |#3| (-174)) (-4458 . T)) 
 ((-2832 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))))) (|HasCategory| |#3| (QUOTE (-372))) (-2832 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-1064)))) (-2832 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372)))) (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-803))) (-2832 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-858)))) (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (QUOTE (-736))) (-2832 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-1064)))) (|HasCategory| |#3| (QUOTE (-377))) (-2832 (-12 (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574)))))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))) (-2832 (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1064)))) (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-174)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-239)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-372)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-377)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-736)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-803)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-858)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1064)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1115))))) (-2832 (-12 (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1064))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-858))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1064)))) (-2832 (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1064)))) (|HasCategory| |#3| (QUOTE (-736))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574))))) (-2832 (|HasCategory| |#3| (QUOTE (-1064))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1115)))) (-2832 (|HasAttribute| |#3| (QUOTE -4455)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1064)))) (-12 (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1192)))))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) 
 (-259 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."))) 
@@ -1116,7 +1116,7 @@ NIL
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-297 S R |Mod| -2230 -4333 |exactQuo|) 
+(-297 S R |Mod| -2967 -2452 |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"))) 
 ((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) 
 NIL 
@@ -1143,7 +1143,7 @@ NIL
 (-303 |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."))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-304) 
 ((|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 
@@ -1239,7 +1239,7 @@ NIL
 (-327 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."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
 (-328 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 
@@ -1560,7 +1560,7 @@ 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 
-(-408 -2041 |returnType| -1574 |symbols|) 
+(-408 -2039 |returnType| -1573 |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 
@@ -1867,11 +1867,11 @@ NIL
 (-484 |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."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
 (-485 |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."))) 
 ((-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115)))) 
+((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115)))) 
 (-486 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)}"))) 
 ((-4459 . T) (-4458 . T)) 
@@ -1887,7 +1887,7 @@ NIL
 (-489 |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."))) 
 ((-4458 . T) (-4459 . T)) 
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+((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-490) 
 ((|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 
@@ -1896,7 +1896,7 @@ 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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-(-492 -4106 S) 
+(-492 -4105 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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-317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-372))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) 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(QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-372))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE 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(LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192))))) (-2832 (|HasCategory| |#2| (QUOTE (-1064))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasAttribute| |#2| (QUOTE -4455)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) 
@@ -2171,7 +2171,7 @@ NIL
 (-560 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-561 R -1395) 
 ((|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 
@@ -2398,12 +2398,12 @@ NIL
 NIL 
 (-617 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)."))) 
-((-4455 -2832 (-2097 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) 
+((-4455 -2832 (-2096 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) 
 ((-2832 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
 (-618 |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."))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-619 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 
@@ -2499,7 +2499,7 @@ NIL
 (-642) 
 ((|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."))) 
 ((-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1918) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1174) (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 (-52))) (QUOTE (-1115)))) 
+((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1174) (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115)))) 
 (-643 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
@@ -2510,7 +2510,7 @@ NIL
 NIL 
 (-645 R A) 
 ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) 
-((-4455 -2832 (-2097 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) 
+((-4455 -2832 (-2096 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) 
 ((-2832 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) 
 (-646 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))}."))) 
@@ -2523,13 +2523,13 @@ NIL
 (-648 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 
-((-2086 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) 
+((-2085 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) 
 (-649 R) 
 ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) 
 NIL 
 NIL 
-(-650 R) 
-((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) 
+(-650 S) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) 
 NIL 
 NIL 
 (-651 A B) 
@@ -2552,8 +2552,8 @@ NIL
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-656 R) 
-((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{LeftModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
+(-656 S) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds if \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
 (-657 S) 
@@ -2600,7 +2600,7 @@ 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)))) 
-(-668 A -2024) 
+(-668 A -2884) 
 ((|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}}"))) 
 ((-4452 . T) (-4453 . T) (-4455 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
@@ -2792,7 +2792,7 @@ NIL
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) 
 NIL 
 NIL 
-(-716 S -3583 I) 
+(-716 S -3584 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) 
 NIL 
 NIL 
@@ -2812,7 +2812,7 @@ 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 
-(-721 R |Mod| -2230 -4333 |exactQuo|) 
+(-721 R |Mod| -2967 -2452 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
 ((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) 
 NIL 
@@ -2828,7 +2828,7 @@ NIL
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
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 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) 
-(-725 R |Mod| -2230 -4333 |exactQuo|) 
+(-725 R |Mod| -2967 -2452 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
 ((-4455 . T)) 
 NIL 
@@ -3091,7 +3091,7 @@ NIL
 (-790 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."))) 
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 (-791 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 
@@ -3228,7 +3228,7 @@ 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 
-(-825 -4106 S |f|) 
+(-825 -4105 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
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(QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-803)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-858)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1064))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-858))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192))))) (-2832 (|HasCategory| |#2| (QUOTE (-1064))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasAttribute| |#2| (QUOTE -4455)) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) 
@@ -3348,7 +3348,7 @@ NIL
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-855 -4106 S) 
+(-855 -4105 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 
@@ -3384,11 +3384,11 @@ 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 (-372))) (|HasCategory| |#1| (QUOTE (-566)))) 
-(-864 R |sigma| -2085) 
+(-864 R |sigma| -2084) 
 ((|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."))) 
 ((-4452 . T) (-4453 . T) (-4455 . T)) 
 ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) 
-(-865 |x| R |sigma| -2085) 
+(-865 |x| R |sigma| -2084) 
 ((|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}."))) 
 ((-4452 . T) (-4453 . T) (-4455 . T)) 
 ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-372)))) 
@@ -3523,7 +3523,7 @@ NIL
 (-898 |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 (-2086 (|HasCategory| |#2| (QUOTE (-1064)))) (-2086 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (-2086 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192))))) 
+((-12 (-2085 (|HasCategory| |#2| (QUOTE (-1064)))) (-2085 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (-2085 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192))))) 
 (-899 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 
@@ -3532,7 +3532,7 @@ NIL
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-901 R -3583) 
+(-901 R -3584) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
@@ -3728,11 +3728,11 @@ NIL
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
 ((|HasCategory| |#3| (LIST (QUOTE -897) (|devaluate| |#1|)))) 
-(-950 R -1395 -3583) 
+(-950 R -1395 -3584) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-951 -3583) 
+(-951 -3584) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
@@ -4131,7 +4131,7 @@ NIL
 (-1050) 
 ((|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.}"))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1918) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1051) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
@@ -4192,8 +4192,8 @@ NIL
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-1066 R) 
-((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{RightModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
+(-1066 S) 
+((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds if \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) 
 NIL 
 NIL 
 (-1067 S |m| |n| R |Row| |Col|) 
@@ -4243,7 +4243,7 @@ NIL
 (-1078) 
 ((|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}"))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1918) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1918 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1079 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 
@@ -4591,7 +4591,7 @@ NIL
 (-1165 |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."))) 
 ((-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1918 |#2|)) (QUOTE (-1115)))) 
+((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115)))) 
 (-1166) 
 ((|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 
@@ -4631,7 +4631,7 @@ NIL
 (-1175 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
 ((-4458 . T) (-4459 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1918) (|devaluate| |#1|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1918 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
+((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#1|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) 
 (-1176 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 
@@ -4662,8 +4662,8 @@ NIL
 NIL 
 (-1183 |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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(QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-922))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-922))) (|HasCategory| |#1| (QUOTE (-372)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-922))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| (-1190 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-146))))) 
 (-1184 R -1395) 
 ((|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 
@@ -4687,11 +4687,11 @@ NIL
 (-1189 |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}."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
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 (-1190 |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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-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
 (-1191) 
 ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) 
 NIL 
@@ -4751,7 +4751,7 @@ NIL
 (-1205 |Key| |Entry|) 
 ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) 
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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 
@@ -4915,11 +4915,11 @@ NIL
 (-1246 |Coef| UTS) 
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 (-1247 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) 
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 (-1248 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 
@@ -4999,11 +4999,11 @@ NIL
 (-1267 |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)}."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
+((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) 
 (-1268 |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}."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
 (-1269 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) 
 (((-4460 "*") |has| (-1268 |#2| |#3| |#4|) (-174)) (-4451 |has| (-1268 |#2| |#3| |#4|) (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) 
@@ -5023,7 +5023,7 @@ NIL
 (-1273 S |Coef|) 
 ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-574)))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-1218))) (|HasSignature| |#2| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3302) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1192))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) 
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-1218))) (|HasSignature| |#2| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3874) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1192))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) 
 (-1274 |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."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) 
@@ -5031,7 +5031,7 @@ NIL
 (-1275 |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}."))) 
 (((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) 
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3302) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3874) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) 
 (-1276 |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 
@@ -5196,4 +5196,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 2268874 2268879 2268884 2268889) (-2 NIL 2268854 2268859 2268864 2268869) (-1 NIL 2268834 2268839 2268844 2268849) (0 NIL 2268814 2268819 2268824 2268829) (-1312 "ZMOD.spad" 2268623 2268636 2268752 2268809) (-1311 "ZLINDEP.spad" 2267689 2267700 2268613 2268618) (-1310 "ZDSOLVE.spad" 2257634 2257656 2267679 2267684) (-1309 "YSTREAM.spad" 2257129 2257140 2257624 2257629) (-1308 "YDIAGRAM.spad" 2256763 2256772 2257119 2257124) (-1307 "XRPOLY.spad" 2255983 2256003 2256619 2256688) (-1306 "XPR.spad" 2253778 2253791 2255701 2255800) (-1305 "XPOLY.spad" 2253333 2253344 2253634 2253703) (-1304 "XPOLYC.spad" 2252652 2252668 2253259 2253328) (-1303 "XPBWPOLY.spad" 2251089 2251109 2252432 2252501) (-1302 "XF.spad" 2249552 2249567 2250991 2251084) (-1301 "XF.spad" 2247995 2248012 2249436 2249441) (-1300 "XFALG.spad" 2245043 2245059 2247921 2247990) (-1299 "XEXPPKG.spad" 2244294 2244320 2245033 2245038) (-1298 "XDPOLY.spad" 2243908 2243924 2244150 2244219) (-1297 "XALG.spad" 2243568 2243579 2243864 2243903) (-1296 "WUTSET.spad" 2239407 2239424 2243214 2243241) (-1295 "WP.spad" 2238606 2238650 2239265 2239332) (-1294 "WHILEAST.spad" 2238404 2238413 2238596 2238601) (-1293 "WHEREAST.spad" 2238075 2238084 2238394 2238399) (-1292 "WFFINTBS.spad" 2235738 2235760 2238065 2238070) (-1291 "WEIER.spad" 2233960 2233971 2235728 2235733) (-1290 "VSPACE.spad" 2233633 2233644 2233928 2233955) (-1289 "VSPACE.spad" 2233326 2233339 2233623 2233628) (-1288 "VOID.spad" 2233003 2233012 2233316 2233321) (-1287 "VIEW.spad" 2230683 2230692 2232993 2232998) (-1286 "VIEWDEF.spad" 2225884 2225893 2230673 2230678) (-1285 "VIEW3D.spad" 2209845 2209854 2225874 2225879) (-1284 "VIEW2D.spad" 2197736 2197745 2209835 2209840) (-1283 "VECTOR.spad" 2196410 2196421 2196661 2196688) (-1282 "VECTOR2.spad" 2195049 2195062 2196400 2196405) (-1281 "VECTCAT.spad" 2192953 2192964 2195017 2195044) (-1280 "VECTCAT.spad" 2190664 2190677 2192730 2192735) (-1279 "VARIABLE.spad" 2190444 2190459 2190654 2190659) (-1278 "UTYPE.spad" 2190088 2190097 2190434 2190439) (-1277 "UTSODETL.spad" 2189383 2189407 2190044 2190049) (-1276 "UTSODE.spad" 2187599 2187619 2189373 2189378) (-1275 "UTS.spad" 2182403 2182431 2186066 2186163) (-1274 "UTSCAT.spad" 2179882 2179898 2182301 2182398) (-1273 "UTSCAT.spad" 2177005 2177023 2179426 2179431) (-1272 "UTS2.spad" 2176600 2176635 2176995 2177000) (-1271 "URAGG.spad" 2171273 2171284 2176590 2176595) (-1270 "URAGG.spad" 2165910 2165923 2171229 2171234) (-1269 "UPXSSING.spad" 2163555 2163581 2164991 2165124) (-1268 "UPXS.spad" 2160709 2160737 2161687 2161836) (-1267 "UPXSCONS.spad" 2158468 2158488 2158841 2158990) (-1266 "UPXSCCA.spad" 2157039 2157059 2158314 2158463) (-1265 "UPXSCCA.spad" 2155752 2155774 2157029 2157034) (-1264 "UPXSCAT.spad" 2154341 2154357 2155598 2155747) (-1263 "UPXS2.spad" 2153884 2153937 2154331 2154336) (-1262 "UPSQFREE.spad" 2152298 2152312 2153874 2153879) (-1261 "UPSCAT.spad" 2150085 2150109 2152196 2152293) (-1260 "UPSCAT.spad" 2147578 2147604 2149691 2149696) (-1259 "UPOLYC.spad" 2142618 2142629 2147420 2147573) (-1258 "UPOLYC.spad" 2137550 2137563 2142354 2142359) (-1257 "UPOLYC2.spad" 2137021 2137040 2137540 2137545) (-1256 "UP.spad" 2134220 2134235 2134607 2134760) (-1255 "UPMP.spad" 2133120 2133133 2134210 2134215) (-1254 "UPDIVP.spad" 2132685 2132699 2133110 2133115) (-1253 "UPDECOMP.spad" 2130930 2130944 2132675 2132680) (-1252 "UPCDEN.spad" 2130139 2130155 2130920 2130925) (-1251 "UP2.spad" 2129503 2129524 2130129 2130134) (-1250 "UNISEG.spad" 2128856 2128867 2129422 2129427) (-1249 "UNISEG2.spad" 2128353 2128366 2128812 2128817) (-1248 "UNIFACT.spad" 2127456 2127468 2128343 2128348) (-1247 "ULS.spad" 2118014 2118042 2119101 2119530) (-1246 "ULSCONS.spad" 2110410 2110430 2110780 2110929) (-1245 "ULSCCAT.spad" 2108147 2108167 2110256 2110405) (-1244 "ULSCCAT.spad" 2105992 2106014 2108103 2108108) (-1243 "ULSCAT.spad" 2104224 2104240 2105838 2105987) (-1242 "ULS2.spad" 2103738 2103791 2104214 2104219) (-1241 "UINT8.spad" 2103615 2103624 2103728 2103733) (-1240 "UINT64.spad" 2103491 2103500 2103605 2103610) (-1239 "UINT32.spad" 2103367 2103376 2103481 2103486) (-1238 "UINT16.spad" 2103243 2103252 2103357 2103362) (-1237 "UFD.spad" 2102308 2102317 2103169 2103238) (-1236 "UFD.spad" 2101435 2101446 2102298 2102303) (-1235 "UDVO.spad" 2100316 2100325 2101425 2101430) (-1234 "UDPO.spad" 2097809 2097820 2100272 2100277) (-1233 "TYPE.spad" 2097741 2097750 2097799 2097804) (-1232 "TYPEAST.spad" 2097660 2097669 2097731 2097736) (-1231 "TWOFACT.spad" 2096312 2096327 2097650 2097655) (-1230 "TUPLE.spad" 2095798 2095809 2096211 2096216) (-1229 "TUBETOOL.spad" 2092665 2092674 2095788 2095793) (-1228 "TUBE.spad" 2091312 2091329 2092655 2092660) (-1227 "TS.spad" 2089911 2089927 2090877 2090974) (-1226 "TSETCAT.spad" 2077038 2077055 2089879 2089906) (-1225 "TSETCAT.spad" 2064151 2064170 2076994 2076999) (-1224 "TRMANIP.spad" 2058517 2058534 2063857 2063862) (-1223 "TRIMAT.spad" 2057480 2057505 2058507 2058512) (-1222 "TRIGMNIP.spad" 2056007 2056024 2057470 2057475) (-1221 "TRIGCAT.spad" 2055519 2055528 2055997 2056002) (-1220 "TRIGCAT.spad" 2055029 2055040 2055509 2055514) (-1219 "TREE.spad" 2053604 2053615 2054636 2054663) (-1218 "TRANFUN.spad" 2053443 2053452 2053594 2053599) (-1217 "TRANFUN.spad" 2053280 2053291 2053433 2053438) (-1216 "TOPSP.spad" 2052954 2052963 2053270 2053275) (-1215 "TOOLSIGN.spad" 2052617 2052628 2052944 2052949) (-1214 "TEXTFILE.spad" 2051178 2051187 2052607 2052612) (-1213 "TEX.spad" 2048324 2048333 2051168 2051173) (-1212 "TEX1.spad" 2047880 2047891 2048314 2048319) (-1211 "TEMUTL.spad" 2047435 2047444 2047870 2047875) (-1210 "TBCMPPK.spad" 2045528 2045551 2047425 2047430) (-1209 "TBAGG.spad" 2044578 2044601 2045508 2045523) (-1208 "TBAGG.spad" 2043636 2043661 2044568 2044573) (-1207 "TANEXP.spad" 2043044 2043055 2043626 2043631) (-1206 "TALGOP.spad" 2042768 2042779 2043034 2043039) (-1205 "TABLE.spad" 2041179 2041202 2041449 2041476) (-1204 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"STEP.spad" 1961352 1961361 1962141 1962146) (-1166 "STEPAST.spad" 1960586 1960595 1961342 1961347) (-1165 "STBL.spad" 1959112 1959140 1959279 1959294) (-1164 "STAGG.spad" 1958187 1958198 1959102 1959107) (-1163 "STAGG.spad" 1957260 1957273 1958177 1958182) (-1162 "STACK.spad" 1956617 1956628 1956867 1956894) (-1161 "SREGSET.spad" 1954321 1954338 1956263 1956290) (-1160 "SRDCMPK.spad" 1952882 1952902 1954311 1954316) (-1159 "SRAGG.spad" 1948025 1948034 1952850 1952877) (-1158 "SRAGG.spad" 1943188 1943199 1948015 1948020) (-1157 "SQMATRIX.spad" 1940860 1940878 1941776 1941863) (-1156 "SPLTREE.spad" 1935412 1935425 1940296 1940323) (-1155 "SPLNODE.spad" 1932000 1932013 1935402 1935407) (-1154 "SPFCAT.spad" 1930809 1930818 1931990 1931995) (-1153 "SPECOUT.spad" 1929361 1929370 1930799 1930804) (-1152 "SPADXPT.spad" 1920956 1920965 1929351 1929356) (-1151 "spad-parser.spad" 1920421 1920430 1920946 1920951) (-1150 "SPADAST.spad" 1920122 1920131 1920411 1920416) (-1149 "SPACEC.spad" 1904321 1904332 1920112 1920117) (-1148 "SPACE3.spad" 1904097 1904108 1904311 1904316) (-1147 "SORTPAK.spad" 1903646 1903659 1904053 1904058) (-1146 "SOLVETRA.spad" 1901409 1901420 1903636 1903641) (-1145 "SOLVESER.spad" 1899937 1899948 1901399 1901404) (-1144 "SOLVERAD.spad" 1895963 1895974 1899927 1899932) (-1143 "SOLVEFOR.spad" 1894425 1894443 1895953 1895958) (-1142 "SNTSCAT.spad" 1894025 1894042 1894393 1894420) (-1141 "SMTS.spad" 1892297 1892323 1893590 1893687) (-1140 "SMP.spad" 1889772 1889792 1890162 1890289) (-1139 "SMITH.spad" 1888617 1888642 1889762 1889767) (-1138 "SMATCAT.spad" 1886727 1886757 1888561 1888612) (-1137 "SMATCAT.spad" 1884769 1884801 1886605 1886610) (-1136 "SKAGG.spad" 1883732 1883743 1884737 1884764) (-1135 "SINT.spad" 1882672 1882681 1883598 1883727) (-1134 "SIMPAN.spad" 1882400 1882409 1882662 1882667) (-1133 "SIG.spad" 1881730 1881739 1882390 1882395) (-1132 "SIGNRF.spad" 1880848 1880859 1881720 1881725) (-1131 "SIGNEF.spad" 1880127 1880144 1880838 1880843) (-1130 "SIGAST.spad" 1879512 1879521 1880117 1880122) (-1129 "SHP.spad" 1877440 1877455 1879468 1879473) (-1128 "SHDP.spad" 1867074 1867101 1867583 1867714) (-1127 "SGROUP.spad" 1866682 1866691 1867064 1867069) (-1126 "SGROUP.spad" 1866288 1866299 1866672 1866677) (-1125 "SGCF.spad" 1859427 1859436 1866278 1866283) (-1124 "SFRTCAT.spad" 1858357 1858374 1859395 1859422) (-1123 "SFRGCD.spad" 1857420 1857440 1858347 1858352) (-1122 "SFQCMPK.spad" 1852057 1852077 1857410 1857415) (-1121 "SFORT.spad" 1851496 1851510 1852047 1852052) (-1120 "SEXOF.spad" 1851339 1851379 1851486 1851491) (-1119 "SEX.spad" 1851231 1851240 1851329 1851334) (-1118 "SEXCAT.spad" 1849012 1849052 1851221 1851226) (-1117 "SET.spad" 1847336 1847347 1848433 1848472) (-1116 "SETMN.spad" 1845786 1845803 1847326 1847331) (-1115 "SETCAT.spad" 1845108 1845117 1845776 1845781) (-1114 "SETCAT.spad" 1844428 1844439 1845098 1845103) (-1113 "SETAGG.spad" 1840977 1840988 1844408 1844423) (-1112 "SETAGG.spad" 1837534 1837547 1840967 1840972) (-1111 "SEQAST.spad" 1837237 1837246 1837524 1837529) (-1110 "SEGXCAT.spad" 1836393 1836406 1837227 1837232) (-1109 "SEG.spad" 1836206 1836217 1836312 1836317) (-1108 "SEGCAT.spad" 1835131 1835142 1836196 1836201) (-1107 "SEGBIND.spad" 1834889 1834900 1835078 1835083) (-1106 "SEGBIND2.spad" 1834587 1834600 1834879 1834884) (-1105 "SEGAST.spad" 1834301 1834310 1834577 1834582) (-1104 "SEG2.spad" 1833736 1833749 1834257 1834262) (-1103 "SDVAR.spad" 1833012 1833023 1833726 1833731) (-1102 "SDPOL.spad" 1830438 1830449 1830729 1830856) (-1101 "SCPKG.spad" 1828527 1828538 1830428 1830433) (-1100 "SCOPE.spad" 1827680 1827689 1828517 1828522) (-1099 "SCACHE.spad" 1826376 1826387 1827670 1827675) (-1098 "SASTCAT.spad" 1826285 1826294 1826366 1826371) (-1097 "SAOS.spad" 1826157 1826166 1826275 1826280) (-1096 "SAERFFC.spad" 1825870 1825890 1826147 1826152) (-1095 "SAE.spad" 1824045 1824061 1824656 1824791) (-1094 "SAEFACT.spad" 1823746 1823766 1824035 1824040) (-1093 "RURPK.spad" 1821405 1821421 1823736 1823741) (-1092 "RULESET.spad" 1820858 1820882 1821395 1821400) (-1091 "RULE.spad" 1819098 1819122 1820848 1820853) (-1090 "RULECOLD.spad" 1818950 1818963 1819088 1819093) (-1089 "RTVALUE.spad" 1818685 1818694 1818940 1818945) (-1088 "RSTRCAST.spad" 1818402 1818411 1818675 1818680) (-1087 "RSETGCD.spad" 1814780 1814800 1818392 1818397) (-1086 "RSETCAT.spad" 1804716 1804733 1814748 1814775) (-1085 "RSETCAT.spad" 1794672 1794691 1804706 1804711) (-1084 "RSDCMPK.spad" 1793124 1793144 1794662 1794667) (-1083 "RRCC.spad" 1791508 1791538 1793114 1793119) (-1082 "RRCC.spad" 1789890 1789922 1791498 1791503) (-1081 "RPTAST.spad" 1789592 1789601 1789880 1789885) (-1080 "RPOLCAT.spad" 1768952 1768967 1789460 1789587) (-1079 "RPOLCAT.spad" 1748025 1748042 1768535 1768540) (-1078 "ROUTINE.spad" 1743908 1743917 1746672 1746699) (-1077 "ROMAN.spad" 1743236 1743245 1743774 1743903) (-1076 "ROIRC.spad" 1742316 1742348 1743226 1743231) (-1075 "RNS.spad" 1741219 1741228 1742218 1742311) (-1074 "RNS.spad" 1740208 1740219 1741209 1741214) (-1073 "RNG.spad" 1739943 1739952 1740198 1740203) (-1072 "RNGBIND.spad" 1739103 1739117 1739898 1739903) (-1071 "RMODULE.spad" 1738868 1738879 1739093 1739098) (-1070 "RMCAT2.spad" 1738288 1738345 1738858 1738863) (-1069 "RMATRIX.spad" 1737112 1737131 1737455 1737494) (-1068 "RMATCAT.spad" 1732691 1732722 1737068 1737107) (-1067 "RMATCAT.spad" 1728160 1728193 1732539 1732544) (-1066 "RLINSET.spad" 1727554 1727565 1728150 1728155) (-1065 "RINTERP.spad" 1727442 1727462 1727544 1727549) (-1064 "RING.spad" 1726912 1726921 1727422 1727437) (-1063 "RING.spad" 1726390 1726401 1726902 1726907) (-1062 "RIDIST.spad" 1725782 1725791 1726380 1726385) (-1061 "RGCHAIN.spad" 1724365 1724381 1725267 1725294) (-1060 "RGBCSPC.spad" 1724146 1724158 1724355 1724360) (-1059 "RGBCMDL.spad" 1723676 1723688 1724136 1724141) (-1058 "RF.spad" 1721318 1721329 1723666 1723671) (-1057 "RFFACTOR.spad" 1720780 1720791 1721308 1721313) (-1056 "RFFACT.spad" 1720515 1720527 1720770 1720775) (-1055 "RFDIST.spad" 1719511 1719520 1720505 1720510) (-1054 "RETSOL.spad" 1718930 1718943 1719501 1719506) (-1053 "RETRACT.spad" 1718358 1718369 1718920 1718925) (-1052 "RETRACT.spad" 1717784 1717797 1718348 1718353) (-1051 "RETAST.spad" 1717596 1717605 1717774 1717779) (-1050 "RESULT.spad" 1715656 1715665 1716243 1716270) (-1049 "RESRING.spad" 1715003 1715050 1715594 1715651) (-1048 "RESLATC.spad" 1714327 1714338 1714993 1714998) (-1047 "REPSQ.spad" 1714058 1714069 1714317 1714322) (-1046 "REP.spad" 1711612 1711621 1714048 1714053) (-1045 "REPDB.spad" 1711319 1711330 1711602 1711607) (-1044 "REP2.spad" 1700977 1700988 1711161 1711166) (-1043 "REP1.spad" 1695173 1695184 1700927 1700932) (-1042 "REGSET.spad" 1692970 1692987 1694819 1694846) (-1041 "REF.spad" 1692305 1692316 1692925 1692930) (-1040 "REDORDER.spad" 1691511 1691528 1692295 1692300) (-1039 "RECLOS.spad" 1690294 1690314 1690998 1691091) (-1038 "REALSOLV.spad" 1689434 1689443 1690284 1690289) (-1037 "REAL.spad" 1689306 1689315 1689424 1689429) (-1036 "REAL0Q.spad" 1686604 1686619 1689296 1689301) (-1035 "REAL0.spad" 1683448 1683463 1686594 1686599) (-1034 "RDUCEAST.spad" 1683169 1683178 1683438 1683443) (-1033 "RDIV.spad" 1682824 1682849 1683159 1683164) (-1032 "RDIST.spad" 1682391 1682402 1682814 1682819) (-1031 "RDETRS.spad" 1681255 1681273 1682381 1682386) (-1030 "RDETR.spad" 1679394 1679412 1681245 1681250) (-1029 "RDEEFS.spad" 1678493 1678510 1679384 1679389) (-1028 "RDEEF.spad" 1677503 1677520 1678483 1678488) (-1027 "RCFIELD.spad" 1674689 1674698 1677405 1677498) (-1026 "RCFIELD.spad" 1671961 1671972 1674679 1674684) (-1025 "RCAGG.spad" 1669889 1669900 1671951 1671956) (-1024 "RCAGG.spad" 1667744 1667757 1669808 1669813) (-1023 "RATRET.spad" 1667104 1667115 1667734 1667739) (-1022 "RATFACT.spad" 1666796 1666808 1667094 1667099) (-1021 "RANDSRC.spad" 1666115 1666124 1666786 1666791) (-1020 "RADUTIL.spad" 1665871 1665880 1666105 1666110) (-1019 "RADIX.spad" 1662792 1662806 1664338 1664431) (-1018 "RADFF.spad" 1661205 1661242 1661324 1661480) (-1017 "RADCAT.spad" 1660800 1660809 1661195 1661200) (-1016 "RADCAT.spad" 1660393 1660404 1660790 1660795) (-1015 "QUEUE.spad" 1659741 1659752 1660000 1660027) (-1014 "QUAT.spad" 1658199 1658210 1658542 1658607) (-1013 "QUATCT2.spad" 1657819 1657838 1658189 1658194) (-1012 "QUATCAT.spad" 1655989 1656000 1657749 1657814) (-1011 "QUATCAT.spad" 1653910 1653923 1655672 1655677) (-1010 "QUAGG.spad" 1652737 1652748 1653878 1653905) (-1009 "QQUTAST.spad" 1652505 1652514 1652727 1652732) (-1008 "QFORM.spad" 1652123 1652138 1652495 1652500) (-1007 "QFCAT.spad" 1650825 1650836 1652025 1652118) (-1006 "QFCAT.spad" 1649118 1649131 1650320 1650325) (-1005 "QFCAT2.spad" 1648810 1648827 1649108 1649113) (-1004 "QEQUAT.spad" 1648368 1648377 1648800 1648805) (-1003 "QCMPACK.spad" 1643114 1643134 1648358 1648363) (-1002 "QALGSET.spad" 1639192 1639225 1643028 1643033) (-1001 "QALGSET2.spad" 1637187 1637206 1639182 1639187) (-1000 "PWFFINTB.spad" 1634602 1634624 1637177 1637182) (-999 "PUSHVAR.spad" 1633941 1633960 1634592 1634597) (-998 "PTRANFN.spad" 1630069 1630079 1633931 1633936) (-997 "PTPACK.spad" 1627157 1627167 1630059 1630064) (-996 "PTFUNC2.spad" 1626980 1626994 1627147 1627152) (-995 "PTCAT.spad" 1626235 1626245 1626948 1626975) (-994 "PSQFR.spad" 1625542 1625566 1626225 1626230) (-993 "PSEUDLIN.spad" 1624428 1624438 1625532 1625537) (-992 "PSETPK.spad" 1609861 1609877 1624306 1624311) (-991 "PSETCAT.spad" 1603781 1603804 1609841 1609856) (-990 "PSETCAT.spad" 1597675 1597700 1603737 1603742) (-989 "PSCURVE.spad" 1596658 1596666 1597665 1597670) (-988 "PSCAT.spad" 1595441 1595470 1596556 1596653) (-987 "PSCAT.spad" 1594314 1594345 1595431 1595436) (-986 "PRTITION.spad" 1593012 1593020 1594304 1594309) (-985 "PRTDAST.spad" 1592731 1592739 1593002 1593007) (-984 "PRS.spad" 1582293 1582310 1592687 1592692) (-983 "PRQAGG.spad" 1581728 1581738 1582261 1582288) (-982 "PROPLOG.spad" 1581300 1581308 1581718 1581723) (-981 "PROPFUN2.spad" 1580923 1580936 1581290 1581295) (-980 "PROPFUN1.spad" 1580321 1580332 1580913 1580918) (-979 "PROPFRML.spad" 1578889 1578900 1580311 1580316) (-978 "PROPERTY.spad" 1578377 1578385 1578879 1578884) (-977 "PRODUCT.spad" 1576059 1576071 1576343 1576398) (-976 "PR.spad" 1574451 1574463 1575150 1575277) (-975 "PRINT.spad" 1574203 1574211 1574441 1574446) (-974 "PRIMES.spad" 1572456 1572466 1574193 1574198) (-973 "PRIMELT.spad" 1570537 1570551 1572446 1572451) (-972 "PRIMCAT.spad" 1570164 1570172 1570527 1570532) (-971 "PRIMARR.spad" 1569169 1569179 1569347 1569374) (-970 "PRIMARR2.spad" 1567936 1567948 1569159 1569164) (-969 "PREASSOC.spad" 1567318 1567330 1567926 1567931) (-968 "PPCURVE.spad" 1566455 1566463 1567308 1567313) (-967 "PORTNUM.spad" 1566230 1566238 1566445 1566450) (-966 "POLYROOT.spad" 1565079 1565101 1566186 1566191) (-965 "POLY.spad" 1562414 1562424 1562929 1563056) (-964 "POLYLIFT.spad" 1561679 1561702 1562404 1562409) (-963 "POLYCATQ.spad" 1559797 1559819 1561669 1561674) (-962 "POLYCAT.spad" 1553267 1553288 1559665 1559792) (-961 "POLYCAT.spad" 1546075 1546098 1552475 1552480) (-960 "POLY2UP.spad" 1545527 1545541 1546065 1546070) (-959 "POLY2.spad" 1545124 1545136 1545517 1545522) (-958 "POLUTIL.spad" 1544065 1544094 1545080 1545085) (-957 "POLTOPOL.spad" 1542813 1542828 1544055 1544060) (-956 "POINT.spad" 1541651 1541661 1541738 1541765) (-955 "PNTHEORY.spad" 1538353 1538361 1541641 1541646) (-954 "PMTOOLS.spad" 1537128 1537142 1538343 1538348) (-953 "PMSYM.spad" 1536677 1536687 1537118 1537123) (-952 "PMQFCAT.spad" 1536268 1536282 1536667 1536672) (-951 "PMPRED.spad" 1535747 1535761 1536258 1536263) (-950 "PMPREDFS.spad" 1535201 1535223 1535737 1535742) (-949 "PMPLCAT.spad" 1534281 1534299 1535133 1535138) (-948 "PMLSAGG.spad" 1533866 1533880 1534271 1534276) (-947 "PMKERNEL.spad" 1533445 1533457 1533856 1533861) (-946 "PMINS.spad" 1533025 1533035 1533435 1533440) (-945 "PMFS.spad" 1532602 1532620 1533015 1533020) (-944 "PMDOWN.spad" 1531892 1531906 1532592 1532597) (-943 "PMASS.spad" 1530902 1530910 1531882 1531887) (-942 "PMASSFS.spad" 1529869 1529885 1530892 1530897) (-941 "PLOTTOOL.spad" 1529649 1529657 1529859 1529864) (-940 "PLOT.spad" 1524572 1524580 1529639 1529644) (-939 "PLOT3D.spad" 1521036 1521044 1524562 1524567) (-938 "PLOT1.spad" 1520193 1520203 1521026 1521031) (-937 "PLEQN.spad" 1507483 1507510 1520183 1520188) (-936 "PINTERP.spad" 1507105 1507124 1507473 1507478) (-935 "PINTERPA.spad" 1506889 1506905 1507095 1507100) (-934 "PI.spad" 1506498 1506506 1506863 1506884) (-933 "PID.spad" 1505468 1505476 1506424 1506493) (-932 "PICOERCE.spad" 1505125 1505135 1505458 1505463) (-931 "PGROEB.spad" 1503726 1503740 1505115 1505120) (-930 "PGE.spad" 1495343 1495351 1503716 1503721) (-929 "PGCD.spad" 1494233 1494250 1495333 1495338) (-928 "PFRPAC.spad" 1493382 1493392 1494223 1494228) (-927 "PFR.spad" 1490045 1490055 1493284 1493377) (-926 "PFOTOOLS.spad" 1489303 1489319 1490035 1490040) (-925 "PFOQ.spad" 1488673 1488691 1489293 1489298) (-924 "PFO.spad" 1488092 1488119 1488663 1488668) (-923 "PF.spad" 1487666 1487678 1487897 1487990) (-922 "PFECAT.spad" 1485348 1485356 1487592 1487661) (-921 "PFECAT.spad" 1483058 1483068 1485304 1485309) (-920 "PFBRU.spad" 1480946 1480958 1483048 1483053) (-919 "PFBR.spad" 1478506 1478529 1480936 1480941) (-918 "PERM.spad" 1474313 1474323 1478336 1478351) (-917 "PERMGRP.spad" 1469083 1469093 1474303 1474308) (-916 "PERMCAT.spad" 1467744 1467754 1469063 1469078) (-915 "PERMAN.spad" 1466276 1466290 1467734 1467739) (-914 "PENDTREE.spad" 1465617 1465627 1465905 1465910) (-913 "PDRING.spad" 1464168 1464178 1465597 1465612) (-912 "PDRING.spad" 1462727 1462739 1464158 1464163) (-911 "PDEPROB.spad" 1461742 1461750 1462717 1462722) (-910 "PDEPACK.spad" 1455782 1455790 1461732 1461737) (-909 "PDECOMP.spad" 1455252 1455269 1455772 1455777) (-908 "PDECAT.spad" 1453608 1453616 1455242 1455247) (-907 "PDDOM.spad" 1453074 1453087 1453598 1453603) (-906 "PDDOM.spad" 1452538 1452553 1453064 1453069) (-905 "PCOMP.spad" 1452391 1452404 1452528 1452533) (-904 "PBWLB.spad" 1450979 1450996 1452381 1452386) (-903 "PATTERN.spad" 1445518 1445528 1450969 1450974) (-902 "PATTERN2.spad" 1445256 1445268 1445508 1445513) (-901 "PATTERN1.spad" 1443592 1443608 1445246 1445251) (-900 "PATRES.spad" 1441167 1441179 1443582 1443587) (-899 "PATRES2.spad" 1440839 1440853 1441157 1441162) (-898 "PATMATCH.spad" 1439036 1439067 1440547 1440552) (-897 "PATMAB.spad" 1438465 1438475 1439026 1439031) (-896 "PATLRES.spad" 1437551 1437565 1438455 1438460) (-895 "PATAB.spad" 1437315 1437325 1437541 1437546) (-894 "PARTPERM.spad" 1435323 1435331 1437305 1437310) (-893 "PARSURF.spad" 1434757 1434785 1435313 1435318) (-892 "PARSU2.spad" 1434554 1434570 1434747 1434752) (-891 "script-parser.spad" 1434074 1434082 1434544 1434549) (-890 "PARSCURV.spad" 1433508 1433536 1434064 1434069) (-889 "PARSC2.spad" 1433299 1433315 1433498 1433503) (-888 "PARPCURV.spad" 1432761 1432789 1433289 1433294) (-887 "PARPC2.spad" 1432552 1432568 1432751 1432756) (-886 "PARAMAST.spad" 1431680 1431688 1432542 1432547) (-885 "PAN2EXPR.spad" 1431092 1431100 1431670 1431675) (-884 "PALETTE.spad" 1430062 1430070 1431082 1431087) (-883 "PAIR.spad" 1429049 1429062 1429650 1429655) (-882 "PADICRC.spad" 1426383 1426401 1427554 1427647) (-881 "PADICRAT.spad" 1424398 1424410 1424619 1424712) (-880 "PADIC.spad" 1424093 1424105 1424324 1424393) (-879 "PADICCT.spad" 1422642 1422654 1424019 1424088) (-878 "PADEPAC.spad" 1421331 1421350 1422632 1422637) (-877 "PADE.spad" 1420083 1420099 1421321 1421326) (-876 "OWP.spad" 1419323 1419353 1419941 1420008) (-875 "OVERSET.spad" 1418896 1418904 1419313 1419318) (-874 "OVAR.spad" 1418677 1418700 1418886 1418891) (-873 "OUT.spad" 1417763 1417771 1418667 1418672) (-872 "OUTFORM.spad" 1407155 1407163 1417753 1417758) (-871 "OUTBFILE.spad" 1406573 1406581 1407145 1407150) (-870 "OUTBCON.spad" 1405579 1405587 1406563 1406568) (-869 "OUTBCON.spad" 1404583 1404593 1405569 1405574) (-868 "OSI.spad" 1404058 1404066 1404573 1404578) (-867 "OSGROUP.spad" 1403976 1403984 1404048 1404053) (-866 "ORTHPOL.spad" 1402461 1402471 1403893 1403898) (-865 "OREUP.spad" 1401914 1401942 1402141 1402180) (-864 "ORESUP.spad" 1401215 1401239 1401594 1401633) (-863 "OREPCTO.spad" 1399072 1399084 1401135 1401140) (-862 "OREPCAT.spad" 1393219 1393229 1399028 1399067) (-861 "OREPCAT.spad" 1387256 1387268 1393067 1393072) (-860 "ORDSET.spad" 1386428 1386436 1387246 1387251) (-859 "ORDSET.spad" 1385598 1385608 1386418 1386423) (-858 "ORDRING.spad" 1384988 1384996 1385578 1385593) (-857 "ORDRING.spad" 1384386 1384396 1384978 1384983) (-856 "ORDMON.spad" 1384241 1384249 1384376 1384381) (-855 "ORDFUNS.spad" 1383373 1383389 1384231 1384236) (-854 "ORDFIN.spad" 1383193 1383201 1383363 1383368) (-853 "ORDCOMP.spad" 1381658 1381668 1382740 1382769) (-852 "ORDCOMP2.spad" 1380951 1380963 1381648 1381653) (-851 "OPTPROB.spad" 1379589 1379597 1380941 1380946) (-850 "OPTPACK.spad" 1371998 1372006 1379579 1379584) (-849 "OPTCAT.spad" 1369677 1369685 1371988 1371993) (-848 "OPSIG.spad" 1369331 1369339 1369667 1369672) (-847 "OPQUERY.spad" 1368880 1368888 1369321 1369326) (-846 "OP.spad" 1368622 1368632 1368702 1368769) (-845 "OPERCAT.spad" 1368088 1368098 1368612 1368617) (-844 "OPERCAT.spad" 1367552 1367564 1368078 1368083) (-843 "ONECOMP.spad" 1366297 1366307 1367099 1367128) (-842 "ONECOMP2.spad" 1365721 1365733 1366287 1366292) (-841 "OMSERVER.spad" 1364727 1364735 1365711 1365716) (-840 "OMSAGG.spad" 1364515 1364525 1364683 1364722) (-839 "OMPKG.spad" 1363131 1363139 1364505 1364510) (-838 "OM.spad" 1362104 1362112 1363121 1363126) (-837 "OMLO.spad" 1361529 1361541 1361990 1362029) (-836 "OMEXPR.spad" 1361363 1361373 1361519 1361524) (-835 "OMERR.spad" 1360908 1360916 1361353 1361358) (-834 "OMERRK.spad" 1359942 1359950 1360898 1360903) (-833 "OMENC.spad" 1359286 1359294 1359932 1359937) 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"DIFFDOM.spad" 272966 272977 273791 273796) (-234 "DIFFDOM.spad" 272129 272142 272956 272961) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 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
+((-3 NIL 2268395 2268400 2268405 2268410) (-2 NIL 2268375 2268380 2268385 2268390) (-1 NIL 2268355 2268360 2268365 2268370) (0 NIL 2268335 2268340 2268345 2268350) (-1312 "ZMOD.spad" 2268144 2268157 2268273 2268330) (-1311 "ZLINDEP.spad" 2267210 2267221 2268134 2268139) (-1310 "ZDSOLVE.spad" 2257155 2257177 2267200 2267205) (-1309 "YSTREAM.spad" 2256650 2256661 2257145 2257150) (-1308 "YDIAGRAM.spad" 2256284 2256293 2256640 2256645) (-1307 "XRPOLY.spad" 2255504 2255524 2256140 2256209) (-1306 "XPR.spad" 2253299 2253312 2255222 2255321) (-1305 "XPOLY.spad" 2252854 2252865 2253155 2253224) (-1304 "XPOLYC.spad" 2252173 2252189 2252780 2252849) (-1303 "XPBWPOLY.spad" 2250610 2250630 2251953 2252022) (-1302 "XF.spad" 2249073 2249088 2250512 2250605) (-1301 "XF.spad" 2247516 2247533 2248957 2248962) (-1300 "XFALG.spad" 2244564 2244580 2247442 2247511) (-1299 "XEXPPKG.spad" 2243815 2243841 2244554 2244559) (-1298 "XDPOLY.spad" 2243429 2243445 2243671 2243740) (-1297 "XALG.spad" 2243089 2243100 2243385 2243424) (-1296 "WUTSET.spad" 2238928 2238945 2242735 2242762) (-1295 "WP.spad" 2238127 2238171 2238786 2238853) (-1294 "WHILEAST.spad" 2237925 2237934 2238117 2238122) (-1293 "WHEREAST.spad" 2237596 2237605 2237915 2237920) (-1292 "WFFINTBS.spad" 2235259 2235281 2237586 2237591) (-1291 "WEIER.spad" 2233481 2233492 2235249 2235254) (-1290 "VSPACE.spad" 2233154 2233165 2233449 2233476) (-1289 "VSPACE.spad" 2232847 2232860 2233144 2233149) (-1288 "VOID.spad" 2232524 2232533 2232837 2232842) (-1287 "VIEW.spad" 2230204 2230213 2232514 2232519) (-1286 "VIEWDEF.spad" 2225405 2225414 2230194 2230199) (-1285 "VIEW3D.spad" 2209366 2209375 2225395 2225400) (-1284 "VIEW2D.spad" 2197257 2197266 2209356 2209361) (-1283 "VECTOR.spad" 2195931 2195942 2196182 2196209) (-1282 "VECTOR2.spad" 2194570 2194583 2195921 2195926) (-1281 "VECTCAT.spad" 2192474 2192485 2194538 2194565) (-1280 "VECTCAT.spad" 2190185 2190198 2192251 2192256) (-1279 "VARIABLE.spad" 2189965 2189980 2190175 2190180) (-1278 "UTYPE.spad" 2189609 2189618 2189955 2189960) (-1277 "UTSODETL.spad" 2188904 2188928 2189565 2189570) (-1276 "UTSODE.spad" 2187120 2187140 2188894 2188899) (-1275 "UTS.spad" 2181924 2181952 2185587 2185684) (-1274 "UTSCAT.spad" 2179403 2179419 2181822 2181919) (-1273 "UTSCAT.spad" 2176526 2176544 2178947 2178952) (-1272 "UTS2.spad" 2176121 2176156 2176516 2176521) (-1271 "URAGG.spad" 2170794 2170805 2176111 2176116) (-1270 "URAGG.spad" 2165431 2165444 2170750 2170755) (-1269 "UPXSSING.spad" 2163076 2163102 2164512 2164645) (-1268 "UPXS.spad" 2160230 2160258 2161208 2161357) (-1267 "UPXSCONS.spad" 2157989 2158009 2158362 2158511) (-1266 "UPXSCCA.spad" 2156560 2156580 2157835 2157984) (-1265 "UPXSCCA.spad" 2155273 2155295 2156550 2156555) (-1264 "UPXSCAT.spad" 2153862 2153878 2155119 2155268) (-1263 "UPXS2.spad" 2153405 2153458 2153852 2153857) (-1262 "UPSQFREE.spad" 2151819 2151833 2153395 2153400) (-1261 "UPSCAT.spad" 2149606 2149630 2151717 2151814) (-1260 "UPSCAT.spad" 2147099 2147125 2149212 2149217) (-1259 "UPOLYC.spad" 2142139 2142150 2146941 2147094) (-1258 "UPOLYC.spad" 2137071 2137084 2141875 2141880) (-1257 "UPOLYC2.spad" 2136542 2136561 2137061 2137066) (-1256 "UP.spad" 2133741 2133756 2134128 2134281) (-1255 "UPMP.spad" 2132641 2132654 2133731 2133736) (-1254 "UPDIVP.spad" 2132206 2132220 2132631 2132636) (-1253 "UPDECOMP.spad" 2130451 2130465 2132196 2132201) (-1252 "UPCDEN.spad" 2129660 2129676 2130441 2130446) (-1251 "UP2.spad" 2129024 2129045 2129650 2129655) (-1250 "UNISEG.spad" 2128377 2128388 2128943 2128948) (-1249 "UNISEG2.spad" 2127874 2127887 2128333 2128338) (-1248 "UNIFACT.spad" 2126977 2126989 2127864 2127869) (-1247 "ULS.spad" 2117535 2117563 2118622 2119051) (-1246 "ULSCONS.spad" 2109931 2109951 2110301 2110450) (-1245 "ULSCCAT.spad" 2107668 2107688 2109777 2109926) (-1244 "ULSCCAT.spad" 2105513 2105535 2107624 2107629) (-1243 "ULSCAT.spad" 2103745 2103761 2105359 2105508) (-1242 "ULS2.spad" 2103259 2103312 2103735 2103740) (-1241 "UINT8.spad" 2103136 2103145 2103249 2103254) (-1240 "UINT64.spad" 2103012 2103021 2103126 2103131) (-1239 "UINT32.spad" 2102888 2102897 2103002 2103007) (-1238 "UINT16.spad" 2102764 2102773 2102878 2102883) (-1237 "UFD.spad" 2101829 2101838 2102690 2102759) (-1236 "UFD.spad" 2100956 2100967 2101819 2101824) (-1235 "UDVO.spad" 2099837 2099846 2100946 2100951) (-1234 "UDPO.spad" 2097330 2097341 2099793 2099798) (-1233 "TYPE.spad" 2097262 2097271 2097320 2097325) (-1232 "TYPEAST.spad" 2097181 2097190 2097252 2097257) (-1231 "TWOFACT.spad" 2095833 2095848 2097171 2097176) (-1230 "TUPLE.spad" 2095319 2095330 2095732 2095737) (-1229 "TUBETOOL.spad" 2092186 2092195 2095309 2095314) (-1228 "TUBE.spad" 2090833 2090850 2092176 2092181) (-1227 "TS.spad" 2089432 2089448 2090398 2090495) (-1226 "TSETCAT.spad" 2076559 2076576 2089400 2089427) (-1225 "TSETCAT.spad" 2063672 2063691 2076515 2076520) (-1224 "TRMANIP.spad" 2058038 2058055 2063378 2063383) (-1223 "TRIMAT.spad" 2057001 2057026 2058028 2058033) (-1222 "TRIGMNIP.spad" 2055528 2055545 2056991 2056996) (-1221 "TRIGCAT.spad" 2055040 2055049 2055518 2055523) (-1220 "TRIGCAT.spad" 2054550 2054561 2055030 2055035) (-1219 "TREE.spad" 2053125 2053136 2054157 2054184) (-1218 "TRANFUN.spad" 2052964 2052973 2053115 2053120) (-1217 "TRANFUN.spad" 2052801 2052812 2052954 2052959) (-1216 "TOPSP.spad" 2052475 2052484 2052791 2052796) (-1215 "TOOLSIGN.spad" 2052138 2052149 2052465 2052470) (-1214 "TEXTFILE.spad" 2050699 2050708 2052128 2052133) (-1213 "TEX.spad" 2047845 2047854 2050689 2050694) (-1212 "TEX1.spad" 2047401 2047412 2047835 2047840) (-1211 "TEMUTL.spad" 2046956 2046965 2047391 2047396) (-1210 "TBCMPPK.spad" 2045049 2045072 2046946 2046951) (-1209 "TBAGG.spad" 2044099 2044122 2045029 2045044) (-1208 "TBAGG.spad" 2043157 2043182 2044089 2044094) (-1207 "TANEXP.spad" 2042565 2042576 2043147 2043152) (-1206 "TALGOP.spad" 2042289 2042300 2042555 2042560) (-1205 "TABLE.spad" 2040700 2040723 2040970 2040997) (-1204 "TABLEAU.spad" 2040181 2040192 2040690 2040695) (-1203 "TABLBUMP.spad" 2036984 2036995 2040171 2040176) (-1202 "SYSTEM.spad" 2036212 2036221 2036974 2036979) (-1201 "SYSSOLP.spad" 2033695 2033706 2036202 2036207) (-1200 "SYSPTR.spad" 2033594 2033603 2033685 2033690) (-1199 "SYSNNI.spad" 2032776 2032787 2033584 2033589) (-1198 "SYSINT.spad" 2032180 2032191 2032766 2032771) (-1197 "SYNTAX.spad" 2028386 2028395 2032170 2032175) (-1196 "SYMTAB.spad" 2026454 2026463 2028376 2028381) (-1195 "SYMS.spad" 2022477 2022486 2026444 2026449) (-1194 "SYMPOLY.spad" 2021484 2021495 2021566 2021693) (-1193 "SYMFUNC.spad" 2020985 2020996 2021474 2021479) (-1192 "SYMBOL.spad" 2018488 2018497 2020975 2020980) (-1191 "SWITCH.spad" 2015259 2015268 2018478 2018483) (-1190 "SUTS.spad" 2012164 2012192 2013726 2013823) (-1189 "SUPXS.spad" 2009305 2009333 2010296 2010445) (-1188 "SUP.spad" 2006118 2006129 2006891 2007044) (-1187 "SUPFRACF.spad" 2005223 2005241 2006108 2006113) (-1186 "SUP2.spad" 2004615 2004628 2005213 2005218) (-1185 "SUMRF.spad" 2003589 2003600 2004605 2004610) (-1184 "SUMFS.spad" 2003226 2003243 2003579 2003584) (-1183 "SULS.spad" 1993771 1993799 1994871 1995300) (-1182 "SUCHTAST.spad" 1993540 1993549 1993761 1993766) (-1181 "SUCH.spad" 1993222 1993237 1993530 1993535) (-1180 "SUBSPACE.spad" 1985337 1985352 1993212 1993217) (-1179 "SUBRESP.spad" 1984507 1984521 1985293 1985298) (-1178 "STTF.spad" 1980606 1980622 1984497 1984502) (-1177 "STTFNC.spad" 1977074 1977090 1980596 1980601) (-1176 "STTAYLOR.spad" 1969709 1969720 1976955 1976960) (-1175 "STRTBL.spad" 1968214 1968231 1968363 1968390) (-1174 "STRING.spad" 1967623 1967632 1967637 1967664) (-1173 "STRICAT.spad" 1967411 1967420 1967591 1967618) (-1172 "STREAM.spad" 1964329 1964340 1966936 1966951) (-1171 "STREAM3.spad" 1963902 1963917 1964319 1964324) (-1170 "STREAM2.spad" 1963030 1963043 1963892 1963897) (-1169 "STREAM1.spad" 1962736 1962747 1963020 1963025) (-1168 "STINPROD.spad" 1961672 1961688 1962726 1962731) (-1167 "STEP.spad" 1960873 1960882 1961662 1961667) (-1166 "STEPAST.spad" 1960107 1960116 1960863 1960868) (-1165 "STBL.spad" 1958633 1958661 1958800 1958815) (-1164 "STAGG.spad" 1957708 1957719 1958623 1958628) (-1163 "STAGG.spad" 1956781 1956794 1957698 1957703) (-1162 "STACK.spad" 1956138 1956149 1956388 1956415) (-1161 "SREGSET.spad" 1953842 1953859 1955784 1955811) (-1160 "SRDCMPK.spad" 1952403 1952423 1953832 1953837) (-1159 "SRAGG.spad" 1947546 1947555 1952371 1952398) (-1158 "SRAGG.spad" 1942709 1942720 1947536 1947541) (-1157 "SQMATRIX.spad" 1940381 1940399 1941297 1941384) (-1156 "SPLTREE.spad" 1934933 1934946 1939817 1939844) (-1155 "SPLNODE.spad" 1931521 1931534 1934923 1934928) (-1154 "SPFCAT.spad" 1930330 1930339 1931511 1931516) (-1153 "SPECOUT.spad" 1928882 1928891 1930320 1930325) (-1152 "SPADXPT.spad" 1920477 1920486 1928872 1928877) (-1151 "spad-parser.spad" 1919942 1919951 1920467 1920472) (-1150 "SPADAST.spad" 1919643 1919652 1919932 1919937) (-1149 "SPACEC.spad" 1903842 1903853 1919633 1919638) (-1148 "SPACE3.spad" 1903618 1903629 1903832 1903837) (-1147 "SORTPAK.spad" 1903167 1903180 1903574 1903579) (-1146 "SOLVETRA.spad" 1900930 1900941 1903157 1903162) (-1145 "SOLVESER.spad" 1899458 1899469 1900920 1900925) (-1144 "SOLVERAD.spad" 1895484 1895495 1899448 1899453) (-1143 "SOLVEFOR.spad" 1893946 1893964 1895474 1895479) (-1142 "SNTSCAT.spad" 1893546 1893563 1893914 1893941) (-1141 "SMTS.spad" 1891818 1891844 1893111 1893208) (-1140 "SMP.spad" 1889293 1889313 1889683 1889810) (-1139 "SMITH.spad" 1888138 1888163 1889283 1889288) (-1138 "SMATCAT.spad" 1886248 1886278 1888082 1888133) (-1137 "SMATCAT.spad" 1884290 1884322 1886126 1886131) (-1136 "SKAGG.spad" 1883253 1883264 1884258 1884285) (-1135 "SINT.spad" 1882193 1882202 1883119 1883248) (-1134 "SIMPAN.spad" 1881921 1881930 1882183 1882188) (-1133 "SIG.spad" 1881251 1881260 1881911 1881916) (-1132 "SIGNRF.spad" 1880369 1880380 1881241 1881246) (-1131 "SIGNEF.spad" 1879648 1879665 1880359 1880364) (-1130 "SIGAST.spad" 1879033 1879042 1879638 1879643) (-1129 "SHP.spad" 1876961 1876976 1878989 1878994) (-1128 "SHDP.spad" 1866595 1866622 1867104 1867235) (-1127 "SGROUP.spad" 1866203 1866212 1866585 1866590) (-1126 "SGROUP.spad" 1865809 1865820 1866193 1866198) (-1125 "SGCF.spad" 1858948 1858957 1865799 1865804) (-1124 "SFRTCAT.spad" 1857878 1857895 1858916 1858943) (-1123 "SFRGCD.spad" 1856941 1856961 1857868 1857873) (-1122 "SFQCMPK.spad" 1851578 1851598 1856931 1856936) (-1121 "SFORT.spad" 1851017 1851031 1851568 1851573) (-1120 "SEXOF.spad" 1850860 1850900 1851007 1851012) (-1119 "SEX.spad" 1850752 1850761 1850850 1850855) (-1118 "SEXCAT.spad" 1848533 1848573 1850742 1850747) (-1117 "SET.spad" 1846857 1846868 1847954 1847993) (-1116 "SETMN.spad" 1845307 1845324 1846847 1846852) (-1115 "SETCAT.spad" 1844629 1844638 1845297 1845302) (-1114 "SETCAT.spad" 1843949 1843960 1844619 1844624) (-1113 "SETAGG.spad" 1840498 1840509 1843929 1843944) (-1112 "SETAGG.spad" 1837055 1837068 1840488 1840493) (-1111 "SEQAST.spad" 1836758 1836767 1837045 1837050) (-1110 "SEGXCAT.spad" 1835914 1835927 1836748 1836753) (-1109 "SEG.spad" 1835727 1835738 1835833 1835838) (-1108 "SEGCAT.spad" 1834652 1834663 1835717 1835722) (-1107 "SEGBIND.spad" 1834410 1834421 1834599 1834604) (-1106 "SEGBIND2.spad" 1834108 1834121 1834400 1834405) (-1105 "SEGAST.spad" 1833822 1833831 1834098 1834103) (-1104 "SEG2.spad" 1833257 1833270 1833778 1833783) (-1103 "SDVAR.spad" 1832533 1832544 1833247 1833252) (-1102 "SDPOL.spad" 1829959 1829970 1830250 1830377) (-1101 "SCPKG.spad" 1828048 1828059 1829949 1829954) (-1100 "SCOPE.spad" 1827201 1827210 1828038 1828043) (-1099 "SCACHE.spad" 1825897 1825908 1827191 1827196) (-1098 "SASTCAT.spad" 1825806 1825815 1825887 1825892) (-1097 "SAOS.spad" 1825678 1825687 1825796 1825801) (-1096 "SAERFFC.spad" 1825391 1825411 1825668 1825673) (-1095 "SAE.spad" 1823566 1823582 1824177 1824312) (-1094 "SAEFACT.spad" 1823267 1823287 1823556 1823561) (-1093 "RURPK.spad" 1820926 1820942 1823257 1823262) (-1092 "RULESET.spad" 1820379 1820403 1820916 1820921) (-1091 "RULE.spad" 1818619 1818643 1820369 1820374) (-1090 "RULECOLD.spad" 1818471 1818484 1818609 1818614) (-1089 "RTVALUE.spad" 1818206 1818215 1818461 1818466) (-1088 "RSTRCAST.spad" 1817923 1817932 1818196 1818201) (-1087 "RSETGCD.spad" 1814301 1814321 1817913 1817918) (-1086 "RSETCAT.spad" 1804237 1804254 1814269 1814296) (-1085 "RSETCAT.spad" 1794193 1794212 1804227 1804232) (-1084 "RSDCMPK.spad" 1792645 1792665 1794183 1794188) (-1083 "RRCC.spad" 1791029 1791059 1792635 1792640) (-1082 "RRCC.spad" 1789411 1789443 1791019 1791024) (-1081 "RPTAST.spad" 1789113 1789122 1789401 1789406) (-1080 "RPOLCAT.spad" 1768473 1768488 1788981 1789108) (-1079 "RPOLCAT.spad" 1747546 1747563 1768056 1768061) (-1078 "ROUTINE.spad" 1743429 1743438 1746193 1746220) (-1077 "ROMAN.spad" 1742757 1742766 1743295 1743424) (-1076 "ROIRC.spad" 1741837 1741869 1742747 1742752) (-1075 "RNS.spad" 1740740 1740749 1741739 1741832) (-1074 "RNS.spad" 1739729 1739740 1740730 1740735) (-1073 "RNG.spad" 1739464 1739473 1739719 1739724) (-1072 "RNGBIND.spad" 1738624 1738638 1739419 1739424) (-1071 "RMODULE.spad" 1738389 1738400 1738614 1738619) (-1070 "RMCAT2.spad" 1737809 1737866 1738379 1738384) (-1069 "RMATRIX.spad" 1736633 1736652 1736976 1737015) (-1068 "RMATCAT.spad" 1732212 1732243 1736589 1736628) (-1067 "RMATCAT.spad" 1727681 1727714 1732060 1732065) (-1066 "RLINSET.spad" 1727236 1727247 1727671 1727676) (-1065 "RINTERP.spad" 1727124 1727144 1727226 1727231) (-1064 "RING.spad" 1726594 1726603 1727104 1727119) (-1063 "RING.spad" 1726072 1726083 1726584 1726589) (-1062 "RIDIST.spad" 1725464 1725473 1726062 1726067) (-1061 "RGCHAIN.spad" 1724047 1724063 1724949 1724976) (-1060 "RGBCSPC.spad" 1723828 1723840 1724037 1724042) (-1059 "RGBCMDL.spad" 1723358 1723370 1723818 1723823) (-1058 "RF.spad" 1721000 1721011 1723348 1723353) (-1057 "RFFACTOR.spad" 1720462 1720473 1720990 1720995) (-1056 "RFFACT.spad" 1720197 1720209 1720452 1720457) (-1055 "RFDIST.spad" 1719193 1719202 1720187 1720192) (-1054 "RETSOL.spad" 1718612 1718625 1719183 1719188) (-1053 "RETRACT.spad" 1718040 1718051 1718602 1718607) (-1052 "RETRACT.spad" 1717466 1717479 1718030 1718035) (-1051 "RETAST.spad" 1717278 1717287 1717456 1717461) (-1050 "RESULT.spad" 1715338 1715347 1715925 1715952) (-1049 "RESRING.spad" 1714685 1714732 1715276 1715333) (-1048 "RESLATC.spad" 1714009 1714020 1714675 1714680) (-1047 "REPSQ.spad" 1713740 1713751 1713999 1714004) (-1046 "REP.spad" 1711294 1711303 1713730 1713735) (-1045 "REPDB.spad" 1711001 1711012 1711284 1711289) (-1044 "REP2.spad" 1700659 1700670 1710843 1710848) (-1043 "REP1.spad" 1694855 1694866 1700609 1700614) (-1042 "REGSET.spad" 1692652 1692669 1694501 1694528) (-1041 "REF.spad" 1691987 1691998 1692607 1692612) (-1040 "REDORDER.spad" 1691193 1691210 1691977 1691982) (-1039 "RECLOS.spad" 1689976 1689996 1690680 1690773) (-1038 "REALSOLV.spad" 1689116 1689125 1689966 1689971) (-1037 "REAL.spad" 1688988 1688997 1689106 1689111) (-1036 "REAL0Q.spad" 1686286 1686301 1688978 1688983) (-1035 "REAL0.spad" 1683130 1683145 1686276 1686281) (-1034 "RDUCEAST.spad" 1682851 1682860 1683120 1683125) (-1033 "RDIV.spad" 1682506 1682531 1682841 1682846) (-1032 "RDIST.spad" 1682073 1682084 1682496 1682501) (-1031 "RDETRS.spad" 1680937 1680955 1682063 1682068) (-1030 "RDETR.spad" 1679076 1679094 1680927 1680932) (-1029 "RDEEFS.spad" 1678175 1678192 1679066 1679071) (-1028 "RDEEF.spad" 1677185 1677202 1678165 1678170) (-1027 "RCFIELD.spad" 1674371 1674380 1677087 1677180) (-1026 "RCFIELD.spad" 1671643 1671654 1674361 1674366) (-1025 "RCAGG.spad" 1669571 1669582 1671633 1671638) (-1024 "RCAGG.spad" 1667426 1667439 1669490 1669495) (-1023 "RATRET.spad" 1666786 1666797 1667416 1667421) (-1022 "RATFACT.spad" 1666478 1666490 1666776 1666781) (-1021 "RANDSRC.spad" 1665797 1665806 1666468 1666473) (-1020 "RADUTIL.spad" 1665553 1665562 1665787 1665792) (-1019 "RADIX.spad" 1662474 1662488 1664020 1664113) (-1018 "RADFF.spad" 1660887 1660924 1661006 1661162) (-1017 "RADCAT.spad" 1660482 1660491 1660877 1660882) (-1016 "RADCAT.spad" 1660075 1660086 1660472 1660477) (-1015 "QUEUE.spad" 1659423 1659434 1659682 1659709) (-1014 "QUAT.spad" 1657881 1657892 1658224 1658289) (-1013 "QUATCT2.spad" 1657501 1657520 1657871 1657876) (-1012 "QUATCAT.spad" 1655671 1655682 1657431 1657496) (-1011 "QUATCAT.spad" 1653592 1653605 1655354 1655359) (-1010 "QUAGG.spad" 1652419 1652430 1653560 1653587) (-1009 "QQUTAST.spad" 1652187 1652196 1652409 1652414) (-1008 "QFORM.spad" 1651805 1651820 1652177 1652182) (-1007 "QFCAT.spad" 1650507 1650518 1651707 1651800) (-1006 "QFCAT.spad" 1648800 1648813 1650002 1650007) (-1005 "QFCAT2.spad" 1648492 1648509 1648790 1648795) (-1004 "QEQUAT.spad" 1648050 1648059 1648482 1648487) (-1003 "QCMPACK.spad" 1642796 1642816 1648040 1648045) (-1002 "QALGSET.spad" 1638874 1638907 1642710 1642715) (-1001 "QALGSET2.spad" 1636869 1636888 1638864 1638869) (-1000 "PWFFINTB.spad" 1634284 1634306 1636859 1636864) (-999 "PUSHVAR.spad" 1633623 1633642 1634274 1634279) (-998 "PTRANFN.spad" 1629751 1629761 1633613 1633618) (-997 "PTPACK.spad" 1626839 1626849 1629741 1629746) (-996 "PTFUNC2.spad" 1626662 1626676 1626829 1626834) (-995 "PTCAT.spad" 1625917 1625927 1626630 1626657) (-994 "PSQFR.spad" 1625224 1625248 1625907 1625912) (-993 "PSEUDLIN.spad" 1624110 1624120 1625214 1625219) (-992 "PSETPK.spad" 1609543 1609559 1623988 1623993) (-991 "PSETCAT.spad" 1603463 1603486 1609523 1609538) (-990 "PSETCAT.spad" 1597357 1597382 1603419 1603424) (-989 "PSCURVE.spad" 1596340 1596348 1597347 1597352) (-988 "PSCAT.spad" 1595123 1595152 1596238 1596335) (-987 "PSCAT.spad" 1593996 1594027 1595113 1595118) (-986 "PRTITION.spad" 1592694 1592702 1593986 1593991) (-985 "PRTDAST.spad" 1592413 1592421 1592684 1592689) (-984 "PRS.spad" 1581975 1581992 1592369 1592374) (-983 "PRQAGG.spad" 1581410 1581420 1581943 1581970) (-982 "PROPLOG.spad" 1580982 1580990 1581400 1581405) (-981 "PROPFUN2.spad" 1580605 1580618 1580972 1580977) (-980 "PROPFUN1.spad" 1580003 1580014 1580595 1580600) (-979 "PROPFRML.spad" 1578571 1578582 1579993 1579998) (-978 "PROPERTY.spad" 1578059 1578067 1578561 1578566) (-977 "PRODUCT.spad" 1575741 1575753 1576025 1576080) (-976 "PR.spad" 1574133 1574145 1574832 1574959) (-975 "PRINT.spad" 1573885 1573893 1574123 1574128) (-974 "PRIMES.spad" 1572138 1572148 1573875 1573880) (-973 "PRIMELT.spad" 1570219 1570233 1572128 1572133) (-972 "PRIMCAT.spad" 1569846 1569854 1570209 1570214) (-971 "PRIMARR.spad" 1568851 1568861 1569029 1569056) (-970 "PRIMARR2.spad" 1567618 1567630 1568841 1568846) (-969 "PREASSOC.spad" 1567000 1567012 1567608 1567613) (-968 "PPCURVE.spad" 1566137 1566145 1566990 1566995) (-967 "PORTNUM.spad" 1565912 1565920 1566127 1566132) (-966 "POLYROOT.spad" 1564761 1564783 1565868 1565873) (-965 "POLY.spad" 1562096 1562106 1562611 1562738) (-964 "POLYLIFT.spad" 1561361 1561384 1562086 1562091) (-963 "POLYCATQ.spad" 1559479 1559501 1561351 1561356) (-962 "POLYCAT.spad" 1552949 1552970 1559347 1559474) (-961 "POLYCAT.spad" 1545757 1545780 1552157 1552162) (-960 "POLY2UP.spad" 1545209 1545223 1545747 1545752) (-959 "POLY2.spad" 1544806 1544818 1545199 1545204) (-958 "POLUTIL.spad" 1543747 1543776 1544762 1544767) (-957 "POLTOPOL.spad" 1542495 1542510 1543737 1543742) (-956 "POINT.spad" 1541333 1541343 1541420 1541447) (-955 "PNTHEORY.spad" 1538035 1538043 1541323 1541328) (-954 "PMTOOLS.spad" 1536810 1536824 1538025 1538030) (-953 "PMSYM.spad" 1536359 1536369 1536800 1536805) (-952 "PMQFCAT.spad" 1535950 1535964 1536349 1536354) (-951 "PMPRED.spad" 1535429 1535443 1535940 1535945) (-950 "PMPREDFS.spad" 1534883 1534905 1535419 1535424) (-949 "PMPLCAT.spad" 1533963 1533981 1534815 1534820) (-948 "PMLSAGG.spad" 1533548 1533562 1533953 1533958) (-947 "PMKERNEL.spad" 1533127 1533139 1533538 1533543) (-946 "PMINS.spad" 1532707 1532717 1533117 1533122) (-945 "PMFS.spad" 1532284 1532302 1532697 1532702) (-944 "PMDOWN.spad" 1531574 1531588 1532274 1532279) (-943 "PMASS.spad" 1530584 1530592 1531564 1531569) (-942 "PMASSFS.spad" 1529551 1529567 1530574 1530579) (-941 "PLOTTOOL.spad" 1529331 1529339 1529541 1529546) (-940 "PLOT.spad" 1524254 1524262 1529321 1529326) (-939 "PLOT3D.spad" 1520718 1520726 1524244 1524249) (-938 "PLOT1.spad" 1519875 1519885 1520708 1520713) (-937 "PLEQN.spad" 1507165 1507192 1519865 1519870) (-936 "PINTERP.spad" 1506787 1506806 1507155 1507160) (-935 "PINTERPA.spad" 1506571 1506587 1506777 1506782) (-934 "PI.spad" 1506180 1506188 1506545 1506566) (-933 "PID.spad" 1505150 1505158 1506106 1506175) (-932 "PICOERCE.spad" 1504807 1504817 1505140 1505145) (-931 "PGROEB.spad" 1503408 1503422 1504797 1504802) (-930 "PGE.spad" 1495025 1495033 1503398 1503403) (-929 "PGCD.spad" 1493915 1493932 1495015 1495020) (-928 "PFRPAC.spad" 1493064 1493074 1493905 1493910) (-927 "PFR.spad" 1489727 1489737 1492966 1493059) (-926 "PFOTOOLS.spad" 1488985 1489001 1489717 1489722) (-925 "PFOQ.spad" 1488355 1488373 1488975 1488980) (-924 "PFO.spad" 1487774 1487801 1488345 1488350) (-923 "PF.spad" 1487348 1487360 1487579 1487672) (-922 "PFECAT.spad" 1485030 1485038 1487274 1487343) (-921 "PFECAT.spad" 1482740 1482750 1484986 1484991) (-920 "PFBRU.spad" 1480628 1480640 1482730 1482735) (-919 "PFBR.spad" 1478188 1478211 1480618 1480623) (-918 "PERM.spad" 1473995 1474005 1478018 1478033) (-917 "PERMGRP.spad" 1468765 1468775 1473985 1473990) (-916 "PERMCAT.spad" 1467426 1467436 1468745 1468760) (-915 "PERMAN.spad" 1465958 1465972 1467416 1467421) (-914 "PENDTREE.spad" 1465299 1465309 1465587 1465592) (-913 "PDRING.spad" 1463850 1463860 1465279 1465294) (-912 "PDRING.spad" 1462409 1462421 1463840 1463845) (-911 "PDEPROB.spad" 1461424 1461432 1462399 1462404) (-910 "PDEPACK.spad" 1455464 1455472 1461414 1461419) (-909 "PDECOMP.spad" 1454934 1454951 1455454 1455459) (-908 "PDECAT.spad" 1453290 1453298 1454924 1454929) (-907 "PDDOM.spad" 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1433185) (-888 "PARPCURV.spad" 1432443 1432471 1432971 1432976) (-887 "PARPC2.spad" 1432234 1432250 1432433 1432438) (-886 "PARAMAST.spad" 1431362 1431370 1432224 1432229) (-885 "PAN2EXPR.spad" 1430774 1430782 1431352 1431357) (-884 "PALETTE.spad" 1429744 1429752 1430764 1430769) (-883 "PAIR.spad" 1428731 1428744 1429332 1429337) (-882 "PADICRC.spad" 1426065 1426083 1427236 1427329) (-881 "PADICRAT.spad" 1424080 1424092 1424301 1424394) (-880 "PADIC.spad" 1423775 1423787 1424006 1424075) (-879 "PADICCT.spad" 1422324 1422336 1423701 1423770) (-878 "PADEPAC.spad" 1421013 1421032 1422314 1422319) (-877 "PADE.spad" 1419765 1419781 1421003 1421008) (-876 "OWP.spad" 1419005 1419035 1419623 1419690) (-875 "OVERSET.spad" 1418578 1418586 1418995 1419000) (-874 "OVAR.spad" 1418359 1418382 1418568 1418573) (-873 "OUT.spad" 1417445 1417453 1418349 1418354) (-872 "OUTFORM.spad" 1406837 1406845 1417435 1417440) (-871 "OUTBFILE.spad" 1406255 1406263 1406827 1406832) (-870 "OUTBCON.spad" 1405261 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(-378 "FINRALG.spad" 601745 601760 603642 603647) (-377 "FINITE.spad" 600897 600905 601735 601740) (-376 "FINAALG.spad" 590018 590028 600839 600892) (-375 "FINAALG.spad" 579151 579163 589974 589979) (-374 "FILE.spad" 578734 578744 579141 579146) (-373 "FILECAT.spad" 577260 577277 578724 578729) (-372 "FIELD.spad" 576666 576674 577162 577255) (-371 "FIELD.spad" 576158 576168 576656 576661) (-370 "FGROUP.spad" 574805 574815 576138 576153) (-369 "FGLMICPK.spad" 573592 573607 574795 574800) (-368 "FFX.spad" 572967 572982 573308 573401) (-367 "FFSLPE.spad" 572470 572491 572957 572962) (-366 "FFPOLY.spad" 563732 563743 572460 572465) (-365 "FFPOLY2.spad" 562792 562809 563722 563727) (-364 "FFP.spad" 562189 562209 562508 562601) (-363 "FF.spad" 561637 561653 561870 561963) (-362 "FFNBX.spad" 560149 560169 561353 561446) (-361 "FFNBP.spad" 558662 558679 559865 559958) (-360 "FFNB.spad" 557127 557148 558343 558436) (-359 "FFINTBAS.spad" 554641 554660 557117 557122) (-358 "FFIELDC.spad" 552218 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377119 377565 377570) (-275 "E04DGFA.spad" 376647 376655 377101 377106) (-274 "E04AGNT.spad" 372497 372505 376637 376642) (-273 "DVARCAT.spad" 369387 369397 372487 372492) (-272 "DVARCAT.spad" 366275 366287 369377 369382) (-271 "DSMP.spad" 363742 363756 364047 364174) (-270 "DROPT.spad" 357701 357709 363732 363737) (-269 "DROPT1.spad" 357366 357376 357691 357696) (-268 "DROPT0.spad" 352223 352231 357356 357361) (-267 "DRAWPT.spad" 350396 350404 352213 352218) (-266 "DRAW.spad" 343272 343285 350386 350391) (-265 "DRAWHACK.spad" 342580 342590 343262 343267) (-264 "DRAWCX.spad" 340050 340058 342570 342575) (-263 "DRAWCURV.spad" 339597 339612 340040 340045) (-262 "DRAWCFUN.spad" 329129 329137 339587 339592) (-261 "DQAGG.spad" 327307 327317 329097 329124) (-260 "DPOLCAT.spad" 322656 322672 327175 327302) (-259 "DPOLCAT.spad" 318091 318109 322612 322617) (-258 "DPMO.spad" 310564 310580 310702 310947) (-257 "DPMM.spad" 303050 303068 303175 303420) (-256 "DOMTMPLT.spad" 302821 302829 303040 303045) (-255 "DOMCTOR.spad" 302576 302584 302811 302816) (-254 "DOMAIN.spad" 301663 301671 302566 302571) (-253 "DMP.spad" 298923 298938 299493 299620) (-252 "DLP.spad" 298275 298285 298913 298918) (-251 "DLIST.spad" 296854 296864 297458 297485) (-250 "DLAGG.spad" 295271 295281 296844 296849) (-249 "DIVRING.spad" 294813 294821 295215 295266) (-248 "DIVRING.spad" 294399 294409 294803 294808) (-247 "DISPLAY.spad" 292589 292597 294389 294394) (-246 "DIRPROD.spad" 282092 282108 282732 282863) (-245 "DIRPROD2.spad" 280910 280928 282082 282087) (-244 "DIRPCAT.spad" 279854 279870 280774 280905) (-243 "DIRPCAT.spad" 278527 278545 279449 279454) (-242 "DIOSP.spad" 277352 277360 278517 278522) (-241 "DIOPS.spad" 276348 276358 277332 277347) (-240 "DIOPS.spad" 275318 275330 276304 276309) (-239 "DIFRING.spad" 275156 275164 275298 275313) (-238 "DIFFSPC.spad" 274735 274743 275146 275151) (-237 "DIFFSPC.spad" 274312 274322 274725 274730) (-236 "DIFFMOD.spad" 273801 273811 274280 274307) (-235 "DIFFDOM.spad" 272966 272977 273791 273796) (-234 "DIFFDOM.spad" 272129 272142 272956 272961) (-233 "DIFEXT.spad" 271300 271310 272109 272124) (-232 "DIFEXT.spad" 270388 270400 271199 271204) (-231 "DIAGG.spad" 270018 270028 270368 270383) (-230 "DIAGG.spad" 269656 269668 270008 270013) (-229 "DHMATRIX.spad" 267968 267978 269113 269140) (-228 "DFSFUN.spad" 261608 261616 267958 267963) (-227 "DFLOAT.spad" 258339 258347 261498 261603) (-226 "DFINTTLS.spad" 256570 256586 258329 258334) (-225 "DERHAM.spad" 254484 254516 256550 256565) (-224 "DEQUEUE.spad" 253808 253818 254091 254118) (-223 "DEGRED.spad" 253425 253439 253798 253803) (-222 "DEFINTRF.spad" 250962 250972 253415 253420) (-221 "DEFINTEF.spad" 249472 249488 250952 250957) (-220 "DEFAST.spad" 248840 248848 249462 249467) (-219 "DECIMAL.spad" 246946 246954 247307 247400) (-218 "DDFACT.spad" 244759 244776 246936 246941) (-217 "DBLRESP.spad" 244359 244383 244749 244754) (-216 "DBASE.spad" 243023 243033 244349 244354) (-215 "DATAARY.spad" 242485 242498 243013 243018) (-214 "D03FAFA.spad" 242313 242321 242475 242480) (-213 "D03EEFA.spad" 242133 242141 242303 242308) (-212 "D03AGNT.spad" 241219 241227 242123 242128) (-211 "D02EJFA.spad" 240681 240689 241209 241214) (-210 "D02CJFA.spad" 240159 240167 240671 240676) (-209 "D02BHFA.spad" 239649 239657 240149 240154) (-208 "D02BBFA.spad" 239139 239147 239639 239644) (-207 "D02AGNT.spad" 233953 233961 239129 239134) (-206 "D01WGTS.spad" 232272 232280 233943 233948) (-205 "D01TRNS.spad" 232249 232257 232262 232267) (-204 "D01GBFA.spad" 231771 231779 232239 232244) (-203 "D01FCFA.spad" 231293 231301 231761 231766) (-202 "D01ASFA.spad" 230761 230769 231283 231288) (-201 "D01AQFA.spad" 230207 230215 230751 230756) (-200 "D01APFA.spad" 229631 229639 230197 230202) (-199 "D01ANFA.spad" 229125 229133 229621 229626) (-198 "D01AMFA.spad" 228635 228643 229115 229120) (-197 "D01ALFA.spad" 228175 228183 228625 228630) (-196 "D01AKFA.spad" 227701 227709 228165 228170) (-195 "D01AJFA.spad" 227224 227232 227691 227696) (-194 "D01AGNT.spad" 223291 223299 227214 227219) (-193 "CYCLOTOM.spad" 222797 222805 223281 223286) (-192 "CYCLES.spad" 219589 219597 222787 222792) (-191 "CVMP.spad" 219006 219016 219579 219584) (-190 "CTRIGMNP.spad" 217506 217522 218996 219001) (-189 "CTOR.spad" 217197 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
author	dos-reis <gdr@axiomatics.org>	2010-06-17 02:36:50 +0000
committer	dos-reis <gdr@axiomatics.org>	2010-06-17 02:36:50 +0000
commit	4c62f989b0c11eb9d3e6c04d966d108fd842fe5d (patch)
tree	58d7faf9768f563e092598279e4f19e1291dbdf4 /src/share/algebra/browse.daase
parent	5b0bfceb3efc34578e1de66194b835bb48009466 (diff)
download	open-axiom-4c62f989b0c11eb9d3e6c04d966d108fd842fe5d.tar.gz